Practice Makes (Nearly) Perfect: Solving ‘Students‐and‐Professors’‐Type Algebra Word Problems

Summary: Three experiments with university students (Ns=40, 36, and 36) who were non-math majors explicitly examined whether repetition in performing ‘students-and-professors’-type algebra word problems, which have been shown in the past to be vexingly difficult even for more advanced students, would spontaneously lead to higher rates of correct answers. Word order and situation model specificity were also examined to determine their effects on the rate of improvement. The strongest predictor of students producing correct equations (i.e., not producing the typical ‘reversal error’) was practice: In all experiments, participants spontaneously improved in equation accuracy almost to ceiling levels as they progressed, despite receiving no feedback. Tentative support is provided for the pedagogical value of repetition in solving problems, along with varying the wording of the problems. Copyright © 2012 John Wiley & Sons, Ltd. In a recent comparison of Common Core standards in mathematics education in the USA (http://www.corestandards.org/) and existing state standards, Porter, McMaken, Hwang, and Yang (2011) also compared the Common Core standards with those of three high-performing countries (Finland, Japan, and Singapore). They found a much greater emphasis on ‘perform procedures’—that is, on doing more problems rather than focusing on higher-level conceptualization—in the highperforming countries than in the US Common Core or state standards. Porter et al. suggested, very tentatively, that this fact may point toward a re-evaluation of the de-emphasis in the USA on solving greater numbers of routine problems. The motivation for the research reported here was to test the degree to which college-aged students’ accuracy in solving ‘students-and-professors’ problems would benefi tf rom repeated exposure to the same sort of problem. This type of problem, for example, ‘Write an equation using the variables S and P to represent the following statement: “There are six times as many students as professors at this university.” Use S for the number of students and P for the number of professors’, has received considerable attention from math educators and cognitive psychologists over the past three decades since Clement and collaborators (Clement, 1982;