Abstract
One of the critical aspects of a mathematics teacher’s work is analysing learners’ mathematical work. Mathematics tasks can prompt the development of different students’ mathematical abilities, and it is of relevance to address the various promoted skills when assessing students’ mathematical work. However, this is a challenging task, given that students’ work is commonly based on procedural knowledge, which is only one of the skills students can work on. Attentive to teachers’ needs to assess students’ learning (summatively and formatively), this chapter uses Kilpatrick J, Swafford J, Findell B, The strands of mathematical proficiency. In: Kilpatrick J, Swafford J, Findell B (eds) Adding it up: helping children learn mathematics [electronic resource]. National Academy Press, Washington, DC, pp 115–155, 2001) model of mathematical proficiency to study examples of students’ work when solving mathematical tasks. From those examples we observe how the five strands of mathematical proficiency are demonstrated by learners as they bring forward various mathematics through their mathematical work. By observing students’ work on mathematical proficiency, teachers are able to acknowledge students’ mathematical abilities, address students’ difficulties, assist students’ knowledge development and, as a consequence, plan and structure their classes and activities focused on students’ needs.
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References
Burkhardt, H., & Swan, M. (2013). Task design for systemic improvement: Principles and frameworks. In C. Margolinas (Ed.), Task design in mathematics education – proceedings of ICMI study 22 (pp. 431–439). Oxford: Springer International Publishing.
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Kilpatrick, J., Swafford, J., & Findell, B. (2001). The strands of mathematical proficiency. In J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Adding it up: Helping children learn mathematics [electronic resource] (pp. 115–155). Washington, DC: National Academy Press.
Swan, M., & Burkhardt, H. (2012). A designer speaks: Designing assessment of performance in mathematics. Educational Designer – Journal of the International Society for Design and Development in Education, 2(5). Retrieved from http://www.educationaldesigner.org/ed/volume2/issue5/article19/
Additional Suggestions for Further Reading
Groth, R. E. (2017). Classroom data analysis with the five strands of mathematical proficiency. The Clearing House: A Journal of Educational Strategies, Issues, and Ideas, 90(3), 103–109.
Suh, J. M. (2007). Tying it all together: Classroom practices that promote mathematical proficiency for all students. Teaching Children Mathematics, 14(3), 163–169.
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Corrêa, P.D. (2018). Observing for Mathematical Proficiency in Secondary Mathematics Education. In: Kajander, A., Holm, J., Chernoff, E. (eds) Teaching and Learning Secondary School Mathematics. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-92390-1_42
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