State Endorses Back-to-Basics Math Standards

The State Board of Education on Monday endorsed a controversial set of no-nonsense standards for math education from kindergarten through seventh grade that emphasize correct answers and lots of practice while discouraging the use of calculators.

The first statewide math standards, the target of attacks by critics who say that they sacrifice thinking for rote memorization, will guide the development of a new state test aimed at monitoring how well California’s public schools are teaching key subjects.

In response to the harsh criticism from some educators and members of a state commission that had taken the first crack at preparing math standards, the board agreed to allow a panel of experts to recommend minor revisions before it takes a final vote next week.

But board members said those changes were unlikely to resolve the fundamental philosophical differences that separate them from their critics. “The differences are genuine,” board member Kathryn Dronenburg of El Cajon said just before the 10-0 vote, with one abstention.

At the heart of the debate is how much emphasis to put on the fundamentals--skills such as memorizing multiplication tables or mastering formulas for finding the area of a cone.

Both sides agree they are important and that American schools have to start teaching them more like their counterparts in Japan and Singapore, whose students come out on top in international tests.

But board members said the initial version of the document prepared by the standards commission did not go far enough.

They voted instead for standards that call for California’s public school students to memorize multiplication tables in third grade and master the age-old routines of borrowing and carrying while adding and subtracting. Long division, a skill that some educators believe is obsolete in an age of calculators, would once again become a staple starting in the fourth grade. And in every grade, the standards call for students to “make precise calculations.”

The standards also frown on the increasing use of calculators, saying that they especially should not be used on state tests.

But members of the appointed standards commission--which had worked for a year preparing a draft of the math guidelines--complained that the board’s revisions overemphasize basic skills while downplaying the need for students to also understand math concepts and be able to use them to solve problems that don’t fit a standard formula.

Standards commissioners were sometimes emotional in expressing their anger. As if trying to take over the very rhetoric that back-to-basics advocates have long directed at current practices, they alleged that the board’s document was “dumbed down” in comparison to their standards.

“The title of our document should be ‘Expecting More,’ while the title of yours should be ‘Expecting Less,’ ” said Judy Codding, the most outspoken of the members of the Commission for the Establishment of Academic Performance and Content Standards to address the board. “I am truly discouraged.”

Board members were equally adamant that they had done no such thing and took offense at the label “dumbed down,” pegging it as a “clever” ploy to undermine support for the math standards among educators.

“The entire state of our children’s education depends on these standards,” Dronenburg said. “All you have to do is read them to see they are incredibly rigorous at every level.”

The state’s 1,000 school districts are not required to abide by the standards. But the standards will be highly influential anyway because they will help shape new textbooks and the statewide standardized tests--the results of which will be highly publicized.

When the board takes its final vote on the standards up to seventh grade, it is expected to act also on standards for the upper grades in order to meet a Jan. 1 legislative mandate. The debate over the content for the middle and high school grades is expected to be equally contentious.

Even the mathematicians in the audience Monday could not agree on whether the board’s standards were superior to those put forth by the standards commission.

Ralph Cohen, a math professor at Stanford University who helped the board write its draft, said the board’s document was clearer in stating what students must know while also presenting the skills in a logical progression from kindergarten to seventh grade.

Students who master its contents will be far better prepared mathematically than most California pupils are today, Cohen said.

“Their skills will be strong, their problem-solving for sure will be strong because they will have the skills with which to solve problems, and certainly their conceptual understanding will be strong because you can’t ask kids to understand concepts without giving them the tools,” he said.

But Dan Fendel, a mathematician at San Francisco State, insisted that students who master the standards will be adept at only one part of mathematics--number crunching.

The document approved by the board “shifts the focus to a very computational look at what math is and that’s not what math is about,” he said. He also opposed the board’s decision to ban the use of calculators on statewide tests--even for computing square roots.

“For anybody to take a square root without a calculator is the height of absurdity,” he said.

The vehemence of the views of both sides reflects the fevered debate over math education that has been building in California and across the nation.

Responding to the fact that relatively few California students take advanced math classes--only one in six now takes more than one year of algebra and only one in three completes geometry--math educators have been trying for decades to find a way to teach the subject in a way that was both interesting and rigorous. For the past decade or so, support has been growing among math teachers for stressing the ways math is used outside the classroom, or trying to make lessons more concrete by using blocks or folded paper to illustrate concepts, for instance, or enlivening lessons with games.

But these so-called reform approaches have been met with growing skepticism among parents and many mathematicians who worry that pupils today are failing to internalize the basics.

Attempting to settle the dispute, the state board last year adopted an advisory policy that sought to balance the competing views. On Monday, though, state Supt. of Public Instruction Delaine Eastin said the new standards tip that balance too far in the direction of skills.

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The New Standards

California’s new math standards for kindergarten through seventh grade have a distinct back-to-basics stamp. Here are some that received tentative approval Monday:

GRADE 1

* Know the addition facts (sums to 20) and the corresponding subtraction facts.

* Use the inverse relationship between addition and subtraction to solve problems and commit them to memory.

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GRADE 3

* Memorize to automaticity the multiplication tables for numbers between 1 and 10.

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GRADE 4

* Solving problems involving division of multi-digit numbers by one-digit-numbers.

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GRADE 5

* Add, subtract, multiply and divide with decimals and negative numbers and verify the reasonableness of the results.

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GRADE 7

* For integers that are not square, determine without a calculator the two integers between which its square root lies.