數學教學轉化之探討——以一位有經驗教師之面積初步概念教學為例

An Exploration of Instructional Transformation of Mathematics Teaching: Teaching Basic Concepts of Area Measurement

本研究根據有效的數學教學之理論，探討一位有經驗教師的圖形大小比較教學案例，分析教師如何使用教科書、數學布題、教學表徵與工具，以及學生解題討論的活動方式，處理教學轉化。研究發現：從樣本教師的數學布題可觀察其課程調整，且教師使用多種來源提供布題，包含：一、自編教學問題且延展教材內容，但是教科書單元設定的學習目標仍為重要的參考來源。二、學生在教學歷程中的學習反應與討論解題表現等形成性評量訊息。口語布題與說明、提供釘板、小白積木、平方公分板等教具操作，以及投影設備，是教師使用以輔助面積教學的表徵與工具。從樣本教師的自編問題，企圖連結學生數學想法與澄清迷失概念的問題提問等師生討論互動，可見其轉化處理。由課程實施中的教學轉化分析，可發現教師的數學學科知識及數學教學內容知識為其轉化處理的重要基礎。

This study examines aspects of instructional transformation based on theories of effective mathematics teaching and a video-taped lesson demonstrated by an experienced teacher for teaching basic concepts of area measurement. These aspects included the use of textbooks, problem posing, the use of instructional representations and aids, and approaches for engaging students in discussion. The findings suggest that the teacher tended to pose problems, which represented curriculum adaptation and tailoring to some extent, by referring to multiple sources. The sources included: a. Problems that the teacher invented coupled with extended materials closely related to learning goals set by the textbook. b. Student problem-solving performance evaluated from formative assessments. The teacher employed instructional representations and aids, verbal language for problem posing, manipulatives (geoboards, 1 cm3 cubes, and grids), and project-equipment. The mathematics problems discussed for the lesson exhibited the instructional transformation, including the math problems and sub-questions used in an attempt to connect with mathematical thinking of students and to clarify any misconceptions. These aspects aforementioned seemed to connect with the teacher’s subject matter knowledge of mathematics and pedagogical content knowledge of mathematics.