Measurement concepts such as volume and surface area provide rich contexts for realworld applications of number processes. Despite their importance, many students and prospective teachers show superficial understanding of measurement concepts. A lack of spatial reasoning and integration of geometric knowledge in problem solving situations may be the cause. This study seeks to determine the connection between spatial reasoning and discourse in influencing students' mathematical reasoning in measurement situations. We analysed 118 year 8 to 10 students' responses on two scenarios: (1) manipulation of 3D relations in 2D format and (2) explanation of changes in the volume and surface area of a shoe box after enlargement. The results showed that successful reasoners demonstrated a connected, integrated abstraction between numerical and geometric schemes, leading to success in reasoning about volume and surface area situations.
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.
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