Teach students to intentionally choose from alternative algebraic strategies when solving problems, after they have procedural fluency¶

Strategy · All strategies
Evidence · no claims cited

Description¶

This strategy has students recognize and generate multiple solution strategies, articulate the reasoning and mathematical validity behind their strategy choice, and evaluate and compare different strategies for the same problem. The guide sequences it deliberately: "the practices proposed in Recom- mendation 3 are most effective if they are implemented once students have some fluency with algebra procedures and strate- gies." Classroom moves include reflective questions for selecting strategies, prompts to articulate reasoning, sample student dialogues comparing two strategies, and small-group comparison activities.

Design Implications¶

Context¶

Requirements¶

• Students should already have some fluency with algebra procedures and strategies before the recommendation's practices are introduced

Constraints¶

• The guide rates the evidence Minimal, and its supporting evidence indicates the practices are most effective for procedural flexibility rather than for conceptual or procedural knowledge

Target Learners¶

• Students learning algebra in grades 6-12 who have some fluency with algebra procedures

Target Learning Goals¶

• Procedural flexibility in choosing among solution strategies
• Articulating mathematical reasoning behind strategy choices

Related Strategies¶

• Repertoire of Strategies
• Comparing Multiple Solution Methods
• Reasoning-Focused Instruction
• De-emphasize Answers, Emphasize Reasoning
• Have learners develop their own problem-solving templates instead of replicating instructor templates

Examples¶

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Key Sources¶

• Star, J. R., Caronongan, P., Foegen, A., Furgeson, J., Keating, B., Larson, M. R., Lyskawa, J., McCallum, W. G., Porath, J., & Zbiek, R. M. (2015). Teaching strategies for improving algebra knowledge in middle and high school students (NCEE 2015-4010). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. https://ies.ed.gov/ncee/wwc/PracticeGuide/20