| Summary: | 碩士 === 國立臺南大學 === 應用數學系數學科教學碩士班 === 104 === This study focused on types of errors high school students may make when learning Equation of Lines in Space, and on what may contribute to these errors, hoping to learn more about students’ difficulties in this unit and to provide teachers with some teaching strategies for reference in the future. The study is mainly conducted with quantitative analysis, supplemented by quantitative analysis of interviews, whose interviewees, all second graders, come from a private high school in Tainan city. When in the second year of high school, many students are found falling behind when learning the second unit in book Ⅳ- Equation of Lines in Space. Though students may have the basic concepts of space learned in the previous unit, Vector Space, their knowledge of space remains the same as that of space plane. What’s more, not only do students not know how to solve the math problem, but they also figure out the problem in wrong ways. As a results, this study aims to find out the blind spots of students when they encounter this unit, and thus help teachers have the know-how to help students learn this unit as well. Accompanied by some interviews, the study reveals the scenarios in which students have difficulty leaning this unit; furthermore, it creates the possibility to fix students’ errors and misconceptions. The results are as follows:
1. What are the common types of errors in Equation of Lines in Space made by the high school students of Tainan ?
(1) They have vague ideas of the definition of parameter form of linear.
(2) The definition of symmetric form of line is not quite clear to them, so confusions and miscalculations can often be seen.
(3) They don’t quite understand the relationship between line and plane：the meaning of line and cross plane and the relationship between the cross product of two vectors and normal vector of plane.
(4) They have no clear conception of the relationship between lines; they are lack of understanding the questions, the characteristics of angle bisector, and the supposed parameter meaning of the linear projection point.
2. The three errors of the unit of linear in space are often made by the high school students of Tainan：
(1) They are insufficient in understanding the definition.
(2) They make errors transforming the equation of linear.
(3) The applications of parameter form are not familiar to them.
(4) They often make errors in the calculation of the cross product.
(5) They are lack of the idea of three-dimensional space.
3. What are the reasons of making errors in thinking and using the lines in space?
(1) Some students have or lack previous cognition.
(2) They ignore the given conditions.
(3) Forgetfulness, careless calculation and slip of pen are common sights.
(4) They don’t have prudent attitude and correct conception in answering the questions.
(5) Inappropriate analogies and false inference and extend can be found, too.
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