Effectiveness of the ‘Change in Variable’ Strategy for Solving Linear Equations Mustafa F. Demir and Jon R. Star, Michig

1. Effectiveness of the ‘Change in Variable’ Strategy for Solving Linear EquationsMustafa F. Demir and Jon R. Star, Michigan State University Results 25% of students used CV at least one question on the pretest and posttest. An analysis of the time that students spent solving each problem indicated that students who used the CV strategy spent less time than students who did not use CV. For example, the average time for all CV users was 3 min 41 seconds to solve CV questions on the pretest and posttest, while the average time for non-CV users to solve the same questions was 4 min 53 seconds, a difference that is significant. CV users also used fewer steps to solve each CV problem, on average. While CV users typically solved CV problems using 3-5 steps, non-CV users solved the same problems using 4-7 transformations. In addition, CV users solved CV problems more accurately than students who did not use CV, as shown in Table 1. In sum, our results indicate that the use of CV enabled solvers to solve CV problems quicker, more accurately, and in fewer steps. Table 1 Comparison of CV and Non-CV Students’ Performance on CV Questions Introduction In this research, students’ strategies for solving linear equations were examined. Of particular interest was the strategy referred to as “change of variable” or CV. CV was found when students rewrote terms such as 3(x + 2) + 6(x + 2) as 9(x + 2). There are very few research studies which attempt to understand students’ strategies to solve linear equations (e.g., VanLehn & Ball, 1987). In these studies, researchers pay little attention about students’ practices of CV strategy to solve linear equations and its effects on students’ solution processes which is the focus of this paper. Method 157 students who had completed 6th grade participated in five one-hour problem-solving sessions on linear equation solving. Students were given a pretest and then a short lecture (20 minutes) in which the researcher introduced four different steps for solving equations (adding to both sides of equation, multiplying both sides of the equation by the same constant, distributing, and combining variables or constants) to solve linear equations. In this short lecture, students did not take any information about using CV. After that, students worked to solve a series of linear equations for three one-hour sessions. References VanLehn, K., & Ball, W. (1987). Understanding algebra equation solving strategies (Technical Report PCG-2). Pittsburgh, PA: Dept. of Psychology, Carnegie-Mellon University. Conclusion CV is an example of an innovative strategy for solving linear equations, but it has received little attention in prior research on linear equation solving. This study represents an initial attempt to investigate the prevalence and use of CV among beginning algebra learners. Further research is investigating the knowledge that CV users developed that enabled them to solve CV more accurately and efficiently and how and whether this knowledge might transfer to non-CV problems. Contact Information Jon R. Star, jonstar@msu.edu; Mustafa F. Demir, demirmus@msu.edu. College of Education, Michigan State University, East Lansing, Michigan, 48824. This poster can be downloaded at www.msu.edu/~jonstar.