Computation Skills, Calculators, and Achievement Gaps: An Analysis of NAEP Items

April 15, 2004

Paper prepared for the 2004 American Educational Research Association Conference, San Diego, CA, April 12-16, 2004

This paper uses data from the National Assessment of Educational Progress (NAEP) to study three issues in K-12 mathematics. It examines national trends in computation skills, investigates whether allowing calculators on NAEP items produces significantly different results compared to not allowing calculators, and analyzes the impact of allowing calculators on the performance gaps among black, white, and Hispanic students.

All three topics are controversial. Computing quickly and accurately is recognized by most math educators as an essential skill, but the question of how much emphasis computation should receive in the K-12 curriculum provokes a heated debate. In its 1989 standards, the National Council of Teachers of Mathematics (NCTM) recommended de-emphasizing computation skills, warning “clearly, paper and pencil computations cannot continue to dominate the curriculum.” The NCTM standards had a profound impact on state curricular policy. By 2000, all but two states, California and Massachusetts, modeled their own curriculum standards on the NCTM’s, and publishers revised math textbooks to conform with NCTM’s prescriptions.

The call to de-emphasize basic skills drew intense criticism from professional mathematicians and parent groups. They argued that the algorithms of arithmetic prepare students for more sophisticated topics and that students apprehend the fundamental structure of mathematics through the mastery of such seemingly trivial operations as long division. In 2000, the NCTM released a revised set of standards, Principles and Standards for School Mathematics. In deference to critics, the language on computation was softened. By the end of fifth grade, the document declared, “students should be computing fluently with whole numbers.” Notwithstanding the document’s more moderate tone, the NCTM standards did not abandon the position that computing skills should be de-emphasized.