This study investigates how well 381 prospective elementary, early childhood, and special education majors solved four arithmetic problems that required using the order of operations. Self‐reported data show these students to be relatively able mathematically and confident in their ability, with no substantial dislike of mathematics. The percentage of answers that were incorrectthat is attributable to order of operations ranged from 21.7% to 78.5%. Overall, fewer than half the subjects answered more than two questions correctly. Of those subjects who performed multiplication before addition, which indicates some knowledge of order of operations, 30.9% performed addition before subtraction and 38.0% performed multiplication before division rather than from left to right, which suggests that instead of using the correct order of operations, these students used the common mnemonic PEMDAS or “Please excuse my dear Aunt Sally “literally, performing multiplicationbefore division and performing addition before subtraction, rather than from left‐to‐right. Furthermore, 78.5% of subjects used the incorrect order of operations to compute −32.

One of the lessons learned from the “new math” reform movement of the sixties is that effecting lasting change requires more than developing curriculum materials at a national level for adoption at the local level (National Research Council 1989; NCTM 1989; Mumme and Weissglass 1989). Lasting reform also requires directly involving teachers in curriculum development so that they have “ownership” of the product (National Research Council 1989). This ownership is necessary because teachers act as curriculum filters (Holmes Group 1986; Porter et al. 1988; Romberg 1988).

The NCTM's Curriculum and Evaluation Standards (1989) called for increased emphasis on promoting students' conceptual understanding of fractions and fraction operations; this call was reaffirmed in Principles and Standards for School Mathematics (NCTM 2000). Currently, many manipulatives, including pattern blocks, fraction circles, fraction squares, geodot paper, and fraction strips, are available to help teachers promote this understanding. This article describes another manipulative, the fraction computer, that I have found helpful for teaching fraction addition and subtraction.

Under certain conditions, any digital computing device experiences loss of accuracy, a problem that has long been a concern to specialists in mathematics and computer science. Now, however, as more classroom teachers use calculators and computers in mathematics instruction, they should know what causes accuracy to be lost and how to prevent it.

Before getting to the main point of this article, I need to make a confession: I am a product of the “new math.ȝ I had the “new math” from kindergarten all the way through high school. The “new math” influenced my understanding of what mathematics is and what doing mathematics means. Most of the time I am not conscious of this influence, but a recent experience made me nostalgic for two, interrelated ideas of the “new math.” I believe that these ideas are just as valid today as they were thirty years ago. More important, as the pendulum of school mathematics reform swings toward the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and away from any residual legacy of the “new math,” we need to retain these two ideas.