研究生: |
陳慶芳 CHEN ,CHING-FAN |
---|---|
論文名稱: |
國中生初學正負數加減運算的解題情形 |
指導教授: |
謝豐瑞
Hsieh, Feng-Jui |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
畢業學年度: | 87 |
語文別: | 中文 |
論文頁數: | 182 |
中文關鍵詞: | 國中 、負數 、加減運算 、概念表徵 、比喻 、數學教育 |
英文關鍵詞: | Junior High School, Negative Number, Addition and Subtraction, Conceptual representation, Metaphor, Mathematical Education |
論文種類: | 學術論文 |
相關次數: | 點閱:324 下載:0 |
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本研究的目的主要在探討學生對不同題目結構之正負數加減運算的解題困難,並進一步分析學生的解題策略及思維;而欲探討的策略及分析的思維含規則與符號法則的運用、比喻的運用、概念表徵的運用等,除此,再將學生所自然浮現的策略和思維加以探討。
研究方法主要是量的研究輔以質的分析,根據上述的研究目的,本研究以初學正負數加減運算的國一學生共1756名為研究對象,樣本遍及14個縣市26所學校。研究工具有二:其一為紙筆測驗卷,藉以探討題型、前後數字關係、進退位、位數及括號等變因對正負數加減運算困難度的影響;其二為半結構性晤談綱要,藉以收集解題策略與思維現象。因此,本研究先進行大規模紙筆測驗,再挑選較具代表性,程度上、中、下均有的學生共31位進行半結構性晤談。
本研究的主要結果有下列幾點:(一)題型、前後數字關係、進退位及位數等變因均會影響正負數加減運算的困難度(p<0.05)。(二)減法題的難度平均高於加法題(p<0.01),各題型的困難度由高到低排列依序為
負-正、負-負、正-負、負+負、負+正、正+負、正-正;而除了負+負和正-負間的困難度未達統計上的顯著差異外,其餘各題型間的困難度均達到統計上的顯著差異(p<0.05)。(三)括號中有無包含運算符號,括號的位置、層數及區分二數之符號為加或減等變因均對正負數加減運算的困難度造成影響(p<0.01)。(四)部分學生在解正負數加減運算時,較常出現的解題思維及策略有:套用符號法則、使用規則、強制性加法、強制性減法、絕對值大的數減絕對值小的數、概念表徵、比喻、去括號、負號提出來再加括號、把負號照抄下來或留下來、答案保留式子中絕對值大的數之符號、括號先算等等;同時也發現部分學生在同一種題型中的解題策略切換頻繁,甚至毫無邏輯或規則可循。
最後本研究依據所發現的結果,分別針對教師教學及教材編寫方面提出建議,同時也為後續研究提供可行的方向。
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