多元表徵的結構化數位幾何課程設計對國民中學學生在學習認知、學習成就及學習態度的影響

Abstract

本研究以國中數學第五冊相似形為主題，採用97課綱為指標，將相似形這個主題課程，對其作內容分析，分為若干個最小可教學單元後，組成一個合理的教學順序網絡，稱為課程拓樸。在課程設計與使用形成性評鑑方法發展完成後，再採用準實驗研究法對學習認知、學習成就及學習態度三個變項進行總結性評鑑。 對於每一個最小可教學單元，採重理解的教學設計(UbD)理念來設計教案，以主要問題的型式出發，漸次的完成每一個最小可教學單元，其間並輔以動態數學軟體Geogebra設計的教材展示及操作，以呈現多元表徵的學習環境。若配合教師於教學歷程中的正確引導，除符合van Hiele的幾何學習理論，也能漸進地進入圖形認知理論所述的知覺性理解、操作性理解、構圖性理解、及論述性理解四種理解面向，最終達成97課綱所規範之幾何核心知識的認識及數學邏輯論述的領會等兩個學習目標。 本研究希望能做到，教學成效依賴課程設計的成份大於教師教學經驗的影響，而能因此推展、並普遍化於一般的教學場域中。因此，本課程設計的目的之一，也在於改進傳統教材章節式編排所呈現知識脈絡模糊的缺點。教案將詳述教學者的策略及學習者的狀態，配合學習單的設計及主軸觀念的評量，最後完成整個大概念的建構。 總結性評鑑的結果顯示，在學習認知變項上有顯著成效，對學習成就的影響較小，對學習態度則沒有影響。最後本研究亦提出包含對教材、評鑑方法與工具、實驗教學環境配置及未來研究方向的建議，供教師、研究者與課程設計者參考。

This study selects similar figures which is a major topic of junior-high-school math textbook volume 5 as the subject matter to conduct instructional design. Based on the 97 curriculum standards announced by Taiwanese Ministry of Education, the author analyzed the subject matter and divided the content into several the smallest teachable units to develop a logical teaching-sequence network also called curriculum topology. After completing the instructional design and formative evaluation, the author employed the quasi-experimental approach to conduct the summative evaluation targeting at students’ learning cognition, academic achievement, and learning attitudes. While designing lesson plans of the smallest teachable units, the author adopted concepts of Understanding by Design (UbD) to define essential questions of each unit and incorporated demonstration and operation of dynamic math software Geogebra into instruction to construct a multiple-representation learning environment. Combined with adequate teacher guidance, the instructional design promotes geometric instruction consistent with the geometry learning theory of van Hiele and facilitates students’ figure comprehension including perceptual apprehension, operative apprehension, sequential apprehension, and discursive apprehension. Therefore, this study can contribute to the fulfillment of improving student understanding about core knowledge of geometry and about representation of mathematics logics emphasized in the 97 curriculum standards. The study intends to achieve a purpose that learning outcomes depend more on this instructional design than on teachers’ teaching experiences so the design can be generalized in different teaching contexts. A focus of this instructional design is to eliminate a flaw of sequential content arrangement of traditional math textbooks, and this flaw is the unclearness of contextual presentation of subject-matter knowledge. The lesson plans in this study detail instructional approaches and learner characteristics and, integrating the lesson plans with worksheets and thematic concept assessment, teachers can enhance students’ construction of big ideas. Results of the summative evaluation indicate that this instructional design significantly improve students’ learning cognition, slightly improve their academic achievement but it has no significant influence on students’ learning attitudes. Finally, this study provides teachers, researchers, and instructional designers with suggestions about design of instructional materials, assessment approaches and instruments, about settings of teaching experiments, and about future research.