A central claim of the current reform movement in mathematics education is that students benefit from comparing and contrasting multiple solution methods. Cognitive science research supports the value of using comparison and contrast to promote general learning: identifying similarities and differences in multiple examples has proven to be a critical and fundamental pathway to flexible, transferable knowledge.

However, few experimental studies have been conducted to demonstrate the value of this approach in math classrooms. Research in mathematics education shows the benefits of a variety of practices advocated by reformers, but we don’t know which of these practices are the most effective for student learning.

The team found that comparing and contrasting alternative solution methods led to greater gains in procedural knowledge and flexibility, and comparable gains in conceptual knowledge, as opposed to studying multiple methods sequentially.

• Procedural knowledge: Comparison helped students become better at solving linear equations. This effect was found on problems similar to those in the study packets, and on transfer problems which differed from those the students had already seen.
• Flexibility: The students in the compare group were able to generate multiple solutions to the same problem. These students were also more likely to use the demonstrated shortcuts during the posttest.
• Conceptual knowledge: The compare and sequential groups did not differ in their knowledge of the big ideas of equation solving – such as the concept of equivalence – but students in both groups showed improvements from pretest to posttest.

Further evidence of the benefits of comparison emerged from the process data Star collected. In their written explanations, students in the compare group almost always referenced multiple methods, focused on the solution method, and judged the efficiency or accuracy of the methods. In contrast, those in the sequential groups were much less likely to do so.

By: Danilo B. Gomez | T-II | Orani National High School Tugatog, Orani, Bataan