臺灣博碩士論文加值系統

實踐開放式教學之研究
─以因倍數題型為例

曾曉馨
國立嘉義大學數學教育研究所
摘　　要

現行的數學教學過分強調算則及程序性知識，與單一解答或單一作法的數學問題，使得學生的思考受限，對數學的理解也有失偏頗，因此，本研究旨在開發因倍數單元的開放式問題，實踐開放式教學，以探討學生解題表現、教師引導討論及學生課後反思的成效。本研究採個案研究法，以立意取樣，挑選六年級學生高中低男女各2名參與研究。
研究發現，開放式教學法，得以幫助教師從多元的切入點引導中低成就學生，而透過高成就學生的解題策略得以幫助低成就學生破除迷思；大部分學生均能啟動後設監控能力與推理能力，並解決具應用性的開放式問題。

The Study of Implementing Open-ended Approach－Exemplar from factor and multiple
Hsiao-hsin Tseng
Graduate Institute of Mathematics Education
National Chiayi University

ABSTRACT
Modern mathematics instruction mainly focuses on the computation ability, the procedural knowledge and the skill for solving single solution mathematical problems. Such notations of teaching and learning not only limit the thinking perspectives of students, but also lead to misconceptions for mathematics. To cope with this problem, this study aims to develop a set of open-ended problems for the “factors and multiples” unit of the mathematics course in elementary schools and to investigate the students’ performance in solving problems, the effectiveness of the discussions guided by teachers, and the quality of the reflections made by the students. The case study approach with purposive sampling is adopted as the methodology of this study. The subjects are two high-achievement, two middle-achievement, and two low-achievement sixth grade students.
From the case study, it was found that the “open-ended approach” was able to assist teachers in guiding the middle-achievement and the low-achievement students from diverse aspects; moreover, it also helped the low-achievement students to resolve miss conceptions in solving mathematics problems with the assistance provided by those high-achievement students. After participating in the learning activities, most of the students’ metacognitive ability and inference ability were promoted, and hence they were capable of solving those open-ended problems.

目次

中文摘要 ……………………………………………………………i

英文摘要 ……………………………………………………………ii

目次 …………………………………………………………………iii

表次 …………………………………………………………………vi

圖次 …………………………………………………………………vii
第一章 緒論
第一節 研究背景與動機 ………………………………………… 1
第二節 研究目的與問題 ………………………………………… 3
第三節 名詞釋義 ………………………………………………… 3
第二章 文獻探討
第一節 開放式教學法 …………………………………………… 5
第二節 因倍數迷思概念之探討 …………………………… 25
第三章 研究方法
第一節 研究架構 ………………………………………………… 29
第二節 研究參與者 ……………………………………………… 31
第三節 開放式教學活動的設計與課堂計劃 …………………… 38
第四節 資料蒐集與分析 ………………………………………… 43
第四章 研究結果與討論
第一節 「合數是否有特例？」實踐結果與分析 …………………47
第二節 「因倍個數知多少？」實踐結果與分析 …………………57
第三節 「因倍互逆我最行！」實踐結果與分析 …………………71
第五章 結論與建議
第一節 結論 ……………………………………………………… 101
第二節 建議 ……………………………………………………… 106
參考文獻
中文部分 ………………………………………………………… 111
西文部份 ………………………………………………………… 113
附錄
附錄一 「合數是否有特例？」教案 …………………………… 117
附錄二 「合數是否有特例？」策略紀錄 ……………………… 122
附錄三 「合數是否有特例？」數字表 ………………………… 123
附錄四 「合數是否有特例？」盤局紀錄 ……………………… 124
附錄五 「合數是否有特例？」課後反思單 …………………… 125
附錄六 「因倍個數知多少？」教案 …………………………… 126
附錄七 「因倍個數知多少？」策略紀錄 ……………………… 132
附錄八 「因倍個數知多少？」數字表 ………………………… 133
附錄九 「因倍個數知多少？」盤局紀錄 ……………………… 134
附錄十 「因倍個數知多少？」選數推測紀錄 ……………………135
附錄十一 「因倍個數知多少？」課後反思單 ……………………137
附錄十三 「因倍互逆我最行！」策略紀錄 ………………………148
附錄十四 「因倍互逆我最行！」數字表 …………………………149
附錄十五 「因倍互逆我最行！」盤局紀錄 ………………………150
附錄十六 「因倍互逆我最行！」課後反思單 ……………………151

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