An exploration of successful students' Problem solving

Jon R. Star

University of Michigan

jonstar@umich.edu

This paper reports the results of a study that explored student solving behavior in the area of linear equation solving. The study seeks to develop better theory, from a procedural perspective, of why some students develop rote knowledge of algorithms while others seem to be able to execute procedures "with understanding."

Ten 7th grade students (50% male) from a large public middle school were recruited to participate. Students (as a group) were given a 15-minute "benchmark" lesson on the basic operators of linear equation solving. Following this initial lesson, each student met individually with a researcher, once a week for four weeks, with each session lasting approximately 30 minutes. Students were given a progression of several types of tasks, including a total of 25 equations to be solved (e.g., two-step problem such as 2x+1=11, progressing to more complicated problems such as 2(x+1)+6(x+3)+5x=4(x+8)+3x). During each session, students were first asked to verbally describe or plan all steps needed to complete each problem. After planning was completed, students completed each problem in writing.

In a close analysis of the videotaped problem-solving sessions, I identified three dimensions of differences among the successful solvers: ability to plan to the solution, language used to refer to operators in planning, and ability to solve in multiple orderings of steps. These results offer preliminary support for the hypothesis that solvers with rote knowledge of equation solving procedures are less likely to show advanced ability in these three dimensions than solvers who are competent.