Stephanie Sawyer gives her view of the flaws of the Common Core math standards:
I don’t think the common core math standards are good for most kids, not just the Title I students. While they are certainly more focused than the previous NCTM-inspired state standards, which were a horrifying hodge-podge of material, they still basically put the intellectual cart before the horse. They pay lip service to actually practicing standard algorithms. Seriously, students don’t have to be fluent in addition and subtraction with the standard algorithms until 4th grade?
I teach high school math. I took a break to work in the private sector from 2002 to 2009. Since my return, I have been stunned by my students’ lack of basic skills. How can I teach algebra 2 students about rational expressions when they can’t even deal with fractions with numbers?
Please don’t tell me this is a result of the rote learning that goes on in grade- and middle-school math classes, because I’m pretty sure that’s not what is happening at all. If that were true, I would have a room full of students who could divide fractions. But for some reason, most of them can’t, and don’t even know where to start.
I find it fascinating that students who have been looking at fractions from 3rd grade through 8th grade still can’t actually do anything with them. Yet I can ask adults over 35 how to add fractions and most can tell me. And do it. And I’m fairly certain they get the concept. There is something to be said for “traditional” methods and curriculum when looked at from this perspective.
Grade schools have been using Everyday Math and other incarnations for a good 5 to 10 years now, even more in some parts of the country. These are kids who have been taught the concept way before the algorithm, which is basically what the Common Core seems to promote. I have a 4th grade son who attends a school using Everyday Math. Luckily, he’s sharp enough to overcome the deficits inherent in the program. When asked to convert 568 inches to feet, he told me he needed to divide by 12, since he had to split the 568 into groups of 12. Yippee. He gets the concept. So I said to him, well, do it already! He explained that he couldn’t, since he only knew up to 12 times 12. But he did, after 7 agonizing minutes of developing his own iterated-subtraction-while-tallying system, tell me that 568 inches was 47 feet, 4 inches. Well, he got it right. But to be honest, I was mad; he could’ve done in a minute what ended up taking 7. And he already got the concept, since he knew he had to divide; he just needed to know how to actually do it. From my reading of the common core, that’s a great story. I can’t say I feel the same.
If Everyday Math and similar programs are what is in store for implementing the common core standards for math, then I think we will continue to see an increase in remedial math instruction in high schools and colleges. Or at least an increase in the clientele of the private tutoring centers, which do teach basic math skills.
Diane Ravitch's blog 
My school district has used Everyday Math for years and I do not like it at all. Like the writer, both my children are quite capable in math so they’ve been able to fare well, but being an art teacher, I have rarely been able to help them when they had questions about homework. I’ve spoken to homeroom and math teachers, and supervisors in my district about this program and they all insist it’s great for higher order thinking, but what good is all the higher order thinking if students don’t have the basic skills down first?
“But what good is all the higher order thinking if students don’t have the basic skills down first?”
That’s an issue our high school English department has constantly voiced as it pertains to the large number of our students who read below grade level. We attempt to mitigate the problem with plenty of vocabulary building and reading comprehension instruction, but it’s an uphill battle.
“But what good is all the higher order thinking if students don’t have the basic skills down first?”
This is the refrain I hear from teachers of most subjects at my school too. Yet we are constantly told that we need to emphasize “critical thinking.”
That math program and Saxon are about the worst. The “spiral” technique ignores concept mastery. It’s okay to review previous concepts, but intense instruction on concepts is more important.
…they all insist it’s great for higher order thinking, but what good is all the higher order thinking if students don’t have the basic skills down first?
I totally agree, and like Alan, I hear the same thing from all subject areas at my school. It’s hard to critically think without a foundation of knowledge and logic.
I agree with this post. I could tell you how much I agree, but following CCSS I need to show you a model. Since I can’t draw a model as a response, I’ll try to describe it ( another CCSS skill)
So here goes;
I agree ____. (I would have drawn a grid 10 boxes by 10 boxes and color all 100 boxes in using my favorite color) Since each box represents 1/100 that you’ll know how much I agree.
Good post . . . she should give concrete examples to make it more real.
mb mbutz24@aol.com
Thanks Stephanie, great comment. I will take it a step further. Do not know your age but at least you have some years outside the classroom. I did not get a license (also in mathematics) to teach until I was 50, spending many years in the corporate world.
Now, with 14 grandchildren and many years of classroom experience, I will do all I can to help change things. Public education is in terrible, deep trouble and everyone seems to acknowledge the fact.
My solution is to Free the Teacher, let them become independent. There are plenty of people and issues to blame but blaming solves nothing. Teaching is no different than running a small business. We must go charter, we must go voucher and get rid of those who pretend to speak for us – the unions. I do not need them, I do not want them.
Dick Velner – Parent, Teacher and Curriculum Principal for the Russian School of Mathematics
Dick,
I agree with your statement “My solution is to Free the Teacher, let them become independent.”. Why is it not possible to do this in Public schools? Charters and vouchers are not the answer and teaching is nothing like running a small business! Maybe you meant that a principal job in a privately run charter school is no different then running a small business? Most charters are run as a small business, only worrying about the profit not the curriculum or instruction.
If a small business does not care about providing a quality service it will not be in business for long!
Tim,
I do not know your background or your experience that developed your conclusions. Teachers are employees of the school district they work for. They have no incentive to improve or provide for excellence in the work they do except their own inner driven values. What makes you think a small business is only concerned about “making a profit”?
I have two sons going into 7th grade and both need help with math – can you recommend a good workbook that is concept driven that I can work them through over the summer? you can e-mail: needleartsguildhhv@gmail.com
Dear Dick and Stephanie,
I am not a math teacher but I am a scientist and University professor. My daughter is now in 3rd grade in a school district in Massachusetts. Many of her classmates go to Russian Math. I am a product of the Russian system and I am not a native here. But, I like the system here and am overall happy with the Common Core. It has its flaws sure, but, so do other systems.
I will say that sending your child to learn math in another system, like the Russian system does not help them truly learn and can be confusing to some.
I also wonder if sending your kids to something like Russian math is doing them a diservice. Do they really know math and understand it or do they just seem like they know it because they are doing math that is 2 years ahead of their peers? If the latter, that is not true knowldege. That’s just cheating, honestly. It also gives them a false sense of security, thinking they know math and don’t have to study. Later, I see them at University, they flop and are unable to think… they can do derivatives like robots but they can’t analyze an experiment…
Another math system may not be the answer, as one of my daughter’s classmates who is in 4th grade equivalent in Russian math but 3rd grade in public school, to her 3/3 are bigger than 2/2. Can I just say, my daughter got that question right thanks to her public school teacher.
Reblogged this on MyWorld as Curriculum Writer and commented:
Thanks Stephanie, great comment. I will take it a step further.
Do not know your age but at least you have some years outside the classroom. I did not get a license (also in mathematics) to teach until I was 50, spending many years in the corporate world. Now, with 14 grandchildren and many years of classroom experience, I will do all I can to help change things. Public education is in terrible, deep trouble and everyone seems to acknowledge the fact. My solution is to Free the Teacher, let them become independent.
There are plenty of people and issues to blame but blaming solves nothing. Teaching is no different than running a small business. We must go charter, we must go voucher and get rid of those who pretend to speak for us – the unions. I do not need them, I do not want them.
Dick Velner – Parent, Teacher and Curriculum Principal for the Russian School of Mathematics
Thanks for the cross post, Dick Veiner!
I agree with your earlier comment about freeing the teacher. I fear that there are many teachers out there who lack the confidence to do so, or just plain fear for their jobs if they don’t follow the district pacing chart lock-step.
And you are totally correct about stopping the blaming; as you say, it solves nothing. At my school, we decided to take that particular bull by the horns and just remediate through whatever high school-level course we are teaching. We do micro-lessons of basic arithmetic skills, then maybe 2 to 3 weeks of starters on those. We also got a grant for web-based subscriptions to ALEKS to give students extra practice at home. Do we actually complete the algebra 1 or algebra 2 curriculum? heck no, but we figure the trade-off – students actually getting the mathematical fundamentals – will pay off in other places. Don’t have any data yet to support that hypothesis since we just started this project this school year, but we will be gathering it and see if it works!
Mr. Velner: I agree with you about deliberate and an emphasis on placing blaming. However, to solve a problem you must find out what is causing it, not the symptoms of the problem, the real live cause(s). So by that required action, you have identified the “blame” and there is no way to hide it; that is, if you really want to solve the cause of the problem, rather than treat the symptoms!
Ron Keister
Here is a classic essay on math education called “A Mathematician’s Lament” by Paul Lockhart.
Click to access LockhartsLament.pdf
@ teachingeconomist: Thank you for sharing that link.
Lockhart’s Lament is an all suffering strawman-filled whine about how math is taught as a computation only course with no inkling of what math is about. His approach may be fine for gifted students but he falls prey to the same things Stephanie has brought out in her comment: he places critical and higher order thinking skills above the basics and does not see that mastery of the basics is essential to get to the lofty tower he enjoys occupying. He is a teacher by the way, at St. Ann’s school in Brooklyn. He teaches gifted and non-gifted students. The gifted students seem to do OK with his course; the non-gifted are in the same boat as the casualty cases from Everyday Math and other atrocities.
Thank you for the link. I had read Lockhart’s Lament some time ago, and had forgotten the name of the essay so it was a pain to track down.
I don’t think it has anything to do with the conversation math teachers are having. The essay takes an antithetical position to a perceived and overly simplistic view of the opposing position. Lockhart basically sets up an easy-to-smack-down strawman. The premise is an unfair characterization (caricaturization?) of people who hold a view that doesn’t agree with his.
Just as many music students learn theory and pieces concurrently, most traditional math curricula do the equivalent. It seems to be a generally accepted meme that whenever someone endorses a mathematics curriculum that uses the adjective “traditional,” it must mean that they think children are just to be taught steps and algorithms in isolation with no context. This simply isn’t the case.
Ms. Sawyer,
Cheap shots at Paul Lockhart, attempting to dismiss him as a guy whose argument rests on straw-man methods is not going to convince many people who’ve read both the essay and book version of his first foray into the public sphere regarding math education, or his more recent book.
It’s also a very predictable tactic to suggest that he’s out in some elite world, out of touch with the vast majority of students. While that might be true, you know nothing of his other experiences, prior to coming to St. Ann’s or parallel to them. You could also suggest, I’m sure, that the late Paul Halmos was living in a dream world when he gave his famous lecture in Scotland in 1973, “Mathematics As A Creative Art” http://www-history.mcs.st-and.ac.uk/Extras/Creative_art.html
Polya, too, was obviously fantasizing when he wrote and spoke about “Let Us Teach Guessing.” According to a recent message I received from someone who knew him at Stanford, my assessment that Polya expected his methods to be used with students before college is correct (though I’ve been told repeatedly by a couple of Mathematically Correct/NYC HOLD members that it’s “obvious” that he only meant them to apply to mathematics majors and graduate students. I’ll stand by my interpretation of his words.
So either we have a world in which most people are incapable of doing anything vaguely akin to what Halmos, Lockhart, Polya, and many others, myself included, would consider “mathematics,” and only the elite and so-called ‘gifted-and-talented’ K-12 students need apply to any classroom going outside the world of rote and computation practice, or that vision isn’t quite true.
Your money appears to be against those mathematicians and those of us who think similarly and, at least in my case, have been introducing problems in various grade bands and in (mostly) some of the highest-needs districts and schools in SE Michigan (including in Detroit, Pontiac, Flint, Willow Run, and their immediate environs).
My current work is a rare exception for me, in that I’m at a progressive (though hardly elite) private K-8 school with an administration, faculty, student body, and parent base that (mostly) trusts that given a solid teacher, the students can do a great deal more than is generally dreamt of in the philosophies of the traditionalist in this country over the last 10-12 decades, if not longer.
No one who knows his/her stuff in math ed dismisses the value or importance of computation, algorithms, and the like. But I do object strenuously to the American obsession with these things to the extent that for the vast, vast majority of the population, including many of our teachers, that is the alpha and omega of K-12 or school math. Lockhart knows it. Halmos knew it. Polya knew it. You seem to represent a very different viewpoint. For some reason, my money, my energy, my work, my efforts, are with the other guys.
Have to reply to myself since there’s no reply option to you, Mr. Goldenberg.
I’ll own that I haven’t read Lockhart’s book, but I am more than passing familiar with Polya and Halmos. I totally agree that mathematics is a creative art as well as a science. Matter of fact, we reference Polya in my classes often regarding the art of problem-soIving. My minor was in history; I get the whole connectedness of the different subjects. I hate how high school has become a bunch of little silos, but I do what I can in my own classes to remedy that.
I just happen to think that we can teach mathematics with a little more balance so that all children can find some success. Some children like to parrot first, think later. Some kids want to figure stuff out first. Imposing one type of philosophy on all children is bound to exclude a chunk of them.
You seem to want to characterize me as some fringe person who just wants kids to memorize a bunch of steps with no context. I don’t think I’ve ever stated anything that warrants a conclusion like that. You are reading a lot between my lines. Good luck with that. I use Alice’s Mad Hatter as my writing guide: I say what I mean. You are welcome to infer all you want, but that doesn’t make your inferences correct.
Having read your posts, I think you would find we agree more than we disagree. But as you’ve already made your judgment (I won’t grace your remarks as actual conclusions), it looks like we are done here.
Ms. Sawyer: do you think I’m misconstruing what you have to say about Paul Lockhart? It seemed rather unfair, and if you’ve not read the book, you are missing some very worthwhile writing. His passion for teaching mathematics is genuine and, on my view admirable.
But he’s hardly alone, and there are real folks teaching mathematics creatively and meaningfully all over the place (too few in K-12 classrooms, unfortunately). Check out James Tanton’s work. Though this year he’s working in DC with either MAA or AMS (I can’t recall off hand) he’s another professional mathematician who has spent recent years teaching mathematics in the K-12 world, quite successfully, though again, like Lockhart, at a private school outside Boston. He’s got great books out, and wonderful free videos on YouTube.
There’s Paul Zeitz of THE ART OF PROBLEM SOLVING fame. Again, free videos on YouTube. Great stuff.
From England, there’s the charming and engaging young mathematician, James Grimes, who blogs at The Singing Banana and has a YouTube channel of that name. And he also can be found as a frequent contributor, with other British mathematicians, on the Numberphile blog and YouTube channel. Almost anything of theirs could be of great interest to K-12 teachers and students, and I have taken advantage of them more than once in the last several months.
And while this is anything but an exhaustive list, I must not leave out the brilliant Vi Hart. My students adore her videos and so do I. They’ve led us to some marvelous classes.
My concern is that we in this country have a huge cadre of teachers who lean towards parrot math (did you use that term? I know a late colleague of mine wrote an essay about that in the KAPPAN a while back) not because it’s what some kids “need” but because it’s how they (the teachers) learned math and because they’re pretty terrified of having to do anything else. I think that’s a huge problem. I think their personal fear and inertia holds millions of children back. I think we can do far better for kids by helping them feel safe to speculate or conjecture (“Let Us Teach Guessing,” as Polya said, though I’m not clear if you agree. And by that he wasn’t talking about repeated wild ‘guess and check’ that I fear has become one of the ways anti-progressive educators have learned to take shots at the progressive reform ideas of the last two decades. The shots are cheap, but too many math educators opened the door for those shots by not making explicit what it means to do mathematical “guessing,” and why it is perfectly respectable and serious).
I work every day to change the direction in which the mathematics teachers I have a chance to influence are working. I KNOW they can do much better, but they won’t as long as they are allowed to think, as so many do, that the problem is the kids (and if not that, then the parents. Or other things, but never the mathematics they teach and how they teach it). I won’t stop doing that work, and I won’t make it easy for teachers to cop out. I’m not suggesting that you do that. I don’t really know what you do. But I do feel that your commentary, while I agree with the overall criticism of the Common Core, barks up a number of wrong trees, assesses blame in ways that will keep us looking backward instead of ahead, and grinds some axes I personally have little use for after 20+ years of Math Wars. I am the first to admit that as a result of those two decades, I am prone to make snap judgments about people who say certain things I’ve tried to show are problematic for a long time. Particularly in the decade and a half from 1995 to 2010, it generally seemed to follow that if people attacked a couple of things in mathematics teaching practice, the rest of their views were pretty predictable.
With the advent of the woeful CCSSI and RttT and other Obama/Duncan abominations (and mind you, I voted for Obama twice), things are getting a bit more complicated. People with whom I’ve NEVER agreed once in two decades about anything in education are suddenly mouthing similar sentiments to my own about Common Core. That’s interesting, but I don’t think many of them have had a revolution in their thinking about education. However, looking at how much Diane Ravitch moved over the last decade, I try to remain open to the notion that anyone can change. Even me.
I am curiouse about how folks would react to my son’s view about math education as a recent high ability high school graduate. One response is here (http://blogs.kqed.org/mindshift/2011/09/is-math-education-too-abstract/) another is a bit of advice to another student here (http://math.stackexchange.com/questions/167294/am-i-too-young-to-learn-more-advanced-math-and-get-a-teacher/167306#167306)
As a parent, I find his last scentence very moving: ” If I seem angry, it is because the material that passes for math in public schools nearly turned me off mathematics forever, and had it done so I would never have realized the sublime beauty of the subject and never felt the peace and joy that has come with understanding it.”
“If I seem angry, it is because the material that passes for math in public schools nearly turned me off mathematics forever, and had it done so I would never have realized the sublime beauty of the subject and never felt the peace and joy that has come with understanding it.”
Can this epiphany possibly come before one masters the basics? Is the problem that the process did not go far enough or that the process was going in the wrong direction? Lockhart’s Lament may seem so appealing, but it’s not what’s going on in schools. There are different levels and types of understanding. I wanted more mathematical (!) understanding for my son, but that had little to do with what his K-6 teachers talked about. Math became more rigorous in high school, but I would like them to put more effort on seeing bigger mathematical ideas. This means more on top, not changing the direction of the process. However, my son has no issue with this limitation. He knows that the beauty of math is built on understanding and mastery of the basics. He is more than happy to master skills with only limited motivation about what it all means. This has nothing to do with rote. It has to do with different levels of understanding. One cannot have K-6 kids learn about place value by first starting to talk about base systems and linear spaces. Also, he is more than able to learn about the bigger picture on his own.
In reality, K-6 educators use essays like Lockhart’s Lament to justify all sorts of trivial ideas of mathematical understanding. It’s used as cover for low expectations. K-6 educators start with conceptual ideas and hope that they will magically drive the mastery of basic skills. It doesn’t happen. Kids are left with vague conceptual ideas that are not strong enough to get the job done.
I suppose the answer to this depends on what are the “basics” of mathamatics.
Teaching economist: I had the exact experience of math in high school that Lockhart writes of, and hence was utterly turned off to the subject. No teacher seemed to notice that I was scoring high on aptitude tests in mathematics (and everything else) and was a straight A student in math (and everything else) until 9th grade (when we were expected to do algebra 1 with zero connection to anything, and I don’t just mean to “the real world,” but to ANYTHING.
No one cared to ask if something was wrong with me. Or with the teaching. Or with the curriculum. I slipped to a B+ in 9th grade math, and as my teacher was also, unfortunately, my guidance counselor, I was put into the middle track math classes for high school, and the teaching was worse, my classmates uninterested, and my performance sank, particularly in my junior and senior years when I essentially stopped making any effort at all (yet still managed a respectable 640 on the SAT math portion, which was about the top 15% nationally. When I took the GRE general math test in 1991, I missed two problems and scored a 780. Guess my “aptitude” for mathematics magically went up in the intervening 23 years).
What got me back on track in math in the 1980s (ages 30 and up) was a number of lucky breaks coupled with my willingness to look stupid in order to stop being ignorant. I now have a masters in mathematics education from the University of Michigan and have been working in various capacities in math ed since the late 1980s. Who’d of thunk it in 1968, when I “knew” I’d never need math or care to learn any? Certainly none of my h.s. teachers.
Yes, I’m angry, too, though time blunts a lot of the personal resentment. My focus is on what’s being denied to the vast majority of kids in this country: the opportunity to even find out if mathematics has anything of interest to them and if they have any talents to bring to mathematics. By continuing to worship at what an Oregon-based colleague, Kirby Urner, properly calls Calculus Mountain, we are pushing rote algebra (algebra devoid of beauty) into lower and lower grades (with little success and much destruction, given that we still for the most part seem clueless about how to teach arithmetic and other areas of math in K-5 in ways that would support algebraic thinking and doing). Instead, we should be reading Lockhart and the others I’ve mentioned (Polya, Halmos) along with high school teacher and veteran of the AP Calculus test committee, Dan Kennedy, whose essay “Climbing Around on the Tree of Mathematics” http://bit.ly/Vddbyp should be required reading to all American math teachers, professors, and those interested parties who view math from the narrow lens of their personal experiences alone.
Mathematics can be practical, it is certainly an exercise in using logical reasoning of a particular type, and it is most decidedly beautiful. We seem to have managed to rid K-14 mathematics of all the beauty and much of the usefulness. I don’t care how loudly the nay-sayers yell and try to get us “back to basics”: the basics are great if they are taught meaningfully. There’s literally NO valid excuse for not teaching them that way. All the showy hand-wringing about the loss of basic skills and the evils of calculators miss the point. Teachers who don’t know math very well are just as bad at trying to teach “conceptual math” as they were/are at teaching rote math/algorithms devoid of sense or meaning. So the pointless squawking of the 20 Years (Math) Wars gets us nowhere as long as conservatives and reactionaries refuse to make room in the K-12 world for mathematical thinking and student investigating, and air-headed, if well-meaning, K-12 teachers try to introduce “reform” mathematics without understanding that no one has ever advocating for throwing babies out with bathwater. Of course you can’t teach math thinking without any math facts or math knowledge. But the assumption, unfortunately, seems to be that kids come to school with empty heads and clean slates when it comes to math. And that is simply not true. Of course, some kids come with much less knowledge than others, for a host of reasons. But After 3-4 years of algorithm-only instruction, almost all of them get the message: math is about calculating, calculating quickly, calculating accurately. Period. If you’re slow, if you make errors, if you can’t do it like the teachers show you, if you have your own ideas, KEEP YOUR MOUTH SHUT. And if you’re not getting it, you’re stupid.
What a marvelous implicit educational philosophy. You doubt that’s what’s going on? Ask why for generations going back at least as far as those born in the 1920s (my parents), the majority of Americans hate and fear mathematics, are woefully ignorant of it, and unashamed of saying so. It ISN’T about calculators or “fuzzy mathematics” teaching. This dog has been hunting for at least 60 years before any of that was an issue.
Wow! Thank you for that insightful and clearly articulated perspective. It’s as if you have expressed what has been churning in my gut for years.
I, at best, had mediocre instruction in mathematics through grade 12. My first experience with math at a community college was more of the same drudgery. Later, at a university, I was fortunate to have excellent instruction that opened my eyes to the beauty of math.
Now with a masters in math ed, I seek to share the wonder, but find myself forced to sit students in front of computer screens where they practice algorithms. Why? Because this program delivers data that the district collects to satisfy RTTT constraints.
I have taught elementary math methods at a local university and seen many cases of college juniors who were unable to solve problems designed for fifth graders.
No wonder students who come to me at middle school are turned off and tuned out- they are past expecting math to make sense – to it having any meaning at all.
Well, at least there are two of us. 🙂
I should not put words into MPG’s mouth but I suspect he would argue that “practicing algorithms” is all most students have ever done, RTTT makes no difference in that respect. Once it was done on a chalkboard, next on dittos, moved on to copies, now it’s on a screen.
Thanks for resisting, but your take on my views is pretty much accurate. I see little evidence of real change in what we’re doing or offering in K-12 math since my own miseducation in the subject in 1955-1968. Certainly, one major area that should be given more emphasis and coverage in K-12, discrete mathematics, is at best paid lip-service to in some state math frameworks (Michigan’s had it in there since the ’90s), but it isn’t tested and hence, it isn’t taught. As the CCSI and its tests take complete control next year (except in Texas and a few other places, and perhaps soon in Indiana, which is rethinking its acceptance of the Common Core), the chances that ANYTHING not on the tests being explored with kids or things looked at through lenses that won’t be considered on the shiny, new, expense, profitable (for Pearson, the ETS, the ACT, McGraw-Hill, etc.) exams actually getting classroom time will approach the zero they’re already at. This is a real tragedy. Given the intimate connections between the topics in discrete math (and its business-oriented cousin, finite mathematics), and computer science and the proof-orientation of post-calculus math classes, when for the most part being a human calculator becomes far, far less important, I cannot for the life of me understand why discrete math isn’t offered in every K-12 district. If nothing else, kids actually like many of the topics, and I’ve had kids who were doing horribly in most math prior to discrete, thriving and acing tests, particularly in graph theory.
My bet is that one factor is the universities and colleges have math departments that pay a lot of salaries through freshman/sophomore calculus classes. Another is that medical sciences make calculus a major hoop, regardless if your family doctor or veteranarian could find the derivative of a constant, let alone a polynomial, today or tell you why it matters to know how. Or that a major sample of U of Michigan calculus students who earned As in the standard course could explain what the derivative of a function means, though they could describe in some detail how to FIND the derivative of a polynomial (isn’t that what it MEANS?)
The other factor that can’t be ignored in any debates about US math or other education is tradition and its cousin, inertia. But that’s another topic for another thread.
It was access to a university mathematics department that saved my son.
Thank you, thank you, THANK YOU! I am a 7th grade math teacher whose students have been using Everyday Math for the last several years. This year, I was given a class outside of the Common Core-driven curriculum to correct these deficiencies. The very first thing I do is play multiplication games with 12-sided dice to increase their proficiency with basic multiplication facts. Then, I introduce them to prime numbers and prime factorization. Then we use that to reduce fractions. Most of my kids didn’t even realize that 21/56 can be reduced because they didn’t know what factors made up 56. And yet, where do we find a focus on prime factorization in the Common Core? Nowhere. Because it’s easier to find GCF and LCM without doing it that way, Prime factorization is not just a trick. It’s about understanding the relationships between numbers. It provides a fundamental number sense that our kids don’t get from Everyday Math.
I think the problem stems from all of the standardized tests our children are bombarded with from a young age. State tests, benchmark tests, progress monitoring tests, etc., etc. They learn to choose the most correct answer from a multiple choice option. And when it is a timed, computer driven test, they have to choose quickly to get credit. A teacher’s job is on the line if students score low (VAM), so They teach them how to do this.
Until we remove these mandates and allow teachers to teach, our curriculum will continue to be driven by Pearson and other corporations who are bleeding public education dry. Educators, not corporations, need to drive the education discussion. The corporate take over of public education has caused this looming catastrophe.
My daughter is also in 4th grade in a NY public school. Last weekend I showed her how to do long division the way I had learned it.
Starting in 2nd grade we’ve had sort of an uncomfortable divide in the class between students whose parents are showing their kids the old algorithms in the course of helping with homework and students who are sticking with the program. I’ve seen students anxiously whispering about whether it was OK to use “stacking” as though it was an illicit black market item.
To me the sad part of this is that there is way to teach the algorithms that does illuminate the concepts. Stacking is a beautiful illustration of the power of zero and columnar organization in a base 10 system. Granted, my 2nd grade teacher decades ago didn’t talk about that, she just said “do this to add up numbers.” But today’s teachers could easily make that conceptual connection.
Watching smart kids flail around improvising 10 steps (each of which could produce an error that is carried over into the remaining steps) to solve a problem that could be done in 3 steps with a classic algorithm is frustrating. I remember it being a good feeling to look at a word problem and just be able to say “Oh, I know just what to do here.” I think allowing today’s students more access to that feeling would actually make the math more “everyday.”
I’ve said it to other teachers, and I’ll say it here: We are raising a nation of test-takers, not thinkers.
Although I hear your frustration and have my own with the CCSS in Math, I disagree with your approach and the focus of your worry. There is nothing wrong with a student in fourth grade using a calculator for long division. I did very well in math before the age of the calculator, but I have to stop and think if I need to do long division without one.
Carole, are you saying that elementary math doesn’t focus as much on how to calculate because there are calculators to take care of that final step? That knowing that the thing is a division problem is “the answer” in the original story above? I would be on board with that as a parent if the students were allowed to use calculators in their classes but I have never seen that.
Also if students don’t have to calculate the answer by hand during standarized tests, the math tests will probably become more like the ELA tests, which is to say, even worse.
I believe the engineers who put our astronauts on the moon used slide rules and knew how to extrapolate. This country did some pretty amazing engineering before calculators and computers. Now we can’t get the correct change in the supermarket without the cash register calculating it
rratto,
I do usually by telling the cashier how much they owe me before it comes up on the screen. They look at me in disbelief and I say it’s just a little math that’s all.
The problem with just assuming kids can do it on a calculator is that a calculator does a kid no good if he cannot set up the problem in the first place. In my state, the powers that be have decided that the CCSS means that there are no remedial classes. The “solution” to kids who are lost is to “give them calculators.” That does no good for my learning disabled son, who doesn’t know how to set up the problem in the first place. There are tons of kids falling into this chasm, and no one seems to care. The kids don’t qualify for special ed, but they’re not on grade level either, and yet they’re shoved into Secondary I classes and expected to pass. I’m afraid at this rate my son won’t graduate from high school.
Elementary students can not use calculators on the NYS assessments
Or they have memorized the algorithm, but have no idea if their answer makes sense. We did a lot of estimating. Since my LD kids could make mistakes with a calculator, I wanted them to know when their answers were in the ballpark.
I disagree with you on calculators, Carol. Students should be given calculators until high school level math or science, if they must be given they at all. So often advocates of calculators fail to address the reality that results when students are given calculators in elementary school. Reality is that students simply plug the numbers into the calculators without taking the time to set the problem up or rationalize whether they’re solving it correctly. They don’t think that maybe they made a mistake when the calculator comes up with a crazy answer because crazy answers are expected. A good teacher will require students to set problems up and show their logic, but how many teachers actually do this? How many teachers above 4th grade even look at homework to see what went wrong?
Calculators, in my opinion, are the root of the problem.
I often ask those who insist that students should never be allowed to use calculators for tedious sums, products, differences, quotients (but I suppose they’ll live with them being used for non-perfect roots), to explain in detail how the method they were taught for doing long division works. Most really don’t know, even if they are proficient at doing such calculations. Virtually none of them recall ever being asked to think about it or being instructed on why the process works.
I find that very telling about our Golden Age before calculators.
Furthermore, while I’m quite adept at mental arithmetic and can certainly do long division with pencil and paper, why would I NOT use a calculator given the chance? Is there something character-building about wasting my time looking for pencil and paper, then going through repetitive process to arrive at something the calculator will give me more quickly, and, if I didn’t miss enter, with perfect accuracy? Baloney.
All this on calculators.. NYS elementary math assessments don’t allow calculators. Kids need to learn the appropriate algorithms before we allow them to use calculators for more complex problems.
It’s like trying to learn how to read without phonemic understanding. ( I’m sure I just open’s up Pandora’s Box with that one)
Stephanie,
You have hit on a very important issue. In my opinion, from what I have seen, the lack of computation skills and understanding comes from the influx of the calculator. I am sure that your son could have done the calculation using a calculator. With NCLB and standardized testing allowing students to use the calculator there has been a “dumbing-down” of the mathematical concepts. Elementary teacher have to teach students to use the calculator, the time spent on calculator instruction takes place of teaching mathematical concepts. They can simply show students how to enter a fraction, push a button and poof, it is reduced to lowest terms. There are many 9th grade students when ask for the product of 8 and 7 will reach for their calculators.
In a recent post on this blog, it was stated that the private schools in silicon valley don’t use the tech devices. That they are learning the concepts and the “why” not just pushing buttons. With the ever increasing emphasis on standardized testing, I only see this problem getting worse. How can a teacher teach rational equations if a student doesn’t understand rational numbers?
Students are not “widgets”! They come to us with not only many social issues but with different educational issues, from different schools, district, states and countries. The teacher’s job has become not just to teach the required material but also deal with the students’ social issues and educational background, making sure they have the background to handle the new material being presented. Can today’s teacher handle all these issues and still get proficient ratings on standardized test? That’s to be determined shortly!
Tim, can you cite any studies that demonstrate that the average high school graduate in, say, 1968 (just happens to be my graduation year), could perform basic arithmetic, sans calculators, better than those who graduated in 2012? I’ll settle for any studies not based strictly on anecdotal evidence or similar nostalgia-filled – kids today are dumber, lazier, blah, blah, blah – kinds of stories, complaints, and fantasies.
As for those all important rational equations: when the majority of students encounter these beasts in high school, most in my experience do not recognize them as “fractions.” Once they do (I’m pretty adept at asking leading questions), they start to dredge up their recollections of how the arithmetic of rational numbers work. But the key issues are not simply whether they mastered those to begin with, but also whether they can generalize to an algebraic situation from an arithmetic one.
When I was in school, I was very good at arithmetic. I also know that many students weren’t. There were no calculators to blame that on, so teachers and students and parents were more likely to blame it on genetics. “Face it: some kids just aren’t good at math.” Or to use a term I particularly dislike but find useful, “Some kids aren’t mathy.”
Well, I don’t think that’s nearly as true as folks would like to believe, and I don’t believe that students who are taught arithmetic conceptually will be hurt by calculators or thrown by the ‘leap’ to algebra.
So why did a lot of students struggle in the ’50s and ’60s (and for many decades before and after), with all this stuff? It wasn’t calculators. And I don’t think it was lack of mathiness. Rather, I think it was mindless mathematics instruction devoid of understanding of why things work as they do. No sense making, just following steps. Those who were good at that (as I was) were deemed bright at math. Everyone else, well, the world needs ditch-diggers, typists, and janitors, too.
The reason the math instruction was bad in past decades is not unrelated to bad math instruction today: the majority of those teaching it, particularly in K-5, don’t know how to teach math conceptually because they were never given a chance to develop any conceptual understanding themselves, by and large. And so I believe a survey of elementary school teachers would reveal a significant percentage of people who fear and loathe mathematics, and who teach a rigid set of procedures they’ve barely memorized (at least in some cases), and cannot dare stray from. Ask people like that to answer any sort of “Why?” question and you will get a look tantamount to your having asked them to put a loaded gun in their mouths and pull the trigger.
How can anyone be expected to really learn mathematics under such circumstances? Calculators are a fortunate tool for those who never get over the hump, but they are also potentially crippling, not in and of themselves, but due to the fact that teachers often are unable to do better than to hand out those calculators. If not used intelligently by the teachers, there’s little doubt that fewer students will grapple with the concepts. It’s a bit like throwing a bone to a dog to get him to stop whining. But you have to throw another bone in short order.
Keeping in mind that powerful arithmetic understanding was NEVER taught widely in this country, that mental math and estimation skills have been given short-shrift for close to a century, if not longer, I think putting too much blame on calculators is a mistake. Better look at the reality that regardless of what era of American education we’re talking about, there simply has not been a lot of sound math teaching in K-5. Without that, even the best 6-12 math teachers will be frustrated in their efforts. But they are not blameless, either. Not by a long shot. I will leave it at that for now, but simply suggest that the American problem with mathematics long predates calculators, NCLB, CCSSI, RttT, ad nauseam. And it will be with us indefinitely because even many people who should know better still insist that the only way to teach mathematics is essentially the way that THEY learned it back in the Golden Age.
Hey MPG, seems you’re everywhere these days. Do you comment on education blogs for a living? I’d like to know how to get into that…
We had a chat a while ago on a different site. Math prof from Canada, remember me?
Anyway, I picked up this book by a proponent of the new methods, written to introduce the general public to them. I thought it would be helpful for the purpose of discussion to have this system laid out carefully by such a one so that we all know what we’re talking about. I think this bit from the preface is quite helpful:
“The introduction of the ‘new’ mathematics into the elementary school grades comes as a direct result of a widespread, long-term study of the mathematics program…[which] was necessitated by important cultural, social, and economic changes into our society….the technological and scientific advances of our times…
…What, then, is new about the mathematics being introduced into the elementary grades? First, the emphasis is now on meaning rather than memorization. Concepts are presented in a meaningful manner, with generalizations growing out of example, exploration, and discovery. Memorization, when it does occur, follows meaning. Second, children are taught in the elementary grades bodies of knowledge in the field of mathematics that were formerly reserved for junior high school or high school…Within the elementary grades themselves, there have been changes in placement of mathematical concepts…simple ideas of geometric shape are now introduced in kindergarten…Third, the name of the subject has changed from the limiting term ‘arithmetic’ to the more inclusive one of ‘mathematics’…
…teachers must reorient their thinking about mathematics. They must take a fresh look at the entire subject and become acquainted with a different terminology. Parents, too, must be prepared to accept the challenge of rethinking [how this subject is approached]…”
Would you say this is a fair summary of what you’re talking about?
R. Craigen: No, I don’t remember prior conversations with you elsewhere. I believe I’ve said as much somewhere on this thread, which has become unwieldy.
I am not a fan of the kind of rigid proscriptions and prescriptions about exactly what math content strand “should” be taught to ALL children of a given age and grade. That’s the tip of a huge iceberg of assumptions about kids that has served many of them quite poorly. But that conversation goes well beyond the particulars of Common Core, NCLB, and the rest of the new wave of education deform laws and documents. To say that I’m less than impressed in that regard would be the politest offering I can make.
As to the need for dramatic change in the beliefs and attitudes of mathematics teachers in K-12 (if not further up the chain), that seems to me to be glaringly obvious. I think that the person/document you cite gets into a lot of trouble despite what are no doubt best intentions by not giving any historical context to what is under discussion.
To speak about memorization and/or rote learning in mathematics without such a context, as well as without a serious look at the strengths and weaknesses of that approach to learning (and the teaching that comes with it) leaves one open to being made to look very foolish.
On my view, as I wrote elsewhere earlier this evening, there’s nothing wrong or particularly right with “rote learning” given no context for where it’s taking place and why, and without examining the limits of what comprises rote learning and the subject one is trying to learn. If mathematics is: a) facts, symbols, terms, and definitions and b) procedures and algorithms, and if there is no sense to why or how the latter work, just as there is no logical reason for the choice of symbols, terms or even some rules (e.g., order of operations, which is a convention, not a logical necessity), then rote learning should be just ducky for making highly successful learners and users of mathematics.
That rote is not even close to being efficient or adequate for producing learners who can do mathematics that requires more than mimicking of procedures and algorithms is indicative that somewhere between teaching elementary arithmetic and teaching whatever comes at the end of high school for a given child, we mostly fail miserably to give that child the tools needed for higher mathematics. Calculus aside, which is only one path, there is a great deal of important mathematics that we could be doing much earlier with children than we do, and that could entail the development over 12+ years of informal proving activities LONG before high school geometry. That we don’t do so is quite telling. We don’t because we do a lousy job of teaching arithmetic sensibly and with meaning. We have far too many teachers who can’t do anything BUT teach it that way, who are terrified of any actual mathematical THINKING or non-routine problem-solving, and who would have heart attacks if asked to work on such things with their students. I’m not speculating: I work with people like that all the time.
When the only things you understand about mathematics are rote procedures, you teach math as rote procedures. Asked to do anything deeper or more challenging, such folks find a million rationalizations: “My kids could never learn that” = “I myself don’t get it, and I would much rather keep doing what I’ve done for the past x years for the remaining y years of my career. PLEASE don’t demand that I actually learn mathematics myself.”
The only paragraph you quoted that I am comfortable with is the last one, and even that doesn’t really say anything at all specific. Having seen the NCTM progressive reform efforts of 1989 on undermined repeatedly by the failure of most of the empathetic teachers to be able to intelligently understand or implement the best ideas from the formative documents, followed by a vicious counter-revolution that lied repeatedly about what the principles were that NCTM called for (mostly by citing anecdotes, real or apocryphal, accurate or grossly distorted and exaggerated, about bozo teachers who said and/or did things with kids that may have represented what those teachers THOUGHT NCTM was calling for, but which in fact were often examples of airy-fairy nonsense.
At this point, it really doesn’t matter if such teachers were real or only figments of the anti-progressives heated imaginations and propaganda. Any real movement to improve mathematics teaching and learning that isn’t “back to basics” nonsense had best be able to get its message across to everyone in ways so clear and unambiguous that any attempt to distort that message will be glaringly false in the eyes of the public, the media, and any fair-minded person. The statements you quoted are all subject to distortion and gross misunderstanding by friend and foe alike. And that sort of failure has been the legacy of the last two decades of the math wars. I’ve got better things to do with my professional work that try to defend the words of people who don’t take the trouble to be precise, careful, clear, and vigilant in the face of organized opposition to anything and everything new.
Finally, I don’t worry about the lengths of my comments or those of anyone else. Why is that important to you? And why should I care?
At my 2nd-tier State U we’ve observed a precipitous drop in the mathematical ability of incoming freshmen. This happened over the last 10 years (I’ve been a math prof for 21 years now), with our remedial math program now enrolling about 50% of the incoming class (up from about 15% of the incoming class 10 years ago). Also, over the last 10 years we’ve witnessed a huge increase of the failure rate in the remedial program. It seems that about 30% of incoming freshmen are not just math illiterates, they are, bluntly put, unteachable. The faculty is stumped, and at the same time the administration has been meddling with the math placement process making a complete mess. So now we fight on two fronts: trying to figure out how to remediate the ever increasing amounts of wholly unprepared students accepted while fending off the administration types who want every “revenue-stream” (a.k.a. student) they create (by lowering the admission standards) to be retained and graduated in a reasonable amount of time (to please the US News report).
And this upheaval at the freshman level has effects later on in higher-level courses with significant mathematical content: my grade distributions have evolved from uni-modal, to bi-modal, to noise…nowadays the situation is so bad that the test average and standard deviation mean nothing.
Last year the students were complaining in the school paper about math tests…one of them actually nailed the problem by saying “I do badly on math tests which when solved by the professor appear to be really easy because these tests are sneaky and not like the homework…I want to take hard tests but you have to train me to take these hard tests.” In other words, this student, at the college level, is unable to do well on tests that are designed to determine whether learning has taken place and is demanding that we instead hold monkey-see monkey-do test-training sessions on the test that he/she will be taking…just like in K-12…
I think the situation is hopeless.
Any possibility that the students coming are drawn from a pool that has gotten a lot larger and, hence, includes people a lot further down the “achievement ladder” than was the case 20, 30, 40, 50, or 60 years ago? Just speculatin’ on a hypothesis. . .
Hi again MPG. In an earlier comment you ask for comparisons to 1968 students. Well, obviously one needs a time machine, or we can test 60 year olds against grade school tots I suppose. But fortunately, I happen to have a time machine, so I’ll take a shot at your challenge.
I happen to be the director of the Manitoba Mathematical Competition, a grade 12 contest aimed at the upper quartile of High School Seniors. We hand out thousands of dollars in prize money, plus scholarships and other honours. We’ve got some nice carrots for these top performers, so those with a bit of motivation tend to take part.
Thing is, a lot of “pretty good” students also like to write, to see how they match up against them, and we encourage wide participation. But … we don’t want to discourage them. So, as with all North American math contests (with the exception of invitation-only olympiads and the notorious Putnam Competition) we ensure that the first few problems are essentially “gift marks” any person with baseline skills ought to be able to score on. The last thing we want to do is to hand out dozens of zeros, out of 100.
So one measure of how student skills — at least among the top quartile — have evolved over the years is the skill-set required to solve the first few questions on a test that has been a fixture over the period in question.
Note that this particular contest is set by a large committee consisting of retired “master teachers” and subject-matter experts, and people with several decades of contest-writing experience. We are intimately familiar with the current skill-level, background and capabilities of the graduating class, and get continual feedback from teachers whose students write our contest. So I assure you that these questions reflect the best judgement of a consensus of experts who are extremely well placed to adjudicate exactly the kind of skill you are asking about.
Oh, and I assure you that on standardized tests like PISA and MPAC, Manitoba students, both now and as far back as we have data, are manifestly typical in North America as concerns mathematical skills.
Here is the first question from the 1968 MMC:
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Simplify: ((a^2-(b-c)^2)/((c+a)^2-b^2) + (b^2-(c-a)^2)/((a+b)^2-c^2)+(c^2-(a-b)^2)/((b+c)^2-a^2)
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Tell me how your grade 12 students do with that one.
Here’s the first question from the 2012 MMC:
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(a) Find three consecutive even integers with a sum of 36.
(b) Find three consecutive integers so that the smallest plus twice the largest is 15 more than the middle integer.
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Double or nothing? Here’s the first question from 1967:
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If g(x) = 3^x – 3^(-x), show that {g(3x)/g(x)-[g(x)]^2}^(-1) = 1/3.
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And from 2011:
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(a) A square has a diagonal 10 cm long. Find the area of the square.
(b) ABCD is a square. AB and CD are increased by 10% while BC and DA are decreased by 10%. By what percent does the area change?
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NOTE: In recent years our first few questions have evolved into two-part problems, each part of which can be solved in perhaps one or two steps because we find anything requiring multiple steps tends to result in a lot of blank papers or plain garbage.
Incidentally, we have achieved some success in this regard. Only about 3% of our contestants scored under 10 out of 100 in 2012. We didn’t fare quite so well in 2011: 10% of our students scored under 10. Only two papers received a zero though. Hurray!
I don’t have result data from the 1960s so I can’t give you the comparable numbers. But, anecdotally, the old-timers who were (and still are) involved setting the contest tell me that most students were expected to get over 50%. Our median score in the last two years was 28% and 39% respectively.
MPG, the last 5 years our administrators have almost doubled the size of the freshman class. They insist that admissions standards have not changed, instead the average SAT scores of incoming students have been going up. They also tell us that students today learn differently than those of decades ago and so it is our fault Johny can’t order 20 numbers given in various formats. Tragicomedy in its purest form.
To R. Craigen: I think you’re onto something. See here: http://www.rsc.org/images/ExamReport_tcm18-139067.pdf
When the RSC report came out in the press we discussed it at lunch and a colleague who works on mathematical problems in chem/bio took a look at the questions and he said the same thing about the old/current differences.
It is possible that both of you are right, as In Hell’s Kitchen is talking about the mean while MPG is talking about the size of the tail of the distribution. My own institution has very fat tails. Faculty who have taught at a variety of institutions almost uniformly say that this university has the best and worst students they have experiencd teaching.
I only just subscribed to this thread today, so I’ve not been seeing follow up comments unless I take the time to return here. Some interesting ideas here. I don’t recall a previous conversation with you, but don’t take it personally: unless we’ve interacted a few times, it’s too easy to lose people and dialogs in the flood.
I wonder about the subjective factor, still, in the selection of problems and the perception of those deciding what and how to test. I need to give more thought to what you’ve written, but the first question that comes to mind is how samples wind up being drawn and if there is fair sampling and reasonable inferences being made from apparent results. According to what I read about PISA, TIMSS, and Math Olympiads, our top kids are still top or nearly so internationally, but our overall population is still lagging when not adjusted for socio-economic factors. A recent piece from the Economic Policy Institute by Richard Rothstein and Martin Carnoy http://bit.ly/WdKHiH seems worth looking at in this regard.
So maybe you should read that and I’ll look more at what you’ve offered here. I’m not convinced that there’s NOTHING to the idea that there’s been slippage of basic computational skills in some segments of the population. I’m very skeptical that there’s been slippage at the top. I’m also very skeptical that things were as generally rosy as many claim and some swear to have evidence of back in their pick for the Golden Age I personally didn’t experience despite having been educated during it at a competitive suburban high school. I doubt a lot of my math classmates in grades 10 – 12 did either, though of course those in the higher tracks no doubt did. However, for all my lack of ability, 23 years after graduation I managed a 780 on the math portion of the general Graduate Record Exam, and a few years later had the equivalent of a near-masters in mathematics and an actual masters in mathematics education from the University of Michigan. My experience is exceptional in the years 1985 on, but I suspect it wasn’t so exceptional in 1955-1977 or so. And that predates both calculators and “New New Math.”
I am a child of the early 50’s. We learned by rote until they screwed us over with “modern math” which absolutely threw me for a loop. Math or arithmetic does not change as far as I can see, It is static. I know my multiplication tables and how to use fractions in most applications, percentages, etc. I can double, triple, and so on multiply and divide. We did not HAVE calculators in school, they did not exist in the everyday setting. We memorized (oh nooooo) and we remembered. Out critical thinking skills developed as we worked our problems.
I have nothing against calculators but I see that our elementary students can use them but cannot use their brains to think critically about how to solve the problem. Not being a math teacher I know I am way out of my comfort zone and my cone of certainty but I think that when students actually work the problems out they are developing those illusive higher thinking skills and will be able to apply them to lots of other situations, not just math. I see students knowing how to plug in a function but not have the vaguest idea of how to perform the function themselve. They simply don’t know the basics. It’s like trying to put words in alphabetical order without knowing the order of the alphabet. One can know there is an order to the alphabet but not know what it is. Not much much progress can go forward from there.
I think we have the balance wrong. Understanding the process is crucial for applying math in the real world, but we have gotten so far into process kids don’t even learn basic facts. Instead they learn strategies (like doubles plus 1) for getting to what should be a rote fact. Beyond that, the way series like Everyday Math work doesn’t insure that kids master the content. we just keep moving on.
I am in my 21st year of teaching sixth grade at the same school. We ‘adopted’ Everyday Math about 5-6 years ago. The group that I have this year has had EM for most if not all of their schooling. It is glaring how poor their computational skills and reasoning are with numbers of any kind (never mind fractions!) compared with the previous groups I have taught. I am forever grateful that I hung on to one copy of the old math series, where computation and concepts were given greater emphasis. I use EM, but in my own way and in my own pacing. If I had not had the number of years teaching math the ‘traditional way’, I wouldn’t know how woefully incomplete EM is and how blissfully unaware the writers of EM are of child development.
I know writers of EM curriculum. They are sincere in their efforts. They are also people who are very comfortable in math and always have been. Where they fail is in their understanding that math doesn’t come as naturally to most children as it did to them.They don’t ‘see’ what is so hard about learning computation, simply because it wasn’t hard for them.
To add insult to injury, when I point this out to administration. His only response is that our test scores in math are good. Sigh.
Stephanie. Actually, the last generation really had an opportunity to be exposed to the old “new math”–which spent a lot of energy teaching kids the underlying concepts involved in mathematics–and arithmetic. If teaching about fractions year after year doesn’t work–maybe it’s because too little time was spent consolidating ideas more appropriate to their age-level, and thus postponing some subjects until they can be more easily truly taught and understood. I’m told that’s “the Japanese way”.
I’ll also bet your sample of 38 year olds (why that age?) was not very scientific.
I’d also like, truly, to know what damage you think it will do those students you teach who don’t do well in algebra. Suppose you fail–what will the repercussions be on their lives, if we didn’t (of course) place artificial obstacles in their path (such as not being able to graduate high school).
Deb
Deb,
I think I must have been part of that generation! I remember learning ideas and algorithms side-by-side. I also remember that first grade was basically about place value, expanded notation, and addition, as well as some telling time and counting money, but not much else. I likely remember because I was scared to death of my teacher, Sister G—–!
I think your reference to the Japanese way is also valid. I think that many regular kids are being exposed to ideas that they are just not ready for, particularly when it comes to fractions. A colleague of mine was telling me he thought his daughter might be slow in math since she was struggling so much in first grade. He showed me a worksheet that was dealing with fractions (only halves and fourths, but still, I thought this was weird for a first grade assignment).
As for my “sample” of 35+ folks, well, that’s just part of my parent-teacher conference schtick. I generally see about 50 parents (and this is my 4th year back teaching) on a night, twice a year, and the fact that I teach in a Catholic high school definitely warps the sample. I’ve also extended it to friends with no kids to see if having children tends to make you review more, but again, hardly scientific. I guess I have a project if I ever decide to pursue a PhD, I suppose.
As for damage to students, I don’t really know where to go with that. I do my best to remediate as we go along the curriculum. Is my algebra 2 class really an algebra 2 class? Probably not. It’s more important to me for students to know and understand a few things well than to just have been exposed to many topics and truly know nothing more than they did when they walked in. And have I failed a few? Probably. No teacher is great to all students. Even teachers who are regarded as not-so-great are great to some kids. At my school, we really do go out of our way to see that all kids graduate. I think that is why we have the reputation we do; parents and kids both know we (teachers, administrators, counselors, staff) care as much as they do about their success and future.
In a school which followed an accelerated curriculum, my kids had a good handle on multiplication and division through second grade. The teacher had the class use calculators beginning in third grade, which back then was the first year of standardized ISAT testing.
By January of that year, my kids’ ability to recall multiplication facts instantly had noticeably diminished. I asked whether calculators were overused. I was told the children were supposed to get comfortable with calculators because of the ISAT tests.
A quick question for all. My district instituted “Singapore” math last year. The little that I saw of it had me baffled, and I come from a family of mathematicians don’t think I ever scored below the 92nd percentile on those math tests way back when.
Where does this “Singapore” math come in in relation to the others mentioned?
In my district the teachers to not know how to teach the core. They are going to workshops two and three times a week, which leaves the children with subs. And of course the subs do not know the material. This has just been a wasted year. Core does not get to the middle of anything. Math is a definite number not a estimate.
Common Core is supposedly pedagogically neutral. Yet, schools, school districts, PD vendors and others are interpreting the math standards as requiring an inquiry-based, problem-based learning and student-centered approach. The 8 Standards of Mathematical Practice are three pages out of 100 pages of standards, and yet, these SMP are looked at as the heart and soul of the standards. The SMP CAN be interpreted to use explicit and systematic direct instructional techniques. The Common Core nowhere mentions “critical thinking”, “collaborative work”, or “inquiry-based discovery approaches” as a necessary part of the standards.
For more, see my article on this at The Atlantic at http://www.theatlantic.com/national/archive/2012/11/why-the-new-common-core-math-standards-dont-add-up/265444/
That’s the problem with Investigations! This is why I have 5th graders sitting in my room who do not know their times tables. And no, the computer game isn’t helping either. This is why I had them get index cards, fill them out with facts, and we practice one fact a week. They love it!
Unfortunately, I would have to hide them if “they” came in my room, because they are not supposed to do “drills”!
Does anyone here think we could construct a set of math standards that would not generate significant criticisms?
TE,
Gonna have to use a technique that I try to get my students to understand and use, repetition.
To answer your question, hell no. That’s an impossibility as Wilson has already shown the problems with any educational standard in his dissertation, see: “Educational Standards and the Problem of Error” found at:
http://epaa.asu.edu/ojs/article/view/577/700
and his shorter version: “A Little Less than Valid: An Essay Review” found at:
http://www.edrev.info/essays/v10n5index.html
Click to access v10n5.pdf
Duane
Hope the nasty wintry mix didn’t find you this time around!
Not likely, and there you’ve nailed it! I admitted I liked CCSM better than the prior standards mess. I just wish there had been more than a passing nod to algorithms and how they can enhance understanding.
I am so reminded of the old phonics-vs-whole language wars. There seems to have been an uneasy truce, in that both are now part of elementary classroom reading strategies. I’d like it if we in math could at least start there.
I’ve been a social studies teacher for 17 years, so I
haven’t studied the CC math standards. My daughter’s 1st grade
teacher and one of my district’s math coordinators explained to me
that the district is likely moving away from Everyday Math because
it currently won’t help our students learn CC math, that concepts
are not taught in depth. Can anyone else speak to this?
Sorry, I should clarify. I haven’t YET studied the CC math
standards. I’m still working on the CC ELA standards. OF COURSE I
teach some math in my social studies classes.
Reading this educationally-conservative (if not reactionary) opinion piece and the vast majority of comments – nearly all of them of the “oh, if only things were the way they were back in the Golden Age” flavor – one might be led to believe a number of possible things before – or after – breakfast.
1) there was a Golden Age of Mathematics Teaching and Learning;
2) text books make or break a math curriculum;
3) there was a single movement/project called “The New Math” that was idiotic, was actually implemented in American schools, and which failed miserably;
4) the ideas proposed in the various NCTM standards volumes starting in 1989 were idiotic, were actually implemented in American schools, and failed miserably;
5) calculators are a tool of the Devil (as is all of educationally technology in mathematics.
There are more statements made explicitly or strongly implied in the above commentary, but I’ll let these suffice and state unequivocally that each of these is utterly or essentially baloney (I’m being polite out of respect for Diane).
There was never a Golden Age. I started school in 1955 and graduated from a very good suburban NJ high school in 1968. The senior class had nearly 800 students and 80% of the graduates went to college. And as one of the mediocre students in mathematics (despite a respectable 640 SAT math score – not bad for someone who slept through math classes routinely) I can say without hesitation that there were a lot of students who left high school with serious deficiencies in their mathematical knowledge, regardless of their diplomas.
My father started school in 1929 and studied aeronautical engineering and then accounting in college. He hated math in school and said that the teachers in his Brooklyn public K-12 classes were uniformly nasty and poor at explaining anything.
My mother and aunt went to school in that same era (my aunt started in 1925, my mom in 1931) and both graduated high school lifelong mathphobes, despite having a father who was a natural genius at mental math (perhaps having left school in 1894, at age six, to work, kept the fabulous teachers of that Golden Age from destroying his abilities).
So unless a quick Golden Era slipped in during the post-war years and then vanished in the mid-1950s (and I have uncles and cousins who would suggest otherwise), I’m just a bit skeptical about the Golden Age.
As for texts, they don’t matter if the teachers are knowledgeable, creative, and fearless. Of course, there’s never been much room for that in this country, and in the current climate such folks are crushed unless they are EXTREMELY clever or teach private school.
There was no single “New Math,” and the crap that was taught for a while in some US schools was probably the least representative material of all the projects that were developing new materials and methods at the time. The best of the bunch, on my view, was Robert B. Davis’ Madison Project (began in Syracuse and then moved with Davis to Missouri). There are materials from that project available for free download. They’re really good. It’s tragic that those weren’t what got published and pushed. But regardless, The New Math was not the problem.
Many of the ideas promoted by NCTM are sound, but few of them are well-understood by the typical American math teacher in any of the K-12 grade bands. Professional development has not been coherent or widely available, and few American teachers seem to take PD seriously enough or see it as a way to truly improve their craft. I could write volumes on that subject, and some people have tried to do so. I will comment below as to what I think the real problem is.
Finally, technology is only as good as the uses to which it is put. Given the fanatic obsession in this country with the bankrupt notion that mathematics is little more than computation, it’s no wonder that so many K-5 teachers have no idea how to use calculators intelligently in their classrooms, and so we entered an era in which one of two extreme and equally wrong-headed notions prevailed: on the one hand, we had that “let kids use calculators for everything, any time” crowd (and yes, I DO hold NCTM partially responsible for that, though not entirely), and the “calculators are the devil” school of thought. A plague on both their houses, in my view, but I hold the second group to be the more blameworthy, because their reactionary attitudes, grounded in a very narrow view of what K-12 mathematics can and should look like (nothing at all like what Paul Lockhart speaks of in his book, or what Paul Halmos described in his famous lecture about math as a creative art, or what Polya strove for, etc.), made them fear and loathe technology. And yet, they are ALL about another technology: paper and pencil. And that is in no small part MORE crippling than electronic technology, because over-emphasis on paper-and-pencil seems to have made generations of teachers in the US eschew teaching or sufficiently emphasizing estimation skills and especially mental arithmetic. And that has truly crippled generations of kids, even many who were able to succeed with all that tedious, procedural number-crunching on paper. Congratulations to those who were successful in becoming a slower, less reliable calculator. But can you actually think mathematically? Can you attack non-routine problems that you’ve not been explicitly given procedures for? If you’re honest, most readers will have to say that they cannot.
So despite all the disparaging of “critical thinking,” the fact remains that mathematics is a mode of thought. And if you’re not exploring mathematical THINKING and true problem-solving with students because you’re so focused on arithmetic as a bunch of black-box magic algorithms, then you’re not teaching mathematics and your students aren’t learning mathematics. They’re learning to do donkey arithmetic and to be thoughtless, mindless little drones. Very good for being cogs in wheels and not thinking for themselves, challenging teachers, classmates, or themselves.
I teach a group of 4th through 8th graders in a mixed-age class for an hour a day at a local private school – no common core, no standardized tests, no one looming over me to tell me that I need to get my kids scores up so we can make AYP.
Last week, after doing lessons on Roman numerals, decimal, binary, octal, and hexadecimal numbers (with a brief look at duodecimal, to which we will return tomorrow), I asked them to think about a couple of things WAY off the map: negative bases, and unit fraction bases. Minds were blown, but we came up with some workable notions of how these might work. We may also look at improper fractional and irrational bases a bit. I know we’ll be taking a look at a problem I was given in a computer programming class at University of Florida in 1979 that requires base 28 for the easiest solution. I think they’ll get it, too.
If someone came in and told us we needed to start prepping for some standardized test or align ourselves with the Common Core or the state curriculum framework the core will replace, or any other nitwit, narrow pile of nonsense, I would fight it, and failing to keep it out, I’d leave. I’ve paid my dues dancing to idiotic tunes, which is one reason I doubt I’ll ever be willing to teach in a traditional classroom again.
But in this regard, the problem isn’t the Common Core (though I very much oppose the entire idea of ANY common core), and those who are focusing on the particulars of this set of “standards” are missing the boat. The specifics aren’t the problem. The problem is the entire institution of American public education. Let me close with a provocative quotation I bumped into this week in that regard:
“It has been customary for fathers to pass on to their sons the creeds and customs which their own fathers had passed on to them. Ancestors have been worshiped and the Old Man has been honored from time immemorial. Education has been chiefly a matter of compelling the child to conform to the ways of his elders. The student has been taught answers, not questions. At least, when questions have been taught, the answers have been given in the back of the book. In the main, knowledge has been given the student, but not a method for adding to it or revising it — except the method of authority, of going to the book, of asking the Old Man. The chief aim of education has been to make of the child another Old Man, to pour the new wines of possibility into the old bottles of tradition. Wendell Johnson, ” PEOPLE IN QUANDARIES, 1946, pp. 24-25.
Perhaps you would like to see my son’s comments on K-12 math. He wrote it just before he left for his first year in college. It can be found here:http://blogs.kqed.org/mindshift/2011/09/is-math-education-too-abstract/
His is the first comment.
Forgive me for a poor memory. Your comment is the first one on his comment. Wish there was a delete button on here.
“Many of the ideas promoted by NCTM are sound, but few of them are well-understood by the typical American math teacher in any of the K-12 grade bands. Professional development has not been coherent or widely available, and few American teachers seem to take PD seriously enough or see it as a way to truly improve their craft.”
You can’t seem to separate the variables of competence, pedagogy, and content. Traditional math was bad because of pedagogy, but the new stuff in math education is not working because of competence?
“…on the one hand, we had that “let kids use calculators for everything, any time” crowd (and yes, I DO hold NCTM partially responsible for that, though not entirely), and the “calculators are the devil” school of thought. A plague on both their houses, in my view, but I hold the second group to be the more blameworthy, because their reactionary attitudes, grounded in a very narrow view of what K-12 mathematics can and should look like (nothing at all like what Paul Lockhart speaks of in his book, or what Paul Halmos described in his famous lecture about math as a creative art, or what Polya strove for, etc.), made them fear and loathe technology.”
When my son was four, I remember thinking about the things I didn’t like about my “traditional” math education. I wanted my son to better learn how all of the pieces fit into a larger idea of what math is all about. Then I found out that our school used MathLand. Later, they switched to Everyday Math. Kids were neither mastering the basic skills or learning about the larger ideas of math. Although you admit to competence as being a big issue, you can’t ignore it and claim that your ideal of math education is better than the reality of any other approach, traditional or “reform”.
Some mathematicians wax eloquent about the wonders of math and how most students are missing the big picture, but in reality, the question is more about whether one can better achieve that ideal from the bottom-up (traditional) or the top-down (reform). Both can work, but the latter requires more effort and is much more risky.
When my son was in fifth grade, a new parent to our (Everyday Math) school wanted to form an after-school math club to study interesting problems. He thought EM was a great idea. He soon found that he was spending all of his time ensuring mastery of the basics. It was just too painful to work on interesting problems when the kids couldn’t do the mechanics even with a calculator. The fundamental flaw of Everyday Math is that teachers are told to keep moving and to “trust the spiral”. The onus is placed squarely on the students. Some kids do well, but teachers never ask their parents what they do at home.
Everybody wants to achieve understanding at all levels, but I doubt that there is common agreement on what that means.
“Can you attack non-routine problems that you’ve not been explicitly given procedures for? If you’re honest, most readers will have to say that they cannot.”
This level of thinking is so incredibly stuck in the world of K-8 Math. What happens at higher levels where non-routine problems require mixing and applying a large number of separate skills? Math is not just a thinking process that solves problems based on understanding larger concepts. I have a very large toolbox of vector analysis skills that I use to solve geometric problems. Those skills are not rote. I know how to do a Gram-Schmidt orthogonalization and when it could be useful. I learned and mastered the technique before I ever applied it to a non-routine problem. I know how to do a simple dot product of two vectors and I know when I might need to use it. When confronted with a non-routine problem, I mix and match tools from my geometric toolbox to solve the problem. Polya assumed that these skills were in place. This is true at all levels of non-routine problem solving. Too many educators, however, talk about how a top-down process can drive mastery of the basics. That doesn’t happen. Even all of the Harkness Table approaches I’ve studied require a lot of basic mastery homework from their students beforehand. This requires more work from the kids. You don’t get something for nothing. Most reform math curricula go through the motions of teaching understanding and critical thinking, but never end up ensuring mastery of the basics because they think those skill are just rote. They are so incredibly wrong. They use critical thinking as cover for low expectations.
Go ahead and give students a problem “that requires base 28 for the easiest solution”. Explain how and when they’ve mastered the needed general skills with bases. Explain when and how all of the other basic skills, required for non-routine problem solving, are learned. It must be as homework if so much of class time is taken up with so few discovery problems. This doesn’t even get into the issue of group learning in class, where some kids go along for the ride and do little work.
“If someone came in and told us we needed to start prepping for some standardized test or align ourselves with the Common Core or the state curriculum framework the core will replace, or any other nitwit, narrow pile of nonsense, I would fight it, and failing to keep it out, I’d leave.”
But your well-prepared students should laugh at these questions. No test prep should be necessary. When I taught my son at home, I never looked at or cared about our state test questions. They were too trivial. I’m not a fan of CCSS; not because of a general dislike of testing, but because I expect that the proficiency level will, as with our current state test, be too low.
SteveH: you really know how to butcher what I’ve written to twist it to your own ends. I’m not going to waste my time correcting every misstatement you made and put in my mouth. What I wrote stands on its own merits, and I’ll leave it to more reasonable people to read it and judge for themselves what I’m saying. Like so many MC/HOLD people and their supporters, you’ve got your mind made up as to what the issues are, and so anything not utterly aligned with your views is apparently impossible to read without spinning it utterly into what it isn’t.
As for what goes on in my classroom, let me know when you want to drop by. Otherwise, your speculations are of no value to anyone but those who share your educational politics and prejudices.
MPG wrote: “What I wrote stands on its own merits, and I’ll leave it to more reasonable people to read it and judge for themselves what I’m saying. ”
It stands on your own strawmen and vague platitudes. It stands on your claim to know the proper way to teach math, but you are unwilling to give more details. At best, we are told that “minds were blown”. This seems to come after a week of “doing lessons” with no indication of how those lessons were done. We see no curriculum or how you adapt for different levels of ability. We don’t see how the school deals with kids in all classrooms, or is this a one-man math department?
“Otherwise, your speculations are of no value to anyone but those who share your educational politics and prejudices.”
I see that you are now using the adjective “educational”. It still doesn’t work.
Steve, I don’t expect you to either be convinced by anything I might say or to actually take the trouble to visit my classroom to find out for yourself. It is SO much easier for you to sneer (a practice at which you’re quite expert).
So not for you but for anyone NOT of your narrow mindset who is interested: I posed the problem yesterday at the end of our fourth lesson on bases. By this point, we’d looked at Roman numerals as an example of a system that doesn’t work like the positional systems we are used to. Then, we examined how decimal, binary, and hexadecimal work, over a couple of days. We also discussed negative and unit fraction bases as a way to stretch our thinking.
A month or so back, one of the students asked if we could watch a short video he’d found on YouTube which turned out to be by a young British mathematician whose math videos I discovered a year or so ago and very much admire (his name is James Grimes, and he mostly posts on his own blog and channel, thesingingbanana; however, this video is on the numberphile channel, to which he is a frequent contributor). I’d not seen it before and it deals with duodecimal or “dozenal” arithmetic, i.e., base 12. I enjoyed it, but my sense was that some of the students were lost, since we’d not done anything that would prepare them, and I hadn’t known in advance that this particular topic was going to arise that day. That is one of the reasons we looked at bases starting last week, in fulfillment of my promise to get back to this area and look at it in more depth.
So yesterday, after looking at octal as a way for me to get some feedback about where students were with what we’d been doing, we returned to the dozenal video, this time with a much firmer ground upon which to discuss it.
With about five minutes left, I posed a problem I’d first encountered in an APL programming class at U of Florida in 1979. It had several parts, but the final piece was what I wanted them to think about. It required that we find a way to alphabetize a list (string) of names of arbitrary length (with an arbitrary delimliter (a comma) between them entries in the original list, plus a space character for “filling out” names so that they would take the same number of columns in the array), having already put the names in that rectangular array (which at least in APL is trickier than it might sound). We knew (and I shared with the students) that APL automatically assigns a numerical value to each letter and character, and so clearly we could turn the names into numbers. There is also a built in function that will arrange a list or array of numbers in ascending or descending order.
The trouble was that turning each letter into its corresponding number in the alphabet (i.e., a = 1, b = 2, . .. , z = 26) wouldn’t solve the problem by itself, I realized. If we had the name “ZO,” it would equal 26 + 1 = 27. But then, so would “OZ”; worse, the name “MO” = 13 + 15 = 28, would come EARLIER than the name “ZA” = 26 + 1 = 27. Something more was necessary. And I left things at that with the students on Monday.
Today, several students who’d been absent on Monday returned, and so I had the full complement of 13. I restated yesterday’s problem along with examples similar to those above illustrating the dilemma, and mentioned that the professor made a strict proscription against using loops or similar structures in the code we wrote.
Immediately thereafter, one student who’d been absent raised his hand and said, “Oh, easy. You just put everything in base 26.” Within about a second, another boy who had been absent said, “No, you need to use base 28.” When I asked why, he said, “Because of the comma and the space.”
After some conversation about these ideas, and agreement that this should work, we tested some of the problematic examples and saw that this approach would assign a unique number to every possible name. Then, some students raised questions about characters we’d not discussed, like hyphens, umlauts, tildes, etc., but we agreed that we could simply pick a larger base to accommodate them if required.
I make no claims about what any of this means, nor would I generalize it to another group. And despite Steve H’s snide commentary, I do not claim that this is THE way to teach math. It happens to be A way that I am teaching math to THIS group of students.
One final note. The first student who suggested base 26 is 11 years old. The boy who suggested that we needed base 28 is 13.
I almost regretted not videoing the class so that I could show it (if I got permission from all necessary parties to do so), but I’m sure that Steve H would explain that I’d fed the right answers to the students in advance. And I mentioned that to them before we moved on. They were amused. As am I, at least partially, at the arrogance of people who know nothing about what I’m doing but are happy to judge it anyway.
I will not reveal identifying details here for a number of reasons, including respecting the privacy of my students. But given the track record of some members of Mathematically Correct, NYC-HOLD, and some of their supporters, I’m very loath to allow anyone to try to stir up trouble, harass my students or their parents or my principal and colleagues. Oh, and yes, Steve: I am the only person who only teaches mathematics at the school. I guess that does kind of make me “the math department.” ;^)
Hurray for APL! if only those stickers would have stayed on the keyboard.
MPG wrote: “I do not claim that this is THE way to teach math. It happens to be A way that I am teaching math to THIS group of students.”
Is that all you are doing in this thread? I’m glad you are in a place where, apparently, parents can choose to be there or not. However, the huge problem in the Math Wars is the fact that most parents have no choice.
Steve H wrote: “Is that all you’re doing on this thread?”
Sorry, you’re becoming both opaque (what’s “that” in your question?) and increasingly disingenuous. I don’t know why you insist on offering nothing but snide comments. Do you have something constructive to say? If so, I can’t recall seeing it here or anywhere else. Like your colleague Mr. Garelick, you’re awfully dismissive of other people’s work without having ever seen it.
If you believe I’m only working in one school, I think you’ll be disappointed to know that as of next week, my evil will be spreading in a public charter, a private school, and a public district in grades 6-12, with likely input into K-5 starting next fall. Bummer, eh?
“That” is:
“I do not claim that this is THE way to teach math.”
You are making a claim about the general approach, and you haven’t said a word about whether you favor parental choice. I’ve said (many times) that people can have different approaches to teaching and different goals. That doesn’t bother me a bit. Some like unschooling. I say “Go for it”. I don’t know what or how you teach personally, but I hear what you say in general about math education. On that level, I will disagree with you because I’ve seen it not work (systemically) first hand. The only times I’ve seen a top-down or understanding first approach work is when students are forced to shoulder a lot of individual homework. That never happens in K-6. Calculators are used as avoidance tools, not as tools for expanding the difficulty of the problems students have to do.
There would be no “Math Wars” if parents had choice and there were real choices to be had. The war exists because schools are forcing their pet pedagogical ideas on all under the guise of “best practices”.
Ah, yes, choice. One of the great red herrings of the current education deform movement, both within and outside of the Math Wars.
Do you seriously suggest that every time a parent decides s/he wants a different flavor of instruction for his/her child than what is currently being offered that a school should provide it? That’s not school you’re talking about. It’s individual tutoring. If you fund it, they may come, but until such time, you sound like you’re dreaming. I only have 13 students in my class right now, with room for one more according to the school policy on class size. If someone isn’t happy with what I’m doing, s/he can go next door. There’s another class I work with only once a week. So far, no child or parent has requested a switch to that other class, but one is hoping to be switched to mine. Nothing to do with the other teacher, who is excellent, but rather a girl who wants more challenging math than he offers, by design and agreement among the principal, the two teachers in whose classrooms I teach math, and me.
Probably the wrong school for you and yours, Steve, but then, you WOULD have a choice to not send your children here at all, as does every parent involved. I did say it was a private school.
In public schools, of course, there’s usually more than one classroom per grade per subject (depends on the size of the district and school of course. I don’t know what to tell you if you’re not happy with the options where you are. Life can be tough. I do know that there’s a vastly greater chance of getting mundane, teacher-centered, computation-oriented math in this country than not. Are you out there advocating for choice for parents and kids who wish they could escape all that? Of course you aren’t. I’ve yet to meet a “choice” advocate in the Math Wars who does. So please, spare me. I’ve been through this nonsense with Bishop and the other full-time professional Math Warriors and I’m utterly unimpressed by the phony call for “choice.” When given a choice, Bishop and his pals have gone into districts and lobbied to throw out the non-traditional books and methods. Perhaps you’re less fanatical.
Being allowed the choice to obtain a mathematics education outside the public school was essential for my son’s mathematical education. We were lucky that the principal of the high school became very cooperative after my son caught a flyer on the MAP math test and scored 298 out of 300 possible points in tenth grade.
Seniors in Michigan can take their required math class at local community colleges and universities for dual enrollment credit, an option I considered for my son this year, but he didn’t like the logistics and took AP statistics instead. If he were planning on a career in mathematics itself, I might have pushed harder. Or not.
I have the distinct impression that my philosophy of parenting is different from that of the typical Math Warrior (not suggesting you are in that set, teachingeconomist).
I wish every school in the country offered discrete mathematics. It won’t happen until people unwrap their heads from the mistaken belief that Mount Calculus is the way to the Holy Grail, if not the Grail itself. I’m confident that a student who has the prerequisites for calculus and has made it through something that exposes him/her to another flavor of mathematics before college will do just fine. Last I checked, there’s a lot of work in the computer field, and discrete math opens pathways and insights to that world. Why is it systematically ignored or marginalized in this country, particularly given how many students I’ve had over the years who really took to it given the chance, but who had not done well in the usual high school math, calculus-bound track? Something’s very fishy, particularly given that mathematicians have pushed for discrete math as an alternate path in high school.
The laudable Michigan policy is choice, allowing students to take classes for credit that are outside building, outside the jurisdiction of the local school board, and take place in a school that is largely exempt from public school regulations.
If it is good for math students as seniors, why not as juniors as well? If it is good for students of mathematics, why not chemistry, English, or physics?
As always, I have to ask: effective choice or token choice? For a kid with the resources, being able to take classes at a college that aren’t available at the local school is real choice. For someone who can’t get there, not so much. Ditto with charters and much else that “choice” advocates sometimes seem not to care very much about. I’m told that it’s “choice” if a kid can take a voucher to the “local St. Sensible’s” (meaning the local Catholic school). Really? Aside from my personal objections to using public money in religious schools, is it a choice for a non-Catholic family? Or the lesser of two evils, rather than a truly desirable option? Compared with the affluent kid who uses the voucher to underwrite the ritzy private school education s/he was already getting, and the middle class kid who now can afford private school, the children of poverty aren’t getting much choice from charters or vouchers in any real sense. But isn’t it pretty to think so?
I certainly agree choices must be real choices. Charter schools offer that possibility, while schools with geographically determined admission standards do not even offer the possibility of meaningful choice.
If only that were true, TE. Do you want to explain, seriously, how that works in, say, Detroit? Because I work there, I know a lot of the charters, and with a few exceptions, most of them aren’t worth the time it takes to say the name of their for-profit management companies.
Friends who are familiar with the situations in NYC, Washington, DC, and LA are also less than sanguine about the overall quality of the for-profit charter schools there. So I’m a bit befuddled by how such schools offer a real choice to parents, if we’re talking about a shot at getting the sort of quality education that, say, kids at Sidwell-Friends get. Or, if the school the Obama kids attend is too high-brow, we could look around NYC, Detroit, DC, and LA and see if there are charter schools – which as we all know get to be much more selective than public schools about special education students, incorrigible students, and others kids who just might bring down test scores, particularly in the NCLB era – available to the populace that are truly outperforming the public schools in town with similar demographics.
The statistics comparing the performance of charters are NOT encouraging. Of course, there are no doubt some truly wonderful charters. And I work with a few in Detroit and have worked with some elsewhere that do good work. But they’re all non-profit managed. And they’re a handful out of a generally bad bunch.
I just don’t see statistics in the cities I’ve mentioned to support the idea that charters, on the whole, offer choice to high-needs kids in inner cities. How they could do so in rural poor areas strikes me as even more difficult logistically.
In all honesty, I think charters – on balance – are worthless. But I’ve never believed they were the real goal. Rather, they’re the wedge to get the true wet dream of deformers and privatizers through the door and into full control: vouchers. And the problems with those, for poor kids, make charters almost look sensible.
This has never been about choice for poor kids and never will be. The power elite couldn’t care less about the poor. What they’re after is simple: billions of dollars. If they have to serve up mass-produced garbage for poor kids in order to get their hands on maximum control of as many public education dollars as they can, so be it. But QUALITY education? Too costly, not profitable, and not really what they had in mind to begin with. After all, a thoughtful, reflective, educated underclass isn’t likely to want to remain the underclass for very long, is it?
The only thing I can tell you about Detroit is that there is not the possibility of meaningful choice in schools with geographically based admissions unless the families can afford to.move or seek to deceive school district administrators ( and I know parents who did both)
I’d say that this state is quite content to leave the vast majority of Detroit citizens, including its children, up the creek sans paddle. I had the displeasure of bumping into a conservative web site yesterday that had dozens of comments from non-Detroiters applauding a supposed decision in the legislature to let Detroit collapse. Probably nothing to do with racism, of course. The general sentiment was that Detroit’s citizens deserve this fate for listening to the advice of “liberals” for so long. The subtext, however, was clear: guilty of living while being black.
The charter school shell game is just that. And no matter which shell the kids in Detroit look under, they’re getting screwed.
I have a suggestion: you two exchange email addresses.
Enough!
Someone putting a gun to your head making you read something here?
Don’t flatter yourself. I stopped reading the two of you long ago- as did others, as evidenced by the absence of interactions.
Unfortunately, my inbox is flooded by this exchange- it has become quite a nuisance.
Please take it elsewhere.
1) unsubscribe from the comments on this thread; 2) put an e-mail filter in place to screen out comments from those you don’t wish to hear from; 3) delete messages you’re not interested in, if you can’t be bothered to filter them into the junk mail automatically.
Those are three reasonable, proactive suggestions that would alleviate your concerns.
MPG wrote:
“Do you seriously suggest that every time a parent decides s/he wants a different flavor of instruction for his/her child than what is currently being offered that a school should provide it?”
“Every time”? Strawman. It’s not just about pedagogy. It’s about expectations. Urban parents in our area fight the educational establishment to open up more charter schools and they say no. The educational establishment especially fears K-6 charter schools that set high standards. Do you think urban parents are stupid or that they cannot choose between school A and school B for their individual child? Do you think that Michigan’s choice policy is wrong? You should see our state. This isn’t just about what you see in your classroom or state.
“Are you out there advocating for choice for parents and kids who wish they could escape all that? Of course you aren’t.”
Wrong again.
“Perhaps you’re less fanatical.”
As usual, you see things as black and white. I’m not part of anyone’s team, although you keep painting me with the same broad brush.
“… the children of poverty aren’t getting much choice from charters or vouchers in any real sense. But isn’t it pretty to think so?”
Have you asked them? I have. It’s heartbreaking when their kids don’t win the charter school lottery. You don’t want to give them any choice because you think it’s not much of a choice? You go tell them that.
“Compared with the affluent kid who uses the voucher to underwrite the ritzy private school education s/he was already getting,…”
Many of which are using the same Everyday Math in K-6 and have the same “traditional” math in high school. You’re mixing up variables here.
“I know a lot of the charters, and with a few exceptions, most of them aren’t worth the time it takes to say the name of their for-profit management companies.”
I know many poor charter schools too, but are you going to deny even that possibility of choice to individual parents? Do you presume to decide for them? What about the other charter schools that work? What does “work” mean? What are you offering as a solution instead? This is a serious question. Without choice, what is your solution? Choice means parental choice, not pedagogue’s choice.
“In all honesty, I think charters – on balance – are worthless. But I’ve never believed they were the real goal. Rather, they’re the wedge to get the true wet dream of deformers and privatizers through the door and into full control: vouchers.”
Here it is. “Wedge.” Don’t listen to urban parents about what they want. You have to fight the hidden political agenda. Why don’t you fight for better charter schools? I do. I fight the educational establishment. They seem to like silly charters that “sludge” off the low end students that the regular public schools don’t want. They don’t like the charter schools they think will “cream” off the most willing and able students. These charters get rejected. That’s why I don’t see many good charter schools in our area.
“This has never been about choice for poor kids and never will be. The power elite couldn’t care less about the poor. What they’re after is simple: billions of dollars.”
If you can’t get past this myopic thinking, you will never come up with any viable solution. Urban students need much more than some sort of math curriculum that teaches them the beauty of math.
I like Every Day Math because it teaches the concepts. When I was a student, we were taught the algorithms, and I was a poor mathematician because of this. I didn’t get fractions etc. because I didn’t understand the meaning behind them.
And this drill and kill mentality doesn’t make sense. I agree with Michael.
And I’m guessing Finland works hard on concepts and how to get answers etc. I don’t like common core, but don’t think the “old” way of doing things makes sense. Instead, I think more teachers need to understand how to teach math.
I know a lot of kids who came up to 5th grade being drilled on math facts and still didn’t have it. So can’t blame not knowing table. Do they need to know math facts, sure but not kill and drill particularly for those who can’t do it that way.
I have no idea where Ms. Sawyer gets the idea that the CCSS “pay lip service” to students learning standard computation algorithms.
Take addition and subtraction, for example. The CCSS expect students in grade 2 to fluently add and subtract within 100. Further, they learn how to add and subtract within 1000 using algorithms based on place value as well as other strategies.
Moving on to grade 3, students must fluently add and subtract within 1000 using algorithms based on place value as well as other strategies.
Finally, in grade 4, after a full two years of building students’ ability to add and subtract with multiple strategies, the CCSS explicitly state that students must add and subtract multi-digit numbers using the standard algorithm.
Where is the lip service? As far as I can tell, they gave two years to conceptual understanding and fluency and now they are giving a full year to procedural fluency. That doesn’t mean you have to like it, but it’s there, and it’s irresponsible to claim that it’s not.
She’s not really responding to what’s in the CCSS, but her fantasies based on her hatred of the progressive reform textbooks of the 1990s. Such people simply can’t look at anything that they didn’t write (or that isn’t approved by the likes of Mathematically Correct and NYC-HOLD), without going into hob-nailed boots mode.
Again, to be clear, my objections to CCSS in math and literacy are more general. I don’t believe there can be a one-size fits all approach to teaching anything. I believe that the very idea of national standards, no matter how well-intentioned some of the contributors may be, is misbegotten at its inception and at its core, and should be abandoned. I have read some insightful specific criticism of the math from folks like Christopher Danielson, and I believe these are serious things that should be corrected, but in the long haul, it won’t matter whether they are or not. The impact of these documents and the concomitant tests to come next year will be the same, and in 10 years, I am 100% convinced, the same issues will on the table about the “failures” of our math students and our schools and teachers.
The true tragedy will be how much good education WON’T take place because districts will twist themselves into pretzels trying to avoid getting their knuckles rapped by the feds. Innovation will be implicitly discouraged, as will be independent action and thought.
The only real hope is in resistance, as we see is taking place in Seattle and which may light a fire that sweeps the nation. Obama, Duncan, et al., and their corporate masters/allies/partners, just can’t seem to get anything right when it comes to public education. Whether Romney had gotten in or Obama continued his insane set of education-for-profit policies matters not that much unless people who are out there on the front lines in the schools stand up to the bribery, bullying, and baloney that is being forced down our throats.
Meanwhile, everyone in the bizarre world of mathematics education and its wars can argue over how many angels are dancing on the end of various pins and what the “right” algorithm is for figuring that out (and if calculators may be used in crunching the numbers). They can argue about whether we rely on Saxon or Singapore, or EM, Investigations, Connected Math, etc., when the very idea of relying on textbooks is being challenged by sweeping technological changes that most of the participants in the Wars prefer to remain blithely ignorant of and incompetent to evaluate. The hip kids will leave the Old Men in the dust. Unfortunately, the poor, the less hip, the more obedient, will be stuck with people who would rather argue over whether math teaching and books in 1953, 1965, 1978, or 1994 was the Golden Age to which we should return, or whether importing math books from Singapore – the land where you can be jailed for chewing gum and publicly flogged for any number of offenses – is the magic bullet.
What a country.
MPG wrote:
“Such people simply can’t look at anything that they didn’t write (or that isn’t approved by the likes of Mathematically Correct and NYC-HOLD), without going into hob-nailed boots mode.”
Hey! That sounds just like you!
The issue for many is choice. We send our kids to public schools and go to open houses where teachers tell us how important it is for little Suzie to explain why 2 + 2 = 4. You have to make a distinction between those who want everyone to follow their beliefs and those who want choice. Which one are you?
“I don’t believe there can be a one-size fits all approach to teaching anything.”
It sounds like you believe in opinion and choice too. Do you think that parents like having “best practices” crammed down their throats and being treated like they are stupid?
“Innovation will be implicitly discouraged, as will be independent action and thought.”
I’m all for unschooling and allowing you to do whatever it is that you are doing, but the key is choice. Affluent parents can send their kids to Phillips Exeter or Phillips Andover. In some high schools, students can choose between IB and individual AP classes. Starting in 7th grade, many students take advanced math classes that make the CCSS standards meaningless.
“The only real hope is in resistance, …”
The only real hope is parental school choice. “Independent action and thought” cannot be limited to just teachers and schools.
“They can argue about whether we rely on Saxon or Singapore, or EM, Investigations, Connected Math, etc., when the very idea of relying on textbooks is being challenged by sweeping technological changes that most of the participants in the Wars prefer to remain blithely ignorant of and incompetent to evaluate.”
Now you’re mixing in opinion. Many of us are quite able to carefully analyze whether “sweeping technological changes” are meaningful or just fluff. I’m just glad to hear that you’re such a proponent of “independent action and thought”.
Steve H.: enough. You’ve got nothing useful or constructive to say to me. You’ve clearly established your rejection of my point of view, as well as your inability and/or unwillingness to: 1) represent it accurately, and 2) respond to points I raise that are a little difficult for your position and your deep-seated need to assassinate my character. Let me note, too, that like so many brave Math Warriors, you’re essentially an anonymous poster. Who is “Steve H,” where does “Steve H.” live, and what qualifies “Steve H.” to evaluate anything at all regarding mathematics teaching or learning?
Until you offer accurate identifying information about yourself and put YOUR butt on the line here, I have no interest in hearing anything you have to say and will ignore it. There is no dearth of cowards in the math wars and you’re just one of many, dealing from the MC/HOLD deck of vituperative and dirt.
bstockus, I have read the standards, in great detail and many times. I do see the logical progression through the grades, and that “strategies based on place value” can certainly be interpreted as standard algorithms. But that can also be interpreted as alternative algorithms (and there are kids who get confused learning 3 different algorithms simply for adding). And that’s the part that seems like lip service. Are 1st and 2nd graders going to be drawing flats and sticks for two years? You, and I, and plenty of teachers understand that we can use the traditional algorithm to reinforce place value and move from the concrete to the symbolic sooner than 4th grade.
But I wonder about the new teacher who sees no use of the word “algorithm” in CCSM for adding and subtracting throughout first and second grade, and who interprets that (or maybe the district coordinator interprets that) to mean “we don’t teach stacking until third grade.” While the standards leave that open in that you can introduce the standard algorithms when you want to, my experience in public school leads me to believe the math standards will be read and implemented literally. I hope I’m wrong.
MPG wrote: “Who is “Steve H,” where does “Steve H.” live, and what qualifies “Steve H.” to evaluate anything at all regarding mathematics teaching or learning? ”
You’ve pulled this on me before. It seems to me that you are willing to give teachers choice, but not parents. So, who gets to decide on what works or not? What qualifications meet your criteria? Should only affluent parents have school choice? Why are they allowed to choose?
I could give you my qualifications, but I will only say that I am not connected to the industry and have no vested interest in products or pedagogy. I’ve already explained that there were many things I didn’t like about my “traditional” math schooling. I am just a parent who had a son subjected to both MathLand and Everyday Math with no choice in the matter. I had to teach and reteach at home. I’ve seen Everyday Math fail because they tell teachers to “trust the spiral”. I’ve tried to work with my son’s schools and have been treated like I’m ignorant of the wonders of critical thinking and problem solving. Apparently, learning educational pedagogy by rote in ed school trumps 35+ years of practicing non-routine mathematical problem solving.
If there were proper school choice, then I would have no problem at all. I also have no problems with schools that try new approaches. I think calculators are wonderful devices. How they are used in schools is not wonderful. My son loves GeoGebra and Mathematica. I think that flipping the classroom sounds interesting, but many of the examples I’ve seen just move the chairs around on the Titanic. Too many think that the are getting something for free. I know all about Harkness Table approaches, but I think they require a lot more individual work and very good teachers. I’ve studied Khan videos and read his book. Nice ideas, but his videos need a lot of work and some manage to screw up his ideas.
You pull out the same tired strawmen and try to paint everyone with the same broad brush. It’s easy to pick on easy targets, but you can’t lump everyone in the same bucket. You also don’t address the issue of choice, but that’s the underlying issue to all of this. Who gets to decide?
Outside of a few large and wealthy school districts, an appropriate math education for the mathematically gifted student will require that they get their education outside of the public school.
The last sentence of the first paragraph elides the distinction in the Common Core between fluency with addition and subtraction and fluency with the standard algorithm. The Common Core requires students to be fluent with 2-digit addition and subtraction in Grade 2, and with 3-digit addition and subtraction in Grade 3. The precise sequence of standards is:
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Notice the progression from strategies to algorithms to the standard algorithm, with fluency in the operations required beginning in Grade 2. It’s up to curriculum developers how to implement this, but it seems to me to be strongly indicated that the standard algorithm would be introduced before Grade 4.
That Common Core MAKES a distinction between “fluency with addition and subtraction and fluency with the standard algorithm” thus taking five years to hash, rehash and rehash yet again addition and subtraction, starting with K.OA.1 and ending in Grade 4, is a shocking dumbing down of the curriculum and flies in the face of US Dept. of Education recommendations. Addition and subtraction have not historically been so perplexing as to necessitate such neurotic repetition and incrementation.
Read “addition and subtraction ad nauseam” at
http://ccssimath.blogspot.com/2012/04/addition-and-subtraction.html
Oh, I see bstockus already pointed this out. At any rate, the quoted sequence of standards might be useful. Feel free to edit my comment.
I have enjoyed following this thread listening to math teachers take each other on. As a special education teacher, I got tapped to teach math at the middle school level. I was left to my own devices since my students were a “lost cause.” We got to go back and tackle all the concepts that they only half understood. They all had weird mnemonic devices memorized for various operations. They hung onto them like dying men since they were the only connection they had with the material. They had no idea why they did anything just that that was the way it was done. It was a painful but rewarding process to build a base of understanding. I really enjoyed the process as well because I had to go back and pull apart my own understanding. I learned so much and really began to appreciate the beauty of mathematics. I am not wired to quickly grasp abstract concepts; I trudge through the material. Since I am not being graded on it, though, I can play, not an option I had as a student. I would like to put a vote in for mathematics as part of the essential liberal arts curriculum. I don’t think we can bemoan the loss of thought provoking literature and not make the same case for the study of mathematics. Both areas have practical applications that we all use more or less depending on our occupations and daily lives. Sc!#%w the practical (not really) and recognize how our minds are stretched by looking at the world from different perspectives: historical, scientific, artistic, musical, mathematical, sociological,… For the record, none of my students were fluent with the basic arithmetic operations, and it really slowed them down. Just like we build a repertoire of skills we do not have to “look up” every time we use them in language arts or music or…, I vote for the same in math.
I am a parent of a couple of actual kids – they are not study subjects put in the classroom so that you can manipulate them to “prove” your own theories. I am not a teacher, but I hold a master’s degree in my own profession.
Parents, if your child is to learn math YOU must teach them, at a minimum, addition, subtraction, multiplication, division, fractions, decimals and positive/negative integers.
“Educators” will always be jumping on some kind of bandwagon in an effort to make themselves feel unique and relevant. So parents, you must be the constant and provide the necessary elementary math education for your child. You cannot trust someone else to do it for you.
Interesting. So you presume that teachers are on bandwagons, not motivated by concern for teaching their students as well as they can? That teachers aren’t parents? That there is a Holy Book that has all the right moves for perfect teaching of any topic to all students, in any combination, that might be thrown at a given teacher on a given day? And that anyone who isn’t following said book is performing manipulations of kids, heedless of consequences, to prove theories.
If I believed any of that, I’d never let my son enter a classroom.
By the way, I am unique. I don’t worry about that. As to my relevance, I can’t say I give it much thought. But perhaps parents, too (of which I am one: I have a 17 y.o. son who is a high school senior), have needs to be unique and relevant. To be “in charge,” and to ensure that their children don’t encounter any “wrong thinking” in schoolrooms. Heaven forfend! What would happen if a teacher told his/her students something with which one or more parents disagreed?
Fortunately, back in 1955-68, that was illegal. Those were the good old days.
Wow, that’s a lot of presuming about what I presume all wrapped up in a straw man argument.
I’m just saying that it is essential that parents (yes even ones who are teachers) teach math to their children rather than relying on a person who may see them for 180 days out of their entire life and is not impacted by any shortcomings that get identified the next year when the child is no longer their responsibility.
I said “educators” jump on the bandwagon. While that encompasses teachers, I don’t think it always originates with teachers, but nevertheless, it has potential to disrupt a child’s education.
It is a lot easier to be proactive and just teach your kid yourself than to have to remediate the problem years later if it turns out they are not prepared for Algebra.
Intriguingly, I intervened very little in my son’s mathematics education despite my personal preferences. He got the much-loathed TERC “Investigations in Number, Data, and Space” curriculum in K-4, then various more traditional books all the way through his current senior year AP Stats class. He managed a 33 on the ACT last June with no help from me to speak of (he tests well, but wasn’t interested in doing a bunch of practice tests so I could share my 30+ years of expertise in standardized test prep. Go figure).
I could have stuck my nose into things in his math classes more than once, but decided that it would serve little practical purpose. Apparently, in spite of my showing that restraint (imagine what sort of irresponsible parent I must be: a mathematics educator who chose not to roil the waters in a mostly traditional school district out of consideration for his son’s emotional well-being and level of comfort with teachers, rather than try to enforce my will on some instructors who were not really very good and a curriculum of which I personally not even vaguely a fan!)
My son can handle all the mathematics he’s had and will have if he continues to pursue a career in the biological or medical sciences as he currently plans. He will not likely become a mathematician (I’ll live, believe me) of any sort, yet I suspect that at SOME point, he’s going to find he has a bigger taste for abstract mathematics than he currently suspects, in spite of the indifferent curriculum and instruction to which he’s been subjected. Had it been necessary, I’d have gotten more involved with his learning mathematics at home. When he asked questions, I did of course endeavor to get him to think about reasonable answers and to help fill in important information. But that’s as far as I went.
But like me, he’s been relatively lucky in spite of some not so lucky things in US math education. I know full-well, however, that we’re the exceptions, not the rule. And I’m doing what I can to change the rule. My ideas and those of educational conservatives and reactionaries differ greatly in this regard. Unlike them, I don’t pay lip-service to helping poor kids and other traditionally under-served populations. I actually work in high-needs inner-city and suburban poor schools with (mostly) children of color and their teachers. I put my money where my mouth is. I’m not in this just for my kid and those of people “like me.” I’m not getting rich doing this. Not by a long shot. I’m not interested in doing so. I’m not willing to settle for mundane math education for the majority and challenging mathematics education for the elite (though, frankly, there’s not nearly as much of that going on for affluent kids, either, on my view).
If I’ve misread you, that may be my inadequacies as a reader, or yours as a writer, or a combination of the two (plus perhaps my having formed a distinct impression of your views from your writing elsewhere). If I’ve really misrepresented your views, my apologies (I’ll await a similar apology from my many anti-fans, but hardly with baited breath, for their repeated twisting of my words and ignoring of things I say that they can’t answer or which contradict the words they want to put in my mouth).
The education wars in general and the math wars in particular get a lot of blood boiling. On my view, there are many reasons: some are of course sincere concern for one’s own children; some have to do with $$ and power; some have to do with religious, social, and political agendas. Mine have to do with a passion for mathematics, its power, relevance, and its beauty, the latter being the most ignored of those three, and for social justice and equity in a nation that increasingly moves to a complete lack of either for the vast majority of its citizens.
MPG wrote:
“.. I’m not willing to settle for mundane math education for the majority and challenging mathematics education for the elite (though, frankly, there’s not nearly as much of that going on for affluent kids, either, on my view). ”
What kind of education, exactly, are the “elite” getting?
They are getting high expectations at school and at home. Many urban kids are getting talk of understanding and low expectations. They are not being separated by ability or willingness to learn.
I want more emphasis on big picture ideas for my high school son in his traditional math classes, although he is quite happy studying things like Fourier Analysis on his own. The big question is whether you can flip the process around and get something for nothing. If you talk about interesting problems in class, when does individual mastery happen? When I tutor kids, we can talk and it seems clear that they understand the concepts and meanings. Then they turn around and make concept mistakes on the problems. Talk is cheap, and group work allows individuals to slide by.
A traditional approach may not get to interesting big ideas in math (there is nothing stopping them), but what is being pushed in many schools is an “understanding” first approach that never ensures individual mastery, and mastery proves understanding. Both directions can work, but many understanding first approaches never see the understanding that comes from mastery of skills. You can tell a lot about a curriculum by looking at the individual homework required. Harkness Table approaches can work, but only if they have the homework and high expectations to back them up.
Here is the problem with Everyday Math, it sets children AND TEACHERS up for failure.
This is a lousy program and math tutors like me get plenty of business when schools use these programs. I suspect for every teacher who loves it, they have plenty of kids either failing OR are in tutoring services.
Now when the school decides to replace the teacher with a computer program, don’t say you weren’t warned.
This program sets you up for failure and when that happens, Bill Gates gets to come in with his TECH buddies and put those kiddies on a computer to learn math the proper way.
You see, the Govt. must BREAK your LEG in order to hand you a crutch and say…SEE WE FIXED IT.
They set teachers up for failure with this program and then come in to save the day with Khan.
How to make teachers obsolete 101.
You and I will never see eye to eye on this. It’s not a “lousy” program. But since you clearly believe it is, and believe that your tutoring business is attributable to it, and not to anything else but the choice of mathematics textbooks, please share what you think a good program is. Further, I am curious if you can provided research that suggests that kids in districts with THAT program (the “good” one) don’t wind up getting tutored for math, or at least need tutoring significantly less than do kids in districts with EM, or other “lousy” math programs.
For close to 20 years, I’ve tried to get people to recognize that textbooks are not bibles, that teachers who use them as such are foolish, and that the best textbook can be useless if used poorly, and even ones I personally don’t care for, if used wisely by solid teachers, can be resources.
In an age when there is SO much material available free on-line – text, video, interactive aps, etc., – it is absurd to make which textbook series gets used THE central issue in assessing the quality of mathematics education in a district, school, or classroom.
I have no dog in the textbook wars. I use materials drawn from a variety of sources, including textbooks, but hardly exclusively so (not even close). I’m tired of hearing about how Textbook X is THE solution to the ills of American math teaching and learning, while Textbook Y is a tool of Satan.
Teachers and parents who belief such myths are fooling themselves and investing a lot of energy for little, if any, meaningful effect.
As for your theories about “the government,” well, you’re welcome to that viewpoint. Did “they” also fake the moon landing and was the government behind 9/11? Did Obama arrange either to fake the Connecticut school shootings or to actually have Israeli commandoes do the murders (I’ve read both those and many other fantasies in the last month or so, several of which I predicted in advance would sprout up on-line)? I’m not convinced.
Does Gates look to make money? You bet. Does he tout Sal Khan to that end? I believe so. I think Gates wouldn’t know quality mathematics or its instruction if it bit him. But if you don’t like Khan or Gates (where we’re in agreement) and also believe that EM (and, no doubt, Investigations, Connected Math, and other progressive math programs) is a “lousy” program, upon what would you rely? Do you believe there are panacea programs? Excellent ones? If so, which? I’m still looking for one, though I believe the search is entirely chimerical.
For my money, the issue is teaching. It’s also the entire belief structure teachers, students, parents, and other stake-holders have about mathematics. Until those things become a lot more sensible, we’ll be spinning our wheels for the most part about math and its teaching and learning. And while I concur that the Common Core, RttT, and NCLB are not helping, far too many voices I hear decrying the Common Core seem to be people who would LOVE it, if only THEY and/or their allies got to write it. That’s what really worries me, as I oppose the very idea of a common core.
Hi again Mike. You never did reply to my question about that summary I quoted from a math text describing the new way to teach. https://dianeravitch.net/2013/01/13/a-math-teacher-on-common-core-standards/comment-page-1/#comment-87987
Key phrase “understanding … before memorization”.
A simple “yes” or “no” would suffice.
You seem to love to dominate column-space with your comments. I wonder if Ms. Ravitch is considering charging you rent. 🙂 I’ll do my best but I doubt I can fill a quarter as much space with the following …
You ask MomWithaBrain here what texts she would propose. I can’t answer for her but I’ll give it a shot — like you I have “no dog in the textbook wars” but as a matter of fact I think you can do a heck of a lot better than EveryDay Math, Investigations and their ilk. Saxon, for example, blows these away in side-by-side comparisons of student outcomes. And Singapore is clearly a better system, with superior, cleaner, less cluttered texts, that also outperforms these in all major assessments.
One could list several others. All of which support understanding, all either incorporating GUIDED discovery or clearly amenable to that instructional approach. In comparison, EDM, TERC and so on prescribe (largely) UNGUIDED discovery, which is, let’s be honest, possibly the worst way to “teach” (i.e., NOT teach) small children, although by high school there is probably some latitude for a certain amount of this approach. As established in cognitive science, “minimal guidance instruction” is not effective with novices (i.e., young children) but can be effective with experts (i.e., adults)
http://www.tandfonline.com/doi/pdf/10.1207/s15326985ep4102_1
That is such an obvious conclusion one wonders why it even requires a body of cognitive science research to support it. But apparently “obvious” doesn’t carry much weight among educational ideologues.
But I think one can do better even than these. Have you heard of JUMP Math? Developed by a mathematician, it may be the best-designed extant set of resources for K-8 math instruction, employing guided discovery and extremely well-scaffoled and structured sequencing of material with an eye to achieving mastery and reinforcing student self-esteem through continual positive feedback via repeated experiences of successful learning accomplishments. Kids, apparently, love that feeling of “Hey! I GET this!” Whoda’ thunk?
JUMP is also attractive because it is inexpensive. It is the only major modern system that I know to be available on a not-for-profit basis. It is promoted through a nonprofit institution, and is a registered charitable organization in Canada. John Mighton, the creator, draws no income from it. Although he is a PhD mathematician, he makes his living as a professional playwright. The teacher resources are available for free. Student workbooks come at slightly above cost and resulting funds are rolled back into the foundation.
Numerous small and medium-scale studies have been done, and the results are universally spectacular. My personal favourite is this one carried out in by a teacher with a split grade 5/6 class, who saw her student performance go from extremely average on standardized core competency assessments to above the 90th percentile. INCLUDING the students at the bottom of the class, who would otherwise be failing. You can read about her experience in the New York Times piece here:
http://opinionator.blogs.nytimes.com/2011/04/18/a-better-way-to-teach-math/
It should suffice just to examine the two graphs shown in that article. You might wonder “is this real”? Well, yes.
This system has been tried in districts around Canada and in Europe. With very talented students and among demographics that historically perform very poorly — with master teachers and math-phobes who dread their own math class and are looking for a way out — and the outcomes are generally the same. I do not use JUMP myself (duh! I’m a university math professor and JUMP is K-8.) But I am familiar with local users of it, with average kids, and we invariably see students rapidly move from unremarkable performance to well above their peers.
More research is cited on the JUMP website:
http://www.jumpmath.org/cms/jump_research
The biggest and most strictly controlled study, unfortunately, is in peer review and because of nondisclosure agreements cannot yet be discussed publicly, but the results are … you guessed it. Very impressive.
Any teacher wishing to examine the JUMP system can download the teacher resources from the JUMP site for free (or purchase it in hard copy at cost). I encourage you to do so, Mike.
EDM and similar expensive COMMERCIAL texts just don’t compare.
There is a concern about length of comment, especially for heterodox comments. Dr. Ravitch has deleted several of my comments in the past because they were too verbose.
Thank you.
R. Craigen: I’ve now answered your inquiry, back where you made it. And it wasn’t a simple yes or no.
As for books, I can’t think of anything worse that Saxon Math. And an ally of the Mathematically Correct/NYC-HOLD folks, UC-Berkeley mathematician H.H. Wu, made some telling comments about Saxon Math at a public hearing in California regarding textbook adoptions that, were I running publicity for Saxon Math, I’d want buried near the earth’s core. In essence, he agreed with my long-held view that the series comprises books with topics thrown together seemingly at random, and that they do not give anyone the vaguest clue as to what mathematics is or how it coheres. But do look for the comments yourself. I can always provide them should you not be able to locate them on-line.
Singapore Math is another matter. The school where I teach uses it, though the choice was made before I came on board. I have spoken with several teachers, and thus far, not one likes it. But my feelings are more mixed. If you feel that a text is necessary, it’s probably okay for addressing some aspects of K-5 mathematics, but it’s very weak in many things I feel should be in any decent math program. I personally would not want to teach from it, but don’t mind that it’s available for kids and parents who want something along those lines. We’ve found a way to use it that is reasonable for now, but if asked, it wouldn’t be the single pillar for K-5 math I’d support.
I know some mathematics educators from Singapore. They’re not quite as sanguine about the books as are some of its most vocal supporters in the USA, and it’s well-known that Singapore itself has been looking to move somewhat in the NCTM-reform direction. I expect that will be a long struggle, particularly given what I know of the government and culture over there, and that it won’t result in wholesale change.
On my view, there’s much to be learned from Asian mathematics books and classrooms, but not some simple message like “THAT’S the magic bullet we need in the US!” Such things simply don’t exist, and despite the lovely things done in Japan, Taiwan, Korea, etc., they don’t have all or even most of the answers. Your mileage may vary, of course, but I’m not sure if you’ve ever spoken with math educators or educational psychologists from those and other Asian countries about their nation’s approach to education and why many of them come to the US to learn things from us they don’t manage to do with their approach but very much desire to see integrated into their systems.
Given your reaction to Saxon and Singapore, it sounds like more about which I’ll suggest we agree to disagree. I’m not optimistic so far that a common set of principles is in the offing for the two of us, but that’s not really necessary.
I do note your sarcasm, by the way, but I can’t say it does much for me. I just wouldn’t want you to think I missed it.
One last thing, R. Craigen: you might note that I give my first name as “Michael.” That is how I like to be addressed and I’d appreciate your eschewing calling me “Mike.” Thanks in advance.
Michael Paul Goldberg:
Never taught in K-12 and never taught at college level full-time. I was a graduate teaching assistant (Master of Accountancy) teaching 2 classes a term for 5 terms. I also taught many Accounting, Tax, and Finance courses as a part-timer at 7 community colleges in 5 states. I never had a perfect and complete textbook. I always supplemented with information on the real world I worked in every day. So I provided the students real, live factual real world information, not the wimpy garbage in most textbooks. In addition, I never used the tests and quizzes in the text book supplements. Again because they were rote memory – no required thinking and logic -regurgitation tests. Anyone who got through my classes had to know the subject and be able to sort through volumes of data to identify the relevant data – again solve real life accounting problems
I also worked on my doctorate in Higher Education Finance in the School of Education where I worked. Finished my courses, but did not get to finish my dissertation due to family medical issues.
I am interested in the education of the K-12 where we retired. So I have been researching and analyzing Common Core. My observation and opinion so far are:
– It has “glowing generalities” that will not help any teacher know what to teach and how to test it.
– I found no curriculum nor tests and wonder how there can be an educational program without these.
But, hey you got to remember I went through a tough program – Accounting – obtaining, AA, BS, and Master of Accountancy degrees, have my CPA and CIA professional certification; was an Internal Audit Manager at AT&T Corp HQ, and Director of Internal Auditing at 2 major state universities (25,000 + students).
Thus, I came looking at Common Core for a quality, relevant, tough set of standards with a quality curriculum and testing. I found none of these. I have great sympathy for you teachers who have to deal with this – to me – obvious very deficient Program forced on you and you will be held responsible for it’s success or failure. This is really very unfair to you!
IMHO!
Another Math Teacher Speaks –
Today I participated in a math PD held in our state capitol. Before embarking on the actual content of the training session, the facilitator had teacher participants read related Common Core Standards. The quiet was broken by occasional gasps, sighs, and moans before the now oft repeated objections were verbalized.
We’ve read them before. Nothing new. And these were same old criticisms and objections that have been raised in previous math PD’s across the country, for sure.
Next, we looked at a few of the sample test items that would be used to asses the new standards.
Seriously??!!
The facilitator, wanting to keep us on track, I am sure, said, “Look, this is way it’s going. We need to get used to it, There is nothing we can do.”
Someone near me table called out, “Yes, there is!”
All eyes turned toward me. Did I just say that?
“What?” I was asked. “What can we do?”
“We are teachers, yes. But we don’t have to be passive – play the part of victims. We are also parents and citizens. We can opt our own children out of testing, and we can talk to friends and neighbors about doing the same. We need to use the power we have as citizens – not just teachers – to turn this around.”
One woman raised her arm with a clenched fist, and stated, “I like that!”
These few words from an “invisible” and “voiceless” teacher who has been empowered through this blog and others in realizing that she is not alone spoke out. It felt good. I just might do it again.
And again.
Thanks, Diane.
Civil disobedience is always a solution, so is using your power through the state legislature. In Indiana, we are close to halting the implementation of the Common Core Standards and related PARCC testing through our state legislature. Senate Bill 193 will stop the implementation and hit the “reset” button in order to allow a revision of the standards and get the input from the local teachers, parents, and newly elected Superintendent of Education Glenda Ritz who defeated Dr. Tony Bennett in November.
Over 500 parents and teachers descended on the Statehouse for a rally to end the common core. We are demanding that education standards and testing remain under the governance of the people of our state. Improvements to our education system will only come from through solutions proposed by those who work closely with our children- not national standards and testing. Our momentum is high and a vote on the measure could happen as early as next Wednesday.
Visit our website at http://www.hoosiersagainstcommoncore.com
What changes to the status quo would you recommend? Would these changes result in the establishment of a web site opposing those changes?
I am not qualified to establish changes to the teaching profession status quo as an individual. The only proposition I would make is that testing and standards be developed and governed by the people closest to the situation. We have established a website which is a forum where research is presented and the public can view information presented outside the influence of corporate and special interests. Indiana has traded a superior set of internationally benchmarked standards for an expensive experimental educational fad with no field testing or credible data to prove the hope of student achievement. An educated parent can see the folly of this decision and fight for reason to prevail. We have had opposition through different media formats from Stand for Children and Students First. The Indianapolis and National Chamber of Commerce is deliberately misrepresenting information in an attempt to undermine our efforts. They can bring it, Hoosiers aren’t buying it.
So I assume you would be in favor of a curriculum designed by each school or teacher, as these are the people “closest to the situation”?
You forgot “or designed by each student” – can’t get closer than that.
Let’s be serious.
As a citizen-parent-teacher in a RTTT state, I have experienced the avalanche of meaningless “data”, wasteful spending, and actual decreased planning and instructional time that has been its result.
We are living “The Emperor’s New Clothes”.
The real victims are the children.
I found that getting a math education for my son required him to go outside public education entirely.
So I assume you would adhere to “… love it, or leave it”?
I prefer “fix it”.
Problems with our educational system are not rooted in Common Core or RTTT, but neither will address its woes.
It is not really a matter of fixing it. It would be very expensive for our public schools here to have provided a suitable education for him and other gifted math students.
It is an injustice that any child is not served- including your son.
Students requiring a personal aide receive the service.
When students’ needs are not met, teachers are the first to know- and, in my experience, generally make the loudest noise.
He was taking an upper level graduate math course as a 16 year old high school senior. Not unique at his school, but rare enough that it would make little sense for the local school district to hire someone capable of teaching him.
I am familiar with one such situation, and firmly believe the school district should have assumed the responsibility of the logistics and expense of the class for your son.
While cases like these in particular are uncommon, the “particular” needs of students – at either end of the continuum- are the responsibility of the public/community school.
I have found myself in situations where I want so much for parents to demand what is right for their child. My pleas, as a teacher, are rebuffed- even scorned.
But parents- sometimes i think they have no idea of the power they posess.
I am in the odd position of defending my school district, but the last class he took as a high school senior was communative algebra, a Ph.D. leval graduate course taught by a full professor of mathamatics at a research 1 university. Outside of the two university towns in my state, I doubt a local school district could find anyone to teach the class even if they were willing to do it for a single student.
If a teacher, school or district has an effective curriculum, they should be allowed to continue it whether or not it conforms to the standardized common core curriculum. Schools should have a variety of testing options from which to choose to validate success. I believe this would allow for innovation and true “choice” amongst our schools.
That would certainly allow for a variety of approaches to education in our public schools, but unless the geographic admission standards used in traditional public schools change, having different approaches to education do the student little good. The students must learn using whatever approach has been adopted by the faculty member, school, or district to which they have been assigned.
The reason I say it is essential to teach your own child is because it is pointless to “roil the waters” and expect anything to happen in time to actually help your own child. Any advocacy of that nature should be kept out of the classroom and should be done for the next generation due to the cumbersome nature of public education.
I taught my children to respect the teacher and the authority that goes with the position. But we thought of Investigations and Connected Math as some secondary source of information and, yes, in some rare instances, a mild for of enrichment. But it was never the primary means of instruction. That was done at home. I never went into the classroom and met with the teachers only on designated conference days. I had no expectation that the teachers had any power except to do what they were supposed to do.
An added bonus was that my children gained confidence when the Investigations/CMP only students came to them in their “groups” . They spent a lot of time reteaching the material to their classmates.
I liked the story about the student who knew that he had to
divide, knew that a division problem could be solved by doing the
opposite of a multiplication, having the self-awareness to be aware
that he didn’t know his 12 times tables well enough to solve it
that way, and created HIS OWN CORRECT algorithm for solving the
problem. I think this is actually a MAJOR success of the math
education he has experienced…. My full response to this post is
here:
http://havingneweyes.com/2013/01/26/adults-can-calculate-with-fractions/
My student would have CREATED his own correct algorithm with the following problems using smaller numbers before he even heard the word division .
Jane uses 3 ounces for each hamburger . If she has 11 ounces of meat, how many burgers can she make.? I am sure he could answer this question easily as a third grader. Suggest making a picture also.
Then : If she has 18 ounces of meat how many burgers can she make?
Jane needs 6 ounces to make a mini meat loaf. If she has
18 ounces how many mini meat loaves can she make?
John uses 12 ounces of meat to make a large meatloaf. If
he has 27 ounces , how many meat loaves can he make? Any
meat left over? Not too hard .
John has 524 ounces of meatl. Can you find out how many
meat loaves he can make?
I bet you could, but it would take too long. That is why we are going to study division.
At this point the student has created his own algorithm for
DIVIDING without even knowing any division tables
But , like the above mother, I would be extremely upset if he encountered her above problem without a knowledge of division
and multiplication tables .
I research how secondary mathematics teachers and calculus students understand division and fractions. I can assure you that despite being able to compute answers to problems stated without context, most of the calculus students I speak to are unable to draw a picture to explain what division means. They also have notions about fractions such as they must be always less than one, and that division always makes smaller and multiplication makes bigger.
This really matters because division is the foundation of understanding rate of change which is essential to understand Calculus and how to apply it to real quantities in science classes. I’m actually taking graduate science classes in addition to my mathematics course work to make sure that I’m not just imagining that having a strong quantitative meaning for rate of change and division is important. I promise you that I see my Geophysics teacher using it every day. I’m not sure if Diane Ravich agrees with this poster, but I certainly hope she is aware that students come to college and high school(I taught high school math for four years) with very few meanings for the computations they know. And I think it is certainly possible that people have been taught how to multiply and divide fractions and forget when they don’t understand them. I know that I have taught students algorithms that they forget despite massive effort and practice on my part.
I’m not suggesting that we don’t teach algorithms or that kids don’t memorize their times tables. However, I think it is awesome that this fourth grader understands more about division than many of the Calculus students who I have interviewed. My results have been accepted to three math and math education conferences and I have video data and analysis to back up my claims.
Unable to draw a picture to illustrate division? Unbelievable!!
We’re they instructed that they could use small numbers rather than the numbers in the calculus problem?
I am good in math. I was the best in my high school, graduated from a highly regarded university with a technical degree and a high gpa, and use math every day as a specialist in quantitative finance.
Years ago, I tutored math and science at the high school level. In every case I found hard working students, trying their hardest, who had scraped by without understand the basics – fractions, graphs, forces, etc.
Now, whenever I hear that someone is “bad in math” at the high school level, I ask if they know their multiplication tables. So far, the answer has always been no.
I agree completely with Cameron Byer that it is absolutely necessary for the kids to understand what they are doing. I also believe it is essential for them to know the tables. If they can get as far as adding, multiplying, and dividing fractions fluently with understanding, and using percentages and decimals well, they have a good math background.
I use fractions and decimals all day long every day. Calculus, a few times a year. I don’t see the point of teaching calculus to students that are weak in fractions.
The system introduces students to advanced material too early at the expense of fluency.
I had good teachers back in the 1950″s. We were taught what division and multiplication were before we had to memorize the facts.
I taught DE math at a community college . My students were afraid of fractions .
Before I taught them how to do 6 : 1/2, I taught 6 : 2 using pictures( using : for div)
6 candy bars divided into groups of 2 gives us 3 groups
6 : 1/2. 6 candy bars divided into halves. How many halves .?
Use a picture of 6 bars. Divide each bar in half. Count the pieces.
I would never use algorithms until they understood what we were doing
They really had trouble with word problems using fractions.:
Mary has 27 yards of ribbon . It takes 3/4 yd. to make a belt.
How many belts can she make. Most of them would just multiply without thinking.
So I told them to temporarily pencil out the numbers and replace them with numbers that would make the problem easy for them:
Mary has 10 yards of ribbon. She needs 2 yards for each belt . How many belts
can she make? Even if you did this problem in your head, what did you do?
Did you multiply? Divide?
Now go back to the original problem and so the same thing.
I used compare and contrast with the same numbers.
1. John has 12 feet of rope. He wants to cut 3/4 of it to use in his garden. How
long will be the piece he cuts?
2. John has 12 feet of rope. He is cutting it into pieces each 3/4 feet long.
How many pieces will he have ?
Problem 1 uses. a. Division. b. addition. c. Multiplication
Problem 2. uses. a. Division. B. addition. c. Multliplication
Everyday Math is not Common Core. It has been around since long before people even began to discuss Common Core State Standards, let alone codify them.
Everyday Mathematics was created by the University of Chicago and promoted by Gates as far back as 2001.
http://everydaymath.uchicago.edu/
http://www.csun.edu/~vcmth00m/nsf.html
“In 2001, for example, the Bill & Melinda Gates Foundation and the William and Flora Hewlett Foundation teamed up to award the San Diego Unified School District $22.5 million, but only under the condition that the school board retain its superintendent and chancellor of instruction so that they could institute educational ‘reforms.’ The two administrators required schools to use a controversial high school physics program, an ineffective reading framework for elementary school, and Everyday Mathematics, an NSF-funded, K-6 series not aligned to the state’s standards.[14] By the next school board election, both administrators had left the district, but San Diego school math scores had already declined relative to the state as a whole.”
In my opinion, it is the best idea for development point of view. Now student is having the opportunity to directly interact with the technology in their early stages.Studying through common core can be the nice option. But, in some scenario, employment issue will raise. When common core like programs replaced highly-qualified teachers, then for surely unemployment issue will raised.
According to me Learning mathematics through online is not the best idea because maths need Practise by your own , by your own mind and hands.Technology can help you only in solving maths equation not to teach a small child. Student can also be distracted; when they Practising over the internet , no one is able to keep an eye on them to check out whether they are doing their work properly or not. I think, learning math on common core standards is not the great idea.But, In some situations we need to study online. So, we should not obsolete the idea of common core tutoring concept what we should need is the change in this latest concept.