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題 名 | 小學生因、倍數問題之解題表現研究=Elementary School Students' Algebraic Strategies for Solving Number Theory Problems |
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作 者 | 陳嘉皇; | 書刊名 | 高雄師大學報. 自然科學與科技類 |
卷 期 | 36 2014.06[民103.06] |
頁 次 | 頁71-90 |
分類號 | 523.32 |
關鍵詞 | 可除性; 質因數分解; 數論; Divisibility; Prime factorization; Number theory; |
語 文 | 中文(Chinese) |
中文摘要 | 本研究旨在透過因數、倍數問題,探索國小六年級學生對可除性與整數乘除互逆概念理解的情形,並分析產出的策略表現,理解學生之數學思考,以促進數學學習的成效。樣本為台灣南部某國小六年級學生33人。研究資料來自學生對作者設計問題的思考與產出之策略,範圍包含教學現場所做的田野札記、教學歷程師生互動的對話、學生作業等。資料分析則根據問題解題之連結、推理與檢驗各階段產出的策略,進行編碼與文字稿轉譯,採用質性方法加以詮釋,編碼。研究發現:一、大部分六年級學生具有因數、倍數、質數和質因數分解的概念,但在解題行動上的應用仍顯困難;二、學生在「找出100以內之質數」問題採取嘗試錯誤、因數分解、概念整合等策略;在「總共有幾個因數?」問題運用逐次試誤、因數分解、概念整合與演繹思考等策略協助解題行動。整合學生解題表現及其困難之處,研究者建議因、倍數問題的教學,可運用多元表徵方式、強調乘除互逆推理與強化質因數分解能力做為重點,以提升學生數學推理的表現。 |
英文摘要 | This study aims to reevaluate students' understanding of number theory, including their understanding of divisibility and multiplication structure of whole numbers. In addition, this study intends to analyze and describe students' mathematical thinking and strategies, and integrate the key findings in teaching number theory to enhance students' ability to solve mathematical problems through the process by which they learn. Thirty-three sixth-grade students completed two problems specifying concepts on number theory. The data collected were analyzed using a qualitative approach of exploring the students' mathematical thinking and strategies in implementing number theory problems. Two major results were obtained: 1) Most of the students understand the number theory concepts but have difficulty in implementing the generalized action; and 2) Students use different strategies, including trial and error, factoring, and combined conceptions to solve number theory problems. These findings can support teachers in successfully engaging students to learn number theory concepts by demonstrating how instruction can be conducted to improve students' algebraic reasoning. |
本系統中英文摘要資訊取自各篇刊載內容。