Bethany Rittle-Johnson, Vanderbilt University
Jon Star, Michigan State University
Howard Glasser, Michigan State University
Kosze Lee, Michigan State University
Abstract: Encouraging students to share and compare solution methods is a key component of reform efforts in mathematics (e.g. NCTM, 2000), but experimental studies that more conclusively demonstrate the benefits of sharing and comparing ideas for student learning are largely absent. In this study, we experimentally evaluated a potentially pivotal component of this instructional approach that is supported by basic research in cognitive science: the value of students comparing multiple solution methods. Seventy seventh-grade students were randomly assigned to learn about early algebra by either 1) comparing and contrasting alternative solution methods (i.e. contrasting cases) or 2) reflecting on the same solution methods one at a time. All students worked with a partner in their regular mathematics classrooms to study and explain worked examples to algebra equations such as 2(x - 3) = 8. Students in the compare group were more accurate and more flexible in their problem solving, and showed comparable gains in conceptual knowledge. In particular, comparison seemed to facilitate attention to and adoption of non-conventional methods.
These findings provide direct empirical support for a common component of reform mathematics teaching. Simple exposure to multiple ways does not maximize learning, underscoring concerns that some teachers' attempts to implement reform pedagogy have resulted in simple "show-and-tell" of student methods without discussion or comparison of the methods. Future research will extend this work to a new task (computational estimation) and to use of teacher-led discussion. Overall, it seems to pay to compare.