State Board May Return Math Classes to the Basics

After three years of controversy over math instruction in California classrooms, the State Board of Education is poised to turn back the clock toward an emphasis on basics by adopting statewide standards that discourage the use of calculators and require memorization of multiplication tables.

Board members say they expect to vote Monday on math standards for kindergarten through the seventh grade that represent a wholesale shift away from the type of lessons used today in thousands of classrooms across the country.

California pioneered some of those very “reform” methods, which downplayed calculating exact answers while trying to make math more fun and interesting. And, until recently, the 11-member state board had seemed willing to accept a balance between the two approaches.

Over the past two weeks, however, board members have taken an aggressive editing pencil to the draft standards presented to them by an appointed commission, putting a decidedly traditional stamp on them.

Members of the Commission on Academic Performance and Content Standards have lobbied against the changes and are expected to show up to protest at what could be a contentious meeting in Sacramento on Monday. Some members of the commission--a majority appointed by Gov. Pete Wilson, who also appoints state board members--have said they may resign if the state board goes ahead.

State Supt. of Public Instruction Delaine Eastin is opposed to the changes, as well, complaining that the board’s proposal “represents . . . a decided shift toward less thinking and more rote memorization.”

She said she will ask the board Monday to delay its decision.

“They’ve deleted verbs like model, understand, estimate, interpret, classify, explain and create and the verb they most commonly substituted was compute,” Eastin said. “Essentially, this comes down to that we are going to teach kids to add, subtract, multiply and divide and we’re not even going to let them use a calculator before the sixth grade.”

The standards commission’s initial proposal, for example, said that second-graders should be able to “create and solve” simple problems. In the board’s revised version, pupils are to simply “solve” the problems.

“Instead of getting a child to have to think by creating a problem, they just want to get the answer,” said Sonia Hernandez, a top Department of Education official who represented Eastin on the standards commission. “I guess in some ways this confirms my worst fears that they really don’t want the tough standards.”

But board member Bob Trigg, who helped craft the revisions, said critics like Eastin and Hernandez are wrong to say the proposed standards overemphasize number crunching.

“It is very easy to throw out words,” he said. “I would hope we could set aside all the flamethrower words and look at the darned content.”

Trigg said the revised standards do not ignore the need for students to understand mathematical concepts and be able to explain their thinking. But “we wanted to have it be pretty clear that it was mathematics that we were dealing with,” he said.

Under state legislation, the Board of Education is required to adopt standards in math and language arts for all grades by Jan. 1. The board enacted the language arts standards last month and is expected to vote on a second set of math standards--for grades 8 through 12--in mid-December.

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

The revisions at issue second-guess the work of the appointed standards commission, which spent a year writing proposed guidelines for math instruction, then previewed them at hearings around the state. But members of the Board of Education thought that the document still lacked “clear, complete and correct” statements about what children should know, according to Marion Joseph, a member of the state board from Palo Alto.

Joseph said the issue is “not about how high the bar is”--the difficulty of the standards--but whether they “call for children to know and do what are the essential elements of mathematics.”

So the revised standards, prepared for full board consideration Monday, call for future generations of California students to memorize the multiplication tables in grade 3 and master the age-old routines of borrowing and carrying while adding and subtracting. In every grade, the board’s proposed standards require students to “make precise calculations,” a skill that math “reformers” often downplay as less important for students than being able to explain their thinking.

Long division, an operation that many believe is obsolete in an age of calculators, would once again become a staple starting in the fourth grade.

The board’s standards writers also took on the increasing use of calculators in all grades. Their revised document specifies that, by the fifth grade, calculators are not an acceptable way to determine an answer to math problems--at least on state tests. Their standards for the seventh grade specifically require students to find square roots without electronic help.

All those requirements represent a sharp shift from the math philosophy that began taking hold in California in the mid-1980s. The state’s math leaders were ahead of the rest of the nation in seeking to make math more accessible to young students by having them use cubes and plastic tiles, for instance, to help visualize numbers.

Though students were still taught to add and multiply, calculators were introduced to relieve students of the drudgery of pencil-and-paper number crunching--the idea being that students would use the time saved to ponder more complex, real-world problems.

In 1989, the National Council of Teachers of Mathematics drew on some of the ideas percolating in California in writing a set of standards that it has pushed aggressively across the country. The point was to encourage more students to take more math. If youngsters could find a better way to multiply fractions--by drawing pictures, for example--they were encouraged to do so. To help them understand a key concept such as the Pythagorean theorem (A-squared plus B-squared equals C-squared), they worked in groups and played games with cardboard triangles and squares.

But that approach drew stinging criticism from traditionalists like Joseph, who derided the reform philosophy as thinking “that the way to get more students to take more math is by lightening it up and making it more like math appreciation.”

Joseph said the state board, in contrast, believes that the way “to get children to do more and better and higher math” is to say to teachers and students “do it, solve it, know it.”

The controversy over the reform approach--dubbed “new-new math”--heightened in California with the adoption in 1994 of textbooks rich in pictures but skimpy on numbers. Later, reform-type methods were blamed for the state’s low standing on National Assessment of Educational Progress exams--even though no one knows how widely those methods were used to teach the students tested.

They are also blamed for the fact that over half of the students admitted to the California State University system are found to need remedial math classes that cover elementary and intermediate algebra. Many of the system’s math professors say too many incoming students grab a calculator when asked to do something as simple as taking 10% of 250.

Concern about reform methods has grown beyond California. Some critics of President Clinton’s proposal for national tests worried this fall that it would stress “fuzzy,” or “whole,” math at the expense of traditional exercises. When the developers of the test urged that students be allowed to use calculators throughout it, Education Secretary Richard Riley disagreed, and his aides pointed out that most Americans remained skeptical of allowing their children to rely on calculators.

Janet Nicholas, a California Board of Education member from Sonoma who was the main author of the latest revised standards, said the new document is not extreme.

“You don’t want to go from one swing to another, and that’s why you absolutely see in here basic skills. But you also see enormous emphasis on problem solving and conceptual understanding--getting kids to know the skills and to use them effectively,” she said.

The proposed standards endorse the notion that mathematical routines must be practiced until they are second nature. Formulas, not drawings or models, are to be used to calculate, say, the area of a cone. Students are expected from the earliest grades onward to be able to figure out whether answers are reasonable.

Another significant shift occurs in the standards’ discussion of statistics and probability. Classrooms today place a heavy emphasis on that area of mathematics from first grade on, recognizing that we are bombarded with the results of political polls and medical studies based on statistical calculations of risk, such as from drinking coffee. So pupils frequently take surveys of their own, interviewing fellow students about their favorite flavor of ice cream, for example, and then making graphs to show the results.

But some teachers fear that such student-conducted surveys take up far too much time. The board’s latest standards all but eliminate them.

Eastin admitted that math reformers in California may have been overzealous in tossing out some basics. But, she said, the board’s proposed standards represent a pendulum swing to the opposite extreme that will anger many teachers and business leaders who are looking for employees who can apply what they know.

“I think this is going to cause a huge firestorm if they try to jam this thing in,” Eastin said.

Trigg, the board member who helped prepare the proposed standards, said he is open to revisions if Eastin or fellow board members have concerns. But Trigg said he wants to steer clear of compelling school districts to follow the current “reform” path because there is little research showing it improves student performance.

“The thing I’m personally interested in is not dictating to a district how to teach this,” he said. “I’m hoping our board will determine what the kids are to learn and give the flexibility to schools how they are going to do it.”