Mate Wierdl is a professor of mathematics in Tennessee and a reader of the blog. He posted this comment:
I think the problems with CC is perfectly described in this blog post which compares a Finnish and a US first grade tests.
Simply looking at the two tests is enough: you can easily understand the Finnish test without knowing Finnish, while you may have to reread some questions in the US one.
Finnish
US
Click to access the-math-test.pdf
The US early emphasis on word problems to connect math with (fake) real life is one of the basic issues with CC. This corresponds to the close reading nonsense. The other basic issue is insisting on kids’ giving logical , detailed explanations for concepts they can easily understand intuitively (such as, they have no problem understanding the difference between 12 and 21, but CC wants kids to explain the difference every time they see it). This corresponds to poem analysis until the poem is dead—as you guys mentioned it before.
If I had to give a single sentence to describe the problem with the CC math: it wants to take art out of math and replace it with logic.
Probably, the same could be said about ELA, but I am not an expert on that.
Diane Ravitch's blog 
Hat Tip to Fred Klonsky …
Perfect!
I’m a first grade teacher. The Finnish test is so much more age appropriate. My First graders have to do so many more complex things then this. The word problems get out of control. So much so that the really hard ones can only be done by the absolute highest achieving in my class. And that’s on a good day.
I couldn’t agree more with the author’s section on explanations. Drives me insane. So many times an intuitive understanding is made, but a formal explanation makes it look like they don’t understand. Children’s brains are developing and need visuals and hands on not just to learn, but also to communicate. Oral and writte. Communication skills are for those with fluency. Many factors of normal development easily explain why linguistic fluency is unobtainable for young children. I could write lots more here.
What the #@*^?! I couldn’t answer some of those ??? the U.S. first grader got wrong, either (& I bet some state legislators & ed. board members who had inked the Pear$on contract couldn’t, either). WHY are Math & Reading Comprehension being linked in FIRST grade? Either one should be testing Math or Reading, but not both. Then, again, the questions are ambiguous–what in G-d’s name is that first one, w/the coins & the cup
that has the #6? Is the answer assumed to be 1 (as in, 5 + 1=6–?). What do coins have to do w/a # on a cup, anyway?!
That’s a GREAT way to start a test: confuse the test-taker from the get-go, rattle ’em, make ’em nervous. The kid taking this test had lots of stamina (or, perhaps, “grit”); I think I would have gotten a lot more wrong than than ones he/she did.
And I’m betting that that 45% (or maybe just those circled wrong; do 1st graders even know %ages-?) made him/her feel just swell.
The quest for “deep understanding” and subsequent “deep explanations” in CC math was fool’s errand. Adding layers of frustration to an already difficult subject for so many students has proven to be a failure of adult responsibility. Ignoring brain development and cognitive learning theory has harmed a generation of young students.
Exactly. Once upon a time many kids struggled to do basic math. Then the authors of Common Core said, “Make the math harder and kids will excel!” Sane people would have predicted a fiasco. In my district, the fiasco has come to pass, especially for the weaker students who are utterly disaffected and, understandably, on the verge of riot.
Like everything else, for mere mortals (unless you are Ramanujan) deep understanding of a mathematical concept normally does not come until after YEARs of exposure and reexposure.
I remember distinctly the first time I understood what calculus was all about and it did not occur until after I had taken several calculus courses beyond the intro course.
The idea that young children are going to have a deep understanding of ANY mathematical concept is just ridiculous and completely ignores how understanding of math develops over time.
Even the so-called “best” math students are really just good rule followers; kids blessed with the right brain wiring. Asking my accelerated 8th graders fundamental questions involving even shallow understanding almost always gets me a shrug of the shoulders.
T: What’s pi?
S: 3.1416
T: The diameter of Earth is approximately 8,000 miles; using pi, and your mental math skills, determine the approximate circumference of Earth at the equator.
S: Huh?
Rage
You are right and even some of the greatest mathematicians of all time could not explain where their ideas came from..
Ramanujan was a perfect example.
He would have hated Common Core and would have been at an utter loss to explain where some of his bizarre infinite series for Pi came from.
Commonujan?
Ramanujan would despise
Common Core in every guise
Making him explain the why?
Of his formulas for Pi
Rage, this is the result of bad textbooks, bad curriculum and bad teachers.
“I attended a lecture at the engineering school. The lecture went like this, translated into English: “Two bodies. . . are considered equivalent. . . if equal torques. . . will produce. . . equal acceleration. Two bodies, are considered equivalent, if equal torques, will produce equal acceleration.” The students were all sitting there taking dictation, and when the professor repeated the sentence, they checked it to make sure they wrote it down all right. Then they wrote down the next sentence, and on and on. I was the only one who knew the professor was talking about objects with the same moment of inertia, and it was hard to figure out. I didn’t see how they were going to learn anything from that. Here he was talking about moments of inertia, but there was no discussion about how hard it is to push a door open when you put heavy weights on the outside, compared to when you put them near the hinge nothing! After the lecture, I talked to a student: “You take all those notes what do you do with them?” “Oh, we study them,” he says. “We’ll have an exam.” “What will the exam be like?” “Very easy. I can tell you now one of the questions.” He looks at his notebook and says, ” ‘When are two bodies equivalent?’ And the answer is, ‘Two bodies are considered equivalent if equal torques will produce equal acceleration.’ ” So, you see, they could pass the examinations, and “learn” all this stuff, and not know anything at all, except what they had memorized.” – Richard Feynman, he was saying this about Brazilian school, but to me this chapter from his “You are surely joking, Mr. Feynman” sounds 100% as if it was written about present day U.S. education.
Richard Feynman famously stated, “My students memorize everything, but they understand nothing.”
“Richard Feynman famously stated, “My students memorize everything, but they understand nothing.”” – Nope, he did not say this about his students. He said it about the Brazilian students whom he observed during lectures and exams.
As you noted it’s the goal…math designed by university math profs rather than math as a tool. In Finland they are teaching kids to use math as a tool…we seem to be basing all our learning on how the apex learned…the upper 4% of learners. The argument is than this is how experts think so it forms the highest standard. I flunked individualized reading in the fourth grade because I would fill out the form after I finished a book…who was the protagonist kinds of questions…this was the 60’s. Have we learned nothing! Math is a toolbox and we need to be competent (basic) at the very least. If you choose to move along as a math prof, so be it! But we need 100% of students to achieve a basic utilitarian view of math, not proofs at 7th grade.
Ramanujan never gave a formal proof of anything but that hardly shows proofs in mathematics are without value. There is value in understanding why a mathematical result is true not just in knowing that it is true. It should also be noted that despite Ramanujan’s extraordinary intuition a substantial percentage of his results are in fact not true. His intuition was by no means infallible.
I guess Grothendieck would be the complete opposite of Ramanujan. Grothendieck always wanted above all to understand why a result was true.
My point was not that proofs are without value.
Only that even some of the greatest mathematicians could not explain how they got their answers and that the fact that one can not explain how one does a problem need not mean one does not know how to do it.
In 5th and sixth grade, two of my my nephew’s were very good at getting the answers to problems but not good at explaining how they got the answers. For simple problems, there is really no point in explaining in great detail, especially not explaining more than one way to get the answer.
They would get back their tests with lots of problems marked wrong, not because the answers were wrong, but because the explanations were not up to expectations.
They clearly knew how to do the problems because they got the right answers.
There is no better way of turning so done off to math than making them do a lot of useless busy work.
I am curious what your definition of a substantial percentage is in reference to Ramanujans incorrect results.
The Wikipedia article on Ramanujan says that of the 3900 theorems that Ramanujan wrote down, nearly all have now been proved correct.
During a lecture at IIT Madras in May 2011, Berndt stated that over the last 40 years, as nearly all of Ramanujan’s theorems have been proven right, there had been greater appreciation of Ramanujan’s work and brilliance, and that Ramanujan’s work was now pervading many areas of modern mathematics and physics.[62][72
I do not want to prescribe what math needs to be in the curriculum and how it should be taught. Here are the basic viewpoints that are definitely wrong (I exaggerate them a bit for clarity).
1) (Utilitarian view) The most important thing is that kids can solve practical problems, such as balance a checkbook or understand investment strategies or convert $ to other currencies.
2) (Rigid Profs’ view) The goal is that kids learn rigorous proofs, because that way they will learn logical thinking, and this can be used everywhere in life, such as in the courtroom or when arguing with our spouses or children.
3) (A mathematician’s view who is blindly in love with math) Kids need to discover everything, (formulas, methods) in math. We shouldn’t rob them them from the pleasures of discovery. Math is beautiful and kids need to see it that way. All kids should learn math as mathematicians do.
4) (Word problem pushers’s view) Math should never be separated from real life. Never ask a kid to plainly calculate 3+2. Naked math is scary to kids. Instead ask: “Juanita had 3 apples, Jia gave her 2 more, how many apples does now Juanita have?”. This is much friendlier, down to Earth, gives an opportunity to teach about non-math values as well, and hence reduces math anxiety.
5) (Militaristic view) Kids need to learn math concepts, formulas, algorithms by rote memorization. Most kids naturally resist this method, so they need to be coerced to do the daily drilling sessions. Whatever coercion the law allows. Drills and rote memorization has been done for centuries, so it clearly is the best method—fantastic for tests and testing. Making sense of formulas and methods can wait till college or even graduate school. Cognitive science supports this method.
The explanations requirement of CC is what irks me the most.
That and the fact that young students (eg, in fifth and sixth grade) are required to explain how they got their answer in not just one way, but several different ways.
Especially in the early grades, the important thing is that someone can get the answer to certain type of a math problem reliably. If they know just one method, that is fine. They will certainly learn more ways as they get older and take more math.
Its unnecessarily confusing to present them with several different ways of doing a problem at a young age when one method would suffice.
First, I’d like to thank you for this worthwhile post.
Why does education always have to be based on one principle and go to extremes? I agree with Mate Wierdl when it comes to early math — rote education is not only acceptable but actually very useful (if we are talking about the “real” world). But starting around middle school, CC math begins to have its place. As formulas become complex, and the memorization is just for the next test and NOT for applying to real world experiences, then its important to use logical reasoning. This way, it’s not about the formula but the thinking process on how you got there.
I teach 8th grade physical science. In my many years of teaching 13 and 14 year old kids relatively abstract topics, I have seen the shift from concrete to abstract just starting to take place around mid school year. Not all but for most students, this new brain capacity is starting to kick in. It has been fascinating to observe this change in kids and I wish those behind CC math had been more understanding of the limitations of the 8, 9, and 10 year old brains of the average child.
What is physical science, exactly? Is it physics? Why not just call it that. This is the problem with American schools – instead of modern-day physics, chemistry, biology, botany, geography, astronomy it teaches “physical science” which is at best a mish-mash of what a 17th century alchemist/naturalist/philosopher would do. People here lament of losing arts to math/ELA, what about real science subjects that have never been taught rigorously in American schools? Physics is not a required subject in most states for high school diploma, it is an elective, and it goes for just one year. It is a joke. In other countries it would last for 3, 4, 5 years covering everything from kinematics to mechanics to gas dynamics to electricity to quantum mechanics.
Physical science at the middle level (grade 8) is one semester of traditional chemistry and a second semester of traditional physics. The term “physical science” is understood to be a combination of these two subjects and is usually the first quantitative science course a student gets before entering high school. If you think science is misrepresented now, just wait until the Next Generation Science Standards kick in. NGSS is intended to result in a fully integrated, K to 8, science curriculum- that is a random mix of unrelated topics that will confuse more than enlighten. This is another standards disaster in the making.
I can’t help but think that if the CC$$ was an actual set of standards instead of a product pretending to be one, we would not be having this or any other major conversations about it. I must point out, yet again, that had the CC$$ been put together the way a real set of standards ( for anything! ) is put together, professional educators and their organizations, such as the NAEYC, National Association for the Education of Young Children would have played significant roles instead of being excluded in favor of reps from the mega testing companies such as Pearson who would not and should not have been involved at all. There is limited utility in terms of student outcomes to having a real, national set of standards, but even that very small advantage has been forgone in favor of a product that makes everything it touches worse. The CC$$ is copyrighted and has an indemnification clause that one accepts as a condition of use. No actual set of standards has or even needs these attributes. The CC$$ was never about education, only about corporate profits via controlling it.
The CC$$ is copyrighted and has an indemnification clause that one accepts as a condition of use. No actual set of standards has or even needs these attributes.
You are correct. But…
The CCSS were first marketed as if they were not intended to be about curriculum (but they were); and then marketed with “publisher’s criteria” for curriculum materials (2011); then those criteria morphed into a system for reviewing curricula, based on absolute compliance with the CCSS, including grade-by grade alignments. That was 2013.
In 2013, the initial criteria for reviewing curriculum materials for CCSS compliance were called “drop dead” (meaning comply with these criteria or do not waste the time of our reviewers). Then the language was softened to “gateway” criteria (2014), but with the same meaning,—comply or else the reviewers will not bother to look at anything else.
By 2015, the promoters of the CCSS had set up a non-profit called EdReports.org to function in the capacity of a consumer-reports rater of published math and ELA materials claiming to comply with the CCSS.
EdReports is said to be the result of a meeting at the Annenberg estate of “the nation’s leading minds in math, science, K-12 and higher education.” I have not been able to find a list of participants in that meeting or the sponsors, but in 2014, professionals in branding and communications were hired to promote EdReports. You can see the strategy and their pride in getting coverage in national news, http://www.widmeyer.com/work/edreports-org.html
including from Peter Greene http://curmudgucation.blogspot.com/search?q=EdReports
In August 2015, the Bill and Melinda Gates Foundation gave $1,499,988 to EdReports for operating support followed in 2016 with more for that purpose: $6,674,956. The William and Flora Hewlett Foundation gave EdReports.org $1.5 million in 2015 and $2 million in 2016.
Ed Reports.org is also funded by the Charles and Lynn Schusterman Foundation, the Helmsley Charitable Trust, the Overdeck Family Foundation, the Samueli Foundation, the Charles and Helen Schwab Foundation, the Stuart Foundation and Broadcom Corporation (an advisor from Broadcom is with EdReports),
You can find more about the absolute continuity from the writing of the CCSS, largely funded by the Bill and Melinda Gates Foundation, to current efforts to impose “approved curriculum materials” for any state that has adopted the CCSS… https://www.edreports.org/about/index.html
So what can be said about the CCSS now, a decade after they were formally launched? About 36 states still have the CCSS (including DC). Ten have made major revisions. Four never adopted and one only adopted the ELA standards.
For an amazing report on the status of tests for the CCSS and who is pulling the strings in which states to keep up the drumbeat for the CCSS and testing see this recent report from a Gates-friendly consultancy. https://education-first.com/wp-content/uploads/2018/02/Education-First-What-Happened-To-State-Tests_April-8-2018.pdf
I am not a teacher of math or ELA but I know this: The investments in these two subjects have distorted the whole of education and are continuing to do so.
The Next Generation Science standards have been tethered to 244 links with the CCSS. Studies in the arts and humanities have been marginalized altogether along with civic education.
The billionaires who funded the standards and still promote them continue to posture as if experts in education or masters of the entire universe of “talent” in education.
From the get-go the standards were designed for use with perfectly aligned curriculum modules for instructional delivery on the internet with continuous adaptive testing and computer friendly coding of every standard. That work is moving forward, even as school libraries are converted to venues for on-line instruction, librarians are vanishing (40% fewer than in 2000), and pushers of online learning conjure ways to save money by hiring fewer certified teachers or none at all.
It is long past time to make the CCSS history. Adapt anything of use, but dump the all the rest.
Thanks, Mate. This is an interesting look at what the math looks like in class. My own soon to be 12 year old comes home with math worksheets like that all the time. She is very perceptive, and some of the work is good for her. Mastery of it is a dubious goal, however good she might be. She is very verbal, so explaining how she got an answer is recreational for her. Her friends, however, may not have that reaction. Nor does her explanation generally mean she understands the concept.
Some years ago, when Tennessee had planned to CC and PARC, we were given a variety of evaluation organs to try out on the students. I had one wonderful student who was a theatre person and read all the time but could not understand the logic of geometry well enough to justify congruence implying equality or how to arrive thereto. I had another wonderful kid who always got the right answers, but could rarely explain why. The former student scored better on the practice PARC, even though she did not understand it as well.
Even as a math teacher, judging who understands best is a difficult task. When Imbecame a history teacher and departed the math thing, it got even worse.
“If I had to give a single sentence to describe the problem with the CC math: it wants to take art out of math and replace it with logic.”
If I had to give a single sentence to describe the problem with the CC ELA: it takes meaning out of ELA and replaces it with decontextualized “text” snippets and oversimplified writing scoring rubrics. So yeah, same thing.
Keep in mind that the purpose of CC is not to reform education in order to make access to it more universal, but to automate education in order to yield more data gold. Follow the money.
Lastly, even though I teach ELA, I’d like to take a stab at the last CC math question in the link, “Write a number sentence for 8 – ___ = 2.” An American city has 8 public schools. 4 charter schools open and quickly close, draining all the funds, carting the money out of the city in convenient takeout bags. 6 public schools are shuttered. The American city is left with 2 public schools. 8 (+4 – 4) – 6 = 2. Did I get that right?
“they have no problem understanding the difference between 12 and 21, but CC wants kids to explain the difference every time they see it)” – I would like to see a specific requirement in CCSSM standards that requires to explain the difference between 12 an 21 every time the kids see it.
As for the test, it is a Pearson test, deeply flawed, made by non-professionals. The mere claim by Pearson that this test is aligned with Common Core does not make the test Common Core, just like the Core-Plus Mathematics having the designation “Common Core edition” does not magically change it from 1990s pitiful context-based algebra-deprived program into something different.
Simply put, a TV set with Energy Star label does not make it Energy Star TV.
Those who claim that the CCS is fine and only its interpretation by teachers, education leaders, testing companies screwed up this modern piece of art, probably need reread this from the 2nd grade math standards
CCSS.MATH.CONTENT.2.NBT.B.7
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
It’s a mistake to think, the standards do not suggest pedagogy. The above passage “strongly” suggests, it’s not enough to teach the addition or subtraction algorithm to kids after introducing it so that the idea behind the algorithm makes sense to them. No, they have to go through the actual motions underlying the method.
How hard is that? Last year, I taught this very stuff to students at the university who wanted to teach in low grades. They protested that there was no way, they needed to go though this, so I showed them the above standard. These were 20 year old students, and most of them ended up understanding the ideas behind the addition algorithm, but drawing the pictures, grouping and regrouping the colored plastic shapes and relating them to steps in the algorithm they simultaneously had to write promoted no understanding at all. They became as mechanical as the algorithm, except the time to complete a calculation took 10 times longer than just doing the algorithm alone—not to mention the gigantic learning curve.
So now imagine doing this as part of solving a word problem (and everything needs to be in terms a word problem), and you start feeling the fires of Hell.
I think the operative expression to use when we talk about teaching math is “make sense to the students” instead of “proof” or even “understanding”. This suggested expression implies that we are not talking about some kind objective, unique standard of understanding, a verification of truth at a fixed level, but an understanding which very much depends on the students such as their age, maturity level or background and perhaps even personality.
When a teacher finds that she needs to explain something differently to a student, she is practicing exactly the above: adjusts explanation of truth to the kid’s mode of understanding.
If they want to use a more formal expression (to make papers on education less readable), they may use the term “intuitive understanding”.
And never ever use “rigorous understanding” or “rigorous proof”. It not only sounds freaky to non-mathematicians but it IS freaky.
@Máté
Yes, one does need to understand how place value works.
No, it is not too early to learn place value in the 2nd grade.
No, it makes no difference whether you add two-digit or ten-digit numbers if you know the concept. In particular, working with numbers within 1000 in 2nd grade is perfectly fine.
No, you do not need to split and graph 12+21 every time you see them, you need to understand the concept of decimal base and place value just once.
Watch this, this guy is amazing in his attitude and humor and some small tricks, but really he does not practice anything different than what has been practised during the last three hundred years: https://www.mathusee.com/parents/updated-books/alpha/ I used his promo videos from YouTube in my own practice, no need to purchase the whole set from him.
I don’t even want to comment on your students.
Oops, wrong link. Here is the video: https://www.youtube.com/watch?v=tvKB4Fp6tFo
Word perfect Mate.
Good clean, straightforward math standards that are developmentally appropriate and aligned with teacher competencies would never produce this degree of frustration, confusion, or debate.
If for a moment you stop thinking of CC crowd as evil Greeks attacking Troy, and consider their position, you will realize that there is no national curricula, and even those who like Diane supported it, have retreated. What do Gates et al do in this case? They try to create “voluntary” standards that look as much as curriculum as possible. The problem of CCSS is not that they are bad, that their creators were not educators, that these standards conflate syllabus with curriculum, etc. The problem is literarlly the size of the whole country: it is that USED cannot by law impose national curricula, this means giving this task to semi-knowledgeable hacks, who impose the standards by other means, like by creating an inter-state conference, then by dangling federal funds for acceptance of the standards.
CCSS is not problem of billionaire wannabe educators, it is the direct result of government inaction. It boggles me that the federal government has half the world under control telling people around the globe what sort of democracy they need and what sort of monetary laws they need to create, yet is completely incapable of imposing a national curriculum in this country.
BA,
I never supported Common Core. I supported the idea of a national curriculum in the abstract. The reality is abhorrent. It seemed like a good idea until it happened. Reminds me of when I was blogging at EdWeek with Deborah Meier. She said she would support a national curriculum if she was in charge of writing it. Me too. There’s the rub.
“I supported the idea of a national curriculum in the abstract. The reality is abhorrent. It seemed like a good idea until it happened.” – it did not happen because Common Core is not a true national curriculum, it is a surrogate. It is better than nothing in my opinion, but it could and should be much better and include all subjects, not just math and ELA.
“Reminds me of when I was blogging at EdWeek with Deborah Meier. She said she would support a national curriculum if she was in charge of writing it. Me too. There’s the rub.” – What does this say about you? That you are as autocratic as Bill Gates, the only difference between you two is that you don’t have his wads of cash.
Back Again, you just violated rule one of the Blog by insulting me. Do it again and you are banned. Deborah Meier made a joke, I made a joke, and you say I am as autocratic as Bill Gates but without the money. You are extremely dense if you don’t understand satire.
I saw a BA post for the first time a few weeks ago where she stated
It is not the Common Core, which is only as set of requirements, it is not a curriculum. It is NCTM Standards, are you people blind to see this?
As far as I am concerned, she started out with an insult to us all. Shortly after, I made it a rule for myself not to respond to this anonymous, possibly paid dudess whose technique is to skim posts superficially and pick out something she feels like attacking with her limited weaponry consisting of “CC is great and you guys dunno what you are talking about”.
“Back Again, you just violated rule one of the Blog by insulting me.” – I did not mean to, was simply commenting on your message. I did not read your blogs on EdWeek, so it was hard to figure out this was a joke. Yes, I am that dense at times.
You don’t have to have read the blogs on EdWeek from years ago to get the point of the joke.
Anything called national standards must be developed over many years by experts who are able to build consensus. Because of our enormous diversity, that consensus is always out of reach. Deborah Meier, who opposes standards, said she would be okay with national standards if she wrote them, which was a joke. I agreed, which was a joke. Hint, hint, hint.