Making math into art isn’t ‘deeper’

Common Core standards are making math education even worse, writes Marina Ratner, a Berkeley math professor emerita, in the Wall Street Journal.

As a sixth grader at a Berkeley public school, her grandson was required to “draw pictures of everything,” she writes.

. . .  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.

Core math requires “convoluted and meaningless manipulations of simple concepts,” Ratner writes.

. .  . 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.

Common Core’s math standards are lower than the standards of high-achieving countries and lower than California’s old standards, Ratner concludes. “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.”

Ratner is wrong on the facts, responds Bill McCallum, a math professor who helped write the standards. Here’s his post on drawings in the Common Core.

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  1. It would be nice if she would use her math expertise to identify the real problem….placement of advanced students in remedial classes. Students should be able to test, if they truly have mastered the lesson.

    What my kid did was take 30 sec to get the sketch done, ten out to bis English lit reading.

  2. Sigivald says:

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

    Someone who wanted kids to actually visualize how it became 1/2, to help them lock in that the numbers are “right”, and that it’s not all just pointless manipulation of symbols?

    Sounds to me a lot like the author is forgetting that kids are learning math, not applying things she’s mastered for decades on end, and that not all the kids are as mathematically inclined as her grandson.

    (I agree with lgm about the Real Problem, too.

    Core Standards, last I checked, require teaching some visualization method or other, early in the processes of learning the basics.

    They don’t specifically require drawing pictures … and they don’t forbid students testing up to a higher grade when they know the material, any more than the Old Standards did.

    Her kid would have been equally bored and wasting his time in the same class while the teacher went over and over the “old way” with the students who don’t already grasp it, until they did.)

    • GoogleMaster says:

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

      Someone who wanted kids to actually visualize how it became 1/2…”

      Except that 2/3 divided by 3/4 is 8/9, not 1/2. How many three-fourths “gazinta” a two-third? That relationship would be devilishly difficult to draw.

      • We did it several times (over time) so that we could understand just what a fraction division problem was saying. Fraction division is fairly tricky to understand, and it’s not that hard to illustrate that the magic formula of flip and multiply works out the same as dividing 2/3 by 3/4 if you draw it a few times. Graph paper helps a lot. I found it very helpful myself. However, I usually find that it’s better to draw a picture about once a day to illustrate something that’s not yet grasped. No need to do it lots of times.

  3. The ed world, at all levels including the politicians) are determined to deny that cognitive ability plays any role in academics – leading to all kinds of silliness and inappropriate policies (like putting kids who read at a 5th-grade level in AP English, as reported by a MD AP English teacher). They almost all admit, though, that not all kids have equal musical or athletic ability. Sigh

  4. Educationally Incorrect says:

    In the ed world so many people suck at math that they believe that the gaussian distribution of an ability (of any kind) is a consequence of “testing.” Without testing the distribution will be a ….. SPIKE OF EXCELLENCE! ( <– trademark 🙂

    Everyone in the spike will go to Harvard AND MIT, and will win all the Nobel Prizes.

    The only thing (in addition to testing) standing in the way is….poverty.

  5. As I’ve said before, writing and drawing pictures about math isn’t going to help students learn it any better, if they don’t have an understanding of the basic principles of math operations.

    IMO, the worst thing that was done to students (besides the calculator) was allowing cash registers to figure out change for cashiers.