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

張景媛(Ching-Yuan Chang)

《教育心理學報》 27期 (1994/06) Pp. 175-200

https://doi.org/10.6251/BEP.19940601.7

摘要

The purposes of the study were to investigate students' misconceptions in dealing with mathematics word problems with the use of qualitative analysis, and further to explore the ways in which the students construct correct mathematical concept. The study was related to qualitate analysis inolving thinking-aloud and thinking-by-questioning methods. The subjects chosen consisted of 90 eighth-grade students. The study intended to analyze the students' misconceptions of linguistic knowledge, schematic knowledge, strategic knowledge, and procedural knowledge in solving mathematics word problems. In addition, it also investigated how the students taught by thinking-by-guiding strategies form their correct mathematical concept.

關鍵字

數學文字題 ； 錯誤概念 ； 語言知識 ； 基模知識 ； 策略知識 ； 程序性知識 ； 放聲思考

並列摘要

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.

並列關鍵字

mathematics wrod-problem ； misconception ； linguistic knowledge ； schematic knowledge ； strategic knowledge ； procedural knowledge ； thinking-aloud