Spatial visualization and measurement of area: A case study in spatialized mathematics instruction

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematical Behavior Pub Date : 2023-06-01 DOI:10.1016/j.jmathb.2023.101038

Danielle Harris, Tracy Logan, Tom Lowrie

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引用次数: 0

Abstract

The purpose of this study was to explore the influence of spatial visualization skills when students solve area tasks. Spatial visualization is closely related to mathematics achievement, but little is known about how these skills link to task success. We examined middle school students’ representations and solutions to area problems (both non-metric and metric) through qualitative and quantitative task analysis. Task solutions were analyzed as a function of spatial visualization skills and links were made between student solutions on tasks with different goals (i.e., non-metric and metric). Findings suggest that strong spatial visualizers solved the tasks with relative ease, with evidence for conceptual and procedural understanding. By contrast, Low and Average Spatial students more frequently produced errors due to failure to correctly determine linear measurements or apply appropriate formula, despite adequate procedural knowledge. A novel finding was the facilitating role of spatial skills in the link between metric task representation and success in determining a solution. From a teaching and learning perspective, these results highlight the need to connect emergent spatial skills with mathematical content and support students to develop conceptual understanding in parallel with procedural competence.

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面积的空间可视化与测量——以数学空间化教学为例

本研究的目的是探索空间可视化技能对学生解决区域任务的影响。空间可视化与数学成绩密切相关，但人们对这些技能如何与任务成功联系起来知之甚少。我们通过定性和定量任务分析研究了中学生对领域问题（非度量和度量）的表征和解决方案。将任务解决方案作为空间可视化技能的函数进行分析，并在具有不同目标（即非度量和度量）的任务的学生解决方案之间建立联系。研究结果表明，强大的空间可视化工具相对容易地解决了任务，有证据表明可以理解概念和程序。相比之下，尽管有足够的程序知识，但由于未能正确确定线性测量或应用适当的公式，低空间和平均空间学生更频繁地产生错误。一个新的发现是空间技能在度量任务表示和成功确定解决方案之间的联系中的促进作用。从教学和学习的角度来看，这些结果强调了将涌现的空间技能与数学内容联系起来的必要性，并支持学生在培养程序能力的同时发展概念理解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Behavior EDUCATION & EDUCATIONAL RESEARCH-

CiteScore

2.70

自引率

17.60%

发文量

期刊介绍： The Journal of Mathematical Behavior solicits original research on the learning and teaching of mathematics. We are interested especially in basic research, research that aims to clarify, in detail and depth, how mathematical ideas develop in learners. Over three decades, our experience confirms a founding premise of this journal: that mathematical thinking, hence mathematics learning as a social enterprise, is special. It is special because mathematics is special, both logically and psychologically. Logically, through the way that mathematical ideas and methods have been built, refined and organized for centuries across a range of cultures; and psychologically, through the variety of ways people today, in many walks of life, make sense of mathematics, develop it, make it their own.