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本研究旨在探索國小教師運用「學習軌道」(learning trajectories,LTs)當成教學工具,比較其學習LTs 前後對課程資源的運用情形?研究問題包含「周長與面積」單元有關教學目標的設定?「周長與面積」LTs 的臆測與數學概念分析?對學習的作業做何種調整的行動?運用何種表徵協助學生學習?如何對學生數學解題的策略進行解釋?研究對象為臺灣中部某公立小學之A 師,採質性描述方式進行探討,分析的資料來自訪談教師之文稿與省思日記。研究發現教師於LTs 學習前之目標設定強調以計算能力培養之課程內容取向,對學生學習軌道之臆測以長方形周長與面積公式之計算應用為主,學習LTs 後則以實測與圖形要素關係理解之學生思考作為導向,學習軌道路徑為:測量與計算線段的長度→理解長方形圖形構成的要素→理解長方形周長公式並應用解題→理解1 平方公分代表的意義→理解長方形圖形面積構成的要素→理解長方形面積公式並應用解題。研究結果對於教師「如何」進行課程資源運用,與教師進行的課程資運運用內容是「什麼」,提供明確、成功的範例。
The objective of this study was to explore whether elementaryschool teachers use course materials in a different manner afterlearning how to use learning trajectories (LTs). The researchquestions concern the setting of teaching objectives for the unit ofperimeter and area in mathematics, the speculations and analysis ofmathematical concepts with regard to the LTs of perimeter and area,adjustments in learning assignments, the use of representation toassist students and the means of explaining problem-solvingstrategies to students. The subject of this study was a teacher servingat a public elementary school in Central Taiwan. We adopted aqualitative approach in analyzing data from interviews with theteacher and the reflections in the teacher’s journal. The findingsindicate that before the teacher learned how to use LTs, the learningobjectives were focused on strengthening the arithmetic of thestudents, and the speculation of student LTs primarily involvedcalculating and applying the formulas for the perimeter and area ofrectangles. However, after learning how to use LTs, the focus shiftedto gauging student understanding on the relationship among shapeelements. The LT was therefore modified to the following procedure:measuring and calculating the length of segments, understanding theelements composing rectangle shapes, understanding the perimeterformula of rectangles and how to use it in problem solving,understanding the meaning of 1 square centimeter, understanding theelements composing the area of rectangle shapes, and understandingthe area formula of rectangles and how to use it in problem solving.The results of this study provide a clear and successful example ofhow a teacher employs curriculum materials and what theemployment includes.
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