Promote the Effective of Learning to Solve Multi-Step Problems by Using Distributive Laws of Algebra

• Main Authors: CHIA-LUN LU, 呂佳倫
• Other Authors: JENG-MING YIH
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/46457195949798929786

碩士 === 國立臺中教育大學 === 數學教育學系 === 101 === Algebra theme of mathematical learning is always the hardest course to understand for students. The related contents of algebra themes are fewer in the old version standards of elementary school mathematics curriculum, resulting in it is more difficult for students to connect the curriculum of junior high school. Therefore, the Grade 1-9 Curriculum Guidelines will explain the solving strategies of algebra theme in more detail, such as multiplication for distributive law of addition and subtraction is one subject of them. Learning of the distributive law is the basis for algebra learning of junior high school. In the factorization, distribution methods and radical operation of algebra topics of junior high school, the maturity degree of using the distributive law is a core of learning. If students can be proficient in the problem-solving strategies of the distributive law in elementary mathematics education stage, it can enable them to develop the ability of simple mental arithmetic and have more smooth sense for the internal logic of number, which is called having the good number sense. The feedback of smooth number sense can enhance students’ confidence, and they are not fallible in simplifying the process of calculating problems to facilitate mathematical learning more efficiency and promote learning interest for mathematical learning. A quasi-experiment was conducted in this study, and the participants were 110 fifth grade students in the researcher’s elementary school. They were randomly assigned to an experimental group and a control group before the experiment, and each of them included 30 students and 80 students, respectively. The self-made test of multi-step problems was used as research tools for experimental teaching. Then, the results of the post-test for the multi-step problems were analyzed by using SPSS software. The ANCOVA analysis and independent sample t-test were used to evaluate the effects of experimental teaching. The pre-test of the multi-step problems was conducted before the experimental teaching, and the post-test of the multi-step problems was implemented after the experiment. The learning effects of students for two groups were investigated by using the quantitative analysis. Finally, operating the real-time services system of on-line cognitive diagnostic tests and analysis based on the application of S-P chart theory to distinguish the learning types of students. According to the results of student’s diagnostic analysis chart, the instructor can identify the students who need to be cared and provide them remedial instruction to promote their learning effects. Based on the analysis of experimental data, the findings of this study are shown as follows: 1.After the experimental teaching, there are significant differences for the experimental group and the control group in the post-test results of the multi-step problems, and the results of the experimental group are better than the control group. 2.After the experimental teaching, there are significant differences for the experimental group and the control group in the difference of time of the multi-step problems, and the degree of time shortened of the experimental group is higher than the control group. 3.The analysis of S-P chart with caution index and the chart of student’s diagnostic analysis show the experimental group includes the different learning types. Instructors can achieve the purpose of improving students’ learning types with appropriate instructional aids. The results and findings of this study indicated the problem solving strategies of distributive law can provide available references and recommendations for the fifth grade teachers and students of elementary school in mathematics teaching and learning for future research.