Comparing and Discussing Multiple Strategies: An Approach to Improving Algebra Instruction

Productive learning of algebra is supported when students reflect on multiple strategies, compare them and discuss the rationale behind and relative merits of particular strategies. Comparison and Discussion of Multiple Strategies (CDMS) is an instructional approach designed to support these processes in math classrooms. In the current study, 16 Algebra I teachers received professional development and supplemental materials to support CDMS when teaching a unit on linear equation solving and 475 of their students completed assessments of their linear equation solving knowledge before and after the unit. Thirteen Algebra I teachers and their 359 students were the business-as-usual control group. CDMS increased how often teachers engaged their students in comparison of multiple strategies, sustained small group work, and sustained mathematical discussions. Students in CDMS classrooms also had higher knowledge of linear equations on the posttest, particularly procedural flexibility, even after controlling for pretest knowledge and school demographic differences. Thus, encouraging teachers to regularly compare and discuss multiple strategies increases students' algebra learning. Findings highlight the need to expand theories of algebra learning to include attention to procedural flexibility, illustrate an instructional theory and method to promote broader learning about algebra, and provide evidence for effective instructional practices.