台北縣國小六年級學生的數學解題方法、對解法可改善性評估與解題信念

A study of sixth grade students’ mathematics problem solving strategies, evaluation of the improvement of problem solving strategies, and beliefs of problem solving in Taipei County

何政松(Cheng-Sung Ho)

指導教授 ： 楊凱琳 ； 楊坤原

中原大學/人文與教育學院/教育研究所/碩士(2008年)

https://doi.org/10.6840/cycu200800479

摘要

摘 要
過去我國的數學教育偏重知識的傳授及演算技能的訓練，以記憶與灌輸的模式教導學生，造成許多學生數學學習的困難與挫折，也可能導致學生具有不同於解題專家的信念。因此，本研究針對台北縣各國小六年級學生進行抽樣調查，以瞭解並探討學生如何評析解法的可改善性，以及探討其與解題行為和解題信念的關係。
正式研究之前，先參考回顧國內外關於解題、解法改善與解題信念的文獻，並整理與歸納出學生常用的數學解題方法與數學解題信念中較重要的特性。依據文獻內容與實際需要編製預試問卷，並抽取100位學生進行預試。針對預試結果加以分析，並做問卷修正後，形成正式問卷。再以「學生解題方法、對解法可改善性認同與解題信念問卷」進行約350位學生的正式施測。問卷回收所得數據經編碼後，採統計軟體SPSS加以分析，結果如下：
一、 本研究發展量表具適切性。
二、 學生最常用的解題方法為建立數學算術式。
三、 以相依樣本單因子變異數分析檢定，得知學生對於隨機試誤或畫圖解法可改善性認同度最高。
四、 採費里曼二因子等級變異數分析，得知大多數學生認為概念的理解與公式皆有其重要性。
五、 用混合設計二因子ANOVA分析不同信念的學生在不同解法上的評估，得知學生的數學解題信念對各種解法可改善性認同度上的看法沒有顯著的影響。

關鍵字

解題信念 ； 解題方法 ； 解法評估

並列摘要

Abstract
Mathematics education in Taiwan over-emphasized the induction of knowledge and training of the calculation technical ability of memory and infusion in the past of mode guidance student. It would cause many students to face the difficulty and frustration in mathematics learning, and also cause the students to have beliefs which are different from the experts’ solution. Therefore, this research carries on sampling to all the six grade students in Taipei County, also inquiring into understanding how students evaluate that if the strategies can be improved, and the relation between the behavior and the beliefs of solution reach agreement.
Before forma study, first make reference to look back a domestic and international concerning solution and solve strategies improvement and solution the cultural heritage of the beliefs, and tidy up and induce students’ common use of mathematics solution of more important characteristic in strategies and mathematics solution beliefs. Draw up to prepare to try a questionnaire according to the cultural heritage content and the effective demand again, and sample 100 students to carry on preparing to try. After aiming at to prepare to try a result to take in to analyze, and doing questionnaire correction, it comes a formal questionnaire. Carry on a formal testing of about 350 students by "The questionnaire of students’ solution strategies, evaluation of solution strategies, and beliefs of solution ".The income data of the questionnaire recovery after coding adopt to statistics software SPSS to take into analysis . Result as follows:
First, this research development meter has appropriateness.
Second, student most commonly used problem solving strategies for establishment mathematics arithmetic type.
Third, by ANOVA, we knew the student regarding stochastically tries by mistake or the painting solution may improvement approval be highest.
Fourth, picks Friedman two-way ANOVA, we knew the majority student thought the concept the understanding and the formula all have its importance.
Fifth, student's in different solution appraisal which analyzes the different faith with mix design two-ways ANOVA, we knew student's mathematics problem solving faith may the improvement approval on view not reveal to each kind of solution the influence.

並列關鍵字

Evaluation of solution strategies ； Beliefs of solution ； Solution strategies

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