| Summary: | 碩士 === 中興大學 === 應用數學系所 === 103 === The purpose of the study aims to discuss the error types of Planes in Space sections of high students with different academic performance and to analyze the cause of the errors when they solve the plane problems, hoping to provide teachers with reference that can assist their remedial instructions and improve their teaching skills.
The methods of the study are to use self-designed Planes in Space tests to investigate and analyze the error types which students have with the calculation process on the test papers. To understand their thoughts when they solve the questions on the tests and the cause of errors, the subjects are seventy sophomores of certain private high school in Taichung City. The researcher drew 70 samples from three groups of students with high, middle, and low academic performance. The research procedure is the following: First, conduct the test in advance. Second, analyze and revise the questions according to the result. Finally, conduct the test officially. Based on the results, we can find that the error types and the cause of errors of answering the questions are the following:
1. Error types:
(1) misunderstanding about the planes and lines in space.
(2) errors in algebraic calculations.
(3) errors in cross product of the vecyors calculations.
(4) errors because of carelessness in understanding questions,writing the wrong numbers, or reading numbers.
(5) guessing answers based on the problems or the messages when solving problems.
(6) formula mistakes or the errors of using improper formulas.
(7) errors in misjudgement of angles.
(8) errors in misjudgement of numbers of answers.
(9) errors in misjudgement the position of the constant term in plane equation.
(10) errors in misjudgement of the four fundamental operations of arithmetic.
2. The cause of errors:
(1) unclear concepts about the definitions related to intercept form in plane.
(2) unclear concepts about the formulas related to distance from a point to the plane.
(3) interactive interruptions of new knowledge and old experience.
(4) insufficient prior knowledge.
(5) carelessness or negligence.
(6) Insufficient ability of computation and miscalculation.
(7) inference based on nothing.
At last, based on the findings, we propose seven recommendations to teach plane in space of math instructions and three suggestions to conduct the further research in the future.
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