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Developing reasoning within a geometric learning progression: Implications for curriculum development and classroom practices
Australian Journal of Education ( IF 2.415 ) Pub Date : 2021-08-05 , DOI: 10.1177/00049441211036532
Rebecca Seah 1 , Marj Horne 1
Affiliation  

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.



中文翻译:

在几何学习进程中发展推理:对课程开发和课堂实践的影响

促进推理是数学教育的目标。虽然可以观察到推理行为,但如何表征它们并促进其成长仍然不明确。在本文中,我们报告了我们在起草学习进度和几何思维模型并使用它们来调查澳大利亚学生的几何推理能力方面所做的努力。这些数据来自大规模研究,用于数学推理的发展。Rasch 分析导致绘制了八个思维区域。我们使用混合方法分析了 446 名 7 至 10 名学生对一项要求他们放大徽标、说明其坐标并计算放大面积的任务的回答。对学生解释的深入、细粒度分析揭示了学生用于推理情况的技能和技巧的范围。研究结果表明,更高层次的推理的特点是可视化技能的提高和熟练使用混合媒介来传达意图。讨论了研究结果对课程和课堂实践的影响。

更新日期:2021-08-05
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