問題題型結構之擬題教學對國小六年級學生分數乘除文字題解題成就之影響

The Influence of Problem-Posing Instruction based on Problem Types Structure toward Sixth-Graders’ Solving Achievement on Word Problems of Multiplication and Divison of Fraction

秦嘉智(Jia-Jhih Cin)

指導教授 ： 楊坤原

中原大學/人文與教育學院/教育研究所/碩士(2012年)

https://doi.org/10.6840/cycu201200155

摘要

本研究旨在探究「問題題型結構之擬題教學法」及「講述為主的教學法」兩種不同教學方式，對學生在分數乘除文字題的解題成就、學習保留、各類題型解題成就、除法顛倒列式等情形之差異，並探討學生對「問題題型結構之擬題教學法」的看法和學習中所遭遇的困難情形。本研究是以量化為主、質性為輔的研究方式，在量化方面，採準實驗研究之不等組前後測設計，以研究者所任教的某國小六年級的一個班級為實驗組，進行問題題型結構之擬題教學，另抽取同年級一個班級作為控制組，進行講述為主的教學，研究者以自編之「數學解題成就測驗前測」與「分數乘除文字題解題成就測驗」兩項量化研究工具，以單因子共變數分析（ANCOVA）、t 檢定、敘述性統計進行量化分析。在質性的部分，針對實驗組學生蒐集其「學習歷程資料」，並抽取8名學生進行半結構式晤談，以瞭解學生對「問題題型結構之擬題教學法」的看法與學習中所遭遇的困難情形。
本研究經由量化與質性資料的分析獲致以下之結果：
一、接受「問題題型結構之擬題教學法」的學生在「分數乘除文 字題的解題成就」後測及其「列式成就」皆顯著優於控制組 學生。
二、接受「問題題型結構之擬題教學法」的學生在「分數乘除文 字題的解題成就」延宕測驗及其「列式成就」之學習保留效 果皆顯著優於控制組學生。
三、接受「問題題型結構之擬題教學法」的學生對整體列式錯誤 率較高的文字題型其解題成就顯著優於控制組學生。
四、接受「問題題型結構之擬題教學法」的學生在正確列式為 「被除數＜除數」時，採用顛倒列式之策略顯著低於控制組 學生。
五、學生肯定「問題題型結構之擬題教學法」在教學策略上的運 用以及對問題的理解與解題有正面的幫助，而學習中所遭遇 的最主要的困難是對題型的分辨不清。

關鍵字

擬題教學 ； 問題結構 ； 分數乘除 ； 解題成就 ； 文字題

並列摘要

This study aims at exploring two kinds of teaching methods, i.e. " problem-posing instruction based on problem types structure" and " lecture-based instruction" in views of students' performance in fraction multiplication and division in text, learning retention, and all kinds of questions and problem solving achievement, division reversed formula in their differences. In addition, it explores students' views on " problem-posing instruction based on problem types structure " and the difficulties encountered on the learning process. This study is conducted mainly by the quantitative research, and supplemented by the qualitative research. At the quantitative aspect, we use ranging group pretest and posttest design of the quasi- experimental study. A sixth grade class taught by the researchers was applied to be the experimental group, carrying out the problem-posing instruction based on problem types structure. Furthermore, another class at the same grade was chosen to be the control group, carrying out the lecture-based instruction, the two quantitative research tools " pre-test of mathematical problem solving achievement test" and "fraction multiplication and division word problems-solving achievement test" designed by the researcher as quantitative research tools, and it also used the ANCOVA analysis , t-test, descriptive statistics to conduct a quantitative analysis. At the part of the qualitative analysis, in view of collection of the "learning process data" of the experimental group students, we chose eight students to conduct semi-structured interviews to understand the students' views on the " problem-posing instruction based on problem types structure " and the difficulties encountered on the learning process.
In this study, both quantitative and qualitative data analyses are used to obtain the following results:
1. At the post-test aspect of the "fraction multiplication and division word problems-solving achievement test" and "formula achievement", students,accepting " problem-posing instruction based on problem types structure ", perform remarkably better than the those students in the control group.
2. At the delay test aspect of the "fraction multiplication and division word problems-solving achievement test" and "formula achievement", students, accepting " problem-posing instruction based on problem types structure ", perform remarkably better than the students in the control group in learning retention effects.
3. At the error rate aspect of the higher overall formula in text question, students, accepting " problem-posing instruction based on problem types structure ", perform remarkably better than those students in the control group in problem-solving achievement.
4. At the division aspect of the dividend an those students in the control group in the application of reversed formulation strategies.
5. In the application of teaching strategies and understanding to questions and problem-solving, students give positive confirmation concerning to help and assistance; however, on the learning process, the main difficulties they encountered are the confusion to the categories of questions.

並列關鍵字

word problems ； problem-posing instruction ； problem structure ； problem-solving achievement ； fraction multiplication and division

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