國小教師對周長與面積單元課程資源運用之研究

A STUDY ON HOW AN ELEMENTARY SCHOOL TEACHER USES CURRICULUM MATERIALS TO TEACH PERIMETER AND AREA

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 elementary school teachers use course materials in a different manner after learning how to use learning trajectories (LTs). The research questions concern the setting of teaching objectives for the unit of perimeter and area in mathematics, the speculations and analysis of mathematical concepts with regard to the LTs of perimeter and area, adjustments in learning assignments, the use of representation to assist students and the means of explaining problem-solving strategies to students. The subject of this study was a teacher serving at a public elementary school in Central Taiwan. We adopted a qualitative approach in analyzing data from interviews with the teacher and the reflections in the teacher's journal. The findings indicate that before the teacher learned how to use LTs, the learning objectives were focused on strengthening the arithmetic of the students, and the speculation of student LTs primarily involved calculating and applying the formulas for the perimeter and area of rectangles. However, after learning how to use LTs, the focus shifted to gauging student understanding on the relationship among shape elements. The LT was therefore modified to the following procedure: measuring and calculating the length of segments, understanding the elements composing rectangle shapes, understanding the perimeter formula of rectangles and how to use it in problem solving, understanding the meaning of 1 square centimeter, understanding the elements composing the area of rectangle shapes, and understanding the area formula of rectangles and how to use it in problem solving. The results of this study provide a clear and successful example of how a teacher employs curriculum materials and what the employment includes.