數學寫作對國中生解方程式應用問題的影響

Abstract

摘 要 本研究的目的是想要瞭解數學寫作活動對國中生解方程式應用問題的成就表現及數學態度的影響，並探討其在解題歷程上的改變。 研究對象為台南地區某公立國中三位不同數學程度的八年級升九年級的學生。研究者對她們進行為期約一個月的數學寫作活動教學，並搭配寫作學習單，以及課後的數學日誌寫作，讓學生逐漸熟悉寫作的各種形式，進而解決方程式應用問題。以放聲思考的方式，收集學生解題歷程的資訊，並以Schoenfeld (1985)的六階段數學解題歷程模式，分析學生在前、後測的解題歷程，再佐以半結構性晤談，來探討學生成就表現、學生解題的想法以及解題歷程的改變，最後再分析情意問卷前、後測的結果，來瞭解學生數學學習態度的改變。 本研究的主要發現如下： 1. 高程度學生的成就表現在前、後測沒有任何差異；中、低程度的學生在後測都有明顯的進步。 2. 三位學生在後測中，花在驗證階段的時間增加。程度較低的學生花在探索階段的時間減少，花在分析和執行階段的時間增加。 3. 三位學生在驗證階段均有明顯的改變(例如增加很多驗證的行為)，程度中、低的學生在分析階段也有明顯改變(例如進行表徵的轉換)，改變後的解題行為有助於求得正確答案。 4. 「解釋性」和「寫一封信」的寫作對解題歷程的執行階段有正向的影響，「長話短說」的寫作對解題歷程的分析階段有正向的影響，「標題寫作」讓學生更加察覺自己的解題歷程，並能時時進行監控，對驗證階段有正向的影響。 5. 寫作活動有助於提升學生學習應用問題的信心、降低學習應用問題時的焦慮；寫作活動也提升了中、高程度的學生學習應用問題的探究動機，卻降低了低程度的學生的探究動機。 6. 參與本研究的學生對這個數學寫作活動，都抱持正向支持的態度，認為進行數學寫作活動有助於數學學習。

關鍵字：方程式應用問題、解題歷程、數學寫作活動Abstract This study aims to understand the influence of mathematical writing activities on junior high school students’ achievement in solving equational word problems and on their mathematics attitude, and also aims to investigate the changes in their problem solving processes. Subjects of this study are three students in some public school in Tainan who have different levels of mathematics. The study is performed in the summer between their eighth- and ninth-grade school year. The researcher engaged the students in mathematical writing activities in her teaching for about a month, accompanied with writing work sheets and mathematical journal writing after class, so they can be familiar with various forms of writing and further solves equational word problems. The researcher collects with the method of thinking-aloud the information during students’ problem solving process, and analyzes the processes in pretest and posttest with Schoenfeld’s (1985) six phases of problem-solving process, and she has semi-structured interviews with the students to investigate the changes in their achievements, in their thinking in problem solving, and in their problem solving processes. Finally the results in the affect questionnaire are analyzed to understand the changes in students’ attitude towards mathematics learning. Following are the main findings of this study. 1. The achievement of the student with the highest level does not vary significantly between pretest and posttest; students with middle and lower levels have significant improvements in posttest. 2. The time all three students spend during verification increases in posttest. The student with lower level spends less time in exploration, and more time in analysis and implementation. 3. There are significant changes by all three students in verification (such as much increased verifying behavior). The students with middle and lower levels have significant changes in analysis (such as performing representation transformations). Their changes of behavior in problem solving helps in finding correct answers. 4. The writing of “explanations” and “letter” have positive influences in the implementation of the problem solving process; the writing of “in-a-nutshell” has positive influences in the analysis of the process; “rubric writing” gives students better awareness of, and helps them monitor, their own problem solving processes, which positively influences verification. 5. Writing activities promotes students’ confidence in learning to solve word problems, reducing their anxieties in doing so; writing activities also promotes the investigation motives of students with middle and highest levels, but reduces those of the student with the lower level. 6. All the students participating in the study have positive and supporting attitude toward this mathematical writing activity, believing it can help mathematics learning.

key words: equational word problem, mathematical writing activity, problem solving process