數學建模教學對國三學生數學學習態度、機率迷思概念及機率學習成就之影響

The Effects of Mathematical Modeling Instruction on Learning Attitude, Misconceptions about Probability, and Learning Achievement for 9th Grade Students in Junior High School

林琬婷(Wan-Ting Lin)

指導教授 ： 洪志成

國立中正大學/教育學院/教育學研究所/碩士(2013年)

摘要

我國數學建模教學研究較少運用在國中機率，此一與日常生活關聯之研究。本研究旨在探討實施數學建模教學後， 其數學學習態度、機率迷思概念及機率學習成就是否有影響。本研究參考者以南部者會區較偏遠地區一所國民中學90 位三年級的學生。採質量混合設計。量化部份採不等組前、後測準實驗研究法， 實驗設計分三組： 控制組為低能力學生的傳統教學， 實驗組一為低能力學生的數學建模教學、實驗組二為高能力學生的數學建模教學。研究工具包含：「數學學習態度」、「機率迷思概念」及「機率學習成就」前、後測，並調查「實驗組」學生對於「建模數學教學法融入機率單元學習意見調查表」。本研究資料分析在量化部份，以描述統計、多變量共變數分析、獨立樣本T檢定、成對樣本T檢定、單因子共變數分析、列聯表、皮爾遜積差相關分析及多元逐步迴歸分析等方法進行資料分析。質性部份採忠實描述與「質性」取向編碼。茲將研究結果分述如下：
1 . 接受數學建模教學之低能力學生在數學學習態度的提升高於接受傳統教學之低能力學生， 其中以「數學焦慮」、「數學有用性」、「學習數學過程」是有顯著差異的。
2 . 接受數學建模教學之低能力學生在機率迷思概念的提升高於接受傳統教學之低能力學生， 其中以「正/負時近效應」的迷思概念是有顯著進步的； 接受數學建模教學之高能力學生在機率迷思概念的提升高於低能力學生， 其中以「結果取向」、「等機率偏誤」、「正/負時近效應」、「有效性誘發」及「忽略母群分配」等五類迷思概念是有顯著進步的。
3 . 接受數學建模教學之低能力學生在機率學習成就的提升高於接受傳統教學之低能力學生。
4 . 數學建模教學下，低能力學生在「數學學習成就」（ 過去10 次數學段考平均）、「機率迷思概念第三大類」、「學習數學的信心」、「機率迷思概念第一大類」對機率學習成就具預測力； 高
能力學生在「數學學習成就」（ 過去10 次數學段考平均）、「機率迷思概念第四大類」對機率學習成就具預測力。
5 . 綜 1~4，量化上，建模不但對機率學習成就具預測力，也可以提升數學學習態度、澄清機率迷思概念及提升機率學習成就，並學會模擬真實世界和形成數學模型。
6 . 接受數學建模教學的高/低能力學生皆對數學建模教學大多持正向積極的信念且在建模循環中會主動討論， 並感到有趣、無壓力及獲得成就感。
7 . 建模活動中，能力高者最有印象/有趣/有用皆為競賽型活動，能力低者則是操作性活動
8 . 接受數學建模教學的學生，能將真實生活情境問題，簡化為真實世界模型，再抽象成數學模型，最後計算出數學結果。

關鍵字

迷思概念 ； 學習成就 ； 數學學習態度 ； 機率 ； 數學建模

並列摘要

In the literature, only a few papers of mathematical modeling instruction applied their research topics to probability courses for junior high schools. To make up the gap, this study is to investigate if applying the mathematical modeling instruction to probability courses can significantly improve the effects on learning achievement, learning attitude, and misconceptions about probability. The participants enrolled in this experiment are ninety 9th grade students from a
municipal junior high school located in the remote district of Chiayi City. Based on the endpoints of the study, those students are thus divided into three distinct groups with 27 low-performing students in control group, 30 low-performing students in experimental group #1, and 33 high-performing students in experimental group #2.
The control group receives traditional instruction, while two experimental groups
receive mathematical modeling instruction. The analysis approaches applied in this
study consist of both quantitative and qualitative researches. For quantitative
research, each enrolled student is required to take tests on “learning attitude”,
“learning achievement”, and “misconceptions about probability” prior to receiving any instruction activities and right after the last class of the course. Besides, the opinion and feedback of the “application of mathematics modeling instruction to probability courses” are collected from students in experimental groups only. Thereafter, the descriptive statistics, ANCOVA model, MANCOVA model, independent t-test, paired t-test, Pearson product-moment correlation coefficient, pivot table, and stepwise regression are applied to analyze the collected data. For qualitative research, the faithful description is the main tool for the collected data. The findings of this study are highlighted as follows.
1. Low-performing students who received mathematical modeling instruction have
significant improvement in “learning attitude” than those low-performing
students who received traditional instruction, especially in sub-categories of
“anxiety”, “usefulness”, and “process”.
2. Within low-performing groups, students who received mathematical modeling
instruction have significant improvement in “misconceptions about probability”
than those who received traditional instruction, especially in subcategory
“positive/negative recency effect”. Besides, high-performing students who
received mathematical modeling instruction have significant improvement in
“misconceptions about probability” than those low-performing students who
also received mathematical modeling instruction, especially in subcategories of
“result oriented”, “equiprobability bias”, “positive/negative recency effect”,
“availability heuristic”, and “overlook of population distribution”.
3. For low-performing groups, students who received mathematical modeling
instruction have better performance in the achievement of probability courses
than those who received traditional instruction.
4. For students who received mathematical modeling instruction, the “past
two-year academic performance”, “subcategories 1 and 3 of misconceptions
about probability”, and “beliefs in learning math” are the predictor variables for
low-performing ones, while the “past two-year academic performance” and
“subcategory 4 of misconceptions about probability” are the predictor variables
for high-performing students.
5. Mathematical modeling instruction not only can improve both attitude and
achievement, clarify the misconceptions about probability, and help build up the
model for real world, but also can be used as a predictor variable for the
achievement of probability courses.
6. Both high-performing and low-performing students in experimental groups have
positive beliefs about the mathematical modeling instruction. Besides, they also
spontaneously join the discussion during the modeling cycle, from which they
feel interesting, relax, and fulfillment.
7. Among all the modeling activities, high-performing students like the
competitive type of activities most, while low-performing students like
hands-on activities most.
8. Students who received mathematical modeling instruction is equipped the
ability to simplify the daily life questions from real world followed by transferring those questions into mathematical models, and then obtain the
results.

並列關鍵字

misconceptions about probability ； learning achievement ； probability ； mathematical modeling ； learning attitude toward mathematics

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