國小高年級學生在立方積木三視圖的推理表現

Fifth and Sixth Graders' Reasoning Performance with Orthogonal Views of Cubic Blocks

陳韻如(Yun-Zu Chen) ； 楊凱琳(Kai-Lin Yang) ； 林福來(Fou-Lai Lin)

《臺灣數學教育期刊》 5卷1期 (2018/04) Pp. 1-34

https://doi.org/10.6278/tjme.201804_5(1).001

摘要

本研究的目的在了解國小高年級學生在立方積木三視圖的推理表現，並探討年級、操作工具和任務類型對學生解題的影響。本研究中，界定立方積木為限制內嵌於2 × 2 × 2的正方體且不得懸空的立體圖形。研究者自編立方積木三視圖測驗，該測驗包括「視圖與立體圖的對應」、「由底層和視圖計數」和「視圖與視圖的對應」三種分測驗，測驗的目的在以三視圖評估學生空間推理的表現。研究樣本為台北市國小高年級學生：五年級學生127名、六年級學生133名。施測時按操作工具的有無將學生以班級為單位隨機分派為積木操作組和心智想像組。研究結果發現：（1）六年級學生的表現顯著優於五年級學生。而操作工具的有無，學生的作答表現並無顯著差異。（2）「視圖與視圖的對應」顯著較「視圖與立體圖的對應」和「由底層和視圖計數」困難。進一步檢驗不同視圖所造成的影響，發現在積木由堆疊產生的情境下，提供俯視圖有助於學生的推理表現。（3）依據學生三視圖的作答表現，共區分出四種類型：試誤法、序列思考、協調，和整合。

關鍵字

三視圖 ； 方塊計數 ； 空間推理 ； 測驗

並列摘要

The aim of this study was to investigate fifth- and sixth-grade students’ spatial reasoning performance with orthogonal views of cubic blocks. The cubic blocks were restricted to a 2 × 2 × 2 structure, with no flying ones. Three variables were considered in the study: grades, manipulatives, and tasks. The developed instrument comprised three categories of tasks: choosing isometric versus orthogonal views, cube enumeration given a base, and a compatibility task. The participants in the study were 127 fifth graders and 133 sixth graders from schools in Taipei, divided into two groups. The first group was assessed using tangible cubes (manipulatives), and the second group was tested without them. The results of the study were as follows: First, sixth graders significantly out-performed fifth graders, but the groups with and without manipulatives exhibited no significant difference. Second, the compatibility task was significantly more difficult than the other tasks. Further examination of the effects of the different given views proved the benefits of the top view. Finally, students were classified into the following four categories based on their performance: trial-and- error, sequential thinking, coordination, and integration.

並列關鍵字

spatial reasoning ； orthogonal views ； instrument ； cube enumeration

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