In the elementary school grades (K-6), this document bars the use of calculators and computers in assessing student achievement vis-a-vis these Standards. In the elementary school grades, these devices serve no constructive purpose in assessing knowledge of mathematics, and their abuse can cause considerable damage to the education of children. They allow students to compute with numerical values having a large number of significant digits, but this only obscures basic mathematical principles, which the use of simpler numbers reveals. Calculators and computers may actually inhibit accurate assessment since these devices encourage overuse of the primitive problem-solving strategy of "guess and check" and thus discourage use of mathematical techniques of problem solving.

It is essential that students have complete facility with all of the arithmetic operations: addition, subtraction, multiplication, and division. These operations arise again in the context of algebra, for example in arithmetic combinations of polynomials, and later in calculus, when the need to manipulate power series arises. Nothing is gained by requiring students to compute by pushing buttons, especially in elementary school, and much can be lost.

The top scoring nations in 4th grade mathematics, according to the TIMSS report, do not allow the use of calculators. The report states: "In six of the seven nations that outscore the U.S. in mathematics, teachers of 85 percent or more of the students report that students never use calculators in class." The full context of these statement is excerpted from the TIMSS report as follows:
 

ARE CALCULATORS AND COMPUTERS MORE COMMON IN U.S. FOURTH-GRADE CLASSROOMS THAN IN OTHER TIMSS COUNTRIES?

"U.S. fourth graders use calculators and computers in mathematics class more frequently than do students in most other TIMSS countries. Use of calculators in U.S. fourth-grade mathematics classes is about twice the international average. In the U.S., teachers of 39 percent of the students report having students use calculators in their mathematics classes at least once or twice a week compared with the international average of 18 percent. Internationally, the teachers of two-thirds of the TIMSS students report that they never or hardly ever had students use calculators in their mathematics classes compared with the teachers of one-third of U.S. students. In six of the seven nations that outscore the U.S. in mathematics, teachers of 85 percent or more of the students report that students never use calculators in class."

"Among the 26 countries that participated in fourth-grade TIMSS, teachers in the U.S. and Canada are among the most likely to report that students use computers in at least some mathematics lessons. Teachers of 37 percent of the U.S. students report that computers are used in at least some lessons, in comparison with 13 percent of students internationally. Teachers in five of the seven countries that outscore the U.S. in mathematics report that they never or almost never have students use computers in mathematics lessons."

"In all countries, fourth-grade students were not allowed to use calculators or computers when taking the TIMSS test."

In the secondary school grades, 7-12, one might hope for basic familiarity with calculators and computers. But here again, that familiarity has nothing to do with assessing knowledge of mathematics. Use of calculators and computers for curve fitting, statistical tests, and other computations, in many cases supplants an understanding of the underlying principles required for these computations.

Whether the use of calculators and computers in instruction boosts student achievement remains an open question. Todd Oppenheimer writes in the July 1997 Atlantic Monthly: "There is no good evidence that most uses of computers significantly improve teaching and learning...."

It would therefore be inappropriate at this time for the State of California to require the use of calculators and computers for the assessment of knowledge of mathematics.