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題名:多元表徵課程對國小四年級學童分數學習成效之實驗研究
作者:王淵智
作者(外文):Iuan-Jyh Wang
校院名稱:國立高雄師範大學
系所名稱:教育學系
指導教授:陳密桃
梁淑坤
學位類別:博士
出版日期:2005
主題關鍵詞:多元表徵課程分數概念分數基模分數解題表現Multiple Representation Curriculum (MRC)Fraction conceptsFraction schemesProblem-solving performance on fractions
原始連結:連回原系統網址new window
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本研究以Behr等人提出之表徵互動系統模式為基礎,設計多元表徵分數課程進行教學實驗以探究其實施成效。所選用之樣本為高雄市市郊一所小學四年級的兩個班級,其中一班 27人為控制組,另一班31人為實驗組,合計58名。兩組學生在教學前施以前測,教學後接受後測,並於三週後接受延宕測驗,以瞭解實驗教學之立即效果及保留效果。實驗組學生並依前測成績排序,選出低、中、高分組各三名,接受教學前及教學後之訪談,以瞭解實驗組不同能力的學生之學習成效。本研究以多變量共變數分析進行量化資料之假設考驗,並利用質性研究的方法進行訪談內容的分析。本研究的主要研究發現如下:
分數多元表徵課程的設計具體可行。以認知心理學中的「表徵」
為基本架構的分數多元表徵課程,能夠引發學生積極參與學習。接受此課程的學童分在數解題表現上也有部分優於一般教材的成效出現。不論是立即效果或保留效果,實驗組在「分數合成與分解」分量表的解題表現均顯著的優於控制組,其他五個分量表的差異則未達統計上的顯著。
數概念發展方面,在分數詞概念的發展顯示出,接受實驗課程的個案,其對於分數詞的認知發展層次有明顯的提昇。其次,在分數的部分整體關係方面,個案在接受教學實驗後,對於分數部分整體關係的口語表徵有所進步,但書寫符號表徵則進步有限。最後,在等值分數概念的發展顯示,接受實驗課程的個案其等值分數概念並沒有明顯的進步。
分數基模發展方面,在等分割基模的發展進步相當明顯,個案
在接受教學實驗後對於「公平」及「耗盡」兩個分割原則能夠清楚掌握。其次,在分數迭代基模的發展上亦有明顯的進步,多數個案能利用真分數找到單位分數,進而迭代出假分數,但對於從假分數找到單位分數迭代出給定分數則仍有困難。至於在遞迴分割基模的發展,則顯示未有明顯的進步。
除上述之主要發現外,根據文獻和本研究之結果,對國小數學教
學、國民小學數學領域課程綱要編修單位及未來研究等三方面提出具
體建議。
A Study on the effects of Multiple Representation Curriculum on
Fraction Number Learning for Fourth Grade Children
Iuan-Jyh Wang
Abstract
The purpose of this study is to investigate effects of Multiple Representation Curriculum (MRC, based on the interactive model for using representational system proposed by Behr’s group) on fraction number learning for fourth grade children. A quasi-experimental design with pretest, posttest, delayed test and interview was adopted. Two fourth grade classes were selected from the suburbs of Kaohsiung City, with a class of 27 children as control group, and the other class of 31 as experimental group. Quantitative analyses included ANCOVA and MANOVA statistical methods for testing hypothesis. For qualitative analyses, 9 cases (three from each of high, medium, and low group) were conducted from experimental group by sorting their pretest scores and conducted interview with them, to evaluate their developments of fractional conceptions and schemes. The findings were as follows:
Development of MRC. It was feasible to apply representation theory of cognitive psychology in the elementary mathematics curriculum development, in order to enhance understanding of children’s fraction learning. In addition, there were only performances of fractional composition and decomposition subscale that were significantly higher than the control group on posttest and delayed tests.
Number Concepts. Children from control group or those who received MRC were performing better in fraction words. In addition, interviews results indicated that children from nine cases were more elaborative in concepts of fraction words and part-whole relation, when compared to prior experimental teaching. However, there was only limited development in equivalent fraction concepts.
Fraction Schemes. The developments of equi-partitioning and iterative fraction schemes of nine cases were facilitated after MRC instruction was applied. Children also understood principles on “fairness” and “exhaustion”. However, there was virtually no major development in recursive partitioning scheme.
Finally, the investigator gave recommendations for teaching, research and administration of curriculum standards.
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