Measures and References: Geometric Reasoning

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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.

Geometry Tasks with Explanation (e.g., Carroll, 1998): Short geometry tasks that elicit reasoning and argumentation through writing, diagrams, and other representations can be used to assess students' understanding and misconceptions of basic geometric properties while giving insight into students' thinking.

KeyMath-3 Diagnostic Assessment (Connolly, 2007): In the geometry subtest, students describe, analyze, and determine the relationship between shapes, and use visualization and formulas to solve geometric problems.


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Booker, G. (2009). Algebraic thinking: Generalising number and geometry to express patterns and properties succinctly. Griffith University Brisbane.

Carroll, W. M. (1998). Middle school students' reasoning about geometric situations. Mathematics Teaching in the Middle School, 3(6), 398-403.

Connolly, A. J. (2007). KeyMath diagnostic assessment (3rd ed.). Minneapolis, MN: Pearson Assessments.

Dehaene, S., Izard, V., Pica, P., & Spelke, E. (2006). Core knowledge of geometry in an Amazonian indigene group. Science, 311(5759), 381-384.

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Huang, H. M. E., & Witz, K. G. (2011). Developing children's conceptual understanding of area measurement: A curriculum and teaching experiment. Learning and Instruction, 21(1), 1-13.

Kaur, H. (2015). Two aspects of young children's thinking about different types of dynamic triangles: Prototypicality and inclusion. ZDM: The International Journal on Mathematics Education, 47(3), 407-420.

Lehrer, R., Kobiela, M., & Weinberg, P. J. (2013). Cultivating inquiry about space in a middle school mathematics classroom. ZDM - International Journal on Mathematics Education, 45(3), 365-376.

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.

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC.

Pittalis, M., & Christou, C. (2010). Types of reasoning in 3D geometry thinking and their relation with spatial ability. Educational Studies in Mathematics, 75, 191-212.

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Tatsuoka, K. K., Corter, J. E., & Tatsuoka, C. (2004). Patterns of diagnosed mathematical content and process skills in TIMMS-R across a sample of 20 countries. American Educational Research Journal, 41(4), 901-926.