An op-ed in the August 6 Wall Street Journal caught my eye. I borrowed the title for this article: “Making Math Education Even Worse.” The subhead reads ⇒

As regular readers know, I take math very seriously. I have watched my students’ math skills decline precipitously over the 3+ decades I’ve taught economics. Today we have students who cannot solve a simple equation like 2x + 3 = 7. (I wish I could say I was joking.)

The op-ed author, Marina Ratner, has quite a distinguished resumé. [1] And it’s hard to argue with this:

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.

But It’s Even Worse

What Dr. Rattner doesn’t point out is the two-edged impact of drawing pictures instead of learning arithmetic. First, the pictures will probably not help many of the students who are math-challenged. Second, and, in my view, more importantly, drawing pictures wastes the time of students who are adept at math. So Common Core is doubly harmful. It holds back the more math-adept students while failing to help many of the math-challenged.

Some Common Core exercises emphasize the use of “friendly numbers.” I have never understood what makes one number friendlier than another. But I have a guess. Numbers that have pointy, sharp corners (7, 5, 4) are unfriendly. Numbers that are nice and round (3, 6, 8, 9, 0) are friendly. I don’t know what to do with 1 and 2. I hope someone who knows Common Core can help me with this classification issue.

[1] 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.