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 Description of Study

This three-year, NSF-sponsored grant research was completed in 2019, and the grant ended in 2020. Please visit our teacher website for more information about our CDMS routine and/or to download copies of our curriculum materials. You can also find out more information about our study by clicking on the “Reports” and “Resources” dropdown menus (above).

This project refines our hypothesis that productive learning of algebra is supported by reflection on multiple solution strategies through comparison and explanation of the reasons behind the strategies. Existing theories of algebra learning focus on building conceptual knowledge and place less emphasis on how students gain expertise with symbolic strategies. Working with symbolic strategies is essential in algebra learning. Students need to develop procedural flexibility – knowing multiple strategies for solving a problem and selecting the most appropriate strategy for a given problem – and understand the conceptual rationale behind commonly used strategies. Knowledge of strategies (procedural knowledge) supports gains in both procedural flexibility and conceptual knowledge of algebra (Schneider, Star & Rittle-Johnson, 2011). In small-scale studies, redesigning lessons on equation solving to integrate a Compare and Discuss Multiple Strategies (CDMS) approach supported greater procedural knowledge, flexibility and/or conceptual knowledge than completing the lessons without a CDMS approach (Rittle-Johnson & Star, 2007, 2009; Rittle-Johnson, Star, & Durkin, 2009, 2012; Star & Rittle-Johnson, 2009). A preliminary set of supplemental materials to support a CDMS approach across the Algebra I curriculum has been developed, with evidence that classroom teachers can implement the materials with good fidelity (Star, Pollack, et al., 2015).

In the current project, our research team is working directly with teachers to integrate a CDMS approach into their Algebra I classrooms. Building off of our previous work, the goal of this project is to undertake substantial modifications in our curriculum, instructional approach, and teacher professional development, and then to document both the feasible implementation and the efficacy for student learning of our improved CDMS Algebra I supplemental materials.

Over the three years of the project, we will:

  • Year 1 (Development): During Year 1, we will work with a small number of teachers to refine our CDMS supplemental materials, teacher professional development, student assessments and fidelity measure. During this development year, teachers will pilot the modifications to our existing CDMS curriculum with close involvement from the research team.
  • Year 2 (Effects of Treatment vs. Business as Usual): In Year 2, we will evaluate the effects of teachers using our materials versus a “business as usual” control group.
  • Year 3 (Scale-Up): In Year 3, we will scale-up our efforts to determine the effect of our materials versus business as usual. We will also study the quality of implementation and impact on student outcomes after treatment teachers have gained some proficiency with the CDMS approach.

Research Hypotheses

Using both quantitative and qualitative analyses, we will evaluate the hypotheses that:

  1. Classroom teachers can successfully and consistently integrate a CDMS approach in their algebra instruction.
  2. Students’ procedural flexibility, procedural knowledge, and conceptual knowledge for a variety of algebra topics can be reliably assessed, and each type of knowledge is positively related and predictive of one another over time.
  3. Integrating a CDMS approach supports better procedural flexibility, conceptual knowledge, and procedural knowledge for a variety of algebra topics than business as usual instruction.