Measures and References: Mathematical Flexibility

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Numerous measures exist to gain a full picture of a student's learning strengths and challenges. Following are examples of measures used to assess this Learner Factor. These measures should be administered and interpreted by experienced professionals.

Informal Mathematical Flexibility Task: Assesses students' Mathematical Flexibility by asking students to perform mathematical Operations and determining how often the strategy they use is the most appropriate for the given problem


Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A longitudinal study of invention and understanding in children's multidigit addition and subtraction. Journal for Research in Mathematics Education, 29(1), 37-50.

Carr, M., & Taasoobshirazi, G. (2017). Is strategy variability advantageous? It depends on grade and type of strategy. Learning and Individual Differences, 54, 102-108.

Geary, D. C., & Burlingham-Dubree, M. (1989). External validation of the strategy choice model for addition. Journal of Experimental Child Psychology, 47(2), 175-192.

Kilpatrick, J., Swafford, J. O., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.

McMullen, J., Brezovsjy, B., Rodriquez-Aflecht, G., Pongsakdi, N., Hannula-Sormunen, M. M., & Lehtinen, E. (2016). Adaptive number knowledge: Exploring the foundations of adaptivity with whole-number arithmetic. Learning and Individual Differences, 47, 172-181.

Siegler, R. S. (1998). Individual differences in strategy choices: good students, not-so-good students, and perfectionists. Child Development, 59(4), 833-851.

Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and Instruction, 18(6), 565-579.

Torbeyns, J., Verschaffel, L., & Ghesquiere, P. (2006). The development of children's adaptive expertise in the number domain 20 to 100. Cognition and Instruction, 24(4), 439-465.