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

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。

The aim of this study was to investigate fifth-and sixth-gradestudents’spatial reasoning performance withorthogonal views ofcubic blocks. The cubic blocks were restricted to a 2 × 2 × 2structure, with no flying ones. Three variables were considered in the study: grades, manipulatives, and tasks. The developed instrument comprisedthree categories of tasks: choosing isometric versusorthogonal views, cube enumeration given abase, and a compatibilitytask. The participants in the studywere 127 fifthgraders and 133 sixthgradersfrom schools in Taipei, divided into two groups. The first group wasassessedusingtangible cubes (manipulatives), and the second group was tested withoutthem. The results of the study were as follows: First,sixthgraders significantlyout-performed fifth graders, but the groupswith 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, studentswereclassified into the following four categoriesbased on their performance: trial-and-error, sequential thinking, coordination, and integration.