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Developing reasoning within a geometric learning progression: Implications for curriculum development and classroom practices

Developing reasoning within a geometric learning progression: Implications for curriculum... Promoting reasoning is the goal of mathematics education. While reasoning behaviours can be observed, how to characterise them and nurture their growth remains ambiguous. In this article, we report our effort in drafting a learning progression and geometric thinking model and using them to investigate Australian students’ geometric reasoning abilities. The data were taken from a large-scale study into the development of mathematical reasoning. Rasch analysis resulted in eight thinking zones being charted. Using a mixed method, we analysed 446 Year 7 to 10 students’ responses on a task that requires them to enlarge a logo, state its coordinates and calculate the enlarged area. In-depth, fine-grained analysis of students’ explanations revealed the range of skills and techniques students used to reason about the situation. The findings suggest that higher level reasoning was characterised by evidence of increased visualisation skills and proficient use of mixed mediums to communicate intent. The implications of the findings for curriculum and classroom practice are discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Australian Journal of Education SAGE

Developing reasoning within a geometric learning progression: Implications for curriculum development and classroom practices

Australian Journal of Education , Volume OnlineFirst: 1 – Jan 1, 2021

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Publisher
SAGE
Copyright
© Australian Council for Educational Research 2021
ISSN
0004-9441
eISSN
2050-5884
DOI
10.1177/00049441211036532
Publisher site
See Article on Publisher Site

Abstract

Promoting reasoning is the goal of mathematics education. While reasoning behaviours can be observed, how to characterise them and nurture their growth remains ambiguous. In this article, we report our effort in drafting a learning progression and geometric thinking model and using them to investigate Australian students’ geometric reasoning abilities. The data were taken from a large-scale study into the development of mathematical reasoning. Rasch analysis resulted in eight thinking zones being charted. Using a mixed method, we analysed 446 Year 7 to 10 students’ responses on a task that requires them to enlarge a logo, state its coordinates and calculate the enlarged area. In-depth, fine-grained analysis of students’ explanations revealed the range of skills and techniques students used to reason about the situation. The findings suggest that higher level reasoning was characterised by evidence of increased visualisation skills and proficient use of mixed mediums to communicate intent. The implications of the findings for curriculum and classroom practice are discussed.

Journal

Australian Journal of EducationSAGE

Published: Jan 1, 2021

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