Once more into the math wars, dear friends. I confess I am an innocent bystander. I have never taught math, and I am astonished at the expectations that our middle school students meet. When I was in high school, I studied Algebra, Geometry, and Trigonometry, but math instruction has moved far beyond what I learned. So I invite math teachers to comment on Wendy Lecker’s new article about what the Common Core math gets wrong. To all the pundits and politicians who ridicule our students and teachers, I have a standing challenge: Take any eighth grade math test and publish your scores.

Lecker writes:

*At parents’ night this fall, a high school math teacher I know begged parents to teach their children long division “the old-fashioned way.” She explained that the new way students had learned long division impedes their ability to understand algebraic factoring. She lamented that students hadn’t been taught certain rote skills, like multiplication tables, that would enable them to perform more complex math operations efficiently.*

*It turns out that brain science supports this math teacher’s impressions. Rote learning and memorization at an early age are critical in developing math skills. *

*A study conducted by Stanford Medical school examined the role of a part of the brain, the hippocampus, in the development of math skills in children. The authors noted that a shift to memory-based problem solving is a hallmark of children’s cognitive development in arithmetic as well as other domains. They conducted brain scans of children, adolescents and adults and found that hippocampus plays a critical but time limited role in the development of memory-based problem solving skills. *

*The hippocampus helps the brain encode memories in children that as adults they can later retrieve efficiently when working with more complex math concepts. The hippocampal system works a certain way in children to help develop memory-based problem solving skills. Once the children pass a certain age, the processes change. *

*The study also found that “repeated problem solving during the early stages of arithmetic skill development in children contributes to memory re-encoding and consolidation.” In other words, rote repetition helps the development of this critical brain system so essential to later more complicated math work.*

*Those who developed the Common Core State Standards clearly ignored brain research in math, as they did in reading (http://bit.ly/1IeIgKm); The Common Core emphasizes conceptual understanding at every phase of math instruction. So, even young children are required not only to conduct a simple math procedure, but to also explain and justify every answer.*

There is more. Open the link and read the rest of the article. Then sound off.

I remember in the 70’s when I was a youngster learning math. We were required to have a calculator. My father went in and told the teacher that he would NOT buy me a calculator until I learned my multiplication and division tables, and that he wanted me to learn to do math on paper. He drew all kinds of pictures to help me understand what I was learning. A few years ago when I went to school to become a massage therapist, we had to MEMORIZE 150 muscles, their origins and insertions and many other facts related to these muscles. MEMORIZE. I’m a great believer in the importance of memorization. You have to have a foundation upon which to build. I often think that requiring students to write in an in-depth manner is not appropriate because they have not read enough and synthesized material. You have to be a reader to be a good writer and you have to be organized. It wasn’t until my later 20’s when I really began to see the “big picture” and make connections between things I had read and put them together in a coherent way. Reading, learning grammar, writing and perhaps more importantly TIME TO REFLECT are the foundations of good writing. I think we are expecting kids to do more than they are developmentally able.

I especially like what you say here about writing. I would just refine it to suggest: kids of all ages do a lot of deep thinking. What’s inappropriate is to move too quickly into objective analysis.

Youngest kids react emotionally & intuitively to new material, relating everything to themselves, their immediate family, developing peer relationships [i.e., their experience]. About as analytical as you want to get is, e.g., ‘what did you learn’ about a story character, ‘what lesson did [character] learn’, ‘was there a page that made you feel that way/ think that” – all open-ended, no ‘correct’ answers.

There is no place in early-grades arithmetic for verbal [LA-style] re-telling of math facts. I even object to teaching them to express math facts w/specific styles of grouping symbols/drawings. Everyone’s brain is busy developing its own inner visualizations/ spatial concepts to understand operations. This approach is just another example of trying to break ‘metacognition’ down into standardized, teachable/ testable skill sets. Just as we see throughout CCSS-ELA.

I think it is a stretch to blame Common Core for this. There is nothing at all in Common Core that forbids the teaching of the time-honored algorithms and shortcuts that we grew up with; nor is using those “tricks” incompatible with gaining a deeper conceptual understanding of mathematics.

And in New York State, the “we don’t teach times tables or long division” battles long predate the adoption of Common Core. Sounds like Lecker’s real beef is with social-justice-obsessed graduate schools of education that abhor “rote learning” and the “mere accumulation of facts.”

Correct; Common Core does not prohibit teaching standard algorithms and in fact requires them. However, the standard algorithm for multidigit addition and subtraction, for example, appears in Grade 4. Up until that time, the standards mention place value “strategies”. CC also does not prohibit teaching the standard algorithms earlier than the grade in which it appears, but that is a fact that, although confirmed by both Bill McCallum and Jason Zimba (lead writers of the CC math standards) has not made it to the ears of publishers, school districts, schools, and test makers. (See http://edexcellence.net/articles/when-the-standard-algorithm-is-the-only-algorithm-taught )

Wendy’s article talks about memorization as a foundation to procedural fluency, it is true, but she also talks about the tendency to have students “explain” their answers as an indicator of understanding. Her reference to a teacher telling parents to teach their students the standard method for long division goes to the interpretation I just mentioned–i.e., that the standard algorithms are postponed until 4th, 5th and 6th grades, since that is where they appear in the CC standards.

Surely you don’t believe what you write? Do you work for an entity that in any way gets money from Gates and Co, or any of the Common Core advocates? Do you have any children currently in grades K-12?

@Lee: Has it occurred to you that the world isn’t operating as a series of competing secret conspiracies in which as soon as someone posts an opinion about something, a hired gun appears to disagree? Maybe there are people who aren’t paid shills for Gates or anyone else who have sound reasons to dispute some of the blanket statements against OR FOR the Common Core. Is that conceivable in your world view? Because I routinely post comments that are critical of aspects of the Common Core Initiative and those that are critical of what I believe are ill-conceived attacks on aspects of the Common Core Standards themselves. And no one is paying or rewarding me in any way to do either.

I hope you read what I just wrote carefully. I don’t make idle claims or careless ones. And I don’t appreciate being accused, even indirectly, of being anyone’s tool. So perhaps you’d do better to craft a substantive response to what Tim stated (which is in my analysis completely accurate) than to try to besmirch his character.

Yes, I believe what I wrote; no, I have no financial connection with Gates or anything that’s even remotely related to education; yes, my children attend a variety of Title I-eligible NYC DOE traditional public schools, where we have had plenty of parent-teacher conferences around the concept of “rote learning” that would seamlessly fit into a Christopher Guest “mockumentary”.

Wher in the standards does it tell teachers what and how to teach? The answer lies in this question: Where in the standards does it say there have to be standardized tests with high stakes on the line? Let’s avoid Arne Duncan’s “Common Core is not a curriculum” defense. We here all know high stakes force teachers to test prep. With annual testing, all debates about teaching pedagogy are permanently ended and decisions are made by the testing monolith.

It’s all well and good to wonder what things would be like if we had ONLY the Common Core standards and not all the stuff that has gone along with them (standardized tests [supposedly aligned with the standards], texts [supposedly aligned], curriculum software [supposedly aligned], etc) but it’s not particularly meaningful in this context because Common Core is a package deal. Has been since day one. It was never even intended by it’s architect and main sponsor to stand alone.

Here’s what Bill Gates said back in 2009

“identifying common standards is not enough. We’ll know we’ve succeeded when the curriculum and the tests are aligned to these standards.

Secretary Arne Duncan recently announced that $350 million of the stimulus package will be used to create just these kinds of tests—next-generation assessments aligned to the common core.

When the tests are aligned to the common standards, the curriculum will line up as well—and that will unleash powerful market forces in the service of better teaching. ”

And here’s what David Coleman, architect of CC said in 2011 “the great rule that I think is a statement of reality, though not a pretty one, which is teachers will teach towards the test. There is no force strong enough on this earth to prevent that. There is no amount of hand-waving, there‟s no amount of saying, “They teach to the standards, not the test; we don‟t do that here.” Whatever. The truth is – and if I misrepresent you, you are welcome to take the mic back. But the truth is teachers do. Tests exert an enormous effect on instructional practice, direct and indirect, and it‟s hence our obligation to make tests that are worthy of that kind of attention.”

When parents, teachers and others criticize and complain about “Common Core”, they are criticizing and complaining about the “package deal”. And with very good reason. It would not even make any sense for them to differentiate between the standards themselves and everything that has gone along with them because they essentially have no choice in the matter.

This is a perfect quote of Gates by our poet, and needs to be reread a few times to appreciate it fully.

“When the tests are aligned to the common standards, the curriculum will line up as well—and that will unleash powerful market forces in the service of better teaching. ”

Gates premise is incorrect: no tests can be lined up with the stated objectives of the CC standards.

But Gates does state something which is generally true and which we can reformulate as

Even if God makes the (necessarily perfect) math standards, if they are tied to high stakes tests, the teaching will be to the tests.

The problem occurs when the tests cannot be lined up to the standards.

NCLB, RTTT, Common Core Crap and High Stakes test ignore a lot more.

What a child remembers has nothing to do with the quality of teaching in any subject or even if the child learned what the teacher taught.

As imperfect humans, we all have this thing called memory and memory is not perfect. In fact, we have no power over what we remember on a day-to-day basis, and what we do remember can be edited and revised while we sleep.

Let me repeat that: what we remember in long term memory can be edited and revised while we sleep. In fact, research shows we can invent memories of events that we never were part of and go through life thinking we were there when we weren’t.

And even when a child remembers what was learned from what was taught, that doesn’t mean the child will be able to access that memory during a high stakes test.

In short: There is short term memory that soaks up what happens to us during the waking hours of a 24 hour period. Then when we sleep, an automatic process decides on its own what to erase and what gets moved to long term memory. If we go without sleep in that 24 hour cycle, our memory is even more faulty. Do you know how many hours the average child and teen sleeps in the U.S.? Studies show that children must sleep more than 8 hours a day for their bodies and minds to function properly.

But, what gets moved to long-term memory is not that easy to access on demand because a number of factors that control accessing what was stored in long term memory. A question on a multiple choice test might not be enough to trigger the memory that would answer that question properly because that memory is linked to a sight or smell or another one of our senses. What happens if a child was doing their homework at night and mom was cooking lemon cake and the house was filled with the scent of lemons so the specific memory of what the child learned while doing homework was linked to the scent of lemons but there was no scent of lemons in the classroom while taking the bubble test?

And what happens when a child comes home and his parents are having a roaring argument and dad hits the mother so the child never does the homework linked to a powerful lesson the teacher taught and then when the child goes to sleep, all he is thinking about is that argument his parents had so no memory of what was taught ends up in long term memory.

For incessant, I taught in schools with poverty rates of more than 70% and sometimes as much as 100%. I wrote the homework assignment on the board. AT the beginning of each class, I required that all of my students copy down the directions for that homework assignment on the paper they were supposed to do the assignment on. I then read the homework directions to them. At the end of class before the bell ran, I reminded them again about the homework and then read it out loud again.

The next day, there would always be several students who insisted I never told them about that homework assignment and yet if we opened their binder—-if they had one—-the directions the copies were there.

Now, let’s imagine what happens when a child is tested on something she was taught and might have learned the year before or even longer than a year.

Great teaching does not guarantee a child will learn what was taught or even remember it months and years later.

Why? Because if humans don’t use those memories, then they fade or are disconnected from the network that makes up long term memory. Long term human memory does not have Google search capabilities or a libraries Dewey Decimal System.

Lecker…”She explained that the new way students had learned long division impedes their ability to understand algebraic factoring. She lamented that students hadn’t been taught certain rote skills, like multiplication tables, that would enable them to perform more complex math operations efficiently.”

There is nothing in the Common Core approach to math that would prohibit a teacher from making sure that their students focused on learning their multiplication facts. It is ridiculous to think that children are no longer expected to learn rote facts during their elementary years.

Children are also still expected to learn the traditional algorithms under Common Core standards. I have been teaching remedial math at the elementary level for many years and I think that there are some good ideas in the Common Core Math Standards. The problems with Common Core Standards are many, but people who do not know what the actual standards are have lots of unfounded opinions.

The BIGGEST problem with Common Core in the United States is the high stakes tests and using the results of those tests to punish public school teachers and public schools by ranking teachers and firing those who fall into the bottom and closing public schools that are labeled failing schools based on the results of those tests.

Finland has Common Core standards too, but they are not linked to high stakes tests that punish children who fall below the arbitrarily line on a field of fill-in bubbles. In fact, in Finland, the standards are left to the teachers to decide how to teach and which ones to teach. In Finland there are NO high stakes tests that label children failures, fire teachers and close schools.

In fact, China has high stakes tests but those tests are not used to fire teachers and close public schools. In China, the FEW high stakes, high stress tests are not linked to Common Core standards and they are only used to rank students to decide who gets into high school or college.

Lloyd, in your mind, is there any difference between the CCSS Initiative and the actual words in the Common Core Mathematics Content Standards and/or Standards for Mathematical Practice? Let me cite the latter in particular:

1) Make sense of problems and persevere in solving them.

2) Reason abstractly and quantitatively.

3) Construct viable arguments and critique the reasoning of others.

4) Model with mathematics.

5) Use appropriate tools strategically.

6) Attend to precision.

7) Look for and make use of structure.

8) Look for and express regularity in repeated reasoning.

If you want the details for the above eight standards, go here: http://www.corestandards.org/Math/Practice/

I would like to know what criticisms you and other readers of this blog have of those eight principles. Because as a mathematics coach, teachers, and teacher educator, I have to say that they capture quite well most, if not all, of the precepts that have informed my beliefs and practices over the last 30 years or so. So if they are not up to snuff in the eyes of others, I very much would like to know how they are wrong-headed, inadequate, or otherwise part of the problem rather than the solution to many of our woes in the teaching and learning of mathematics.

Please do not cite specific curricular materials from publishers like Pearson, McGraw-Hill, etc., as those are not the same as the above. Publishers have been free to put any words they like on their products for decade after decade. In the 1990s, the words paid lip-service to the NCTM Standards of 1989. In the 2000s they claimed to be aligned with NCTMs 2000 volume, Principles and Standards for School Mathematics. Now the magic words are “Common Core State Standards.” But printing those words on a book don’t make the words true. And in the case of all those sets of standards, there was enormous leeway for how authors & publishers (even the ones who actually were trying to tell the truth when they claimed to be aligned) to interpret and try to embody the standards.

Yes, there is an even longer set of standards in Common Core Mathematics, namely the content standards. But a careful reading of those shows that there is much room for authors to be creative in what they do. From what I’ve seen thus far, there’s much that could be improved on what has been offered by publishers. And meanwhile, I’m sure that the authors of the standards themselves will struggle with one another and any new participants in their committees to improve the particulars in the content standards. No volume of mathematics standards I’ve ever seen, including CCSS-M, is written to be static or permanent.

I write the above as someone who has been critical of the Common Core initiative and who is no fan of universal content standards in the first place (at least not mandatory ones). Frameworks are fine as long as people are free to depart creatively and appropriately from them. And the Common Core Initiative itself is highly problematic regardless of how good the actual standards offered thereby might be. The politics of how the Common Core was created, promulgated, and enforced are widely known to readers here and need no recapitulation from me. The high-stakes tests are terrible, but even if they had lived up to what was promised back in the early days of Obama’s first administration, they would still be a very bad idea. So again, I’m not defending any of that and have no interest in revisiting arguments against them. I was well ahead of the curve in criticizing those aspects of the CCSSI and have not changed my views in that regard.

What remains is my concern as a mathematics teaching professional that the old guard (as evidenced by the Garelick/Beals propaganda piece in the ATLANTIC and the puff piece written about it by Wendy Lecker) are using concerns of serious educators and parents as a way to continue their 1990s attacks on progressive mathematics education. Blindly supporting their viewpoint is an enormously shortsighted mistake that will, if successful, throw us back to the ignorance of previous “back-to-basics” eras like the 1970s/80s, the very rigidity and foolishness that fueled NCTM’s attempts in the late 1980s and early 1990s to move us away from primarily procedural learning as the be-all and end-all of K-12 mathematics teaching and learning. As always, be careful what you wish for: you might just get it.

I think I made myself perfectly clear that it is the high stakes tests that are WRONG, and that the Common Core Standards should be left up to teachers to teach anyway they see fit and also exclude any standards they don’t want to teach just like teachers are allowed to do with Finland’s standards. There should be no mandatory scripted curriculum linked to the standards that teachers are FORCED to use.

The testing mania to rank teachers, rank schools, rank children—and then punish them—MUST end now!

If we want children to be college and career ready, then the most important GIFT we could teach children is to enjoy and love reading and that is free because of public libraries. Something, I’m sure, is not wanted by the autocratic, for profit, corporate public education demolition derby. In fact, I’ve heard and read that these same privatization forces want to privatize and profitize our public libraries too, so readers have to pay to check out a book and read it.

For instance, the December 2015 Costco Connection features Stan Lee, who is the creator of Marvel Comics superheroes. He was born to poverty. He grew up in poverty. He’s 92 today and highly successful with a net worth of $50 million. The imagination and creativity that led him to this success comes from his love of reading books—-not a list of standards linked to high stakes tests that rank and punish. Click the link and read the interview with Lee and discover that a love of reading books is so much more important than Common Core Standards and high stakes tests.

http://www.costcoconnection.com/connection/201512?pg=29#pg29

@Lee: I’ll ask again: to what in particular in the actual Standards for Mathematical Practice do you object? Why won’t you answer that question? And if your answer is that there’s nothing in them to which you object, shouldn’t you state that directly?

I agreed that the testing is highly problematic and even that is an understatement. The overall CCSS-Initiative will always be deeply flawed because of, among other things, the linking of a screwy assessment system to assessment-neutral standards of practice and (separately) content standards.

I’d personally be fine if the content standards were either deep-sixed or redone in a host of important ways (not the least of which is to make them voluntary). But the mathematical practice standards are another matter entirely. And I guarantee that regardless of what is said publicly, much of the opposition from educational conservatives to the Mathematics Standards has to do with those 8 standards for mathematical practice. Those I do not believe can be voluntary. They form the core of an approach to thinking about mathematics and its teaching and learning that is absolutely central to the question of whether we will continue to spin our wheels for another century or actually begin to make progress in mathematics education for all our citizens.

Can you not step outside your focus on the assessment issues long enough to comment one way or another on the Practice Standards? I am confident that no one will suggest that you’ve sold out your overall opposition to CCSS-I by so doing.

“Mathematics Standards has to do with those 8 standards for mathematical practice. Those I do not believe can be voluntary. They form the core of an approach to thinking about mathematics and its teaching and learning that is absolutely central to the question of whether we will continue to spin our wheels for another century or actually begin to make progress in mathematics education for all our citizens.”

How the math standards are taught must be voluntary and teachers must be allowed to decide what methods and curriculum are used to teach them. No scripts. The standards cannot be copyrighted. They must be open source. Any technology used, must be the teachers’ decisions who teach math.

No, I stand against the mandated mathematical practice linked to these 8 standards. Math is not the key to lifelong learning. Literacy is. Literacy and a love of reading MUST be the focus. Once a child has a love of reading and a high level of literacy, they are a lifelong learner and if needed, can return to learn the math later in life.

How many jobs require all 8 standards of mathematical practice?

In 2012, about one-third of jobs were in occupations that typically require post secondary education for entry.

Forty percent of jobs only require a high school education and 26% don’t even require that. Only 18% require a Bachelor’s Degree.

It’s through a love of reading that children develop imagination and imagination is crucial to critical thinking and problem solving. Once a child has a high level of literacy, I repeated, they are a lifelong learner and can return to school to pick up any math they forgot or never learned.

Jesus, Lloyd. Read what I wrote and asked. You’re answering/refuting things I’ve not said. I have no interest in a mandated set of materials. I don’t particularly like the notion of a mandated set of topics, subtopics, etc. That pretty much does away with both meanings Americans ascribe to the word “curriculum.” And I have repeatedly stated my general dislike of the assessments and how they are misused and abused.

So, that leaves a set of 8 principles of what it means to do mathematics, know mathematics, learn mathematics, and teach mathematics (with implications for what we should, as teachers and learners, be assessing if we want to be able to say we’ve learned mathematics).

I’m a former English teacher, so you’ll get no argument from me against literature, reading, literacy, writing, etc. Trying to bait me along those lines is going to be a losing proposition.

But let’s not make the mistake of trying to prioritize one sort of thinking and learning over another. Who is to say that there are not more ways through the woods than one? You seem to be willing to throw mathematics under the bus because you value the power of literacy. I don’t denigrate the power of literacy – far from it. But I would be very chary of limiting education such that mathematical thinking is placed on a lower rung. There are too many children who would be hamstrung if we arbitrarily insisted that mathematics, science, art, or music were not on a par with reading and writing. And that seems somehow to be where you’re headed. And in that regard, how many jobs require competence in science, music, or art? Or history? Or political philosophy? That seems like a very poor criterion upon which to decide how to structure curricula. And isn’t that whole “college/career ready” propaganda a huge part of how Common Core has been marketed to us? Seems odd for you to be using it here.

Sadly, someone’s perception of math and its utility seems influenced by those teachers who did teach anything they wanted in any way they they wanted. The result is pretty predictable.

The standards for mathematical practice simply define good mathematics teaching and learning. That’s a big “simply”

The thing is—if a child has a high level of literacy and loves to read but doesn’t want to go to college, that child is still college ready if they change their mind later in life. I know because I did. I loved to read. Hated school. Didn’t want to go to college and then in my early 20s I changed my mind.

As for math, how did the world survive for centuries without these 8 CC principals of math? How did the U.S. send men to the moon and bring them back? How did the U.S. win World War II? How did the U.S. become the wealthiest most powerful country on the planet—for a few decades anyway?

Lloyd, I prefer arguing/discussing/exploring these issues with people who want to work towards productive goals rather than prove how stingingly clever they can be via ignoring what their “opponents” are actually saying. So if it makes you happy to think you’re “winning” something here by continuing to twist my words into bizarre claims I’ve never made and never will, be my guest. Much joy may it give you. More reasonable people have been thanking me for what I’ve been saying here. You figure they’re all nuts?

I hope you’ve read C.P. Snow’s THE TWO CULTURES. I’m one of those weirdos with one foot firmly planted in each, so I don’t need to choose a side. You’re blinded to the power, beauty, efficacy, and personal utility (in terms of answering meaningful questions about the world) that mathematics provides.

“La filosofia è scritta in questo grandissimo libro, che continuamente ci sta aperto innanzi agli occhi (io dico L’Universo), ma non si può intendere se prima non s’impara a intender la lingua, e conoscer i caratteri ne’ quali è scritto. Egli è scritto in lingua matematica, e i caratteri son triangoli, cerchi, ed altre figure geometriche, senza i quali mezzi è impossibile a intenderne umanamente parola; senza questi è un aggirarsi vanamente per un oscuro labirinto”

Galilei, Il Saggiatore 1623

“Philosophy [nature] is written in that great book which ever is before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.”

And for something more up to date, try my hero, Richard P. Feynman:

Or don’t: you can lead a person to knowledge, but you can’t make him think.

Correct me if I’m wrong but you think that part of the math standards you advocate as better than anything else ever used before should be mandatory for every math teacher in the country—no choice. Am I wrong about that?

I have no problem with any math teacher who likes the math standards or any part of them and wants to follow them. But I don’t agree with any top-down mandatory edicts that don’t give teachers choices on teaching methods, curriculum and material used for any subject. For instance, if a teacher wants to use Pearson material to teach, then that is the individual teacher’s choice.

I thank I have made it clear that I am totally against any top-down mandates from Washington DC and I extend that to state capitals and even elected school boards when it comes to teachers having the freedom to teach their subject without micromanagement from above, and this extends to all subjects.

If you think some or all of the math standards are better than any other method of teaching math, that is your opinion but your opinion should not be mandatory for all other teachers. That means you have to the right to promote those standards as an advocate only.

Management in education should be office managers and their job must be to support teachers—not order them around like generals sending troops into combat.

I taught from 1975 – 2005. I taught English, reading and journalism and for most of those thirty years, I decided how I would teach the material. When I started teaching, the state required that we test our students on every skill we taught, but we were required to create our own quizzes and we had to come up with a lot of them. We didn’t have to send that data to any central authority that would then rank us and punish us based on the results. That was a top down mandate that interfered with teaching.

If you do not like the way I respond to your thinking, then consider this. I was born with severe dyslexia and a test said I would never earn to read or write. I probably have attention deficit disorder because I’m easily distracted, but thanks to the harshness of Marine Corps boot camp discipline they literally pounded into the recruits, I learned to set goals and focus on them to overcome that ADD. I also returned from Vietnam with PTSD.

So you are debating someone who overcame severe dyslexia thanks to a mother who refused to accept the verdict that I would be illiterate all my life and she literally beat reading into me with a wire coat hanger until I fell in love with fiction that I wanted to read.

I’m one of those kids who was difficult to teach. The teachers who reached me—-and there were several of them from K – 12—were teachers who were free to decide how to do that without somebody else ordering them to do it only one way.

The first teacher was the one who ignored the verdict that I was a lost cause and she gave my mother advice on how to teach me reading at home—the coat hanger wasn’t part of that advice.

What kind of teacher was I? Well, that’s in my memoir—the one that I wrote from a detailed classroom daily journal I kept for one full school year in 1994-95. And for thirty years, I was a thorn in the side of those top-down management types who thought they knew what was best for all teachers. It’s called Crazy is Normal, a classroom expose.

It’s all about choice and empowering teachers to make the choices for themselves—-with support from other teachers—-on how to teach the subjects they teach and what material to use.

There aren’t federal mandates. There is federal funding provided by all US taxpayers. if states and localities want to avail themselves of that funding (~10%), then they can follow some basic rules. Such as don’t discriminate based on race or religion. Or uses some of that money for school in poor neighborhoods. Or actually require teachers to instruct based on quality standards.

Your state is free to turn down that funding. Go for it.

Virginia, what do you mean that the federal government can require teachers to instruct based on quality standards. The federal law explicitly states that no officer of the federal government may do anything to direct, control, or influence curriculum or instruction. That has been in the law since the 1970s.

Diane, states can devise their own curriculum and instruction. But they can’t receive money for using watered-down standards. If states decided that the only competency they wanted their high school graduates to achieve was simple addition and phonics awareness, the federal gov’t is well within its right to withhold federal funding.

If the feds tell the states how to go about teaching their standards, then I agree they crossed the line. But note that Virginia (and Texas I believe) never adopted CC and the feds had no problem with that. At least after Virginia upgraded its watered-down math standards around 2011/2012.

Virginia, I am not aware of the federal government withholding money from states because they didn’t approve of their standards and tests. Cite sources.

Good that you asked as I’ve been researching all these decisions for my VDOE case. While Washington state had its ESEA waiver pulled because it refused to evaluate teachers on student growth, Oklahoma’s waiver was pulled because it reverted to inferior standards.. Those standards did not comply with the rigorous standards required by ESEA (Common Core complies but so do the nonCC standards of Virginia, Texas and others). Oklahoma was essentially put on probation in 2014-2015 and since Oklahoma made “progress”, had its waiver restored for 2015-2016. More likely, given the new ESEA bill in Congress, US DoE just capitulated to avoid exacerbating the debate.

As to withholding funds, see Deborah Delisle’s letter to Oregon, specifically point #3. They can pull administrative funds and even programmatic funds.

VIRGINIA, in the new ESSA, the Secretary has lost his power to compel states to adopt the standards, curriculum, and assessments that she or he favors.

True, you won this round. Hasn’t been passed yet, though.

It will pass tomorrow, Virginia

Lloyd, have you considered what it means to teach mathematics in a principled manner – taking into consideration what people who actually use and/or do mathematics at some level beyond primary school bring to the various tasks that engage them? Those 8 principles pretty well some up what gets done. So if you’re going to teach or learn mathematics with no regard to those principles or some similar set, you’re almost certain to be selling yourself or your students very short.

Nowhere have I demanded that every student become a professional mathematician or a high-end user of mathematics (e.g., physicist, economist, engineer, etc.). But I would like to believe that every student is given the tools to go as far as his/her interests care to take him/her. You’re all about literacy tools and I’ve yet to see anyone suggest those aren’t important. But you seem perfectly willing to dismiss out of hand numeracy tools. And in so doing you really do propose to doom yourself and countless students to a monocultural view of the world and its possibilities. The fact is that mathematical imagination and maturity inform our ability to make sense of and accomplish things in this world just as much as do reading and other aspects of literacy. We can’t learn all the languages on the planet, but if we have one natural language, that’s a start. But no natural language will be adequate for dealing with mathematics or science or the things that depend heavily upon them. So why not try to make education give students at least the minimal tools for becoming well-versed in those areas for which natural language cannot possibly do the trick?

As for your latest switch to the issue of teacher choice: this is the old Mathematically Correct/NYC-HOLD ploy, not all that different if you probe deeply enough from the reactionary and greed-mongering rhetoric behind “school choice.” People like Mercedes Schneider talk about “choice” in ways that sound very reasonable and democratic until you look at what they’re advocating through the lens of, say, teaching evolutionary biology vs. creationism or intelligent design. The latter are not reasonable or adequate alternatives to real science. And teaching mathematics as a bunch of disconnected procedures that make little or no sense and merely need to be memorized long enough to pass some test of procedures is not teaching mathematics at all. It’s teaching kids to be machines, and we now have machines that are vastly better at number crunching than any human being can or needs to be. What the machines can’t do is actual mathematics. That’s where human beings come in. And the principles for mathematical practice (which look a lot like the much older NCTM process standards, not coincidentally) are a sound framework for teaching human beings, not future drones.

So where is the “choice” that you’re so concerned about, Lloyd? Which textbook series to use? I couldn’t care less about textbooks or publishers. Most are grossly inadequate to the task of teaching and learning school mathematics in the ways that matter in the long haul. A century or more of rote learning of mathematics in the “best” Prussian tradition of factory schooling should have taught us by now that the “choice” of which you speak will simply allow many teachers to continue to teach mathematics in the way it was taught to them. But math teachers are exceptions, not the norm. And the average American fears, loathes, and basically cannot do mathematics or think mathematically. Why should teachers have the option to perpetuate a failed approach that serves a minority of students, namely the ones most able to imitate their teachers?

There are more than tree million public school teachers in the United States. How can you prove that they are all using failed approaches to teaching math or any other subject?

Teacher training in the United States is all over the map. Every state sets its own standards from the flawed and inferior TFA approach with 5 weeks of training in a lecture hall to year-long full-time residencies.

California, for instance, requires teachers to keep up-to-date with teaching methods, curriculum, classroom management, etc. by requiring that they take workshops or classes and prove it to renew their teaching credential every few years. I think medical doctors do this too. No one mandates what workshops. lectures and classes they take as long as they are approved.

The myth that all teachers are using the same teaching methods and classroom management that teachers have been using for centuries is wrong. That is only a myth.

Possibly the answer is not a mandatory method or curriculum based on standards to teach math or any other subject, but better initial teacher training that never ends.

But the trouble with that is we return to the top-down mandatory do it our way or else we will punish you in some way, we return to a few people at the top who think their ideas are the only ones that work. Like Bill Gates who never attended a public school and never taught.

The alternative is to compare teacher training programs from worst to best. In fact, Dana Goldstein attempted to do that in Chapter 10 of her book “The Teacher Wars”.

The title of that chapter: “Let Me Use What I Know: Improving Education by Empowering Teachers”

We can’t empower teachers when someone—anyone—mandates how it must be done.

That way, if the element of the standards that you think is superior is superior then it should win out in the long run. When the powers at the top—Bill Gates, Congress, Governors, state legislatures, the President—don’t trust teachers and mandate it for them, that will not work in the long run.

Finland has standards but the govenrment of Finland does not mandate how those standards are to be taught or which ones the teachers should focus on. That is left up to the teachers. It’s called trust and treading teachers like the professionals they are.

By all means, support what you think is the best way to teach math, but don’t attempt to make what you think works best mandatory for all the other teachers.

The United States is ranked 4th or 5th in the world for the ratio of its citizens that have college educations.

You ask, “Why should teachers have the option to perpetuate a failed approach that serves a minority of students, namely the ones most able to imitate their teachers?”

Yet, according to NMS.org, 44% of high school graduates are ready for college level math courses and 36% are ready for college level science.

You ask about choice. Children make choices too. They are the ones who decide what to major in. If they are not interested in a STEM major, that is their choice. According to NMS.org only 38% of students do NOT graduate with a STEM major. Subtract and that means 62% do graduate with a STEM major.

Do you advocate taking away the right of college age students to make choices of the majors they want to graduate in? I question some of the claims made in the NMS.org paper, because bls.gov reports that only 18% of the jobs require a Bachelor’s degree but 30.4 percent of people over age 25 in the United States have at last a BA. In fact, the number of College graduates—many of them with too much student debt to pay off—in the United States with a BA or better is increasing at a dramatic rate.

https://www.nms.org/AboutNMSI/TheSTEMCrisis/STEMEducationStatistics.aspx

http://www.bls.gov/careeroutlook/2014/article/education-level-and-jobs.htm

If you think there is a STEM shortage due to K-12 math teachers using the wrong methods of teaching, then maybe you should read this from The Atlantic.

“Because labor markets in science and engineering differ greatly across fields, industries, and time periods, it is easy to cherry-pick specific specialties that really are in short supply, at least in specific years and locations. But generalizing from these cases to the whole of U.S. science and engineering is perilous. …

“there continues to be a large pool of top science and math students in the U.S. OECD data on ‘high-performing’ students suggests that the U.S. produces about 33 percent of the world total in this category in the sciences, though only about 14 percent in mathematics.”

THE WORLD TOTAL – did you read that?

The population of the United States is less than 5% of the world total, yet we produce 33% of the world total in STEM majors and 14% in math.

http://www.theatlantic.com/education/archive/2014/03/the-myth-of-the-science-and-engineering-shortage/284359/

Obviously, a lot of math teachers K – 12 are doing something right even if they aren’t doing what you advocate.

Lloyd, any time you would like to have a conversation in which you stick to what I’ve actually said or implied, that would be ducky. I’m not going to refute straw-man arguments in which you turn me into the Scarecrow.

Take a look at Japan, Lloyd: I’m never going to suggest that we could ever be Japan nor that it’s desirable that we try to become Japan. But they know some things about mathematics education we appear unable or unwilling to grasp. One of the most important is that having an underlying set of beliefs of what it means to know, do, learn, and teach mathematics is a good idea. When you grasp that that is NOT tantamount to some nightmare of Math Commissars controlling and/or scripting teachers’ every move, then we’ll possibly be able to have a meaningful conversation about mathematics teaching and learning.

For a guy who comes out of a military background, you seem terribly loath to consider that every discipline and profession has some standards and operating principles. If freelancing and freewheeling approaches to mathematics teaching looked like the sorts of things that crop up from the teachers on the list of bloggers I offered earlier, I’d be all for it. But they are the exception, not the rule, and all of them are very much operating with the framework of the principles I listed, regardless of whether they ever read them. It’s like the notion that most medical professionals would come to accept the Hippocratic Oath’s precept of “First, do no harm” because, like the Golden Rule, it’s simply “right.” As someone who has never taught mathematics, you seem powerfully invested in disputing a set of principles that every competent mathematics teacher I’ve ever worked with or learned from has to some extent incorporated in his/her practice. I find that very odd indeed. And dyslexia just doesn’t account for what you’re doing, on my view.

Let’s not forget that the Japanesegot much of what they do now in math education from our NCTMStandards in the 1990s.

Peter, the give and take between the US and Japan (as well as other Asian countries) has been on-going for decades, and it would take a historian of mathematics education with access to information from the relevant countries to determine chicken-and-egg issues. Japanese lesson study does not appear to have a precedent in the US, but there are clearly ideas from the 1989 NCTM Standards that appealed to mathematics educators and educational psychologists from Asia (I know that directly from having met with some of those during my graduate work at U of Michigan from 1992-98). At this point, it’s a little hard to say who has been the bigger influence on whom, but my personal take is that Asian countries are more adaptable: if they see something works, they’re quick to try to implement it. And in countries where there is a reasonable degree of homogeneity (economically, ethnically, culturally etc.) and/or centralization of education (but not the Common Core top-down sort, but more of a flowing back and forth between rank-and-file teachers and ministries of education), it’s feasible for change to occur in terms of classroom practices.

Where it’s been much harder to effect change in Japan and some other Asian countries is in the role of Big Tests, which function for students in ways truly unimaginable to Americans even now. Nothing here competes with the importance for students of the national examinations for college entrance in Japan, China, and some other Asian countries. I wrote about this in 1993 and have yet to see evidence of significant change, despite much lip-service being paid towards the idea of reducing the significance of these tests (ironically during the quarter century when political and financial interests have been successful at pushing us closer to a model that leads to truly young children being physically and psychologically sickened by high-stakes tests) and despite burgeoning cheating scandals in places like Mainland China.

It’s still really difficult to get any sort of wide-spread adoption of the sorts of ideas that are inherent in the NCTM Process Standards and CCSS-M Standards for Mathematical Practice (yes, the ones Lloyd decries). Reading the Lecker article and the one she admiringly cites, comments from some folks here, and it’s not that difficult to understand the problem. If Common Core had never happened, the Math Wars would still be raging, but without Obama, Duncan, Coleman, Pearson, et al. to pin blame on or give praise to. I’ve been writing about that for much of the Obama Era, but the underlying resistance to progressive mathematics education principles and practices is so entrenched (and, on my view, NCTM did such an incompetent job of promoting its own best ideas, and then doubled down on its poor judgment by uncritically accepting the Common Core Initiative, not unlike the premature endorsement of Obama in 2012 and Hillary Clinton now by teachers’ unions – if not the rank-and-file membership) that I’m not confident that we’d be any further along in the process of improving things than we are. But as I’ve been saying here, what worries me isn’t the demise of the Common Core, but the idiocy that will come in its wake. More fundamentalist/right-wing and politically correct/left-wing censorship of K-12 textbooks and fiction reading? Another dance with the back-to-basics dragons? Further rejection of progressive history texts and teaching? Equal time for “creation science/intelligent design” in our science classrooms? When the dumbth triumphs, we all lose, and from what I’ve seen of much of the reactionary opposition to Common Core (along with some of the left-wing opposition), defeating the Common Core is not about to usher in any sort of enlightened era of curriculum, pedagogy, policy, or anything else in public education.

Here’s how I interpret your statement: “Lloyd, any time you would like to have a conversation in which you stick to what I’ve actually said or implied, that would be ducky.”

This means you control the parameters of the conversation. Most of what I wrote reflects on your allegations that teaching math in the United States must follow at least one element out of the Common Core standards.

It is arguable that I made my case—by going outside of the parameters you want to stick to so you can control the arrangement—-that it isn’t necessary for every K-12 teacher in America to teach how you think they should teach.

How about a simple answer to one short question—I think I’ve asked this a number of times now and you just keep accusing me of strawman arguments?

Do you want to mandate, using an element of the CCSS, how all math teachers in the US teach math? Please keep your answer short.

Yes, well, call me crazy, but it find it difficult to debate someone who asks me if I’ve stopped beating my wife, if I still support the fascist control of everything that goes on in classrooms, or if I would prefer to see students flayed alive or merely drawn-and-quartered.

I have no interest in controlling what you post, Lloyd, nor do I harbor any illusions about being able to do so. But when you respond to what I write with a bunch of straw person arguments, that’s simply not something I care to support. Is that unreasonable of me? Is that “controlling” things too much for your taste?

I’ve more than adequately described what I’d like to see happen in our classrooms when it comes to teaching mathematics. Unfortunately, you’re unwilling or unable to hear it. More importantly, I have spent about 25 years now seeing almost nothing that looks like what I’d call effective and principled teaching in mathematics classrooms. And that’s giving a rather large amount of room for what comprises both “effective” and “principled.” And I’m hardly alone in that regard. I had a memorable conversation on this issue more than a decade ago, in 2004, with James Hiebert, co-author of THE TEACHING GAP (http://bit.ly/1ND7QF7) five years after that books appeared. I asked him about how much of what I’ll call ‘progressive-reform’ math teaching was going on in the USA (you might prefer NCTM-style math teaching, constructivist mathematics teaching, or something else): his answer was that if we randomly selected a city, school, and classroom at random on a map of the United States, the probability that we’d see a reasonable instance of the sort of teaching he and James Stigler wrote admiringly about in their book was effectively zero. I have seen little in the ensuing eleven years to make me believe that the number is much higher today. Too many people like Katherine Beals, Barry Garelick, etc. helping to support teachers who have little or no inclination to change at anything but the most superficial of levels. And despite NCTM’s fond fantasy that going along with the Common Core as uncritically as they did would bring about the reforms they’d hoped for in the 1990s thanks to the power of the US Department of Education and many state governors getting behind the Common Core, they badly miscalculated once again. They preserved their track record of rarely missing an opportunity to miss an opportunity to seize the momentum in the effort to really improve what goes on in mathematics education in the US.

“I’ve more than adequately described what I’d like to see happen in our classrooms when it comes to teaching mathematics. Unfortunately, you’re unwilling or unable to hear it. More importantly, I have spent about 25 years now seeing almost nothing that looks like what I’d call effective and principled teaching in mathematics classrooms.”

True, I’m not interested in your ideas about math. What I’m interested in is if you support mandatory top-down management that orders teachers to use one method of teaching math that’s linked to the Common Core Crap—as I like to think of it.

Instead, you keep leaping on your allegations of me making straw man arguments and not sticking to the narrow confines of what you want others to agree to.

No mention of that fact that the U.S turns out 14% of the world’s college math degrees while the U.S. has less than 5% of the world’s population. No mention of the fact that about a third of college graduates in the US earn STEM degrees and the U.S. is ranked 4th or 5th in the world for the ratio of college graduates and probably is #1 for the raw number of college graduates with a BA or better.

As for straw man arguments, in the previous comment, you offered only a conversation you had years ago with one person who alleged that he could pick a school at random out of almost 100,000 public schools, 15,000 public school districts that teach more than 49 million students and not find one math class being taught the way he and you want math taught.

You have offered a perfect example of someone who wants top-down management all based on what you think and you could be wrong.

Lloyd, you’re a prisoner of your own paranoid fantasies. I work my ass off to ensure that teachers aren’t put under the thumb of the Common Core or the particular curriculum assigned to them.

And that’s all you need to know about me. Accusing me, even obliquely, of favoring top-down management absent substantive proof is a clear indication of how little you know what you’re talking about. I’ve worked against that sort of nonsense my entire career. Sorry you feel like you’re in a position to cast aspersions towards my professional integrity simply because we disagree on whether the Principles of Mathematical Practice are a sound basis (note the indefinite article there, Lloyd) for building principled teaching and learning of mathematics.

You have something better to offer perhaps? Something nearly as good? Of course you don’t, because you’re not a mathematics teacher and you apparently border on the seriously clueless when it comes to what sound mathematics learning or teaching is about. That’s okay. Ignorance isn’t illegal. But being way out of your depth and pretending to have some sort of expertise is intellectually dishonest and fundamentally unethical. Kind of like driving without a license only a lot more people are likely to be hurt in the long run.

You don’t see me insulting your experiences as an English teacher. But you sure seem to think that you have me pegged as some sort of “math Nazi” because I won’t submit to your know-nothing comments about mathematics and its teaching and learning. Give up while you’re behind.

Instead of attacking me again, all you had to do was say, “No, I don’t support any top down management that tells teachers how to teach or what curriculum or materials they use.” It was that simple.

Yeah, Lloyd. I’ll keep that in mind the next time someone recklessly accuses me of holding views 180 degrees opposite of everything I believe in. Because after all, you meant no offense or harm is so doing and were just waiting for my assurances. How could I have been so blind as to what you’ve been up to all weekend on these issues?

On Sun, Dec 6, 2015 at 9:33 PM, Diane Ravitch’s blog wrote:

> Lloyd Lofthouse commented: “Instead of attacking me again, all you had to > do was say, “No, I don’t support any top down management that tells > teachers how to teach or what curriculum or materials they use.” It was > that simple.”

Correct me if I’m wrong, but I don’t remember that you ever clearly stated that you were against all top down mandated methods of teaching in any subject.

And where did I accuse you of holding views 180 degrees opposite of everything you believe in?

Lloyd, Michael: enough! You are both smart, thoughtful, articulate–and on the same side. Get a grip and shake hands. No more verbal fisticuffs.

So I’m guessing that every ELA teacher should be allowed to teach reading or composition or grammar or punctuation or literature any way they feel appropriate and teach any content they feel appropriate?

And further we shouldn’t bother with literature – novels, poetry, whatever – because so few actually read these after schooling?

I’m hearing the very attitudes of someone that were created by not being taught good mathematics and not taught it well.

The great problem is that many adults rightfully remember their experiences in dull, boring, meaniningless math classes.

What is not right is that they seem to want children, even their own, to have the same experience.

Sort of like having to read Elegy Written in a Country Churchyard and expecting a kid to like poetry.

@Peter Smyth wrote in part: “I’m hearing the very attitudes of someone that were created by not being taught good mathematics and not taught it well.”

Indeed. It’s like the blind led by the blind, then advocating for putting the eyes out of all sighted people. Sounds like a marvelous plan for ensuring that we move steadily backwards towards complete innumeracy, except for the elite.

Nothing against the Marines for building marvelous fighting machines where human beings once stood, but my previous mention of Prussian education was not intended as praise for that particular 19th-century incursion into American classrooms and schools. Far from it. I’m sure that the whole “few good men” thing is a great idea, with the emphasis on “few”: I have no objection to those who self-select into that sort of training to do so (well, to be honest, there’s nothing I can do about preventing people from seeking that sort of thing, regardless of my opinion of it), but I’m sure as hell not interested in seeing military training principles inform public education on the whole. I don’t recall democratic core values being central to the sort of blind obedience drilled into the military. How intriguing that someone with that background would oppose the sort of mathematics teaching and learning that promotes independent thinking and confidence in individual mathematical power.

In a nation where math education has been a consistent disaster for well over a century (check the history of American reform initiatives in math & science education throughout the course of the 20th century), you’d think that by now the hard-liners would have to admit that they can’t get the job done. Instead, they just double down on all the wrong ideas and demand that after every attempt to move us an angstrom or so towards progressive math education (which they fight furiously every step of the way and thereby succeed in undermining for all intents and purposes) we take three steps backwards to the tried and failed drill and kill approaches. It’s almost a miracle that anyone at all takes a single mathematics course once s/he reaches the minimum requirement.

@M.P.G.

“I would like to know what criticisms you and other readers of this blog have of those eight principles.”

I don’t think the criticisms are of the principles themselves but the insistence by many that these practices are the best.

Good math teachers use many avenues to instruct their students. As a math teacher of over 25 years, I resent being mandated to teach math using on method over another. I am always willing to try new methods but if I don’t feel that the method is good for my students, I won’t use it.

Having students use modeling when teaching fractions is a useful strategy but having students model algebraic equations (outside of special ed) is crap.

What practices? I don’t see any practices. I see principles. How you or students put those into practice is quite a varied matter. If you can show me where in that list there is a specific practice, I’d like to know. I’ve been teaching for over 40 years, and mathematics for about 35 in one capacity or another. Everything in that list makes sense to me and represents things I feel extremely comfortable with as undergirding any sensible, effective teaching or learning practice.

And I beg to differ about modeling of algebraic equations being crap. But then, you’re not very specific at all about what you mean by “modeling.”

Diane,

Okay.

Anyone have a link to the place in the Common Core Standards for Mathematical Content or Mathematical Practice that explicitly suggests students should NOT learn basic math facts.

I’ll wait.

Garelick and Beals are still fighting the Math Wars c. 1992. Lecker blindly supports them with the fashionable buzz words “brain research.” For a cherry on top of this garbage sundae, we get the shop-worn Math Wars phrase “doesn’t add up” (if someone had only thought to copyright that in the early 1990s, she’d be very wealthy today).

But since nowhere does the Common Core Standards call for students not learning basic mathematical facts, this entire argument is nonsense. Just as it was nonsense when earlier versions of it appeared from groups like Mathematically Correct and NYC-HOLD and their off-shoots in the 1990s, claiming that the National Council of Teachers of Mathematics (NCTM) was calling for the replacement of arithmetic with calculators and replacement of all teacher-centered, explicit instruction with student-centered, discovery-based “constructivist” mathematics (“constructivism” is to “Math Warriors” like Garelick and Beals” what “communism” was to Joe McCarthy: a scary term they either don’t understand or deliberately misuse to terrify laypeople like Wendy Lecker and the average parent).

It’s one thing to be critical of specifics in the Common Core Mathematics Standards, as many knowledgeable, experienced mathematics educators and teachers have been (before the “Math Warriors” and many of those same politicians Ms. Lecker criticizes in her headline discovered that there was treason lurking in a general outline of mathematics content for K-12 education). It’s quite another to suggest that the professionals who developed those standards were clueless.

What he said.

I second that and reserve the remainder of my time for MPG!

@Stiles: very kind of you.

You state that CC standards are not the problem but how accurately are any of the items you list measured in a standardized test? Isn’t the problem that CC standards are tied to the tests? Aren’t the tests, then, the curriculum? Who develops the tests? The very same professionals that developed the standards?

1) Make sense of problems and persevere in solving them.

2) Reason abstractly and quantitatively.

3) Construct viable arguments and critique the reasoning of others.

4) Model with mathematics.

5) Use appropriate tools strategically.

6) Attend to precision.

7) Look for and make use of structure.

8) Look for and express regularity in repeated reasoning.

@Michele: do you see no meaningful difference between the standards for mathematical practice and any particular set of tests that a state, district, or school chooses to administer (or mandate)?

The two assessment consortia affiliated with CCSS-I were SUPPOSED to be creating tests that would align better with the principles of the practice standards. I would say (and I’m hardly going out on a limb here) That they failed rather dismally. No doubt that failure was close to inevitable given how politics and profit conspired to control assessment affiliated with CCSS-I.

But it is not inevitable that assessments have to work at cross-purposes with progressive standards for mathematical practice. NCTM has worked on this issue with varying degrees of success since the early 1990s. Had NCTM been more effective as an organization at promoting its best ideas about mathematics education rather than being depressingly naive about the backlash it engendered and how to reach out to the general community in the face of concentrated and well-organized opposition, we might already have a large repository of good-quality assessments to examine.

However, as I tried to suggest in an earlier comment, no amount of success at designing truly good tests will matter in the face of bad political manipulation of the uses to which assessment is put. Period.

Thus, it’s really not a useful question to ask whether we see much or even any reflection of the Standards for Mathematical Practice in the high stakes assessments making the rounds within or without the context of the big testing consortia: the question is in fact irrelevant. In that context, nothing in the way of quality matters, only those with the power to control assessments and the uses to which they are put can matter. In the face of wrongful abuse of tests, even the best assessments become an abomination.

From my perspective, CCSS-I will pass, probably sooner than many people imagine. The high-stakes testing is doomed. People will learn sooner or later how to work around the bullshit. But meanwhile, it is vital that we not dump everything in a feverish attempt to “cleanse” ourselves of a perceived evil. The Practice Standards are sound. We need them. And it would be tragic if we allowed reactionaries to convince us to do away with them by appealing to our dislike, however legitimate, of other elements in the Common Core Math Standards.

“The Practice Standards are sound. We need them.”

I disagree. The only thing we need in life is food, air, water and shelter. Money is optional since hundreds of millions of people around the globe survive without cash. Hopefully, the food, air and water will be clean and safe.

I repeat, every child does not need the practice standards that you advocate. You might want children to practice those standards but those children don’t need them.

The children don’t need them and teachers don’t need to follow them or be mandated to teach them.

What jobs and how many jobs require the knowledge those standards are alleged to provide? For instance, do the hundreds of thousands of gardeners who mow lawns and clean up yards NEED those math standards? What about all the drivers who deliver the US mail, FedEx or UPS? What about all the military troops who make the military a career? What about auto mechanics? What about all those clerks in the service industry that work for Target, Costco, Wal-Mart? What about all the people who work for small business in the retail service industry? What about carpenters? I’m a woodworker (my hobby) and general math is more than enough for me to build a house or a table. I don’t need algebra or Trig or geometry or calculus to do that.

Back to the most important skill for lifelong learners—a high level of literacy and a love of reading books. We don’t need mandatory standards and high stakes tests for developing a love of reading.

Lloyd, you are deliberately misinterpreting my point. If we go in the direction you’re insisting upon, I’ll just go you one better: who are you to determine that children need ANY of the things you list? My point was that to learn the sorts of thinking and habits of mind that allow one to learn mathematics meaningfully and effectively, those practice standards are essential. If a kid chooses not to learn mathematics, I can’t and won’t force him/her to do so. But I can ensure that we don’t make the possibility of learning mathematics an irrelevant torment.

On the other hand, there are children who choose not to pursue the pleasures of literature and literacy. Who are you to insist that they must? And if you have the right to promote that learning, why is it wrong to promote the learning of mathematics? Something is deeply inconsistent in what you’re saying as far as I can see. Whether it comes from a willful distortion of what I’m getting at or simply a strange disconnect between “the two cultures,” I’m not sure, but I can’t find a coherent argument in what you seem to be advocating.

Okay, so children don’t NEED to learn to read to survive. After all, my older brother survived to age 64 before he died and he was illiterate all his life. He was never homeless. He always had car and a place to live.

Lloyd, if I wanted to continue a pointless argument with someone who refuses to respond to what I’m saying and instead twists every point into absurdity, I’ll know whom to look up.

Lots of luck to you in the world of utter sophistry. I’ll be working with kids and teachers to ensure that the latter give the former maximum opportunities to become numerate and aware of and open to the usefulness and beauty of mathematics. I can’t imagine that your paths and mine will ever cross outside of the Internet, given as how we apparently live on entirely different planets.

Thanks for taking the time to lay out the argument in a way that those who do not teach math might understand.

@bmarshall: you’re welcome, although I don’t know that I did the argument justice quite yet in this particular thread. It’s very complex, and one thing I’ve found in the latest phase of the Math Wars (that is, the Common Core phase of the Math Wars) is that complexity and nuance aren’t welcome. We’re supposed to have picked a team/side by now and determined that CCSS is 100% evil and deserving of permanent abandonment. Most commenters here would no doubt agree with that sentiment.

And yet, despite being an early critic and non-adopter of CCSS-I, I can’t simply reject everything in the Math Standards (as a former English teacher, I’ve steered clear for the most part of the literacy wars, pre- and post-Common Core, though I’m now eagerly awaiting information on which rejected literary theory is at the heart of CCSS literacy), but when someone tries to entirely dump on those math standards, my annoying inability to not take an absolutist position keeps kicking me in the shins and saying things like, “Are you seriously going to let that go by unquestioned and unchallenged?”

Why I haven’t learned by now to be a good little soldier and accept unquestioningly that the label “Common Core” guarantees Satanic motivation and content therein eludes me. I want to be a True Unbeliever: really, I do. I want to be able to simplistically eschew rational thought. It’s so much easier than actually sorting through things and asking questions like, “So after all this is gone, Obama and Duncan are distant memories, and some new era has arisen, what then?” Because from much of what I read, the goal of some of the fiercest critics of the mathematics standards is to get “back to basics.” And as we read here earlier this evening from Veritas, to the time when kids did as teachers told them, unquestioningly, and men were men, women were women, and all was right with the world.

I went to school in 1955-1968. I missed that era. Anyone here live through it? My parents missed it in the 1930s-40s. When did it sneak in?

I have reflected most of the day on the conversation we had yesterday on this blog. I must admit much of what you said is correct and I came to this conclusion when I recalled some difficult classes that I took but was unable to do well in them. For most of the math classes I took, including calculus, I could earn an A by doing problems but not really understanding what was going on mathematically. This weakness showed up when I took a college business calculus class and still shows up when I do probability. Needless to say, I am glad to have realized this and think it is imperative that I research more of the websites you have referenced here. Along those lines however I do feel there is a place for memory and even drill and kill. But I must admit that I do like some parts of common core at the high school level; I said some parts. I do like how we are teaching mathematics as related to the real world and not just problems that only have relevance in a mathematics classroom. Above all, today I recalled many times over a long career where I have put the question to the students: Does this make sense to you?

Interesting, Veritas. Now I have to reflect on what you just wrote in the light of what I see all the time as a coach and teacher, and what I read from the (mostly) young mathematics teacher/bloggers whose ideas and practice I find so inspiring and admirable. I’ll get back with you soon.

There’s two kinds of math. One where you solve equations, and one with lots of words. Common Core seems to lean heavy on the word side. Still, a lot of it boils down to rote memorization of terminology, which doesn’t mean deeper understanding of math.

What’s the opposite of 7? LIke, what’s a pile cap? Very important terminology to memorize or just peripheral mental debris?

Pardon me, TC, but if you don’t think understanding what the “opposite” of 7 is matters, you don’t know much about mathematics. And in fact, there are two opposites of 7: the additive inverse, which is -7, and the multiplicative inverse, which is 1/7. Both are vital pieces of knowledge that undergird the foundations of arithmetic and algebra.

I recommend eschewing the word “opposite,” which is ambiguous out of context, and using additive or multiplicative inverse where appropriate.

And I recommend not making ridiculous overgeneralizations about the mathematics standards in Common Core. Despite the current doctrine most generally espoused here, the problem isn’t the standards for the most part. And confusing various publishers’ attempts to rake in $$ via their “aligned” textbooks with what is actually written in the Mathematics Standards documents bespeaks intellectual laziness (if you’ve not actually read them) and the sort of lock-step ignorance that continues to keep the United States spinning its wheels when it comes to improving mathematics education for all Americans.

Hey, I’m not the one stamping Common Core aligned on the texts and tests.

@TC: I guess you agree with me that knowing what additive and multiplicative inverses are is important, as you did not attempt to refute my claim. I appreciate the agreement and assume you’ll want to withdraw your previous comment, at least in part.

“Opposite” of 7 means nothing outside the context of the axioms and theorems in play. I can establish a system where the concept of opposite of 7 is a happy face. Rote learning is better addressed as fluency. Human working memory is severely limited. Only if students understand concepts to the point they are second nature can they move on. Example. If students know long division by rote only, they struggle when understanding polynomial division later to get asymptotes.

Common Core is incoherent and rambling. Standards by definition are MEANT to restrict freedom and stifle innovation. Teachers need the flexibility to reach into the tool box and pull out what works for a student – memorization, concepts, repetition, reasoning. Common Core, VAM, and misuse of technology isolates the teacher from the students and forces us to apply what we know are junk sciences. If we do not use the garbage Common Core and VAM mandate, the Reformers seek to push you out and find another who will without question. It is a no win.

Yes, I agree that math concepts are important and knowing the additive inverse and multiplicative inverse are important. My argument is with semantics. I could do division and calculus. If you tested me ought of high school or college what the divisor or dividend was, I couldn’t tell you.

Memorized mandatory semantics for math by grade. Where’s the list?

Happy to sound off! I get very tired of the Black-white thinking and “throw the baby out with the bath water” arguments of our US society.

Math Wars refers to the back and forth we have experienced in US education between math as practice and memorization, and math as understanding numbers and numerical literacy. Why does it need to be an either/or argument? Personally and professionally, I want my children and students to do both. If we were arguing how much of each, when to do each, how often to use memorization versus conceptual understanding, THEN I could agree with the authors of these arguments. Teachers AND parents want their children to not only be fluent in needed math practices like addition, subtraction, multiplication, and division but also want them to UNDERSTAND what those operations mean mathematically, when to apply them, and WHY to use one method over another in any given circumstance. Why do we always think it is either one or the other when it comes to American education? These types of arguments cloud the very real and important research and discussions that we should be having.

I welcome Common Core in both reading and math because it brings meaning back to the purpose of why we do these things. That is not a bad thing and I would be shocked if someone tried to say that it is. Balance is the key people! Should Common Core be revised to support what we best know about developmental ages and leaning? Certainly. Should we shut it down because there may be some standards that are off the mark? No.

We need to have discussions and build practices and evidence to define HOW MUCH of each is needed for a solid math learning experience for all children. To argue one or the other is like the phonics versus whole language reading wars. Both are based on faulty white-black thinking. Any experienced and successful teacher knows that while teaching phonemic awareness, you better also instill a love of words, a practice of seeking to understand the words beyond sounding them out. Otherwise, why bother reading?

My point here is we seem to think in education (and most other spheres of US society) that we can only argue at the two extreme positions when depth of thought actually occurs IN BETWEEN the two extremes. We need to start asking the questions: How much? What works best at each developmental level? Which method of instruction works best with this type of material? We need to stop asking either/or garbage questions that lead to opposing sides and unending arguments that are not real to actual educational practice.

I don’t think “we” really care about a lot of things that are supposedly scientifically proven or indicated. “Brain research” indicates that children learn foreign languages at an early age yet most schools still start teaching languages in the middle grades. Research indicates that high schoolers need to sleep later yet most schools still start too early in the morning. So, what really matters in the end is money and who will pay not “scientifically proven” and what is indicated by “brain research.” And Lloyd, I totally agree with what you say about memory in the above post!

Diane, I think most on this board would agree that you need both.

Repetition is needed in some cases. Just like an athlete trains his body to perform an action from muscle memory, kids should learn things like multiplication tables (up to 9×9 and 9+9 at least) so they can perform other tasks like multiplication.

However, once the basics are covered, conceptual understanding is needed. I played basketball extensively for 25+ years. I felt the ball was an extension of my hand. Now, when I pick up a basketball, I have to focus on being able to dribble under control. Memories can fade. There is only so much one can memorize and it fades over time.

I am now teaching my child greatest common factors and least common denominators. I was brainstorming on how I could visually explain GCF. I’ve settled on using the area representation of multiplication. In other words, when you multiply two numbers, you are really just creating a rectangle whose lengths are represented by the two numbers and taking the area. In finding the GCF, you are making rectangles of equal width from each number where that equal width is as large as it can be. From there, you can compare the relative heights of each.

Let me give an example with 48 and 36. They can be factored into 2^4 * 3 and 2^3 * 3^2. We can create rectangles of 12×4 and 12×3 to represent the two numbers. Our rectangles can’t get any wider and still have the same width for each number. We can now see that the first number is 4 units tall and the second is 3 units tall. The first is 4/3 of the second one.

Now, I teach my child to find the prime factorization of each number and then find all the common terms first. That’s the algorithmic approach and is needed to solve problems rather quickly. But she may forget that part. When she understands that GCFs are just finding the largest width that can be used to make rectangles out of two numbers so we can compare their relative size, that concept is not easily forgotten.

If I were to teach other kids GCF algorithms without teaching them this concept, they would forget within a few days. But since our brains retain pictures (think about tricks to remember names) and concepts more easily than algorithms, a conceptual understanding is needed.

The same applies to virtually every math topic taught in schools today. And it’s why we need teachers who really understand this stuff. It’s not fair to ask an English major to teach a conceptual understanding of math when they likely never were taught math in a conceptual way (or have an intuitive feel for it).

But make no mistake, the emphasis on conceptual learning is critical. We can’t abandon all the algorithms, but concepts are key.You make a great argument for smaller classes and freedom from restrictive standards and the Damocles sword of VAM testing. Standards, by definition, inhibit freedom and stifle innovation. VAM testing forces certain process and approach to how conformance to the standards.

But because one concept works for your small sample, does not mean it easily extends to a classroom of 30. Then throw in students with challenges and outside influences. Some children are not visual and do understand procedures and process better. Others like to be told how it works or learn by examples. Still others love the abstraction and axiomatic reasoning. Reformers have such a hard time understanding that teaching is very much an experimental, human activity not easily replaced by simple minded metrics or algorithms. There is no single right way.

I agree with MathVale. Some students just want the bottom line and want to get through the problem. In fact, many of my gifted math students would rather learn the procedure then connect back later.

I know tons of students who would like to just be told the answer and not have to think. I know plenty who would like to not have to take mathematics at all. I know quite a few who would prefer to stay home and play video games and listen to music all day.

I’m all for taking student preferences into account up to a point, but I won’t let them dictate what it means to do principled teaching. They’re mostly too young, too inexperienced, and too corrupted by what passes for education in this country (“go for the grade, not the learning”) to have a clue.

Great idea for a simple visual for GCF!

You could also do that with denomination of currency from a funny bank that can issue it in any integral denomination. So, you want two stacks for each number using the greatest denomination (fewest bills).

You could also represent the bills by rectangular units, and the stacks would be the same rectangles you got. I like the rectangle visual.

This or something like it should have been in a widely distributed text years ago! You shouldn’t have to re-invent freakin’ wheel after freakin’ wheel, pardon my carpentry jargon. Nor should any teacher.

Actually, the CCSS for Math contain standards that address fluency in math facts for grades 1-5. Additionally, 4th and 5th grade standards address the need to master the standard algorithm for multi-digit and division. It’s all right there in the CCSS. Surprised the author didn’t bother to do this basic bit of research.

So, if a high school teacher needs to beg parents to teach their kids long division, it’s not because of the Common Core.

My issue is more about the sheer number of standards and the often abstract difficulty of those standards. We are flying through concepts in order to cover everything in the third grade. Multiplication/Division fluency is in there, but so is everything else. It’s too much, too soon, and it’s really harming my students with special needs.

Does anyone have the link to the Stanford study Wendy Lecker cites? As a person working in educational neuroscience, I’m not familiar with that study, and she chose not to link to it in her article. There are few things more common in contemporary journalism than getting neuroscience wrong. (BTW, I’m personally all in favor of kids learning arithmetic facts, just not convinced this is a matter of neural determinism.)

BTW, with respect to a previous commenter’s claim that neural factors cause children to learn languages better at an early age: Not only does this mischaracterize “brain research,” but behavioral research suggests that age of acquisition may be less of a factor than the amount of use and exposure and dedicated practice of the new language–at no matter what age a person starts to learn it. (see Flege et al, 1999 in the Journal of Memory and Language)

Russell, here is the link to the study. The author posted it in the comments section.

http://www.ncbi.nlm.nih.gov/pubmed/25129076

Russell, thanks for the tip on the Flege et al study. Thorough & illuminating (tho I think you overstate the results; it certainly supports early start). I’m currently browsing a 2011 paper which addresses this & other overlooked angles of acquiring L2: “A Critical Review of Age-Related Research on L2 Ultimate Attainment”, by Muñoz & Singleton.

This post show a real misrepresentation of “brain science” and misunderstanding of how we actually learn math.

But maybe it’s a misunderstanding of what comprises math.i would not hold up the traditional method of long division as math: it’s arithmetic, and it’s just an algorithm.

@Peter Smyth: you appear to have noticed, as I and others have, that “brain science” has become a new chant with which to dismiss whatever some people dislike or promote what they favor.

Wouldn’t it be refreshing if we were more intellectually honest and careful about using popularizations of science instead of actual science? And more cautious about citing single examples social science research as if it could be taken as absolute proof of sweeping generalizations (usually just the ones that fit prejudices and preconceptions)?

MPG, I almost just said “brain science?” and left it at that. I, too, expect more intellectual honesty and maybe avoidance of junk science on this blog.

Agree, the skeletal info acquired from the study about hippocampal activity hardly justifies the leap into application to math curriculum. At most, it simply seems to reflect what we know already from observation: memory is at its apex in young children. As a teacher of for-lang to the very young (w/continuing students), I can confirm also that ability to mimic precise sounds is at its peak then, reflected in superior accent to those who begin FL later; also that info learned via music/rhythm at that age is retained thro many yrs of disuse.

The takeaway for me is simply that early yrs present memorization opportunities in math & all learning. But as so many parents & teachers point out at the comment thread to Lecker’s referenced Atlantic article, CCSS-Math itself does not discourage memorizing times tables etc, it merely emphasizes getting the concepts across. The duel between concept & rote is over once we dispense with stdzd annual testing & it’s test-prep materials, which will always lean to extreme/fad/push to buy new matls. Returning judgment to local schools as to best balance of curriculum.

“Our children only go through school once. Their brains only develop once. To jeopardize their growth because of some unfounded idea a policy maker thought might be neat is criminal.” Awesome statement from the article.

As a middle school math teacher in Portland, Oregon, I am outraged by what is being done to our curriculum by the “common” core. Math concepts that were previously taught in higher grades have been pushed down to lower and lower grades. Elementary school teachers are now expected to teach higher-level math concepts that they themselves may not fully grasp. This is nightmarish for sixth grade teachers, who must try to “unteach” the ideas and practices incorrectly taught by people who lack mathematical backgrounds.

Supposedly, kids are being taught deeper concepts earlier. In reality, they are being *told* more earlier, at best without understanding, and at worst with deeply – embedded erroneous beliefs about how math works.

Though, some of the misfire may not be with the teacher’s understanding of math or how to teach it, but with the fact that these higher level math skills are not developmentally appropriate for younger children who lack context and sophisticated processes to make sense of it.

In an attempt to “challenge” kids in the 90’s and 2000’s, we started shoving grade level material into younger grades. No matter how “smart” a child, there just is a point that they are not developmentally ready to grasp certain mathematical principles. Funny how non-educators seems to be the ones making the calls on these decisions.

These “higher level math skills” are being taught to Korean, Chinese, Swiss, etc kids 1-3 years before we are teaching them to our kids.

The fact that virtually no K-5 teacher has a STEM degree is the reason why math is taught so poorly in elementary school. CC was an attempt to at least have teachers convey the relevant concepts. Instead of trying to learn math themselves prior to teaching it, they loudly resist being forced to teach concepts they themselves don’t even understand fully.

There is a simple answer to this. Many post-docs are working in STEM universities for $40K. Pharmacists often don’t earn high wages. Yet, when you add pensions into teacher compensation, many start at $45K+ min and in my district, a masters degree teacher (only 5 years of college) starts at $64K/yr for working 200 days/year. If we simply publish private sector equivalent pay for teachers and are willing to hire STEM majors instead of education majors to teach K-5 math, much of this issue will dissolve away on its own.

Virginia, how many STEM majors would work for a teacher’s salary? How many STEM majors are competent to teach children in K-5? Have you ever thought of trying it for a week? I doubt you would last three days. Why don’t you try it?

@Katy: please. Anyone who is certified to teach K-5 mathematics should be able to teach any mathematical idea, concept, or procedure that appears in K-5 and should have a working knowledge of mathematics through basic algebra. If not, then his/her mathematics teaching in whatever elementary grade s/he works will be mechanical and disconnected. And in fact, that’s a pretty fair description of what many of our mathematics teachers do, sad to say.

How true. The answer is to either hire math specialist teachers in K-5 or replace the existing K-5 teachers altogether with STEM majors.

To me, as a special educator trying to make sense of Common Core Math Standards for third and fourth graders, the problem arises in both the specifics- specific standards that are simply developmentally inappropriate for many (not all) kids-and the sheer amount of standards. Here in Illinois, our old standards were about 7 pages for PK-12 and not even dense text. The old standards covered multiple grades (early elementary, intermediate elementary, middle grades etc….) not individual grade levels. They were outlines, general guidelines to show what topics to cover. Different curricula and individual teachers had a lot of leeway in deciding how to tackle those topics.

The Common Core standards, on the other hand, are 52 pages long for math alone! (see: http://www.isbe.state.il.us/common_core/pdf/math_common_core_standards.pdf ) They are highly prescriptive and require very specific teaching techniques. For example, for third graders (these are 8 years olds!) one standard says, “CC.3.OA.8 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).)” These are some really hard concepts for kids many of whom developmentally are still thinking concretely. Say nothing about our students with special needs. And we’re asking them to do straight-up algebra. There are also multiple concepts in this one standard: mastery of all four operations, two-step word problems, creating algebraic expressions, rounding answers, and using mental math strategies. Seriously, this is ridiculous! By forcing this kind of complicated and abstract thought on kids who aren’t ready will make kids turn off to learning. And just wait ‘til you see the tests like PARCC that accompany these standards. They looked like college course exams instead of tests for elementary students.

Let’s talk about the amount of standards. For third grade alone, there are 35 of these complicated standards. There are less than 37 weeks of school in the Chicago Public Schools calendar, and in schools like mine, up to 15 weeks of that time is interrupted due to testing. (See http://mskatiesramblings.blogspot.com/2015/02/how-up-is-parcc.html ) The pacing is way too fast for many kids. The amount of standards required per grade level leads to a whirlwind of concepts being thrown at kids who are often aren’t ready for them even if they were given sufficient time.

And my kids with special needs are especially damaged by these standards. Their education is being warped in order to comply with these federal mandates. Teachers everywhere feel the tension around teaching concepts we know kids aren’t ready for, and what we’re being forced to do every day just to keep our jobs. The Chicago Public Schools IEP system won’t even let us put in standards from lower grade levels for our students to work on-they say it has to be the chronological grade level of the child regardless of where they are currently functioning.

I’m tired of people saying, what’s wrong with the “mathematical practices”? Nothing, if that’s all the standards were. It’s the other 52 pages that is harming students, especially in the younger grades and kids with special learning needs. There were no elementary teachers or special educators included in developing these standards, which is very evident in practice.

Common Core sets kids up to fail. That’s not the kind of teaching I believe in.

Excellent comment, Katie. This connects well with what I see in middle school.

Great comment. It sure looks like the distinction between standards as guidelines and curriculum in the sense of the specifics taught in the classroom has been blurred by the Common Core standards. I’ll remember this the next time I read that Common Core are just standards that don’t have anything to do with curriculum.

KatieOsgood, nobody is claiming that CC standards are developmentally appropriate for ANY special education student. The fact that we refuse to track kids by ability so that the faster learners can be on pace for college, the average students learn material that is relevant in a non-college-prereq career, and the slower kids receive the extra help they need iswhy this problem exists.Are you really suggesting that all students should be held back so that every one of your kids can learn at a pace that is comfortable? Or are you saying that tracking is appropriate and that state educators should stipulate different standards for different tracks?

Katie,

I appreciate the frustration you are expressing. The CC standards are a long document. When you actually look at the number of pages for each grade level, it is actually much more manageable although certainly not as meager as 7 pages for all the grades–which sounds to me more like a list of topics rather than standards.

My experience is this:

— CC is new and teachers/parents are having a hard time changing to what is new

–the math is particularly daunting to educators who have relied on their own algorithms rather than a clear conceptual understanding of what those algorithms do

–making the switch requires really good and ONGOING professional development to help teachers along with the unfamiliar parts of the standards

–many materials claiming to be Common Core are confusing the issue and making it harder for teachers by providing pages of materials that actually confuse rather than help with conceptual understanding

–many textbooks over-teach what is actually required and if teachers follow those texts page by page, they will be overwhelmed and frustrated

–Common Core is sometimes being confused with testing as accountability and although many proponents of one are proponents of the other, they are not the same thing

I hope you will give Common Core math more time for you to digest it. Try things out without being too hard on yourself. Some of your special ed kiddos will take to concepts and LOVE them. Others will certainly respond better to learning the steps of an algorithm. Special Education is always the hardest area of implementation and I respect what you do immensely.

Bonita

@educhange Thank you for your thoughtful comment, but I disagree. I don’t need more professional development in order to teach developmentally inappropriate standards. And no one ever mentions the pacing required to cover everything-it leaves our kids with disabilities far behind. In fact, since the general education curriculum has changed so significantly, myself and many colleagues are having to rethink Least Restrictive placements for some students with disabilities. I teach special education at a Title 1 neighborhood school on the south side of Chicago, so my students are often some of the most vulnerable kids in our system. And Common Core is harming them. We are seeing behavioral and academic consequences to implementing an experimental, inappropriate set of standards.

But to take a step back, we know Common Core was not primarily written or pushed by educators, but by the testing industry and proponents of neoliberal education reform. Seem from that point of view, where schools like mine need to “fail” in order to promote privatization and to extract profit from our public K-12 system, the Common Core’s difficulties are not a fluke, but done by design.

I agree, Katie, despite my comment above supporting CCSS-Math as regards its not discouraging rote learning of math facts. And I disagree somewhat with educhange below. I speak only as a parent, a teacher in an unrelated field (for-lang), w/a past career in engrg support services. There are too many stds per grade– & the ‘per-grade’ bit presents its own problems.

I’d much rather see what educhange disparages as a content outline– grade span– with scaffolding. I think it quite possible to move algebraic concepts earlier if done in a grade-appropriate fashion. Teachers could glean the age-appropriate pedagogy if intermediate goals were specified, flow-chart style.

Math teachers correct me, but the way I read CCSS-Math for primary, it’s as tho the overall direction, with its scaffolding, intermediate, & end-goals are hidden from view. What’s left for teachers to follow is what in engrg proposals we’d call the “take-off”: the list of items reqd to get there. Which leaves teachers unable to tweak curriculum as needed, while understanding the big picture.

Katie Osgood: props.

The high-stakes testing “aligned” to the CCSS standards are meant to measure and punish—or as I see it, if truth be told, test to punish and fail. In other words, failure brought to scale is a feature, not a bug, of CCSS.

While I have found the discussion on this thread of the standards and their [abstract or concrete] implementation informative, let’s get down to the hard reality of what drives CCSS.

Unimpeachable, well-informed, sometimes exceptionally plain speaking charter member of the self-styled “education reform” movement. A “thought leader” of rheephorm that, in contradistinction to almost all his peers, can actually be called one without the quotation marks.

Dr. Frederick Hess, American Enterprise Institute, end of 2013:

[start]

In truth, the idea that the Common Core might be a “game-changer” has little to do with the Common Core standards themselves, and everything to do with stuff attached to them, especially the adoption of common tests that make it possible to readily compare schools, programs, districts, and states (of course, the announcement that one state after another is opting out of the two testing consortia is hollowing out this promise).

But the Common Core will only make a dramatic difference if those test results are used to evaluate schools or hire, pay, or fire teachers; or if the effort serves to alter teacher preparation, revamp instructional materials, or compel teachers to change what students read and do. And, of course, advocates have made clear that this is exactly what they have in mind. When they refer to the “Common Core,” they don’t just mean the words on paper–what they really have in mind is this whole complex of changes.

[end]

Link: https://deutsch29.wordpress.com/2013/12/28/the-american-enterprise-institute-common-core-and-good-cop/

Click on the link to the blog of deutsch29 (the redoubtable Dr. Mercedes Schneider) for more contextual info.

The clincher: Dr. Hess anticipated the last paragraph of your comment under your comment by two years.

I am sure that it was entirely unintentional, but how much more of an endorsement of your POV can you get?

That’s how I see it…

Heartfelt thanks for all you do.

😎

@Krazy TA: I’m certainly not arguing against your points about the purposes of the Common Core Initiative. I am sure Hess is right in what he describes and I’ll be very pleased to see the whole sorry mess collapse under its own despicable and corrupt weight.

But nothing I’ve written here or elsewhere today or ever has disputed any of that. What I continue to ask, Ms. Schneider and others notwithstanding, is what y’all plan to do about improving mathematics education after the dust settles. And if Ms. Scheider’s is the paradigm for what most folks who follow this blog have in mind, I believe we’re in for another couple of decades of math hell.

Anyone can tell us: “Throw out everything in the Common Core.” But I’m not hearing any sensible, concrete suggestions about what happens when you’ve done that, especially since most of the actual mathematical content of the Common Core is, after all, the same content that we’ve considered to be K-12 mathematics for decades. If Schneider, you, or someone else who wants to toss it all out has a new curriculum in mind for school mathematics, I’ve missed it. Any links to share? Because if not, then I’d argue that my point about trying not to be psychotic when it comes to getting rid of anything and everything that has been labeled “Common Core Math” is worthy of serious consideration. It would be sad to dump a few millennia of learning down the crapper because the New Inquisition has deemed that if the Common Core label has been applied to something, it’s Satanic.

Michael Paul Goldenberg: I thank you, and everyone else, for their comments on this thread.

I must decline your invitation to contribute on the pedagogical side of the “math wars” because I do not consider myself equipped, due to lack of experience and training, to make sensible and informed comments.

I am reading and learning. And in this case, as I see it, the heat on this thread is generating (at least as far as I’m concerned) a lot of light…

😀

However, I will add: the whole corporate education reform approach downplays, avoids, deflects and eliminates such discussions in favor of a frenetic push to sell products. Or when rheephormsters do chime in, they ignore that old saying: I’m a modest person that has a lot to be modest about. Being experts on subjects they know nothing about is a hallmark of rheephormistas.

That said, I will simply add: I tend to dismiss CCSS rhetoric as simply Rheetoric. Whether or not the words sound fine, it’s about as helpful and useful to a discussion like this as the usual rheephorm clinchers like “studies show” and “that’s just anecdotal.”

So I urge y’all: keep on keepin’ on. I have a front row seat and don’t plan to miss a moment of the action.

😎

Instead of waiting for a politician to accept the Common Core Test challenge, perhaps we all should take an eighth grade common core math test and post our own results. I’ve seen some social studies common core tests, and they are very daunting.

The problem I see with this sort of argument is it is black and white, throw the baby out with the bath water, mirroring what we see often in current US society.

Education is not either/or. It is not either learning or memorizing math algorithms OR understanding the conceptual use of mathematics. It is not using phonics to sound out and read words OR understand the meaning and layers behind a text. What parent or teacher would support that kind of learning? I think we all want more for our children.

When people produce arguments about educational practices that sound more like political polarization, I know they are not really thinking very deeply about educational practices. Thinking deeply means understanding that teaching and learning is multifaceted and layered, and explaining/discussing/researching teaching and learning with depth means to be asking and answering important questions: What should be learned? How often? When is this developmentally appropriate? How much should we do of this or that? What is the right balance to help the most children along? What do we do when what we are doing does not seem to be helping a given student or sets of students?

Throwing out Common Core standards is pandering to the polarization of educational thinking. Learning with the CC standards and revising appropriately, holding publishers and curriculum folks to actually FOLLOWING the standards and not making up their own versions, and holding districts/schools/teachers accountable to understanding and implementing the standards with appropriate materials, THAT is what will help us to revise and improve upon the Common Core standards.

The so called “math wars” are about people who just want to polarize and not really deeply understand learning and teaching. The so called “reading wars” are the same. Practitioners, those of us teaching (and learning) on the front lines, know that all of the above is needed: phonics AND whole language; math algorithms AND math conceptual practices. Anyone that only wants to do one or the other should not be teaching.

My apologies. I posted twice. My first post was delayed and I thought lost:(

In broad brush, who could disagree?

I suspect most of the polarization comes from the fact that CCSS was presented fait accompli, in fact presented as ‘copyrighted’, without preview, w/no feedback loop for revisions (no subtractions, only additions & those limited to 15%). State DOEds in fact bought in before the first draft was issued. Implementation– despite the fact that these stds represented a major change in approach–subject to high-stakes testing affecting careers & institutional futures– was put in place at all grade levels simultaneously (as reqd, so as to acquire RTTT monies). So you immediately have a situation where students are being taught & tested, say in 8th grade, to a std which was not preceded by teaching to CCSS-grades 3-6.

The polarization of the discussion was predicated on the all-or-nothing manner in which CCSS & its associated hi-stakes tests & data-collection-system were imposed at buy-in.

So now some of us can discuss pros & cons in the breathing space afforded by some states which just now agreed to moratoriums on deciding whether teachers &/or schools are ‘failing’ based on CCSS-aligned stdzd test scores. But other states have put in place a nearly-identical set of re-branded stds, & press on with hi-stakes decisions, & presumably will keep it up despite ESSA cutting strings w/fed DOEd.

FWIW, in my opinion the CCSS-ELA is horrible compared to our previous NJ stds. NJ was among top state-ed performers for decades w/o CCSS, & this lit major can tell you that they are grossly age-inappropriate in early grades w/o reference to the phonics/whole-lang debate; they undermine reading comprehension, stifle early-reading & writing interest, & inculcate learners with a backwards [debunked mid-20thC.] approach to lit analysis.

I’m a mathematics educator now, but in another life (c. the ’70s) I did doctoral work in literature. So I’ll bite: what’s the debunked mid-20th century approach to literary analysis to which you refer?

Hi, MPG! Enjoy reading your comments here, & admire your blog. The creaky old theory is New Criticism. There’s a fair amount online complaining about its dominance of CCSS-ELA. That Rosenblatt’s 1938 gauntlet- throw down (“Literature as Exploration”– eventually, reader response theory) is often brought into the discussion shows just how hoary the debate. I like Dan Katz’ article for clarity & specific CCSS-ELA cites:

http://danielskatz.net/2014/09/19/dear-common-core-english-standards-can-we-talk/

Love Dan Katz’s article! Thank you for posting it. I love that he gets specific by showing where he sees the problems within the ELA standards and fully analyzes/explains his reasoning. So the question becomes, are the CC so bad they should be thrown out and we should start over? Or is revision possible to accommodate and value student voice and ideas within the standards? I agree that current tests need major overhaul, revision, or tossing out. I also agree that it is appalling to use these tests as measures of teacher efficacy-a very poorly thought out idea. Nevertheless,it is the standards themselves that I do like and feel with revision we could make them more effective and answer the concerns of many opponents. I guess I am coming from the previous California Standards (and tests) which valued a thinner sort of reasoning. I would be sad to return to that. Maybe that is why I do not find Common Core distasteful in math nor ELA. I do see many teachers and publishers promoting math ideas that are questionable and not necessarily in the standards at all.

Bad news: while I appreciate the compliment, I’m a fan of the New Critics. Of course, I don’t believe for a nanosecond that David Coleman knows what New Criticism was about even if he actually ever mentions it, and I’m pretty damned sure he didn’t take two courses in the history of literary criticism that would have given him some sort of basis to understand what the New Critics were about.

That said, now that you’ve told me what I already suspected was the case, would you like to explain what is wrong with New Criticism as a literary critical theory? Because on my view, the New Critics made enormous strides towards freeing literary analysis of a bunch of really bad ideas (historicism, psychologizing, biography, etc.) that threatened to put the emphasis on just about anything but the actual texts that readers interact with.

Asking students to give evidence for their thinking about a text rather than simply state what they think without any regard at all to what’s written seems to me a rather reasonable idea. Of course, how that works in K-3 is decidedly different from how it works in 10-12. Just as giving justifications and explanations for mathematics thinking and reasoning in K-3 differs greatly from what should be considered a reasonable job of proving something in high school.

There is a metacognitive thread that runs through my notions of learning. It’s grand to have something to say, but it’s far greater to have some actual reason for saying it, preferably one that has some connection to what other people might be able to understand (even if they disagree). People are entitled to their emotional reactions to a poem, play, story, novel, movie, etc., but if they hope to get anyone else to understand what they’re talking about or why, they’d better be able to in some way connect their views to the actual words or images. I may passionately believe that the sum of any two odd integers is always an even integer, but if the best I’ve got going in the way of evidence is the intensity with which I feel or state that belief, I honestly don’t see why anyone else should agree with me. On the other hand, if I can make a simple drawing, craft a physical representation, or make some other sort of valid (however elementary) case for that true fact, then I can move the world.

Here’s a comment I just made on Dan Katz’s blog regarding New Criticism and “reader-response” theory:

“David Coleman is a poor representative for the brilliant New Critics. And despite what some people write, New Criticism has not been “discredited,” at least not by those of us who actually get it. There’s nothing inherent in New Criticism that is incompatible with a reasonable interpretation of “reader-response theory, either. If we let an idiot like Coleman lead us to make a knee-jerk rejection of New Critical theory because he pretends to have a clue as to what that is, and then use “reader-response” theory as an “antidote” to something that is not a problem to begin with, then we’re being led by the noses at the hands of a political opportunist and fool. I couldn’t care less what David Coleman thinks about anything. His famous comment about no one caring what “you” think or feel says it all.

But having taught literature in university and high school, I can tell you that there are generations of instructors who would kill to get students who actually have some understanding of what it means to illustrate an assertion about a literary work with textual evidence. If “reader-response” theory were as simple minded as some people appear to want to have it, then we’re providing rationalizations for lazy students who don’t have the first idea how to analyze what they read and feel that anything whatsoever they state about a novel, poem, play, story, movie, etc. is “valid” because they “feel” that it’s true. I would never debate with a student what s/he “feels” while reading or viewing something: that’s psychology, not literary analysis. But if the student can’t provide the slightest textual support for their reaction, then frankly, why should ANYONE else care? It’s not that no one cares about personal experiences, but literature class isn’t group therapy, folks. If you want to recount your dream and tell me what it means, then if I’ve made a commitment – personal and/or professional – to listen, so be it. If I’m your English teacher, however, I have an obligation to help you develop some sense of how literature works, how writers write, and why it simply is NOT the case that “anything goes.”

I refute fools like E.D. Hirsch who claim that there’s ONE correct interpretation of any text – namely that of the author, but he wasn’t a New Critic: he was, in fact, guilty of one of the cardinal sins the New Critics exposed: the Intentional Fallacy. The New Critics worked to give us freedom from narrow extrinsic interpretations of texts as well as ridiculous claims to be able to reduce a text to a single authorial interpretation. “Reader-response” theory added tools to the arsenal of the serious reader and critic, but not license to claim that an interpretation is sensible because “I feel that way.”

Glad you like the Katz article, educhange. And appreciated your post to it, MPG, maybe it will spark some new discussion there. I see New Criticism as an extreme (& necessary) pendulum-swing attempting to rein in previous tangential excesses into romance, morality, etymology, symbolism, et al including my pet peeve, interpreting a work of art via the author’s biography (to which we seem to have returned!). And transactional theory as an extreme swing the other way. Kind of like Eliot vs Pound, orDickinson vs Whitman: you have to find a balance. Just as you point out re: math wars.

I probably agree more than not about balance. I certainly never wanted the imprimatur of the likes of David Coleman on close textual analysis nor did I think we needed it. I had very good English teachers in high school (c. 1965-68) and they would have spat in Coleman’s idiotic face given some of the absurd pronouncements he’d made in the last decade.

I also had the privilege of taking the penultimate undergraduate Shakespeare course taught by the late Irving Ribner before his untimely death in 1972. He was a historical critic (as were many of those on the faculty at University of Florida when I did my graduate work in literature there in the mid-1970s). I learned a great deal from being in his class and never regretted the time I invested under his tutelage. But I also learned from those experiences why the historical lens was inadequate for what I considered then (and would consider now) to be, yes, principled and effective literary criticism. By 1975, I was very aware of the notion of respecting a text on its own terms, something that only a few of the professors there seemed to believe or practice. I will be eternally grateful to my primary mentor there, William R. Robinson, for helping me quickly wean myself from the teat of psychological criticism and turn to a more respectful stance towards works of art. Nothing in what I learned from him or a few others there (or in my undergraduate education at Goddard College in ’68-’69 and ’72-’73) made me averse then or now to the notion that how readers interact with texts is vital to meaningful criticism. And there is room to bring in more extrinsic ideas in a respectful and productive manner. But it is vital to avoid both reductionism and self-indulgence. I’m not convinced that some of the reaction against “New Criticism” isn’t a desire for the latter and that I cannot and will not ever abide as a reader or a teacher. (Luckily for those who have decided, with or without any actual grounding in the critical theory of the New Critics, that all of what they said must be rejected, I haven’t taught a literature class since 2000 and doubt I will be doing so again anytime soon). 🙂

MPG it is a pleasure to converse with someone who cares a darn about literary analysis. My ed is limited to a BA in Fr&Sp [‘Romance’] Lit from Cornell. I see my allowed course selection in retrospect as a salad, a meatball, & an excess of desserts. For me that meant huge servings of for-langs & their lits, w/a large dollop of art history –& as little Hist, hard & soft sciences as I could get away with.

I now understand I was schooled in strict ‘explication de texte’, Euro-style, no doubt very close to New Criticism. Little place to practice this [hi-sch Fr teaching was decades ago] but have long run an annual poetry session for book-club members, & find my emphasis (while partly instruction in forms & techniques used) is mostly on helping those unused to poetry to pin their emotional response to specific passages.

So it may seem disingenuous that I lambaste Coleman’s [CCSS-ELA’s] preoccupation w/New Criticism. You have studied the real thing post-grad; I assumed he was passing on an authentic version (as I noted he studied poetry at Oxford). So for example when I observe his repeated emphasis on ‘authorial intent’ (another bugaboo for me), I figured that was ‘New Criticism’. I see I have much to learn. But I am glad to note you find value added in the reader-response theory, if held within New-Crit-style framework.

But I still have trouble w/the idea that we need New-Crit-drenched CCSS-ELA stds [albeit Coleman’s faulty interpretation] to correct an imputed prior free-for-all, emotional, unrestrictedly self-referential era of LA writing instruction. This was not the NJ ELA of my kids’ ’90’s-’00’s public ed. They were routinely [tho perhaps formulaicly] taught to cite chapter & verse supporting every opinion. Such was introduced gradually as age-appropriate, starting toward 4th-5th gr. There was plenty of room in K-3/4 to freely express one’s spontaneous reactions to text. Whereas CCSS-ELA insidiously inserts the reqt that every reaction be text-referenced starting in K.

I took Diane’s dire warnings to heart, that Common Core is not a legitimate standard at all and no corrections are permissible. They aren’t interested in what any of us think about it, and so they must be stopped and the standards replaced wth legitimate ones.

Here’s my 12 minute video:

https://jgiambrone.wordpress.com/2015/11/13/common-core-hostile-takeover/

Every math teacher’s best friend is simply this: give me a child that is at grade level. If you don’t do that, then we are all playing Russian Roulette.

I thought we were paid to teach the students we have, not the students we wish we had, Veritas. Why don’t we just ask for students who already know the course material we’re asked to teach? That would make things even easier, right?

I’ll share your thoughts with my colleagues. Last year was “Introduction to Common Core” for all staff.

This year, they’re being drilled in their evaluations for not being able to make the change fast enough. They’re also veterans and have been on the top of the pay scale for some time. The skids are being greased.

Once again, to be crystal clear: I do not advocate for the Common Core. I have no dog in that fight; if it collapses and disappears, I won’t shed a single tear for its passing. What will bother me deeply is if the back-to-basics crowd wins in the aftermath.

I’m with MPG on that.

I think it is more than reasonable to expect most 15 year olds to know more than a third grader.

As far as getting paid to do the job, I more than earn my pay working against those who would rather cater to children who can learn but who choose not to. I was hired because my superiors knew I would “teach them where they’re at.” It’s sad that the public education system allows student failure early on. It’s the same thinking that says abortion on demand is a right, but when innocent people are massacred in a hail of bullets, the first thing they ask is “why don’t we value life any more?”

Please don’t presume that my pay grade somehow forces me to accept the nonsense that has occurred when teachers have been undermined by a system that makes the child the center. When you went to school, you didn’t get a choice if you wanted to fail or not; you did the work, bucked up, and grew into a man. The policies the grew out of this perverse philosophy has robbed children of right to an education and has robbed them of learning the virtue of hard work, and, yes, that dreadful virtue of “obedience.” So, now we need you.

Today, we make teacher prowess the in-thing. We let kids choose to fail, but we pretend they’ve mastered the material and pass them on through the system regardless. We build a huge safety net and then wonder why the kids won’t work hard or memorize some things from time to time. The high school counselor and administrator thinks the teacher is bad when she’s not; they’ve just bastardized her attempt to make kids grow. We don’t have a choice anymore, we now MUST work differently.

We have no choice now but to teach the way you and NCTM want us to teach. I mean, when a third of your students, non-minority and not poor, can’t do basic arithmetic, we’re forced to teach in non-traditional ways.

Now, the teacher is a puppet on a string to folks like you who deify Common Core, and a conceptual, discovery based learning. The table was set a long time ago.

From nothing comes nothing. No, from nothing comes Common Core. Truly, those here who complain with me on this, sadly don’t see how they’ve set the stage for it.

Nothing is easy. Let’s make it easy for kids. I mean, learning should require no sweat, blood, or tears.

Yeah, that abortion vs. mass shootings argument is sure to capture a lot of hearts and minds.

We had someone here post that her school insisted upon everyone having a calculator in the ’70s. How far back exactly ARE the “good old days” when math was math and you, ahem, “did the work, bucked up, and grew into a man”? Anyone grow up to be a woman? Did women even TAKE math back then? Maybe they (and their abortions) are the problem?

By the way, to whom are you addressing “folks like you who deify Common Core”? Haven’t seen anyone doing anything of the kind here. Mostly a lot of criticism from everyone.

You seem a bit bitter, Veritas. Reality seems to be treading heavily on your toes. But surely a pro like you should be in demand at a nice suburb or tony private school where boys are young men and math is math and teachers are gods. And all those concepts, all that understanding nonsense, is not part of the equation. So to speak.

Don’t assume that those who don’t agree with you or the workings of a system that has stopped working, don’t care about those who are being held down.

So, I am bitter when I see people being set up to fail. Especially children.

I do work in a nice suburb, bub. The kids can do better, but they are allowed to self destruct. They admit that they don’t have to do any lifting; they can be Kobe Bryant without the hours and the sweat. The brass are content to con the public that kids have measured up when we teachers at the end of the line, know they haven’t. I’ve also taught in a tony (what the hell is that?) private school, a “comprehensive” private school, so I can make comparisons.

How do you explain a student who is well fed, who comes from a seemingly functional family, well-dressed, comes to high school without the pre-requisite skills for a course in Algebra 1? How do you explain that each year, most of the students you will see during the day are just like him?

Enter Common Core. I present a complex problem for students to ponder. some kids can’t understand just what the words say. Most all can’t think long or hard enough to benefit from the problem. Do you teach high school kids like this? All day long? Every day of the school year? Or, do you work at the college level? What exactly are your credentials in the trenches?

@Veritas, that’s “Mr. Bub,” to you.

“Do you teach high school kids like this? All day long? Every day of the school year? Or, do you work at the college level? What exactly are your credentials in the trenches?”

Here are some of the places where I’ve worked since 1998: an alternative high school in a working-class suburb of Detroit, teaching (mostly) mathematics and one literature course per semester. The South Bronx. Flint, Pontiac, Detroit, Warren, and Ypsilanti, Michigan.

All in K-12.

You see a lot of college teaching in there? (I’ve done some, but only one year full-time since 1991-2). Get the sense that I’m living in an Ivory Tower? Want to hear about the high school kid I had in Pontiac, not deemed special education, who (and I am not making this up) did not know the order of the counting numbers between 1 and 20 (I gave up at that point).

How about the 9th grader I worked with two weeks ago who told me, “I don’t know anything about division”?

Here’s one other key difference: I don’t think any of this is new. I don’t blame it on the NCTM Standards or Common Core because I saw the same sorts of things when I was a student in the 1950s and 60s. I saw teachers who you would probably see as exemplary who had no business in the classroom teaching mathematics at any grade level as far as I’m concerned. I’m sure they thought they were fabulous. I’m sure they were able to rationalize the students who weren’t learning as being culpable for their own failure, just as you are able to do. And there were no NCTM Standards, no calculators, no Common Core to blame it all on. Just smug teachers who could say, “I taught it well. They just didn’t choose to learn.”

I don’t blame it simply on teachers who are lazy or incompetent. I think the problems are far more systemic. Far beyond the schoolhouse doors. But if you seriously think that there’s something new going on, that you’re victimized by teaching in a decadent era, that things were just rosy once upon a time, I’d say you need to study the history of American education a lot more vigorously than you have. Study the reform documents and initiatives in mathematics education over the entire 20th century (I did so in graduate school and it was a real eye-opening experience). That’s a pursuit I would assume Diane, a historian of education, would appreciate. Before you convince yourself further that the fault is in our stars rather than in ourselves, consider what might account for the sad picture you describe, but in the context of this hardly being new. Why would so many American students from varying backgrounds, including affluent ones, be so indifferent towards education over the course of at least a century?

HInt: it’s not video games, computers, and the Internet. It’s not television. It’s not Hollywood. It’s not radio. It’s not the NCTM or the Common Core State Standards. It’s not lazy parents. It’s not drugs. It’s not any of the rationales you seem to seize upon. Think harder. And don’t call me “bub.”

Now that was quite a litany. We need a lot more than Common Core to turn it around. A lot more than the science of teaching. I think you’ve made that clear.

Now think harder.

@veritas: not much of a reply, and what little there is looks like nothing more but a dodge. What gives you the bizarre sense that I’m an advocate for the Common Core? Or that I ever have vaguely suggested that it is the cure for anything at all? I have opposed national standards for going on three decades now. I’ve opposed high stakes testing used to punish teachers and students and to destroy public education longer than most folks on this blog. I wonder where you were when I was warning people about the dangers of standardized testing and curriculum in the 1990s, while at the same time trying to help teachers better prepare students for improving on such tests without the teachers having to sell out their notions of principled mathematics teaching to the testing juggernaut.

It never ceases to amaze me how quickly people try to label anyone who doesn’t decry everything in the Common Core as developed by a team comprised of Satan, Saddam Hussein, Osama Bin Laden, Hitler, Stalin, and Pol Pot as “pro Common Core.” It’s reached the point where I attempt preemptive warnings on many things I post. But I know they won’t be heeded, and today’s experience has simply added a few more examples.

I know, too, that to fail to toe the party line means being challenged on “experience in the trenches” (oops, I think I might just outrank you there) or whether one has children (sorry, my son, despite my being on Medicare as of July, is only 2 1/2 years past his graduation from a public high school. Foiled again).

But I won’t give up. I’m not going to roll over to either the Standardistas or those who oppose them without nuance or careful analysis. Anyone can whip the crowd into a lynch mob. Stopping such a mob is a little more difficult and far more risky. But I’ve always been stupid that way.

I think I get where you’re coming from, but I’m not sure. My only high-school experience was in a ’70’s private school, but it was an odd one: I taught in the first few yrs of a school created from the melding of a [just-closed] military academy & a ‘country day school’. So we had about 40% former military academy, 40% privileged suburbanites, & 20% refugees from declining local ps schools.

The former military kids were ave intelligence but were there to work hard and learn. You could say the same of the refugees from ps. But I observed a distinct schism among the privileged suburbanites (those who’d been w/the country day school since K). They were uniformly of above-ave intell & comfortable SES. The elder of these were well-prepared.

But those who’d graduated 8th-gr in ’69 were notably unprepared for Fr I or II. Convo among colleagues revealed this group had been taught reading via some early variant of the whole-language approach; ‘reading via osmosis’ was how it was described to me. Whatever the fad was, it eschewed grammatical instruction. I understood what I was up against when in Sept, a student asked plaintively, ‘But Mme, what IS a pronoun?’ Apparently the kids had been passed up grade to grade despite what for a significant cohort was a tenuous hold on reading in English, which left them in dire straits for starting on L2.

I might add that this group (unlike their elders) had a serious attitude problem. Their aggressively anti-intellectual demeanor would have been recognized by me today as defensive. They knew they didn’t get it, weren’t sure why, & saw the teacher as enemy.

Had I known then what I understand now after 14 yrs teaching PreK/K for-lang, I would have known how to start where they were actually at, educationally, & would have adapted lessons accordingly. But if I had had those students today– & if FL-ed were subject to CCSS-studs/assessments, I would be up a creek w/o a paddle.

@MPG: talk to me, I think I get it. I am just an old lady out there on my own, teaching for-lang enrichment to PreK/K kids of parents who have a clue beyond American Exceptionalism. With a curriculum drummed up from EU folks looking to connect & a CA group committed to teaching conversational Spanish [TPR/TPRS].

Motivated by watching my own kids– who have FL genetics up the wazoo, plus musical ears– turned off to FL by century-old U.S. methods developed for long-distance reader-writers, still taught in ps today.

Even in those school districts clued-in enough to start FL in early grades, just look how they do it: in your 3rd-gr kid’s backpack, you’ll find a mini-book w/fill-in written exercises, proving that the teacher does not start w/ listening-speaking, but jumps right to written exercises.

I can’t stress to you enough how absolutely idiotic Common Core math is and what a total waste of time it is. My 4th granddaughter comes home every day with one page of long division broken up into many segments, taking her 1/2 hour for what should take five minutes. Same thing with multiplication last year: continuous adding to get to a number. There’s absolutely nothing gained from this. Some things need to be rote like using your times tables for long multiplication and division and use the freed up time to teach real history, science, current events, critical thinking, and more. Teacher directed classes are the worst thing possible if it’s not combined with meaningful interaction and reaction from students. If children are not part of the learning process, they become bored and hate school like my granddaughter now does–a child who loved it in first grade before the district bought into the Common Core nonsense. Teaching to the test all day is a total, total waste of a child’s time in the classroom.

@shar: why does the standard multiplication algorithm work? Better yet: why exactly does the standard algorithm you learned for doing long division work? Could you explain it to your granddaughter?

Please note: I am not asking you to explain the steps for doing division. I can find that in any book, on countless web pages and in dozens of free online videos: the procedure is not in question.

But countless American children leave high school without the first clue as to why that procedure works. Why does it make sense to do those steps in that order? What does the decimal remainder mean?

Now, I’m not saying that the textbook your granddaughter uses is good, bad, or indifferent. For one thing, I’ve not seen it (nor am I particularly interested in knowing which one it is). Instead, I suggest you find an elementary school textbook somewhere from the last 115 years that explains long division sufficiently that you could then explain why the method works to a 4th grader.

If you have trouble finding one, then maybe the issue isn’t “Common Core math.” There’s no such animal. No new mathematics was invented for textbooks in the Common Core era. The problem I’m highlighting is that no one has written a textbook that I’ve seen that explains how/why these sorts of algorithms work to kids. So in what should be a complete non-surprise to anyone keeping score at home, American kids and adults today, from 9 to 99, can’t tell you – with the rarest of exceptions – how and why long division works. I strongly suspect you can’t, either. But you can rail against asking kids to do repeated subtraction. . . or repeated addition. . . so you must be an expert on mathematics and its teaching and learning. And yet, I bet you cannot answer my question about division. Not without doing a lot of research. And quite possibly not even then.

Michael Paul Goldenberg, you point is very valid. i live in a state that eschewed CC and we are woefully behind where the kids should be. My daughter is in first grade and I don’t think they’ve started long division yet. But the personalized learning they assign for homework allows them to advance ahead so she began to encounter it.I know the algorithm taught for long division but I could find no great conceptual understanding (didn’t actually look but just no intuitive one). So I told her to ignore that one and only divide a positive integer (as the divisor) into the dividend. One can simply multiply both the divisor & dividend by 10^x so that the divisor is a positive integer (e.g. 100/100).

if I had taught her to align the decimals as they normally do, I couldn’t expect her to remember it for long. She would need multiple exposures to that algorithm before internalizing it and would be likely to forget it later in life. But everyone can understand how to divide a positive integer into another number.

There’s a reason that many of us 1) don’t use many of these algorithms in our daily life but 2) could perform extremely well on high-school tests even to this day. It’s because we

fundamentally understand math concepts. We don’t think they are that difficult to learn (until you get to the advanced principles) and can even be fun. We want all kids to enjoy math and be able to retain a large core of the K-12 math curriculum. That is why we teach concepts. The fact that most of the folks on here preaching algorithms and calculators can’t explain (may not even understand) the concepts should speak volumes.Tim, point taken. But that MET study showed the teachers with high VAMs also had high student enjoyment of class and critical thinking test scores (open ended tests). Those teachers in the study knew they were being measured on VAMs so wouldn’t they have attempted to “game” the tests if it were that easy? Nothing is perfect and there are margins of error, but I haven’t seen anything that suggests consistent bias. If you have, please share.Wow. So much for thinking there was any unity of thought in the DR blog followership.

Much to say myself, but these comments have gone on for so long.

Diane, any possibility of starting a new post: “Common Core Math Standards – Good for students or Not? Evidence-based responses only, please.” (and maybe posters can identify themselves by whether or not they teach math and at what level…)

just a suggestion…

Alice, when I don’t know the answers, I let the discussion rip.

@MPG… At risk of being jumped, I must say I agree with you and appreciate your effort to keep putting out reasoned and moderate points. Whether CCSS are manna or sulfurous is a Sisyphean argument: much like wrestling a pig in the mud, you both get dirty but he enjoys it. Meanwhile, many of the points you made got me thinking about how to ask such questions about our practice. Teacher-to-teacher reflective peer learning is is powerful and must be supported. The intellectual honesty and quality of the questions we ask of ourselves and each other about our practice and our students’ outcomes is what matters. Thank you for posing such questions.

Thank you kindly, Lisa. Here’s the thing: I had dinner with a 5th- grade teacher and his wife this evening. I’ve been very informally mentoring on math education for a couple of years via Facebook and we finally got to meet tonight when they decided to take a day trip to Ann Arbor. At the end of the evening I mentioned the debate on this post and said that what keeps me sane is the knowledge that there is a growing cadre of mathematics teachers for whom the Math Wars are utterly irrelevant because they’re far too busy developing an online community of excellent practitioners who share their ideas, lessons, questions about teaching, etc., in a somewhat amorphous nexus of blogs, Twitter posts/conversations, and, occasionally, actual meetings at conferences they arrange themselves. They don’t depend upon NCTM, they don’t seem terribly concerned about the Common Core, they don’t talk much about high stakes tests: they seem to focus on problems of practice, conversations about math, math lessons, reaching students, and so forth. I’m deeply impressed by many of the ideas they come up with and comforted to know that they exist. There aren’t enough of them to yet pose a clear threat to established mathematics educational practice, but they are definitely having an impact. They are technology and media savvy, and they aren’t going to sit around debating whether such things should play a role in the classroom because: 1) it’s obvious to them that the horse got out of the barn a long time ago; and 2) they’re perfectly comfortable figuring out how to make the most of that instead of bemoaning some imagined Golden Age. Were I of a religious bent, I’d say, “Thank Gods for them.”

“”At the end of the evening I mentioned the debate on this post and said that what keeps me sane is the knowledge that there is a growing cadre of mathematics teachers for whom the Math Wars are utterly irrelevant because they’re far too busy developing an online community of excellent practitioners who share their ideas, lessons, questions about teaching, etc., in a somewhat amorphous nexus of blogs, Twitter posts/conversations, and, occasionally, actual meetings at conferences they arrange themselves. They don’t depend upon NCTM, they don’t seem terribly concerned about the Common Core, they don’t talk much about high stakes tests: they seem to focus on problems of practice, conversations about math, math lessons, reaching students, and so forth. “”

Too cool. This is how I hope the future of education will be. I have worked with teams of teachers who work like this and it is awesome for math, for reading, for writing, for science, AND especially for students!

Oh, I can only hope for such a future among for-lang teachers. Tho there are such teachers in my immediate (central-NJ) area, they are a tiny majority. Before the movement of FL conversational-ed teachers [as opposed to the mainstream teachers of century-old methods supported by mainstream pub-ed] can spread their wings & fly, there needs to be recognition in U.S. that for-lang SPEAKING ability is as important to global competition as STEM prowess. It’s not just about our lack of Arabic-speakers for the CIA. Two decades ago, my elec-engr husband brushed up his hi-sch Span-IV in order to conduct negotiations w/ the Puerto-Rican power authority.

Much as US & UK would like to think English is the global sine qua non, if you can’t understand the background conversation in a global meeting, you cannot hope to negotiate effectively.

Michael Paul Goldenberg would you please post a few of those blogs or sites you mentioned (from the amorphous nexus)?

My two cents:

The rush to create and implement the standards, any standards, was a big strategic mistake, because without fleshed-out curricula and resources for it, you invite ongoing potential disasters, and simply put more care should go into creating sets of standards, period.

I don’t think the answer is ramping things up in the earliest grades and K. Many schools are starting semi-formal instruction in K, with students not yet 5. Consider what is done is most other countries. Kids in general are at least 6 or 7 before anything like that begins, I believe. Correct me if I’m wrong. If I’m wrong, by the way, then the world is quickly going insane.

I doubt the answer is more STEM majors in teaching, though education being so warped at this point in this country, I’m not sure I want Ed majors at all. If there were appropriate texts and resources and training, you wouldn’t need the STEM majors in low grades. Right now, maybe you do. But even STEM majors can’t perform miracles or finish building planes in mid air. That’s why there is such a press for distracting explanations and proofs everywhere, and weird methods and diagrams. If this were done right, explanations and justifications would only be demanded at appropriate and meaningful times, or they would be embedded in tasks already in other, better, forms. And, yes, there must be places and times for practice and drilling to some degree, for memory, mechanical fluidity and to gain familiarity with all possible twists and turns, when possible.

As it stands, this was a big opportunity cost. There was a chance to have done something really, really well, that states could have benefited from as they saw fit. Well, we have to forge on and pick up some of the pieces, toss off some of the trash and deeply deformed bits.

Well, there’s no choice for now. In the earliest grades, we definitely need lots of Ed and child psych/dev majors, regardless of the politicization and state we’re in. Didn’t mean to imply otherwise. Just vented there.

One fast way to do this is to go to Dan Meyer’s blog, dy/dan (http://blog.mrmeyer.com/) and look at his blog roll. To mention just a few others I like (this is barely the tip of the iceberg):

Christopher Danielson’s two blogs – Talking Math With your Kids, and Overthinking My Teaching;

Michael Pershan: Math Mistakes (http://mathmistakes.org/);

Sam Shah: Continuous Everywhere, Differentiable Nowhere (http://samjshah.com/)

Fawn Nguyen: Finding Ways (http://fawnnguyen.com/)

Raymond Johnson: Mathed.net (http://blog.mathed.net/)

Kate Nowak: f(t) (http://function-of-time.blogspot.com/)

That’s a good, short starting list, but it’s nowhere close to exhaustive, and I find new ones of value just about every week. Some of the above have multiple blogs and I may have listed only one.

Thank you so much Michael!

Happy to be of assistance.

What does Wendy Lecker know about math, the teaching of math, or the hippocampus?

Even more, why would she use a junk science term like “brain science”.

There are no actual scientists who would call themselves brain scientists.

Maybe she thinks neuroscience is over our heads?

Thanks. Flerp !

The discussion/debate regarding math standards is about to be thrown back at the states as the federal (de-facto) requirement for implementation of Common Core math or ELA standards will be in the hands of 50 different state legislatures.

There seem to be four options:

1) Continue using Common Core standards

2) Revert to NCLB standards

3) Adopt NCLB standards from MA (or any other state)

4) Start from scratch

Regardless of choice, far more important will be providing teachers with curriculum, textbooks, and activities that are aligned with their standards in addition to having highly qualified teachers/math specialists in place at the elementary level.

Here in NYS we could simply revert to our ‘old’ NCLB standards including our pre-Common Core HS math program. There is no great mystery to it as schools across the country have been using the NCTM principles and standards as their framework for decades.

One of the major problems with CC math was the ridiculous notion that elementary and middle school children needed a math program that twisted the “how”, ignored the “when” yet over-emphasized the “why”. Inundating concrete learners with abstract math concepts was a recipe for frustration and failure. It’s no wonder the pendulum always swings, “back to the basics”.

I would like to look at the CC standards to which you refer so that I can more deeply understand what you are saying. Could you please share an example of a CC standard that does one or all of the following:

-twisted the “how”

-ignored the “when” yet

-over-emphasized the “why”

I truly want to hear what people mean about this. I am not being sarcastic.

Common Core math standards are extremely prescriptive (the how) and have placed a developmentally inappropriate emphasis on understanding “why” algorithms work.

And like math education has for years, Common Core math treats arithmetic and computation as and end instead of a means. Math students, even the majority of good, successful ones, continue to see math as mostly pointless number games. One of the best things we could do would be bring back industrial arts programs.

“And like math education has for years, Common Core math treats arithmetic and computation as and end instead of a means. Math students, even the majority of good, successful ones, continue to see math as mostly pointless number games.”

Intriguing, since it’s precisely the alleged failure to treat computation and arithmetic as the be-all and end-all of school mathematics in K-5 or so that so aggravates many people here and throughout the country. Are there TWO sets of Common Core math standards?

Or is something else going on here? Maybe Common Core Math is like the elephant and the blind men.

Rage, there is another option. Review and revise the Common Core standards. Use them when they are improved, if you choose to do so. Get rid of the tests and use a generic test that is not “aligned” to the standards. If a student is prepared in a subject, it should not be for a specific tests but for any tests. That’s like learning to drive in one neighborhood but not knowing how to drive in any other neighborhood or on the highway.

Diane

Common Core standards are copyrighted. Not subject to change. Besides the consensus opinion is that CC math pushed standards down one to two grades making the developmentally inappropriate, especially at the elementary level. Not sure if we would want that as a starting point. Why not just adopt the MA math standards pre CC?

Here are just a few samples of comments on the “STOP COMMON CORE TESTING” Petition2 Congress. There are literally hundreds of similar complaints about Common Core math. This petition is now at 8,060 emails/letters sent to Congress and President Obama.

I am a world renowned engineer and am furious that the education system has gotten this bad! Common Core math is proof that the education department is being lead by people with lack of brain power! The fact is the reason it exists is about kick backs from the companies that are selling our kids’ futures down the river!

Absolutely the most insane math method I have ever witnessed. This will inevitably create a dumber generation than we have ever seen. We should all be very concerned about our children’s future based on the kind of “thinking” this program produces.

When I was in elementary school, I excelled in math and reading despite the fact that I suffered with ADHD. Even in high school, I was getting straight A’s in honors/ap classes.

Then came the common core. Kids with learning disorders learn alternate methods to learn things but the common core only gives one method and fail you if you don’t use it even if you get the right answer and my grades plummeted from a 4.0 GPA to a 3.0. This system hurts everyone but it is most detrimental to children with disorders. Please, we’re all begging you, end this stupid system

when I have to Google instructions to help my first grader do her math homework… something is wrong. what white collar pencil push came up with this*****backwards way to do math.

Coming from a family with multiple advanced degrees in engineering and math, I see absolutely no benefit in common core math. It has increased my child’s frustration with math, making her dread her homework and learning.

Common core is ludicrous. Why force a child to do so much extra work that is unnecessary. It is an inefficient method to teach math. There is no just reason to force teachers and children to adopt this method.

When I was in school, standard math was what I practiced, and I have to say that I excel at math. Math was my best subject in school, and still is to this day even into college. As I looked into common core math, I started to see the struggles kids could have with this type of math. And then comes my almost 8 year old brothers parent teacher conferences. Where my parents were told he is falling behind drastically. In what subject you ask? Math. Which he excelled in last year and has a good understanding of. But he cannot do the common core. His teacher is not even in support of it, but is forced to teach it to them. She suggested us to help him. While I am the only one who can grasp it in my family, how am I, or any adult supposed to be expected to help the younger generations with this type of math when we were not taught ourselves. His stress levels with school have increased, he’s hesitant to do his homework now that he’s being taught this. And for what? So he can do math better in his head? I’ll tell you this. Is did it in his head before this. And now all this has done has made his life hard and he doesn’t know how to handle it. And he was not the only student who had this problem in his class. This needs to be removed from schools. It does nothing more than complicate simple math, by adding in uneccissary steps that do not lead to better results.

My son is an exceptional student testing n the 99th percentile in some areas. Even he is struggling with this common core math. It has got to go!

Common Core adds many unnecessary and illogical steps to solve a problem. When this generation is grown and working the jobs that we adults currently hold, will they be sitting down every time they have a math problem that they have to solve and writing out all of these steps to get to an answer that the generation before was able to solve simply and quickly in our heads? Has anyone considered the adverse reactions of raising our children to rely on such a ridiculous method. My son is in 1st grade and is being faced with common core teaching. He is required to write sentences each day regarding geometry. Sentences including words that he not only hasn’t learned how to spell, let alone what the meaning is: equator, hemisphere, continent. He not only has no clue what he is doing, but is getting frustrated to the point of crying. He is losing his interest in school and learning and is having difficulty focusing. The new guidelines governing No Child Left Behind and requiring Common Core are leaving more children behind than ever before. This needs to stop.

http://www.petition2congress.com/15080/stop-common-core-testing/view/2

I did love industrial arts and agree it would be great to have it back. Still, in terms of the standards I cannot find what you are describing. The petition certainly shows the frustration that people are feeling, no doubt. In the next posting you provide a great example of that frustration. The example refers to problems with the testing (I am in agreement) and the implementation of the standards through choices teachers and publishers make (again, I have no doubt that teachers and publishers often over emphasize things to the detriment of others). I do not say this to pick on teachers. I have been teaching for decades in both middle income and Title I schools. I say this because I think if we rage against CC standards, it would be important to clearly define examples of the standards themselves and where they go astray, rather than in people’s feelings about the standards, or in how selected teachers, schools, and districts might be implementing them. Also, I believe it is important to separate the standards from the testing which are two different things in education. I hear people on this thread say it is all one package, but that has NOT been my experience as a teacher. I have loved standards as they have often freed me from prescribed programs and curriculums without fear that my students are not getting what they need for the next grade level.

“My son is an exceptional student testing n the 99th percentile in some areas. Even he is struggling with this common core math. It has got to go!”

Hmm. Just those sentences raise a lot of questions. 1) How did you determine that your son is an exceptional student? In what is he in the ’99th’ percent? How confident are you that the assessments that told you that are correct, but everything/anything affiliated with Common Core must be incorrect? 2) What is “common core math”? I ask this question and never get a meaningful answer. Is it EVERYDAY MATHEMATICS, a curriculum that has been around for several decades and long predates the existence of the Common Core State Standards? How about Singapore Math, which was developed outside the USA, again long before CCSS-M?

Is it Engage-NY/Eureka Math? How do we know that that commercial program embodies the essence of Common Core Math? From what I’ve seen of the secondary materials for that program, it’s got some interesting stuff but is a mismatch in many ways for the district where I’m currently working. Only its affordability makes it very appealing to administrators in financially-strapped districts. So maybe the problem isn’t quite as simple as “this is a bad program in every sense for every kid in every district”? Any chance of that?

The reality is that anyone can write and publish a textbook and label it “Aligned with the Common Core State Standards,” just as happened in 1989-2008 with various incarnations of the NCTM standards and before that with various state standards. Publishers – wait for it – lie. All the time. And there’s no one to stop them from doing so. Never have been, quite possibly never will be. Saxon Math and INVESTIGATIONS IN NUMBER, etc. from TERC both claimed to be aligned with the NCTM Standards. If you’ve looked at the two series, you’d have to wonder in what universe that could be possible, as these two approaches to the teaching and learning of mathematics couldn’t be more different.

Here’s the reality: no matter what is in the Common Core, publishers are going to find ways to get their products sold. They will make cosmetic revisions to existing textbook series if they can get away with that, or they will roll out new ones with familiar authors’ names (Ron Larson, for example). They will do what they need to do to make $$. For the most part, they have no philosophy of education, certainly no philosophy of mathematics education, and big publishers offer textbook series for mathematics that are, from a theoretical perspective of pedagogy, antithetical to one another. Whatever it takes to capture the lion’s share of the market in the most profitable manner possible. If back-to-basics became the law of the land tomorrow, McGraw-Hill, Pearson, and Houghton-Mifflin would be ready to profit. If NCTM-influenced teaching were to become absolutely mandated, same thing. If Common Core lives, they’re ready. If it dies, they’re ready. They’ve been the real power between what is available in the vast majority of American mathematics classrooms for decades, and only a relatively small number of districts, schools, administrators, and teachers have what it takes to slough off the influence of big publishing. And that was true LONG BEFORE ANYONE EVER WROTE THE WORDS ‘COMMON CORE STATE STANDARDS.’

The major difference between what was going on 20 or 40 years ago and now is that there are fewer choices in the way of publishers, but most of the giants have a menu from which to choose. The tests are now the whip and gun behind it all, but even before Big Testing was so powerful, Big Publishing was determining what went on in most classrooms and few schools or teachers really objected. Parents, either. Oh, sure, once in a while there was overreach – the New Math freaked out a lot of folks, though mostly because the one program that was widely implemented was too abstract and as has become the predictable rule no one really bothered to try to get parents OR teachers on board with what was going on.

But as I’ve tried to get others to address, I’m curious how it is that you became an expert on teaching and learning mathematics. Seems like loads of people are, even if they have no real background in teaching, educational research, or even mathematics. Makes a fool like me who has spent over a quarter century in classrooms working with kids and teachers on mathematics wonder why I bothered to do graduate work in the field: I could have just weighed in as a former pupil, a parent, or concerned citizen. All that time I spent studying mathematics content, methods, and issues of pedagogical content knowledge? Waste of time! Looking at comparative international mathematics curricula? Ridiculous! Studying the history of reform efforts in math and science education in the US? I could have been fishing!

So I likely should stop weighing in here and elsewhere. Everyone knows more than I do. My professional record? Meaningless! No, it’s time to smell the flowers, collect my Social Security check for as long as people who know better than I do allow me to do so, and wait for the Reaper.

MPG

Please don’t take your math book and go home. Your contributions are valuable, but like most teachers, you talk too much. If you were named the Grand Puba of Ameicam math education (K to 12). – what specifically would you prescribe? Short and sweet if you can.

I’m not interested in being the Grand Poobah of anything but my own life, thanks. And if I talk too much, no one is obligated to listen in my experience.

But if you want short and sweet, here’s two words: discrete mathematics.

I find the discussions about Common Core frustrating. (And I’m disappointed in Diane Ravitch seeming to support this article.) While I think the testing should be abolished, I think the standards have a lot to offer. And I really disagree with Lecker’s premise that memorization is the key to later learning algebra: absolutely not. Truly understanding the numbers you’ve manipulated is the key to then learning how to manipulate abstracts.

Cassi, don’t be disappointed if you read something you don’t like. That dissonance makes for a stimulating discussion and we learn from one another. Life is not a multiple choice question with only one answer.

p.s. to Rage: that lengthy comment about five or so above this one IS yours, isn’t it? Too much talking?

Don’t worry, no one is going to make you the Grand Poobah of math education. That wasn’t meant to be taken literally. Your input and expertise here is important to help further the possibilities of school life beyond Common Core math. Can you summarize “discrete mathematics” so that it could become the foundation of our 2ist century math standards. How about brief scope and sequence?

K – 2 ?

3 – 5 ?

6 – 8 ?

9 ? 10? 11? 12?

This part of the article is right on

“… when certain mathematical procedures become automatic, it frees up the brain to progress to more difficult math concepts. Forcing children to explain every simple procedure distracts students from this vital transition. In a Wall Street Journal article last year, engineering professor Barbara Oakley explained that much like focusing on every aspect of a golf swing impedes the development of the swing, forcing children to stop and continually prove their understanding can actually impede their understanding. ”

Once the concept behind an algorithm is understood, there’s no reason to modify the algorithm to test student’s understanding of it every time it’s used. Unfortunately, that’s how CC is interpreted and implemented as far as I can see.

On the other hand this statement by Oakley is highly questionable

“Expertise comes with repetition. True mastery, she explains, is the ability to pull out a chunk of knowledge quickly and use it.”

This is the exact argument that is used by the makers of SAT, ACT, and most other tests to make math tests that test speed more than anything else. I dare to ask: Is this kind of mastery of all the crazy math stuff kids presently learn needed?

Not accidentally, Oakley’s “mastery” argument is used to justify excruciatingly boring math lessons: “here is the New Concept for today, now here is Example1, Example2, …, Example 20, now go home and do 20 more problems at home using Concept.”

I also argue that for most people, rigorous understanding of math concepts is not beneficial at all even in high school. It’s enough to make concepts plausible and appealing to kids. In fact, this is where most math teachers fail, in my opinion: instead of taking time to make a concept plausible and fascinating, they rush through some kind of rigorous argument to support the concept, and then they spend most of their time on giving applications of the concept.

I add (or: admit), kids (especially young ones) don’t always have to understand a concept or algorithm at all, and they may still be fascinated by it. It’s like skiing or skate boarding: kids don’t have to understand why certain moves work, but that doesn’t stop them from enjoying the learning and application of the moves.

Do anything to keep the wonder and curiosity alive. But we have always known that, haven’t we?

Máté, I really appreciate your comment. I love teaching math in a way that gets kids excited about the math! It is a joy to have a class full of students who are intrigued by what they are learning. My hope is to light the fire, not to just fit the next concept into students’ brains.

Making a math concept, let’s say solving by proportion, “plausible and appealing” can only be achieved with interesting applications that students can relate to. Otherwise, its still just tricks with numbers.

As long as students are required to compute, calculate, or derive barren quantitative responses (numbers only) without unit labels – we will continue to raise an inumerate population.

Yes, RageAgainstTheTestocracy, though by math concept I meant something more complicated than ratio. Of course, for many people, the sexappeal of math disappears when they start feeling that math is just a bag of tricks to calculate stuff.

I was thinking about a more complicated tool such as

“the three lines we get by connecting each corner of a triangle with the midpoint of the side opposite to it intersect in a single point”

Many math teachers prove this, and move on to applications of it, or, worse, they would squeeze another result of geometry into the class. Instead, spending a class to help the students discover the result and appreciate it is what would benefit most kids. I don’t think proof is important in this case.

I suspect, many readers of this blog don’t realize (or remember), for example, that this geometric result is the basis for the the concept of the center of gravity: that any physical body, such as a plate, has a single point where it can be perfectly balanced.

Ah, I read you, Maté. And this coming from one who who was surprised to find (in her 20’s– on looking to take the GMAT) that tho her verbal was too off-the-charts to be measured, her math had sunk to F. [After 6 mos of studying old GMAT tests, managed to raise it to C-].

Math to me was an intriguing puzzle I could not solve. As a young French teacher, I audited a colleague’s algebra classes, sure that now mature, I would understand. It was as though there was a veil I could almost penetrate, but not quite– the same experience when attempting a grad-level Eco class [having passed the GMAT].

I had a wonderful Algebra teacher in hs who spent every day with me after school, & I did learn just enough to pass that Regents exam.

The feeling I had from 3rd grade on (that’s when they introduced fractions) was that I never had enough time to understand a math concept before they moved onto the next one.

Back in the ‘90s, the NYCBOE asked the CEOs of some of the most prestigious Fortune 500 companies what they wanted most from the NYC high school graduates.

The answer: We can put a calculator on every desk for next to nothing. We need problem solvers.

So the NYCDOE scrapped all the existing math programs in both general and special ed and got into “The New Math”. Process over product.

It was completely inappropriate for my special needs kids, most of whom would never see the inside of a Fortune 500 office complex. I tried going back to my much more effective remedial method, but was stonewalled by my AP. She told me that, if she saw me using those books again, she would personally burn them.

The NYC Dept of Education asked the business world how we should be teaching our kids. The business world gave the DOE their marching orders. If not the beginning, this moment was definitely indicative of a hierarchy that’s become firmly entrenched and is still growing, today.

I am not a teacher of math, but I have been called on to teach arithmetic processes. Having little knowledge of how students were taught in grades one to five, I did wonder why they had so little ability to multiply/divide in grade six, seven, and even eight. I recalled being unable to retain seven times eight and six times nine when a seventh grade student, but I knew how to figure it out! My students had no idea what multiplication was about and could not come up with an alternative strategy to memorization! This bothered me more than their not having the times tables memorized.

Understanding what you are memorizing is fundamental. Otherwise you are just memorizing nonsense. And this lack of concept seems to me why the students have not accomplished memorization.

Generally, I just pulled out a ton of pencils and had the student physically represent what multiplying would look like. Same with division. I suppose the next step would be to have the student explain the process to someone.

One Algebra teacher found he could raise math scores by insisting on the memorization of the times tables. (This when calculators could not be used for standardized tests.)

If a student does not understand multiplication and division, s/he will be unable to do anything else.

i just scrolled through the older comments. What a revelation. I didn’t know. This war is as vituperative as the “reading wars.”

In all honesty, you aren’t seeing the Math Wars in its full “glory” here, as there’s no one weighing in consistently who is, for example, playing the “liberal racism” card. That’s what some traditionalists say about progressive mathematics educators like me when we argue for any sort of non-traditional sort of pedagogy, text, resource, technology, etc. in the context of minorities, women, or other groups and individuals who have generally been poorly-served by an exclusive diet of teacher-centered, lecture-driven direct instruction . It turns out, according to such “Math Warriors,” that progressives are the “real” racists, not they. It’s part of the larger “Culture Wars” that no doubt can be traced back at least to the 1960s.

I, too, was not aware of the Math Wars phenomenon.

I do know that my daughter transferred to a different high school specifically because of the lack of competent math teachers in the school she’d been attending. It was a good move.

Question: would you say that there’s a general rule of thumb when it comes to math instruction?

I ask because the special needs kids I worked with had very little in the way of arithmetic skills. This mirrored a general lack of structure in their lives, for the most part. I would always give real world parallels (keeping a checkbook ledger, drawings which showed groups, etc), but rote memorization definitely helped them when the word problems started to become more complex. Having the basic computational skills down made it much easier for them to concentrate on the more complex problem at hand. Otherwise they’d get frustrated and give up.

A general rule of thumb is pretty broad, but here goes:

All math instruction should be built around the idea that the child does the thinking and learning.

It should be built into expectations and the tasks we engage them in

The second idea is that struggle is good’ it’s ok to make mistakes. That’s how we learn.

Show and tell by a teacher is the least effective strategy for a teacher’ it can be the most effective when students do it.

gitapik, howdareyou say there was a lack of competent math teachers! Why, according to all the observation-based evaluations of teachers in every state, we know that 99%+ of teachers are outstanding! Thus, it simply couldn’t be true that your child had more than one ineffective teacher.Why, if what you are saying is true, then maybe we need to rethink teacher evaluations. Maybe we need to base evals on objective metrics rather than just a principal who has interests in both the ratings of her staff and their friendship. Maybe, just maybe, for the important subject that is math, we need an evaluation metric based on how teachers effect student growth after discounting factors such as SES, class size, and prior knowledge.

I wonder if anyone has ever devised this type of metric…. maybe Diane can tell us.

Virginia, schools have long had a shortage of math and science teachers. I urge you to offer to teach at your local public school–oops, forgot that you are barred from entering the school. Or some school where they don’t know you. Surely your extensive STEM education would make you an excellent teacher, that is, if you know how to communicate with the children of 6-15, and if you know how to hold the class’s attention.

What are the objective metrics that you believe should be used to measure teacher effectiveness? It can’t be test scores, because we have tried that now for five years, and it hasn’t worked anywhere.

Diane, I must admit, that was a pretty good one on my being banned from school. For those that don’t know the story, you can read about it (here and here and here and here and here and here. But interestingly, I can attend Veterans Day assemblies throughout my district and even be asked onstage including giving remarks, just not at my kids’ school.).

Diane, your readers may be interested to know that a state circuit court judge tried to sanction me with $6500+ fines for trying to hold Imagine School’s “undisclosed lobbyist” and chairman of the school board Eric Hornberger accountable for not declaring his conflicts of interest. Hornberger works directly for Dennis Bakke of Imagine and pushes charter schools in my district (Imagine desperately wants in) but never disclosed his conflicts. Too bad the judge and opposing counsel can’t read the very first rule in the book. Over 60+ years of legal experience against a pro se STEM major …. and the winner is…well, you know that one. More on this one as the appeals play out.

Back to evals: for those subjects that have sequential material (must learn concepts in sequence and thus one can measure progress over time), growth in test scores are the most reliable method. Student surveys are another key part of the mix as are observations by trained 3rd-party evaluators (from outside the school).

Why would you say that “we’ve tried it for five years, and it hasn’t worked anywhere”? ESEA only required decisions to be made from evaluations based on student growth in the 2014-2015 school year. That was just this past year. And for the CC states, they received a waiver for an additional year. So maybe your math is better than mine but by my calculations, there haven’t been any consequential decisions based on objective student growth (VAMs) outside of a couple early state leaders.

Maybe you can reply to

gitapik‘s assertion that one high school had weak math teachers. Could that be possible? Why haven’t the observation-based evaluations identified those teachers (99% of teachers rated effective)? Do parents just have unrealistic expectations?You previously mentioned that it was not possible to hire as many STEM graduates as schools would need to teach math & science (still need to respond to that post). But have we really tried? TFA targeted many such STEM majors and 80-90% of their applicants couldn’t find placement. Maybe there will be high churn as STEM majors discover if they can really teach and whether they enjoy it. But why not open up alternative paths to teaching and really recruit in the engineering schools. We should be recruiting at every single engineering school in the nation. School districts do not recruit outside of education colleges. Why not? How do we know STEM grads won’t find their calling inspiring our youth until we actually try? And for STEM majors, they have a fallback if it doesn’t work out. We don’t have to worry about asking a STEM major to move on from being a teacher as they can obtain a job in their native STEM fields.

“Show and tell by a teacher is the least effective strategy for a teacher’ it can be the most effective when students do it.”

Thank you, Peter. I understand this in theory AFTER the skill has been modeled for the student. I’ve always made lots of room for trial and error, whether working with students with autism, emotional, or learning disabilities. Academic, social, and living skills. Are you suggesting that a teacher not model prior to having the kids experiment with and, potentially, master the skill(s)?

virginiasgp: Math WARS it would seem to be.

The middle school that my daughter attended was excellent in ELA. As a very, very good writer, she flourished there. In math they were hit and miss. Her 6th grade math teacher was not so great, so we worked with her at home and were able to get the content delivered through that combination of school and family.

Her 7th grade math teacher was fantastic. I remember him saying, “People think it’s ok to say that they weren’t great in math in school but you rarely hear anyone say they weren’t very good at reading”.

She chose to transfer because, after researching the credentials of her future math teachers at that school, she realized that the schools’ focus was much more ELA oriented. So she checked out the bios of teachers at other schools and ended up transferring to one with a better balance of expertise within the different subject areas.

I think it’s important to understand nuances in conversations and situations, virginiasgp. My daughter would’ve done pretty well at that first school, but it was slanted more towards ELA. So she moved on. Saying that the entire system is a shambles that needs to be completely revamped seems to me to be the equivalent of saying that nothing should be changed. Neither side addresses the nuances. It’s not all good and it’s certainly not all bad.

gitapik, I’m not saying it’s all bad. But based on your observations, it’s simply not credible to say that 99% of math teachers are “effective”. Maybe 75% are or even 90% if we are generous. There are probably 15 math teachers in a middle/junior high school (3 grades * 5 teachers each). According to the eval data, all of these teachers are effective. The VAM eval models only predict that 1-2 of these 15 teachers are ineffective. Are you seriously suggesting that not even 1-2 (or more likely 4-5) of your daughter’s 15 potential math teachers were ineffective? Btw, a single teacher (daughter’s 6th grade teacher) represents 7% which is the same target for the VAM models in NY.And yes, knowledgeable parents can fill in the gaps like you have. But what about kids who don’t have knowledgeable parents? Shouldn’t they have an effective math teacher rather than teachers with “excellent” evaluations when they are clearly ineffective?

I might ask how did she determine which teachers were effective based on their bios? Could she have looked for math teachers with a STEM major? That makes sense to me but not to many school administrators who only hire education majors until high school.

Nobody has claimed that the majority of teachers are not effective. We are essentially arguing over 5-20% of the teachers who many view as ineffective. In many occupations, the rest of the team can cover up for their lack of performance. But in education, is it fair or ethical to overlook a teacher’s inability to relay math skills simply because many don’t want to rock the boat? That’s the question before us.

I’m not sure that it’s even meaningful to discuss what comprises an effective mathematics teacher (let alone who is or isn’t one or what percentage of US mathematics teachers in K-12 are in fact effective) without working definitions of: 1) knowing and doing K-12 mathematics; 2) teaching K-12 mathematics; or 3) teaching K-12 mathematics effectively (though I’d argue that a good working definition of the last one is, “giving students the opportunity and means for #1.

So the whole shebang really does depend on what we call knowing and doing mathematics (which probably leads us to a prior question of what mathematics actually is.

As long as the vast majority of parents, politicians, school administrators, students, and K-12 mathematics teachers have a badly warped and crippled picture of what mathematics is, we’re pretty much doomed to another century of bleakness for most people regarding mathematics. Our current conception is absurd: we have come to believe that mathematics is computation and vice versa. In fact, computation, while a useful tool in applications of mathematics and as a building block within some areas of mathematics, is basically the booby prize. Emerge today from K-14 (so I’m including basic calculus here) with nothing more than the ability to calculate reasonably well and congratulations! you’re an obsolete bag of water that does something slowly and poorly compared with a host of microchip-based devices including your cell phone. What an achievement!

It is simply criminal to allow children to spend 13 years in school and emerge from the experience with absolutely no sense whatsoever as to what mathematics is or what mathematicians actually do. And as long as we focus almost exclusively on computation and pushing some symbols around vapidly for the last couple of years of K-12 (what passes for “algebra” education in this country), we pretty much guarantee that no one who doesn’t need to take higher mathematics for professional or academic requirements will do so.

I’m hardly pushing for all kids to be pushed towards a career in pure mathematics. But if you graduate high school without the slightest idea what pure mathematics is and why people do it, you’ve been robbed.

There’s a step even before modeling for students, and I think it’s a launch problem that sets the stage for the learning. If they’re about to learn the tools to do meaningful stuff (that might rule out tests), it would help to know what problem they’re learning the tools for.

I think that’s what motivates most adult learning. It certainly drives how I learn technology. It’s not, of course, the way we do professional development.

Yes, I understand that. Say I’m doing a unit on subtraction. I might enact a scenario where I’m wanting to buy something for my kid (something that I know the students would love, too). The kids see me doing the math in my checkbook ledger to see if I can afford it.

In that situation I’m showing a practical application of the skill and getting their interest. Next step is to model the skill, using the same materials.

Virginia: I don’t condone slackers. The vast (and I do mean VAST) majority of my colleagues feel the same. I’m not “seriously suggesting” anything. I’m talking from personal experience. After witnessing almost 2 decades worth of propaganda and outright lies about my profession trumpeted through the media, I’ve learned not to take all that I’m fed from that vein too seriously.

Regarding STEM majors and why they’re not teaching:

I have no doubt that some would make excellent teachers. Why would they not get accredited, if that’s what they want? They’d certainly be welcome. I spent a considerable amount of money on my masters degree in special ed when I chose it as a second career. I learned a LOT and earned a 4.0. Those classes along with the experienced mentors I worked with in school were essential in preparing me for life in the classroom. It’s one thing to be able to talk to talk. It’s a whole ‘nuther to be able to walk it. That might sound corny…but it’s true. If someone wants to become a teacher, then let them earn the right by taking courses that are related to that art/skill. It’s not easy. At all. No matter how much knowledge you have, imparting it to a classroom of kids is challenging even in the most positive of environments.

I have to disagree with some fights about Common Core Standards in Mathematics. I am a former math teacher and stayed home when my children were born. In that time I have been able to study and one of the topics I have learn is common core in math. The greater change suggested by common core is to let students understand the concept being taught in each mathematical area. It asks for teachers to let students discover the mathematics in real word settings instead of just giving out a mathematical formula to remember. The reason for doing this is to let students apply their learning in the best possible way in every real word mathematical problem they encounter. Once students understand the concept, they still need to memorize their facts. Children are not only asked to know and understand the “old division”, but all the ways they can do division. The hard part of this type of teaching comes in middle school and high school, since teachers are used to teach the formulas and now preparing class is really hard. I am not underestimating teachers, what I want to say is that common core does not change what needs to be taught in math, but how it needs to be taught. The greater change in adopting common core standards is not for students, but for the teachers!

My son began his Kindergarten grade with common core, you should see what he is able to do in 3rd grade, and he does know his facts by heart, but he can do amazing things in math that I wish I could do as fast as he does, and I hope I had his mathematical understanding when I was 8 years old. When I see him in action I can understand how hard it could be for a middle school teacher! The sad thing about Common Core are not the standards, are the tests, since standardize testing cannot asses conceptual comprehension. This is the reason for common core to ask for explanations, since there are children that can have a great conceptual comprehension and miss a calculation, and there are others that have a great procedural comprehension (the steps to solve an algorithm), but have no clue how to adjust this to real life or to explain what each number means.

Change is hard and there are several things wrong in the educational system in the US at the time. But I do believe the changes created by common core mathematics are positive. We just need to fight for a fair testing system!

Good points, Maria. There are two obstacles. Teachers need time, resources, support to develop lessons that support good mathematics. The second is that for too many teachers, they exist in a culture that does not see this as what teachers do.

We seem to think that teaching just happens.

Even without being a math teacher, I know Maria is correct in principle. A lifetime of studying logic has taught me that learning even very basic arithmetic can be approached in several ways. (Therefore “math wars” are inevitable.)

Also, I agree with Maria that in principle it is better to learn why something is true than to learn an algorithm (a calculation process) without knowing why it works. Both the “new math” of my childhood (I’m the son of a math professor), and from all accounts the Common Core today try to get children to see the reasons why.

But it is harder to understand why something is true than to apply an algorithm. Complete explanation of why the arithmetic algorithms work is appropriate for well-motivated college math or philosophy majors. (Therefore “math wars” are bitter fights over deeply held matters of principle.)

For a creative teacher, there is an unlimited number of ways to teach math. Visual aspects or experiential projects might be differently emphasized for different problems. Algorithms, pictures, or deeper understanding might get emphasis in different contexts. Hypothetically, a creative teacher would mix approaches, depending on individual students’ needs, what gets their attention, and what is fun.

If the Common Core standards are imposed on teachers, however, this tends to work against teachers’ creativity. This tends to undermine the good intentions of teaching students the reasons why.

I doubt there’s any way of teaching math well that doesn’t rely on the creativity of teachers.

@Aaron, there’s a world of difference between asking a K-5 student to “prove” in any sort of formal or ‘rigorous’ way why arithmetic algorithms work and trying to help students understand why they work so that they can explain the rationale behind the steps involved. There’s also an enormous difference between the first sort of formal proving and asking a student to explain his/her thinking and methods in trying to solve a problem, particularly a non-routine one. So we are NOT asking students to operate on an undergraduate level in either mathematics or philosophy of mathematics. That would be irresponsible and unproductive.

Asking for a proof of why a negative integer times a negative integer must be a unique positive integer is inappropriate for K-5 students and I know of no one advocating that teachers do so. Asking students to demonstrate, model, or offer an argument for why the sum of two odd numbers must be even is within the power of most third graders, if only we bothered to ask.

MP Goldenberg writes “Asking students to demonstrate, model, or offer an argument for why the sum of two odd numbers must be even is within the power of most third graders, if only we bothered to ask.”

At that level, it’s enough if they observe the pattern on specific examples and accept the general statement as true.

Asking 3rd graders to demonstrate why the sum of two odd numbers is odd just scares most of them.

“Asking 3rd graders to demonstrate why the sum of two odd numbers is odd just scares most of them.”

That would scare me, too, since I know that that sum is even. But it would actually be fascinating to claim that the sum is odd and see what students said.

I would suggest, however, that in classrooms where students are routinely asked to explain their thinking and why things that they are learning in mathematics are true, fear isn’t the typical response. In most US classrooms, they aren’t expected to actually think, their ideas and methods aren’t valued, and so of course suddenly having to justify in ANY way why something in mathematics is true would be likely to scare a lot of students.

So is the reasonable conclusion to never ask such questions or, in fact, to make asking such questions routine?

I have seen 3rd graders tackle answering why odd + odd is even, by the way. I’m not simply speaking theoretically. Of course, the question arose in a context and in a classroom culture where they knew that such questions were fair game. They weren’t asked to write a formal proof a la Russell & Whitehead’s PRINCIPIA MATHEMATICA, or even the sort of proof one sees in a typical basic algebra text: just to explain in whatever manner they chose to justify the claim. No heads exploded and the ensuing conversation was, to put it mildly, amazing. Among other things, it resulted in a student hypothesizing that some numbers are both odd and even. That wouldn’t happen in a classroom culture where students weren’t led to express their ideas or where they felt unsafe to go out on speculative limbs like that. The conversation that his notion engendered was the sort of thing that could happen if kids learned to engage in accountable talk about mathematics (and other subjects) and if teachers learned to be “less helpful.”

Actually, that’s not the only thing I screwed up. What I meant to write was

Asking 3rd graders to demonstrate ON A TEST why the sum of two odd numbers is even just scares most of them.

You are correct in that asking 3rd graders to explore whether the sum of two odds is even is perfectly suitable for their age.

Physical models are highly appropriate. The same ones they used to understand odd and even numbers. Sadly it may be beyond the way the teachers were taught. They’re the scared ones.

I respectfully disagree that third graders would find this frustrating. I work in a Title I school and I have noticed that when the teachers set up good discussion and exploration structure and when they provide tools for thinking, third grade students love figuring out and trying to prove things. It is all in the set up of the lesson and the “mistake” perceptions that have been either rewarded and regarded or used to dismiss a student’s thinking. Kids can figure and think and if the right classroom environment and structures are in place, they thrive at this.

educhange, as I wrote, I messed up. I left out the part that it makes no sense to ask 3rd graders to explore this question on a test.

Oh. Sorry I missed your follow up! Completely agree on the testing issues!

@Michael Paul Goldenberg

I would be excited to see 3rd graders talk about why odd + odd = even, or odd X odd = odd, or negative x negative = positive.

Such deeper questions arise *everywhere* in math, even the most basic math, which seems to be the same as you say. So we are in agreement.

The next problem, though, is harder: given a pair, (teacher, student), find the right approach for teaching x, for all x.

@Aaron: in my experience, there is no such x in the real world. Maybe in the complex one or the surreal or hyperreal world. And I don’t search for such an x.

Here’s a link to the conversation I was talking about:

http://deepblue.lib.umich.edu/handle/2027.42/65013

Enjoy.

Funny, I read information about that same Stanford study and it came to the conclusion that using problem solving techniques to arrive at computational knowledge INCREASED students rote memorization AND gave them more tools to work with on less familiar problems. This editorial sounds more like spin to me. I believe in building understanding before memorization, which is a strength of CCSSM. Now the tests designed to assess this, that’s another thing entirely. I think authors on the Common Core need to identify if they are against the tests or the standards, they are NOT one in the same.

There’s no doubt that common core math does address some problems in math education. What I don’t understand is why reinvent the wheel when it comes to giving out a math advisory for the nation? Why not just import the Finnish math standards?

Here they are, I cut them out from the original document

There is a good amount of overlap with CC math, but the language it’s written in is simple, concrete, almost jargon free hence straightforward to understand.

The math “standards” for kindergarten are strikingly different from CC’s

Of course, don’t attach any tests or strings to the standards. Trust the degree of adoption to teachers and their peer review system.

The effect of these kinds of federal standards can be similar to national health advisories about tobacco or sugar: states will adopt it if they see the value in it.

Arithmetic? or Mathematics?

Numbers? or Theory?

Computation? or Relationships?

Calculating? or Comparing?

Like, Spelling v. Writing

The complaint that K to 12 does not present “real math” could be solved by re-structuring the curriculum. Mathematics could be infused into the HS disciplines or be taught as a separate course. However the general complaint or concern regarding students and “math” certainly has nothing to do with theoretical mathematics. When kids can’t do basic arithmetic and have no number sense – the fix does not involve the introduction of true mathematics. One of the biggest mistakes in the Common Core approach was trying to develop a “deeper understanding” of abstract concepts in children that, with a few rare exceptions, are strictly concrete learners. Most people do not need much beyond a solid mastery of 8th grade topics. A good statistics class would be more beneficial than algebra for most.

When my daughter was in college, one of her friends was an elite, world class math student, probably on of the top ten students in his age group; a true math genius. And a really nice, regular, unassuming kid.

When I first met him I said in passing, “You must be a real numbers guy”. He shook his no, smiled and said, “Math has nothing to do with numbers.”

This encounter was my somewhat embarrassing introduction to this comparison.

I think it would make sense to give kids an exposure to this in HS, but clearly the theoretical mathematicians find themselves with or without it.

I would just rephrase that to “numbers don’t make it math”. Calculus, statistics. Geometry, may use numbers, but but numbers are just part of the language.

I can’t speak for general ed or HS, but the above post is pretty much where I’m at regarding the teaching of mathematics in my special needs classes. The admins did a great disservice to my kids when they took away the computation based remedial series I was using along with my ability to “tweak” it, according to the class needs and interests. The scaffolding was tightly packed, the concepts were expressed in both diagrams and numerically, and word problems were being introduced in their simplest form.

It wasn’t an accelerated program. It wasn’t even grade level. But the kids I teach are just simply not ready for that kind of challenge. They may never be. The question, it seems to me, is whether that’s “ok” or not. Is every child supposed to be college and career ready by the time they exit high school or should there be respect and places for those who choose not to or simply cannot follow a path that involves abstract concepts and/or careers that require mid to high academic achievement.

It sounds like you’re doing something we all need to do – try to take ownership of what you teach.😀

(The above post I was referring to was Rage’s original one:

“Arithmetic? or Mathematics?…”)

RageAgainstTheTestocracy writes “However the general complaint or concern regarding students and “math” certainly has nothing to do with theoretical mathematics. ”

I believe, this statement is incorrect. Here is what doing theoretical math looks like in 8th grade

Now, please explain why this couldn’t or shouldn’t be done in any grade.

Some other questions,

Why does this need to be a separate class from the usual TFM=Test Fitted Math currently taught in K-12 and beyond?

Do kids really need TFM or rather the video’s art like activities should dominate their math classes?

This video is awesome – you have to listen to the subtle language.

So 8th graders doing permutations and combinations. I see this as a great launch into a whole unit on counting.

The thing is – BTTC (Before the Testing Craze) this is where we were heading 25 years ago with the NCTM Curriculum and Evaluation Standards, the Middle Grades Math Project, Marilyn Burns, Deb Ball, Maggie Lampert …

It is stunning to think what could have been had the last 20 years not been wasted.

But videos like this give me hope.

Kids constructing their own mathematics. Instead of being shown how to solve the problem.

Good mathematics, taught well – Glenda Lappan

That’s a fantastic video, Mate!

We’re never going to get anywhere when people insist upon conflating calculation with mathematics. And when people fail to see the mathematics that underlies calculation and hence do not teach that except by accident.

Suggesting that you can’t have kids doing mathematics if they haven’t mastered arithmetic is somewhat shortsighted. Given the right questions, any class with any kids can move from drill and practice of facts and algorithms (done without any connection to anything whatsoever of interest to the students – and by that I do not mean strictly so-called real-world problems) to actual mathematical thinking and investigations. The video Máté provided gives some evidence to that effect, but there is lots of great stuff out there for younger students. Enslaving kids to calculation über alles is an excellent way to ensure that very few kids will or will want to learn mathematics. And a four-function calculator outperforms all but the most skilled of human computers if all we need is numbers crunched at speed with accuracy.

Of course, Máté also raises the 500 lb. gorilla in the room – high-stakes testing. As currently implemented and constructed, such tests have no connection to anything that matters to anyone inside schools or to many parents. They serve solely the interests of politicians and enemies of children and learning. Other than that, of course, they’re FABULOUS!

😀😀😀

One of the points of the video is that the participating kids do practice the use of a few formulas. So what kids traditionally do by working out dozens of boring examples of the same stuff is also accomplished by the the kids in the video, but these kids don’t even notice that they are in the process of committing formulas and their proper use to long term memory.

When the teacher at the end says “not the result but the process is important”, you can translate it to “the video shows the process of committing the material to long term memory” for the cognitive scientists. But we all know that much more is going on which is not describable by precise science, and certainly cannot be captured by any tests.

“Given the right questions, any class with any kids can move from drill and practice of facts and algorithms (done without any connection to anything whatsoever of interest to the students – and by that I do not mean strictly so-called real-world problems) to actual mathematical thinking and investigations.”

I say this with respect, Michael: Have you ever taught a class of severely emotionally disturbed/learning disabled kids? Physical fights at least once a period if they’re not engaged? Or children with autism?

I can see that I’m way over my head on this topic, as I’m not a mathematics teacher, per se. But I do know what sparks the interest of the students I teach. It’s not just drill and teach, either. There’s more involved than that. I’m always open to new methods and would be happy to hear of one that would better serve and reach my kids. It’s just that I’m in alien territory on this one and it would seem, from what you’re saying, that I’ve got a lot of company.

No argument about the testing, btw. It’s an aberration and it’s just getting worse. The “fix” (“Personalized Learning”) just takes education a few steps further into the depths of oblivion.

500 pound gorilla is an understatement. I’d call it a 54 ton Abrams tank. Capable of so much more damage.

What a great discussion. Thanks to all you folks for some interesting views of the Common Core. I even found the word Geometry once. Only once.

Which brings us to the CC and Geometry. With its emphasis on transformations and its insistence on a Cartesian approach, it becomes less rigorous logically and perhaps even less influential in creating students who can reason. Traditionally, the course called Geometry built it self, logical piece by piece, until some students were able to follow a very few principles to some really sophisticated conclusions. Then the CC approach was forced on teachers through high stakes testing. Who knows how this will turn out. I am trying as hard as I can. I feel like one of those incompetent teachers described above.

Roy, what, exactly, is “the Common Core approach”?

As for geometry, I would say that teaching it from a purely axiomatic/deductive perspective had been on the wane long before there was any such animal as a “Common Core.”

Finally, there’s never been any really sound reason for making high school geometry THE place for students to first (and last) encounter proofs in mathematics. As I’ve suggested already, there is plenty of room for introducing students to notions of “proving” results far, far earlier, and then helping them deepen their sophistication with proof over the rest of K-12. It puts far too much of a burden on geometry to make it the sole repository for proof in K-12, it takes away from other ways of learning and thinking about geometry, and it makes geometry more forbidding to some students who aren’t ready for proof at the level often seen in traditional geometry classes. Horses for courses. . . and courses for horses. I’d say that we should be sharing proof more evenhandedly throughout the K-12 years and doing geometry with proof, but not exclusively so.

I regret that I did not see this two months ago, I was having surgery then.

I am a retired Pk, Kg, primary teacher who became the math coordinator in a Pk -Grade 3 school. Math is these grades and into the middle grades needs to begin with the concrete, not the auditory and the abstract. Math has traditionally been taught with the teacher explaining the procedure on chalkboard or screen. This is a behavior approach.

Children learn because they are told. Piaget’s stages include concrete operations (approximately age 7 to 12.). Students need experiences, They need to be asked questions to enable them to see relationships . And they need to be told the labels – the math terminology.

In second grade my son was doing excellent work in math and reading. He was out of school for three weeks ill. When he returned, he had no idea what the teacher was doing with 31 – 7. When he came home I took out pegs. Toothpicks work just as well.

I bundled them into tens. “Let’s subtract,” I told him.. He told me,. “You can’t do it.” .

I asked , “Why not? 31 is more than 7.” He told, me he had to take a rubber band off.

He did and we also put the paper work down as the teacher was telling the class. We did a second problem the same way -with concrete objects..As I began the third problem my son said, “I do not need those, Mom. I get it, I understand it.” It took less than five minutes with concrete objects for him to understand the procedure and regain his confidence.

I have taught addition and subtraction as word problems with children drawing the first number in one line and the second one in the next line. The third line is the equation, such as, 76 +2 = ____ or 6 + _____ = 8 with drawing 2 in the next line to n make a total of 8 or ____ – 2 = 8 etc. The answer is put in the blank.

Materials used to develop math facts are a 20 bead string, a math rack or a redenek,

addition of 8 or 9 + cards from Origo Education in which a ten frame is used and one the lower counters is moved up into the ten frame to make 10 and one less than the original number . Fractions are taught using pattern blocks, a Pk-Kg staple. Etc. etc.

Marie, a retired math primary teacher, now a trainer and consultant

” And they need to be told the labels – the math terminology.”

Which is way overdone nowadays.