The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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An application and development of an activity lesson guessing a population ratio by sampling with replacement in 'Closed box'

'닫힌 상자'에서의 복원추출에 의한 모비율 추측 활동수업 개발 및 적용

  • Received : 2018.10.15
  • Accepted : 2018.11.21
  • Published : 2018.11.30
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Abstract

In this study, I developed an activity oriented lesson to support the understanding of probabilistic and quantitative estimating population ratios according to the standard statistical principles and discussed its implications in didactical respects. The developed activity lesson, as an efficient physical simulation activity by sampling with replacement, simulates unknown populations and real problem situations through completely closed 'Closed Box' in which we can not see nor take out the inside balls, and provides teaching and learning devices which highlight the representativeness of sample ratios and the sampling variability. I applied this activity lesson to the gifted students who did not learn estimating population ratios and collected the research data such as the activity sheets and recording and transcribing data of students' presenting, and analyzed them by Qualitative Content Analysis. As a result of an application, this activity lesson was effective in recognizing and reflecting on the representativeness of sample ratios and recognizing the random sampling variability. On the other hand, in order to show the sampling variability clearer, I discussed appropriately increasing the total number of the inside balls put in 'Closed Box' and the active involvement of the teachers to make students pay attention to controlling possible selection bias in sampling processes.

Keywords

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[그림 1] 활동수업의 개발 과정 [Fig. 1] The development process of this activity lesson

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[그림 3] 활동수업의 주요 흐름 [Fig. 3] Main flow of this activity lesson

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[그림 2] ‘닫힌 상자’의 예 [Fig. 2] An example of ‘Closed Box’

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[그림 4] 뚫린 구멍을 통해 무작위로 선택된 공의 색을 관찰하는 학생 [Fig. 4] A student watching the colour of a ball chosen at random

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[그림 5] 표본비율의 대표성에 대한 의심 [Fig. 5] Doubts about the representativeness of sample ratios

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[그림 6] 표집 변이성의 인지 [Fig. 6] Perception of the sampling variability

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[그림 8] 표집 과정의 편의 가능성 인지 [Fig. 8] Perception of the possibility of sampling bias

[표 1] 모둠별 표본비율과 추측한 모비율 [Table 1] Sample ratios and guess values of the population ratios by groups

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[표 2] 발표 및 활동지 서술의 질적 내용분석 결과 [Table 2] The result of QCA of students' presentations and activity appreciation

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[그림 7] 표집 변이성에 따른 모비율 추측의 난점 인지 [Fig. 7] Perception of the Difficulty in estimating the population ratios due to the sampling variability

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[표 3] 가상의 모비율 추측값 [Table 3] Guess values of the population ratios in a hypothetical situation

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