A State Board That Can’t Do the Math

If you want to understand the war over standards for our schools, you have only to look to the battle over math.

On one side is California’s academic standards commission, which recently completed its math standards. On the other is the State Board of Education, which was charged with considering the commission’s work and adopting standards based on it. The board gutted the commission’s recommendations and made its decision final Thursday.

The commission spent a year and a half carefully analyzing the standards used in countries such as Japan and Singapore, whose students year after year perform at the world’s highest levels in mathematics. The commission’s premise was that California deserved such high standards and could afford no less.

When the state board took a knife to the commission’s standards, it cut out almost everything that was not related to computation and the memorization of formulas.

What was gained? Nothing. The commission hadn’t ignored the basics. Its standards required, for example, that all students memorize the multiplication tables by the end of the third grade. It made it clear that students had to be able to do their arithmetic accurately without calculators. No fuzzy math here. The commission’s insistence that our students learn their math facts and know the basic formulas by heart was unrelenting.

But the commission’s careful study of the success of nations where high achievement is the rule led it to add certain elements to the basics--elements that other nations consider vital. There is nothing new about this math--it is the math that students in other countries have been taught and have used to outperform American students for years. The state board, in its desire to institute standards that would fit the 1950s, ignored what is essential today.

What the state board deleted or weakened were standards intended to make sure that students understand the key concepts underlying mathematics, standards making students apply math facts and formulas to problems not quite like the ones at the end of the chapter in the textbook, and--most important--standards that demand that students put problems from everyday life into mathematical form so that they can be solved with math facts and formulas.

Several years ago, the federal government did a survey of people in their teens and early 20s. Almost all of these young people could add a column of figures and take a percentage of the sum. But surprisingly few could add up a restaurant check and calculate the tip. How could this be? The algorithms involved--of addition and the multiplication of fractions--are the same. These young people just did not understand that the math facts they had learned could be applied to this real life problem.

Comparing a Japanese math textbook with a standard American one is remarkably instructive. The American text introduces the topic with a set of definitions and algorithms to memorize. The rest of the chapter is basically a set of problems for the student to solve. The Japanese text instead concentrates on explaining the broad topic and its conceptual underpinning. The Japanese text treats only a few related topics a year in some depth, while the American text races through many apparently unrelated topics, covering each very superficially. The American student is not expected to understand the concepts underlying the material; for the Japanese, it is the conceptual mastery that is most important.

The student who has achieved real conceptual mastery can apply that understanding to a wide variety of problems, even those of a type he or she has never seen. The student who does not have conceptual mastery will fail to see that the restaurant check is a problem in addition and fractions in disguise.

The state board’s insistence on reducing mathematics to facts and formulas will deny California students an opportunity to master concepts that Asian and European students routinely master, and to learn to solve problems that their counterparts in other nations can easily solve. What has been lost in the board’s actions is almost everything that gives children in the highest performing nations their competitive edge.

Why did the board remove from the commission’s recommendations almost everything that the most successful nations have decided is necessary? Board members said they removed what was experimental and untried, leaving the traditional, the tried and true. In fact, what they left out is traditional in the countries whose students perform at the highest levels in math. In fact, what they have settled for was traditional in this country in 1920.

That is a retreat to the old in the face of the requirements of today. It will be a great shame if California’s children and the future of the state’s economy are sacrificed to the state board’s misplaced nostalgia.