創意教學活動「四邊形的獵捕」——包含關係的推理

Creative Teaching “Catching the Quadrilaterals”－Reasoning on Inclusion Relation

此教學活動最主要的內容，乃是藉由遊戲競賽的方式，讓國中生在對幾何形狀的特徵與性質分析上，能充分運用數學辨證、推理和溝通的技巧，進而發展「四邊形包含關係」的學習。學習活動的設計理念依據，採用van Hiele 之幾何思考的五個學習階段（five sequential phases of learning）來參酌，並做為課室實際執行的依據。最後，經過研究者對活動歷程的分析發現，透過此遊戲的進行，協助了國一學生釐清對不同四邊形定義、特徵與性質的迷思概念，並主動以非形式推論的方式建構且理解「正方形、長方形、菱形均包含於平行四邊形中」，至於「正方形包含於長方形」、「正方形包含於菱形」與「長方形與菱形共同會包含到的圖形是正方形」的概念，研究者在本文的反思與建議中，亦提出了活動歷程中可採取的機制方法。

The major focus of the teaching activity is, through the model of conducting games, to make the students in junior high school able to analyze the characteristics and quality of geometric shapes with the use of mathematical argument, reasoning and skills of communication, in order to develop the learning of the inclusion relation of quadrilaterals. The notion of the design is based on the five sequential phases of learning by van Hiele, which is also the criteria of conducting the teaching. The researcher finds that with the analysis of the process of activities, the conduction of the games assist junior one students in clearing the misunderstanding of the different definitions, characteristics and qualities of quadrilaterals. Furthermore, it actively constructs and recognizes the notions of ”parallelograms include squars, rectangles and rhombuses”. In the end, the researcher proposes the adoptable organic solution to ”rectangles include squars”, ”rhombuses include squars” and ”squars are the overlapping of rectangles and rhombuses” during the process of activities in the suggestion.