A Study of the Equality Axioms Instruction on the Sixth-Grade Students

• Main Authors: Fong-mei Ke, 柯鳳梅
• Other Authors: Chi-Tsun Yeh
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/43519060173751633432

碩士 === 國立臺南大學 === 應用數學研究所碩士班 === 100 === The purpose of this study was to investigate how the instruction of equality axioms influenced sixth graders’ performance in problem solving and to evaluate the researcher’s lesson plans. Adopting a nonequivalent pre-test/post-test control design of a quasi-experiment, the research took the homeroom class as the experimental group and conducted an experiment with the self-developed instruction of equality axioms. Another class of sixth graders, the control group, on the other hand, received regular instruction of the designated edition. Research methods, which included a teaching experiment, written tests, semi-structured interviews and statistical power analysis, were applied to collect and analyze data. The results were as follows. 1. Students in the experimental group performed well in written tests. The self-developed instruction pushed stragglers ahead and at the same time helped the high-fliers maintained their level. 2. ANCOVA assumed significant difference in learning effect between the experimental and control groups, so the self-developed instruction may prove effective. 3. Judging from their solving strategies on applications problems in written tests, students of the experimental group not only accepted but made use of the concepts introduced in the self-developed instruction. 4. Experimental group students lost patience with the problem solving strategies of equality axioms. Even though they understood the concepts, they usually neglected the basic arithmetic operations and were quick in solving every problem with one-line formula. Not in the habit of solving problems with algebra, they turned to arithmetic, a strategy they were more familiar with. 5. They tended to miss brackets when making equation. Nor did they have a grasp of the equivalence of equality signs. 6. Sixth graders could not fully understand inverse operations. Teachers would have difficulties explaining the meaning of inverse operations to them, which could only result in more confusion and mistakes in problem solving. 7. Students were slow of reading comprehension. Some were below the general level and showed no interest in math. For those who showed an attitude of indifference, they either gave up answering questions or muddled with their work.