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.

Mathematics textbooks sometimes present worked examples as being generated by particular fictitious students (i.e., person-presentation). However, there are indicators that person-presentation of worked examples may harm generalization of the presented strategies to new problems. In the context of comparing and discussing worked examples during extended classroom instruction, the current study compared the impact of person-presentation to strategy labels on students' posttest accuracy and ratings of strategy generalizability. Five algebra teachers and their 168 students used worked examples either presented using fictitious students or with a strategy label during a multiweek unit on equation solving, with teachers randomly assigned to condition. All students compared and discussed the worked examples. In this context, we found no effect of condition on student accuracy at posttest, nor on their ratings of the generalizability of the presented strategies. We discuss why previously found negative effects of person-presentation may not have extended to this context.

The current article focuses on efforts to understand how a basic learning process—comparison—can be harnessed to improve learning, especially mathematics learning in schools. To harness the power of comparison in instruction, we must investigate three core decisions: what, when, and how to compare. Comparing different strategies for solving the same problem or easily confusable problem types is particularly effective for supporting mathematics learning. Comparing examples early in the learning process can be challenging, but delaying comparison can reduce procedural flexibility. Indeed, comparison is resource demanding, so it is more impactful when carefully supported (e.g., side-by-side visual presentation, explanation prompts). To bridge from research to practice, we communicated research findings to teachers and policymakers and developed curricular materials, instructional routines, and professional-development materials to help math teachers leverage these learning processes. We conclude this review with key open questions. (PsycInfo Database Record (c) 2021 APA, all rights reserved)