Reacting to the proliferation of calculators in elementary school, the State Board of Education on Thursday adopted new guidelines for mathematics instruction that discourage using the devices in the classroom until children show that they can add, subtract, multiply and divide on their own.
The state board’s unanimous decision to emphasize traditional computational skills using pencil and paper marked a sharp reversal from a previous “framework” for mathematics adopted seven years ago.
At that time, the state’s top school policymaking panel declared that calculators had become equivalent to electronic pencils and suggested that all students have them at hand for lessons, homework and tests.
Calculators, it was said, were crucial for an empowering math program.
Since then, the stumbling performance of California students on state and national math tests has prompted a backlash against a reform movement that had emphasized the development of students’ abilities to think conceptually about math over their ability to perform math procedures like long division.
The immediate impact of Thursday’s vote was unclear. In a state with 1,000 school districts, 8,000 public schools and countless competing visions of school reform, it is rarely possible to switch course merely by decree from Sacramento.
The new guidelines already face stiff resistance from many teachers who say that they put too much stress on rote memorization--turning the students into machines.
Judy Anderson, president of the California Mathematics Council, representing thousands of teachers, denounced the new guidelines in a letter to the board as “narrow, biased and backward.”
Hung-Hsi Wu, a mathematician from UC Berkeley who was in charge of editing the guidelines, replied that the old policies were nothing but “a lot of hand-waving” and “big words” without precision or rigor.
The fierce conflict reflects a long-running educational debate that also touches on subjects such as reading and science: Should mastery of facts, skills and procedures take priority? Or should students be freed from many of the traditional classroom drills to explore projects and ideas, learning the necessary facts and skills along the way?
Thursday’s ratification of the new math framework and a companion document that elevates the role of phonics in reading lessons put the state squarely in the camp of the traditionalists. Now, board members said, the nation’s largest state school system, with 5.7 million students, has to start delivering world-class results.
“We have a very difficult road ahead--an arduous road,” said board member Janet Nicholas. “It’s about more than basic skills. Average isn’t good enough. We’re aiming higher than average. It’s really a measured path of how to raise the level of student achievement.”
Setback for Supt. Eastin
The 10-0 vote approving the math framework and 10-0 vote on reading were the state board’s last major actions before Gov.-elect Gray Davis, a Democrat, takes the place of Gov. Pete Wilson, a Republican, in January. Next year, as Davis begins to name replacements to the 11-member board, many school policies could shift.
But Davis has shown no inclination to abandon or dilute the demanding new academic standards in reading, math, science and social sciences approved during the past two years by Wilson’s board. Rather, Davis has said he supports more summer school for students who fail to keep pace.
The state board’s vote on math defied state Supt. of Public Instruction Delaine Eastin. At the meeting, Eastin scolded the board for not taking another month to assuage critics. “You could have done more to promote the buy-in of teachers,” she said.
Evidence abounds about the state’s math failures. A nationwide math test in 1996 found that California’s fourth-graders trailed their peers in 40 states; its eighth-graders were behind those in 32 states. Well over half of the schoolchildren who took the statewide Stanford 9 math tests last spring scored below the national average. In March, California State University announced that a record 54% of entering freshmen needed remedial math.
Many of the state’s troubles in math, experts say, stem from the high numbers of students who are not fluent in English and who live in poverty.
Nonetheless, the new math guidelines exhort teachers and administrators to push for better results from all students so they are ready for algebra and geometry. The foundation for this approach was laid a year ago when the state board approved an exhaustive list of benchmarks for what students should learn about math from grade to grade. In kindergarten, students are expected to “understand and describe simple additions and subtractions.” In second grade, they are to memorize the multiplication tables of 2s, 5s and 10s, up to “times 10.”
The document approved Thursday amplified on the standards by giving teachers detailed advice on how to help students reach them. Although the standards and the framework are voluntary, schools will have powerful incentive to follow them because they will influence textbooks and tests.
The state’s previous math guidelines, approved in 1991, encouraged teachers to make frequent use of calculators. They were even published with pictures of smiling children holding calculators and an image of a scientific calculator on the cover.
The new guidelines assert the primacy of brainpower over battery power. One passage criticizes textbooks that assert a calculator can be used in the seventh grade to “prove” the irrationality of a number such as the square root of 2. Instead, the guidelines say, students should master the precise definition of irrational numbers, which are those numbers that cannot be represented as an exact ratio of two integers.
In another blunt passage, the guidelines warn: “It is imperative that students in the early grades be given every opportunity to develop a facility with basic arithmetic skills without reliance on calculators.” However, at the last minute, the board backed off on a proposed stance against any classroom use of calculators until sixth grade. Board members said elementary teachers should be given some discretion on lessons for mathematically gifted youngsters.
Wu, the UC Berkeley mathematician, said in an interview that he did not want to discourage the judicious use of calculators, especially for advanced studies in middle school and high school. In fact, the state of Virginia last year purchased 200,000 graphing calculators for eighth-, ninth- and 10th-grade students. Computers, too, are beginning to play a wider role in math teaching.
But, Wu said, there is no hard data to prove the benefits of calculators and much anecdotal evidence to suggest that too many students lean on the devices to conceal their defective knowledge. “The calculator is a powerful instrument,” Wu said. “It can do a lot of good, and it also has the potential to do great harm.”
But Anderson, president of the mathematics council, said that even primary grade students can benefit from learning how to make machine-powered calculations.
“Calculators are very much a part of our world,” Anderson said. “I think calculators can be used to do some pretty sophisticated problem solving.”