Three-domain taxonomy of algebra learning outcomes: conceptual knowledge, procedural knowledge, and procedural flexibility¶

Theory · All theories
Evidence · 3 claims (3 for) · 1 study (1 review), q2 · 0 of 1 report an effect size · 3 claims rest on one study

Description¶

The guide organizes the knowledge and skills algebra students are expected to master into three outcome domains used to classify study results. As printed, "the different types of knowledge and skills that algebra students are expected to master are classified into three domains: conceptual knowledge, procedural knowledge, and procedural flexibility." Conceptual knowledge covers understanding algebraic ideas, operations, procedures, and notation; procedural knowledge covers choosing and applying operations and procedures to reach correct solutions; procedural flexibility covers identifying and implementing multiple methods and choosing the most appropriate one. The guide uses these domains to report which recommendations have evidence in which outcome area.

Design Implications¶

Context¶

Requirements¶

• Outcomes from studies must be classified into the three domains using the definitions and sample items in the guide's Appendix D

Constraints¶

• The guide notes some recommendations are more effective in certain domains than others, so domain-level effects are not uniform across recommendations

Target Learners¶

• Students learning algebra in grades 6-12

Target Learning Objectives¶

• Conceptual knowledge of algebraic ideas and notation
• Procedural knowledge of choosing and applying algebra procedures
• Procedural flexibility in using multiple solution methods

Claims¶

• Alternative Strategies Most Effective For Procedural Flexibility [+M]
• Teaching reflective questioning or using graphical representations improves procedural and conceptual knowledge across diverse populations [+W]
• Studying solved problems improves algebra achievement compared to solving practice problems alone, though the evidence base is rated minimal and one study found negative effects [+W]

Related Theories¶

• Bloom's Taxonomy
• Bloom's Taxonomy cognitive domain as a six-level framework for classifying examination questions

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