The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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A case study on student's thoughts and expressions on various types of geometric series tasks

다양한 형태의 등비급수 과제들에 대한 학생들의 생각과 표현에 관한 사례연구

  • Received : 2018.08.21
  • Accepted : 2018.10.15
  • Published : 2018.11.30
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Abstract

This study started with the following questions. Suppose that students do not accept various forms of geometric series tasks as the same task. Also, let's say that the approach was different for each task. Then, when they realize that they are the same task, how will students connect the different approaches? This study is a process of pro-actively confirming whether or not such a question can be made. For this purpose, three students in the second grade of high school participated in the teaching experiment. The results of this study are as follows. It also confirmed how the students think about the various types of tasks in the geometric series. For example, students have stated that the value is 1 in a series type of task. However, in the case of the 0.999... type of task, the value is expressed as less than 1. At this time, we examined only mathematical expressions of students approaching each task. The problem of reachability was not encountered because the task represented by the series symbol approaches the problem solved by procedural calculation. However, in the 0.999... type of task, a variety of expressions were observed that revealed problems with reachability. The analysis of students' expressions related to geometric series can provide important information for infinite concepts and limit conceptual research. The problems of this study may be discussed through related studies. Perhaps more advanced research may be based on the results of this study. Through these discussions, I expect that the contents of infinity in the school field will not be forced unilaterally because there is no mathematical error, but it will be an opportunity for students to think about the learning method in a natural way.

Keywords

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[그림 1] 교수실험의 도식 [Fig 1] Figure of teaching experiment

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[그림 2] $\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{1}{8}$ + ⋯에 대한 그림 모형 과제 [Fig 2] A model figure for $\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{1}{8}$ + ⋯

[표 1] 교수실험에서 제시된 주요 과제 [Table 1] Key task of teaching experiment

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[표 2] $\sum_{n=1}^{{\infty}}\frac{9}{10}(\frac{1}{10})^{n-1}$의 풀이에 대한 학생들의 반응 [Table 2] Students' responses to $\sum_{n=1}^{{\infty}}\frac{9}{10}(\frac{1}{10})^{n-1}$ 's solution

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[표 3] $\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{1}{8}$ + ⋯의 풀이에 대한 학생들의 반응 [Table 3] Students' responses to $\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{1}{8}$ + ⋯'s solution

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