I first encountered the Common Core State Standards last fall, when my grandson started sixth grade in a public middle school here in Berkeley, Calif. This was the first year that the Berkeley school district began to implement the standards, and I had heard that a considerable amount of money had been given to states for implementing them. As a mathematician I was intrigued, thinking that there must be something really special about the Common Core. Otherwise, why not adopt the curriculum and the excellent textbooks of highly achieving countries in math instead of putting millions of dollars into creating something new?

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.

Martin Kozlowski

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.

For California, the adoption of the Common Core standards represents a huge step backward which puts an end to its hard-won standing as having the top math standards in the nation. The Common Core standards will move the U.S. even closer to the bottom in international ranking.

The teaching of math in many schools needs improvement. Yet the enormous amount of money invested in Common Core—$15.8 billion nationally, according to a 2012 estimate by the Pioneer Institute—could have a better outcome. It could have been used instead to address the real problems in education, such as helping teachers to teach better, raising the performance standards in schools and making learning more challenging.

*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.*