Sunday, August 10, 2014

Coring out the math standards

A renowned math teacher charged the Common Core curriculum of substantially weakening math standards in a recent column published in the Wall Street Journal. Dr. Marina Ratner wrote:


Reading about the new math standards—outlining what students should be able to learn and understand by each grade—I found hardly any academic mathematicians who could say the standards were higher than the old California standards, which were among the nation's best. I learned that at the 2010 annual conference of mathematics societies, Bill McCallum, a leading writer of Common Core math standards, said that the new standards "would not be too high" in comparison with other nations where math education excels. Jason Zimba, another lead writer of the mathematics standards, told the Massachusetts Board of Elementary and Secondary Education that the new standards wouldn't prepare students for colleges to which "most parents aspire" to send their children.

I also read that the Common Core offers "fewer standards" but "deeper" and "more rigorous" understanding of math. That there were "fewer standards" became obvious when I saw that they were vastly inferior to the old California standards in rigor, depth and the scope of topics. Many topics—for instance, calculus and pre-calculus, about half of algebra II and parts of geometry—were taken out and many were moved to higher grades.

As a result, the Common Core standards were several years behind the old standards, especially in higher grades. It became clear that the new standards represent lower expectations and that students taught in the way that these standards require would have little chance of being admitted to even an average college and would certainly struggle if they did get in....

It remained to be seen whether the Common Core was "deeper" and "more rigorous." The Berkeley school district's curriculum for sixth-grade math was an exact copy of the Common Core State Standards for the grade. The teacher in my grandson's class went through special Common Core training courses.

As his assigned homework and tests indicate, when teaching fractions, the teacher required that students draw pictures of everything: of 6 divided by 8, of 4 divided by 2/7, of 0.8 x 0.4, and so forth. In doing so, the teacher followed the instructions: "Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for 2/3 divided by 3/4 and use a visual fraction model to show the quotient . . ."

Who would draw a picture to divide 2/3 by 3/4?

This requirement of visual models and creating stories is all over the Common Core. The students were constantly told to draw models to answer trivial questions, such as finding 20% of 80 or finding the time for a car to drive 10 miles if it drives 4 miles in 10 minutes, or finding the number of benches one can make from 48 feet of wood if each bench requires 6 feet. A student who gives the correct answer right away (as one should) and doesn't draw anything loses points.

Here are some more examples of the Common Core's convoluted and meaningless manipulations of simple concepts: "draw a series of tape diagrams to represent (12 divided by 3) x 3=12, or: rewrite (30 divided by 5) = 6 as a subtraction expression."

This model-drawing mania went on in my grandson's class for the entire year, leaving no time to cover geometry and other important topics. While model drawing might occasionally be useful, mathematics is not about visual models and "real world" stories. It became clear to me that the Common Core's "deeper" and "more rigorous" standards mean replacing math with some kind of illustrative counting saturated with pictures, diagrams and elaborate word problems. Simple concepts are made artificially intricate and complex with the pretense of being deeper—while the actual content taught was primitive.

Yet the most astounding statement I have read is the claim that Common Core standards are "internationally benchmarked." They are not. The Common Core fails any comparison with the standards of high-achieving countries, just as they fail compared to the old California standards. They are lower in the total scope of learned material, in the depth and rigor of the treatment of mathematical subjects, and in the delayed and often inconsistent and incoherent introductions of mathematical concepts and skills.

Ms. Ratner is professor emerita of mathematics at the University of California at Berkeley. She was awarded the international Ostrowski Prize in 1993 and received the John J. Carty Award from the National Academy of Sciences, of which she is a member, in 1994. Rest of column

12 comments:

Anonymous said...

Wonder how Common Core stacks up against Mississippi's "previous standards"?

Johnny Weir said...

Bad at math? You may have been born that way, according to recent research. Dyscalculia -- a disorder that makes it difficult to understand numbers -- is estimated to affect five to seven percent of the population.
Not all of us are fortunate enough to just be able to do something by simply trying really, really hard. Sometimes things come down to a literal matter of capability. It is a disorder. That's how disorders work. It makes me so sick seeing so many people, to use your word, marginalizing this. Go tell a color blind person to try really, really hard until they can see red and green.Lots of famous smart, people were horrible at math. Many famous people were bad at math. Inventor Thomas Edison was had trouble in school because he was said to be "too dumb," particularly when it came to math. But Edison went on to patent over 1,000 inventions, including the light bulb, making him one of the most famous inventors in American history. Math only makes up 1/3 of the SAT test.

Anonymous said...

I've seen some of the math test questions from Common Core - they are absolutely absurd and measure nothing relevant.

No one can be that incompetent as to design a curriculum and tests this useless by accident.

Anonymous said...

Very sad. And very glad I grew up in California. Excellent math instruction. I am amazing at math compared to others. What the heck is the government thinking?

Anonymous said...

I'm a bit surprised at the professor's reaction to visual learning techniques.
Not all students are left brain dominant.
To present learning in such a way as to allow all students to learn and stimulate the weak side of their brains in the process as well isn't a bad thing.
Young people's brains are still developing along with their bodies.
We know a human isn't limited to and thus doomed to their level of development at 5 or 12 or 15 just like we know some boys are great athletes in junior high and stop growing while some athletes weren't good in junior high and later become stars.
If a teacher relies on one method of learning, as the professor charges was the case for her grandson, that's not good.
But, those adults who turn right 1.7 miles past the 3rd stoplight can also learn to turn right at the white house with the green shutters and vice versa. Engineers can learn to write coherently and English majors can learn to balance their check books.
In the past several decades , our education system has rewarded those who memorize well. Unfortunately, memorizing is unrelated to comprehension. And, we've focused so on specialization that interdisciplinary communication has been lost.
The latter seems evident in the professor's opinion piece. She might should be spending time with the neuroscience professors.

Anonymous said...

Evidently the "visual" aspect of common core is designed to teach students how to understand the keyboard at McDonalds, ie Big Mac vs Happy Meal rather than how to add, subtract, multiply and divide. Who are the idiots who come up with this and we are idiots if we let it happen

Anonymous said...

That's cute, 7:04.

What you don't mention and what the good professor touches on is what's included on the test. The CC supporters will tell you is that CC has nothing to do with how (read that as method) the kids are taught they just want them to answer the test questions correctly. They are adamant that it is up to the local districts on how to instruct the kids. That part is true. But what they aren't telling you is that the districts have a choice between a scantron and a written test. If the test demands the kids to show their work using one specific method, what are the rest of us right brainers supposed to do?

CC is nothing but the ugly baby produced by a cabal of personal data seekers (do you honestly think Gates is benevolent?) and test/textbook producers.

Anonymous said...

7:29 Answering the test questions correctly is dependent on those being tested knowing the answers.
So what you are saying is that like with all testing, there's a minimum standard of knowledge that is expected.
If the methods of imparting that knowledge are left up to the local districts, then why does the professor object to her grandson's method of being taught math as if that has anything to do with CC?
And, you're point about how the tests are graded is what exactly? You object to technology of grading papers faster because you think this allows information to be gathered that isn't already gathered?

I don't doubt there are glitches in CC. Even in the business world, getting a new project off the ground or making changes requires getting enough people behind it in the beginning.

Frankly, I do think it's in Gates interest to have well educated employees and there is more than a little evidence that he's very disturbed by how poorly those who graduate even at post graduate levels are able to problem solve and evaluate.

And, it is a source of frustration to Gates and others , that these days, we have a tendency to nitpick at details and criticize rather than to problem solve.

What is true is that our educational system is not competitive anymore and we must to something and perhaps try different things until we find that " something".

But, frankly, it's not the educators or entrepreneurs that concern me. It's all the people who think their anecdotal experiences make them experts.

Ophelia said...

Johnny Weir, while dyscalculia is just as valid a diagnosis as dyslexia, there should nevertheless be standards of core learning established, and, yes, the bar should be set high.

I hated math, and was very bad at it, all through childhood. It wasn't dyscalculia, it was pure-D boredom. I'd hide a juicy library book behind my dry old algebra text, while the dry old teacher droned on about quadratic equations.

But I wanted to escape Mississippi reallllll bad, and knew I'd need some fancy-lookin' credits on my record to get into one-a-them Yankee colleges, so I took trigonometry. Had a truly inspired teacher, and something went "click" in my non-math-lovin' cranium. Aced the course with an A.

I went on to do calculus in college, and aced that, too. I'd suggest that perhaps skill with numbers, like many other skills, may develop at different rates in individuals. No reason to "dumb it down" to make it less challenging. Just as dyslexics must learn to read, somehow, dyscalculics must figger out how to figger.

Or have a big ol' hole in their learning.

RandomHero30 said...

Common Core is DESIGNED to make kids dumb as hell. The answer doesn't matter so much as how the problem made you FEEL inside and how that emotion can be applied to seeking "social justice" for left handed, Asian, transgender midgets. Gates is about as benevolent as stage 4 liver cancer and let's not forget that Bill "Kill your parents" Ayers had some input too. CC is designed to make the kid rely on the STATE for help, not the parent (because we want kids to be good little statists in order to bring communism.) 2x2? You find that by drawing out blocks, shading in 3 of the squares, subtracting fart.23 pi. Proponents claim "its just a set of standards"....then why do a lot of these "standards" involve 6th graders having to read books about an uncle raping them? Its all either perverts getting off on kids reading filth, outright praise of communism (with the requisite brainwashing) distortion of the Constitution on revisionist history designed to MAKE THE NEXT GENERATIONS HATE AMERICA, or simply dumbing kids down so all they need is Cheezits and the latest episode of Dance Moms. Get this scumbag garbage out of my state.

Kay said...

2:37: Public school teacher here-- I've taught both the "old" MDE math standards and the "new" Common Core math standards and they're pretty similar. The main difference is that the CC standards work at a slower pace, but with greater depth. The CC standards also focus more on the problem-solving process and on the students justifying answers.

6:51: I've heard lots of people going a little crazy with the fearmongering ("I heard if a student says that 2 + 2 = 5 but he can explain his answer, then Common Core says he's right!! PANIC!") Not true. It's more like if a student randomly memorizes how to find an answer but can't explain why, he doesn't get full credit.

If you are panicked or just curious, you can read the standards here:
http://www.corestandards.org/Math/

Obviously no set of standards is perfect, but our old standards were pretty relative to the rest of the country (especially in high school and especially in reading). If I lived in a state like California, I might be irritated about implementing a new set of standards. But in a state like ours, it's nice to be put on an even playing field with the rest of the country without having to spend tons of resources writing our own standards. It's unfortunate that so much of what goes on in the classroom will still be determined by standardized testing, but that was going on way before Common Core.

A couple more annoying misconceptions:

1. It's not a curriculum. Teachers / schools / districts get to choose how to teach the standards (i.e., what texts to read). So if you see a news story about COMMON CORE FORCING CHILDREN TO READ ABOUT HITLER, it's not a real thing.

2. Most of the "Common Core test questions" you've seen on the Internet have come from workbooks or other teacher-assigned work. Hardly anyone in the country (myself included) has seen actual PARCC assessment questions. Now after we give that test this year, we'll talk about whether or not the questions are crazy.

Sincerely,
A teacher who isn't Common Core's biggest fan, but who is irritated by the misconceptions

Anonymous said...

That's a lovely dissertation 10:03. Tell me, if that same kid answers 2 + 2 = 4 but cannot write a justification for it, does that make his answer any less correct?

The answer to my question is simple: nope.

13-7=6 isn't a five step process, despite what CC says.

And FTR, I was one of those "crazy" parents posting pics of her children's math homework on FB last year. As a finance major, I was unable to help my 1st grader with her homework. Because in CC's world, 12-5 equals advanced logic and B.S. in journalism to get full credit for an answer.

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