| Summary: | 碩士 === 國立臺南大學 === 應用數學研究所碩士班 === 100 === The purpose of the study was to aim at the problem-solving performance in multiplications of fractional questions of the fourth graders in different question representations (written symbols v.s. static pictures), different meanings of fractions (continuous v.s. discrete), and different types of multiplication(equal-group v.s. multiplicative comparison v.s. rectangular area). Besides, the researcher analyzed the significant interaction effects of different question representations and different meanings of fractions involving multiplications.
A survey was used as the research method. The study was done on 4 classes of fourth graders of an elementary school in Xinshi Distriction in Tainan City. The researcher chose 118 fourth graders from this school. After completing the self-developed questionnaire, “Multiplications of Fractional Questions” in different topics representations, the researcher applied SPSS 19.0 to analyze the data and report descriptive statistics, t-test, one-way analysis of variance, and two-way analysis of variance. The result of the study was in the following：
1. (1) In the representations of written symbols, the performance in solving problems of the students was better than those in the model of continuous quantity than in the model of discrete quantity. The interior difference of the continuous quantity was smaller than discrete quantity. (2) In the representations of static pictures, the students’ performance in the model of continuous quantity was superior to those in the model of discrete quantity. The interior difference of the continuous quantity was smaller than discrete quantity.
2. The representations performance of the students was significantly better in written symbols than in static pictures in multiplications of fractional questions.
3. The students’ performances were much better in the model of continuous quantity than in the model of discrete quantity in multiplications of fractional questions.
4. As a whole, the result of the representations performance of the students in multiplications of fractional questions was that multiplicative comparison was the best, equal-group was the second and rectangular area was the worst. There was significant difference among different types of multiplications: (1) There was significant difference between the model of multiplicative comparison and that of equal-group in the students’ performance in multiplications of fractional questions. (2) There was significant difference in the model of multiplicative comparison and that of rectangular area in the performance of the students in multiplications of fractional questions.
5. There were no significant interactions between different question representations and different meanings of fractions.
|
|---|
