- 學位論文
國中生數學方程式文字題解題困難及迷思概念之研究
A study of misconceptions and the difficulties in solving mathematical equation word problems of junior high school students
摘要
本研究主要目的是探討國三學生在數學方程式文字題的解題困難及分析其迷思概念。研究對象為新竹縣某國中96名國三學生，蒐集資料以兩個階段進行，第一階段以研究者自編之「數學方程式文字題測驗」及「數學方程式文字題解題困難檢核表」進行測驗。第二階段根據紙筆測驗結果挑選具迷思概念代表性學生進行半結構性訪談，分析學生的迷思概念。本研究獲致之結果如下。 一、整體國三學生於方程式文字題中最多人覺得困難的是「解題計畫 及監控」階段及「不知如何列式」。 二、不論數學學業成就高低，「解題計畫及監控」是最多人感到困難 的階段；而在解題困難題項中，不同數學學業成就學生的解題困 難題項不盡相同，中、高數學學業成就學生認為解題困難為「不 知如何列式」，而低數學學業成就學生認為解題困難為「缺乏解 題步驟計畫」。 三、學生在數學方程式文字題解題中四種知識的迷思概念分述如下。 （一）在語言知識的迷思概念有：1.不清楚日常生活的數學相關 用語；2.不了解句中隱而未顯的主詞；3.對字義的錯誤直 譯；4.受題目前後句的銜接而誤判題意；5.對字詞的誤 解；6.不了解假設語句的意思。 （二）在基模知識的迷思概念有：1.倍數關係的迷思；2.因果關 係的迷思；3.無法區分與解題相關的資料；4.未知數數量 的迷思；5.幾何圖形的迷思；6.對等號的迷思。 （三）在策略知識的迷思概念有：1.逆推策略的使用迷思；2.習 慣以算術方式解題；3.假設方式的迷思。 （四）在程序性知識的迷思概念有：1.移項法則的迷思；2.同分 母分式的迷思；3.加減消去法的迷思；4.開平方的迷思； 5.使用括號的迷思。 本研究之研究結果如上所述，期望能對教師個人、學校、教育行政機關及後續研究提出建言，以作為日後課程設計、教學及補救教學之參考。
並列摘要
The main purpose of this research is discusses the difficulty in solving problem and misconception of mathematics equation word problem on the junior high school students. The object of study for 96 third-grade students of one of junior high school of Hsinchu County. The collection material carries on by two stages, the first stage from arranges to carry on the examination for “mathematics equation word problem examination” and “the check-list of the difficulty in solving problem on the mathematics equation word problem” by the researcher. The second stage is according to the written records examination result, and choice to the most representative students of misconception to carry on semi structure interview and analyzes the misconception of students. The research results were as follows： First, the most third-grade students conceived it difficulty in solving problems of mathematics equation word problem in this research are lie in “solution planning and monitoring stage”, and they even “did not know how to arrange the algorithm”. Second, no matter the mathematics studies achievement height, the most students conceived it difficulty in solving problems occurs in “solution planning and monitoring stage”. However, there are different difficulties in solving problems in the topic item between different students of mathematics studies achievement. The height mathematics studies achievement student's difficulty in solving problems is “did not know how to arrange the algorithm”, and the low mathematics studies achievement student's difficulty in solving problems is “lacks the solution step and planning”. Third, the misconceptions of the knowledge in mathematics equation word problem solving are description as follows. A. The misconceptions of linguistic knowledge: 1.Unclear mathematics vocabularies of daily life ;2.Not understood the subject which hidden in the sentence;3.Wrong literal translations of mathematics vocabulary; 4. Misinterpret of the implication of mathematics equation writing topic problem result from ; 5. Antithetical couplet word misunderstanding; 6. Does not understand the supposition sentence meaning. B. The misconceptions of schematic knowledge includes:1. Misconception of multiplier relationships; 2. Misconception of causation relationships;3. Unable to differentiate the information of problem solving ; 4. Misconception of unknowns; 5. Misconception of geometric figures; 6. Misconception of equal sign. C. The misconceptions of Strategic Knowledge includes: 1. Misconception of retroduction ; 2. Custom by arithmetical mode problem solving; 3. Misconception of supposition ways. D. The misconceptions of the procedural knowledge includes:1.Misconception of removal of term; 2. Misconception of the same denominator fraction abbreviate; 3. Misconception of the gaussian elimination method; 4. Misconception of rooting number; 5. Misconception of use parenthesis. According to this research as stated above, researcher expected the conclusion could be helpful in course design, teaching, and the remedial tutoring that some concrete suggestions were offered to teachers, schools, the educational administration, and the future study.