數學文字題錯誤概念分析及學生建構數學概念的研究

The Analysis of Misconceptions of Mathematics Word-Problem and the Way of Students' Constructing Mathematics Concept

本研究主要目的是以質的研究方法探討學生在數學文字題上所產生錯誤概念，並探究學生如何建構出正確的數學概念。受試為國中二年級55名學生。此項研究採用放聲思考和問題思考法來分析學生解答數學文字題時在語言知識、基模知識、策略知識、及程序性知識等四方面的錯誤概念。研究者並以引導思考教學策略來瞭解學生如何建構出正確的數學概念。

The purposes of this thesis were:(1)to explore the lexical andconceptual representations of Chinese-Englis bilingual university students,namely,to test the'concept-mediation hypothesis'and the'word-association hypothesis';(2)to compare the patterns of lexical and conceptualrepresentations of bilingual university students with differentlevels of English proficiency,namely,to test the'intermediate hypothesis';(3)to compare the'subtraction method'paradigm and the'semantic/associative priming'paradigm in testing the above hypotheses.Twenty English non-proficient subjects participated in experiment 1.They were required to perform in two kinds of tasks:Chinese wordstranslating,pictures naming(in English),and words and pictures categorizing(in Chinese).The subtraction method paradigm was used.The results showed that the reaction time difference between wordstranlating and pictures naming is significantly smaller than that ofwords categorizing and pictures categorizing.These results supportedthe prediction of'word-association hypothesis'.In experiment 2,twenty English proficient subjects were asked toperform in the same tasks as in experiment 1.The results were in linewith those of experiment 1,also supporting the prediction of'word-association hypothesis'.Twenty-four subjects participated in experiment 3,adopting the'semantic/associative priming' paradigm along with lexical decision task.The results showed that the priming effects were not significant whenChinese target words were used.However,the priming effects weresignificant when English words were used as target words.Since'between-language repetition effect'was equal to'within-language semantic/associative priming effect',and both were greater than'between-language semantic/associative priming effect',the predictionof'word-association hypothesis' was again supported.