Measures and References: Geometric Reasoning

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Measures

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.

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.

References

Arıcı, S., & Aslan-Tutak, F. (2015). The effect of origami-based instruction on spatial visualization, geometry achievement, and geometric reasoning. International Journal of Science and Mathematics Education, 13(1), 179-200.

Beery, K. E., Buktenica, N. A., & Beery, N. A. (2010). The Beery-Buktenica developmental test of visual-motor integration: Administration, scoring, and teaching manual (6th ed.). Minneapolis, MN: NSC Pearson.

Boakes, N. J. (2009). Origami instruction in the middle school mathematics classroom: Its impact on spatial visualization and geometry knowledge of students. RMLE Online, 32(7), 1-12.

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

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.

DeJarnette, A. F., Walczak, M., & Gonzalez, G. (2014). Students' concepts- and theorems-in-action on a novel task about similarity. School Sciences and Mathematics, 114(8), 405-414.

Dindyal, J. (2004). Algebraic thinking in geometry at high school level: Students' use of variables and unknowns. In 27th Annual Conference of the Mathematics Education Research Group of Australasia Incorporated (MERGA 2004) on "Mathematics Education for the Third Millennium, Towards 2010", (pp. 183-190)

Dvora, T., & Dreyfus, T. (2004). Unjustified assumptions based on diagrams in geometry. International Group for the Psychology of Mathematics Education.

Fitrianna, A. Y., Dinia, S., Mayasari, M., & Nurhafifah, A. Y. (2018). Mathematical representation ability of senior high school students: An evaluation from students' mathematical disposition. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 3(1), 46-56.

Fujita, T., Kondo, Y., Kumakura, H., & Kunimune, S. (2017). Students' geometric thinking with cube representations: Assessment framework and empirical evidence. The Journal of Mathematical Behavior, 46, 96-111.

Gal, H., & Linchevski, L. (2010). To see or not to see: Analyzing difficulties in geometry from the perspective of visual perception. Educational Studies in Mathematics, 74(2), 163-183.

Keller, J. (2002). Blatant stereotype threat and women's math performance: Self-handicapping as a strategic means to cope with obtrusive negative performance expectations. Sex Roles, 47(3-4), 193-198.

Kyttala, M., & Lehto, J. E. (2008). Some factors underlying mathematical performance: The role of visuospatial working memory and non-verbal intelligence. European Journal of Psychology Education, 23(1), 77-94.

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.

Mabotja, S., Chuene, K., Maoto, S., & Kibirige, I. (2018). Tracking Grade 10 learners' geometric reasoning through folding back. Pythagoras, 39(1), 1-10

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(_2), 191-212.

Santos, L., & Semana, S. (2015). Developing mathematics written communication through expository writing supported by assessment strategies. Educational Studies in Mathematics, 88(1), 65-87.

Sinclair, N., & Bruce, C. D. (2015). New opportunities in geometry education at the primary school. ZDM: The International Journal on Mathematics Education, 47(3), 319-329.

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.

Yang, K. L. (2012). Structures of cognitive and metacognitive reading strategy use for reading comprehension of geometry proof. Educational Studies in Mathematics, 80(3), 307-326.