| Summary: | 碩士 === 國立中興大學 === 應用數學系所 === 107 === The purpose of the study aims to discuss the mistakes which the seventh-grade students in the Taoyuan City make when solving “Greatest common divisor and least common multiple” problems, specifically to explore the error types and analyze the causes of the errors. We hope to provide teachers with reference that can formulate appropriate teaching strategies, assist their remedial instructions, and improve their teaching skills.
The methods of the study are to use self-designed greatest common divisor and least common multiple tests to investigate and analyze the error types which students have and to interview them to understand their thoughts when they solve the problems in the tests and the cause of errors. The subjects of the study are fifty-nine seventh graders selected from a junior high school in Taoyuan City. The steps of the study are as follows. First, pretest the students. Second, based on the test results, make statistical analysis and modification on the test questions. Finally, let the students take a formal test. The findings of the study are as follows.
1. Error types :
(1) Not fully understand the definition and mathematical style of greatest common divisor and least common multiple.
(2) Not familiar with basic operations.
(3) Guessing answers based on the problems or the messages when solving problems.
(4) Misuse or mixed up formula.
(5) Similar questions are confused or cannot be extended.
(6) Do not understand the meaning of the problems, or misunderstand the meaning of the problems.
(7) Condition not noticed, or mistakes in calculations due to carelessness.
(8) Casually guessing an answer.
(9) Leaving a blank answer.
2. The causes of errors :
(1) Unclear concepts about the definitions, formulas, and terms related to greatest common divisor and least common multiple.
(2) Lacking in prior knowledge which resulted in errors of computation.
(3) Confusion of the characteristics of greatest common divisor and least common multiple.
(4) Disable to do link and inference of common factor and common multiple with greatest common divisor and least common multiple.
(5) Using false concepts or formulas to solve the problems.
(6) Carelessness or negligence.
(7) Insufficient computation or miscalculation.
(8) Mutual interference of old experience and new knowledge.
(9) Misunderstand the meaning of the problem.
(10) Not capable of answering the question due to lack of problem-solving
strategies.
In the end, based on the findings, I make eight suggestions on the teaching of ” greatest common divisor and least common multiple” and four suggestions for future research, which can be provided to prospective educators and researchers as a reference.
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