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.

Flexibility in problem solving (Star & RIttle-Johnson, 2008): Measures students' knowledge of multiple strategies and strategy efficiency in equation solving.


Booth, J. L., & Koedinger, K. R. (2012). Are diagrams always helpful tools? Developmental and individual differences in the effect of presentation format on student problem solving. British Journal of Educational Psychology, 82(3), 492-511.

Brenner, M. E., Brar, T., Durdn, R., Mayer, R. E., Moseley, B., Smith, B. R., & Webb, D. (1995). The role of multiple representations in learning algebra. In Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (17th). Columbus, OH.

Bulgar, S. (2009). A longitudinal study of students' representations for division of fractions. The Math Enthusiast, 6(1), 165-200.

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

Jansen, A. (2006). Seventh graders' motivations for participating in two discussion-oriented mathematics classrooms. The Elementary School Journal, 106(5), 409-428.

Jansen, A. (2012). Developing productive dispositions during small-group work in two sixth-grade mathematics classrooms: Teachers' facilitation efforts and students' self-reported benefits. Middle Grades Research Journal, 7(1), 37-56.

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

Levav-Waynberg, A., & Leikin, R. (2012). The role of multiple solution tasks in developing knowledge and creativity in geometry. Journal of Mathematical Behavior, 31(1), 73-90.

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.

Panaoura, A., Gagatsis, A., Deliyianni, E., & Elia, I. (2009). The structure of students' beliefs about the use of representations and their performance on the learning of fractions. Educational Psychology, 29(6), 713-728.

Robinson, K. M., & Dube, A. K. (2013). Children's additive concepts: Promoting understanding and the role of inhibition. Learning and Individual Differences, 23(1), 101-107.

Schneider, M., Rittle-Johnson, B., & Star, J. R. (2011). Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge. Developmental Psychology, 47(6), 1525-1538.

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

Star, J. R., & Rittle-Johnson, B. (2009). It pays to compare: An experimental study on computational estimation. Journal of Experimental Child Psychology, 102(4), 408-426.

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.

Webb, N. M., Franke, M. L., Ing, M., Wong, J., Fernandez, C. H., Shin, N., & Turrou, A. C. (2014). Engaging with others' mathematical ideas: Interrelationships among student participation, teachers' instructional practices, and learning. International Journal of Educational Research, 63, 79-93.