[논문]통계적 문제해결 과정에서 예비 수학교사들의 탐구 질문 분석

김소형; 한선영

doi:10.7468/mathedu.2021.60.3.363

통계적 문제해결 과정에서 예비 수학교사들의 탐구 질문 분석
Analyzing research questions from pre-service mathematics teachers in statistical problem solving process 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.60 no.3, 2021년, pp.363 - 386

김소형 (성균관대학교 대학원) , 한선영 (성균관대학교)

초록
AI-Helper

통계를 의미 있게 학습하기 위해서는 실제 데이터로 통계적 문제해결을 경험할 수 있는 기회를 제공해야 한다. 특히 문제 설정 단계에서의 탐구 질문은 학생들이 통계적 문제해결 과정의 시작부터 결론까지 성공적으로 안내하는 데에 중요하다. 이에 본 연구는 문제 설정 단계에서 예비 수학교사들의 탐구 질문에 대해 혼합연구방법을 실시하였다. 그 결과 일부 예비 수학교사들은 통계적 질문을 분류하는 과정에서 질문의 의미나 변수가 명확하지 않거나 통계 지식에 대한 오개념으로 인하여 통계적으로 해결할 수 없는 질문을 분류하였다. 또한 예비 수학교사들의 50%만이 통계적 문제해결에 적합한 6가지 조건을 모두 충족시켰으며, 나머지 50%는 일부 조건만 충족시켰다. 따라서 이러한 결과는 예비 수학교사들에게 교사 교육을 통해 통계적 문제해결 과정을 경험할 수 있는 기회를 제공해야하며, 그 중 문제 설정 단계는 매우 중요하므로 문제 설정 단계도 일련의 세분화된 과정이 필요하다는 점을 제안할 수 있다.

Abstract ▼ AI-Helper

To learn statistics meaningfully, we must provide an opportunity to experience the process of solving statistical problems with actual data. In particular, exploration questions at the problem setting stage are important for students to successfully guide them from the beginning to the conclusion of the statistical problem solving process. Therefore, in this study, a mixed research method was carried out for the exploration questions of pre-service mathematics teachers during the problem setting stage. As a result, some pre-service mathematics teachers categorized incorrect statistical questions because they did not clearly define the meaning or variables of the questions in the process of categorizing them from possible questions. In addition, questions that cannot be solved statistically were categorized due to misconceptions about statistical knowledge. Second, only 50% of the pre-service mathematics teachers met all 6 conditions suitable for solving statistical problems, while there maining they met only a few conditions. Therefore, the conclusion of this study is as follows. First of all, they should be given the opportunity to experience all the statistical problem solving processes through teacher education because they do not have enough experience in statistical problem solving. Secondly, since the problem setting stage is very important in the statistical problem solving process, a series of subdivided processes are also required in the problem setting stage.

주제어

표/그림 (18)

그림 [Fig. 1] PPDAC 모델(Mackay & Oldford, 1994)
표 [Table 1] Issues in statistical solving process (Wild & Pfannkuch, 1999, p.226)
표 [Table 2] Four components of statistical solving process (Franklin et al., 2007, p.11)
표 [Table 3] The link between the type of investigative question and the nature of the data, school level (Arnold, 2013, p.37)
그림 [Fig. 2] The triangulation design method in this study
표 [Table 4] Information about pre-service mathematics teachers
표 [Table 5] Issues and components carried out at each stage of the population mean estimated project
표 [Table 6] Analysis standards in this study
표 [Table 7] Comparison of results analyzed with the intent of the 3 questions
표 [Table 8] Results on the analysis of the added questions into 3 of the intentions
표 [Table 9] Comparison of statistical terms used
표 [Table 11] Analysis results on 'Is the population clearly represented in the question?'
표 [Table 10] Analysis results on 'Is the question clearly describe the variables available?'
표 [Table 12] Analysis results on 'What is the intention of the question?'
그림 [Table 13] Analysis results on ‘='Is this a question that can be answered with the given data?'
표 [Table 14] List of questions that are not known by the given data
표 [Table 15] Purpose of the question
표 [Table 16] Analysis results on 'Is that a statistical question?'

참고문헌 (41)

Arnold, P. M. (2013). Statistical investigative questions: An enquiry into posing and answering investigative questions from existing data. (Doctoral dissertation). The University of Auckland, New Zealand.
Arnold, P. M., & Pfannkuch, M. (2019). Posing comparative statistical investigative questions: International perspectives. In G. Burrill & D. Ben-Zvi (Eds.), Topics and trends in current statistics education research ICME-13 Monographs (pp. 173-195). Switzerland: Springer Nature.
Bae, H. J., Lee, D. H. (2016). An Analysis on Statistical Units of Elementary School Mathematics Textbook. Journal of Elementary Mathematics Education in Korea, 20(1), 55-69.
Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning: The Solo Taxonomy. New York: Academic Press.
Creswell, J. W., & Plano Clark, V. L. (2011). Designing and Conducting Mixed Methods Research (2nd ed.). Thousand Oaks, CA: Sage.
Creswell, J. W. (2017). Qualitative Inquiry and Research Design: Choosing among Five Approaches 3rd edition(Cho, H. S., Jeong, S. W., Kim, J. S., Kwon, J. S., Trans.). Seoul: Hak-Ji Sa. (Original work published 2013).
Doyle, L., Brady, AM, & Byrne, G. (2016). An overview of mixed methods research - revisited. Journal of Research in Nursing, 21(8), 623-635. DOI: 10.1177/1744987116674257

상세보기
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-k-12 curriculum framework. Alexandria, VA: American Statistical Association.
Frischemeier, D., & Leavy, A. (2020). Improving the quality of statistical questions posed for group comparison situations. Teaching Statistics, 42, 58-65.

상세보기
Graham. A. (2006). Developing thinking in statistics. London: The Open University in association with Paul Chamman Publishing.
Go. S. M., Kim, M. S., Jung, J. K., Cho, W. Y. (2017). Analysis of the Problems in Statistics Units of Middle School Textbooks for the 3rd grade in terms of Statistical Literacy. School Mathematics, 19(4), 731-749.
Hwang, H. J. (2020). The Development of the Items on Mathematical Instructional Evaluation based on the Teacher's Practical Knowledge. J. Korea Soc. Math. Ed. Ser. E: Communications of Mathematical Education 34(4), 507-523.
Jang, A. R.. (2016). A Comparative Analysis on Statistical Reasoning Questions in Textbooks: focused on the first year of middle school. Graduate School of Education Chonnam National Univerisy, Gwangju.
Jeon, H. W., Kim, R. Y. (2019). A Comparative Study of Statistical Processes in Korean and U.S. Middle School Mathematics Textbooks. School Mathematics, 33(4), 425-444.
Jeong, S. J. (2019). An analysis on Statistical Literacy of Mathematically Gifted Students through Context Centered STEAM Education. Graduate School of Education Korea National University of Education, Chung-Buk.
Ju, M. K., Kim, S. Y., Bae, K. T., Jeong, H. S., Jung, S. Y. (2018). An Analysis of High School Students' Statistical Literacy: Students' Achievement and Mifficulties of Statistical Inquiry. School Mathematics, 20(4), 661-683.

상세보기
Kang, H. Y., Shin, B. M., Ko, E. S., Lee, D. H., Sim, S. Y., Kim, J. J., Ku, N. Y., Jung, I. S., Choi, K. S., Hong, J. H., Lee, S. B. (2014). A study on the improvement of mathematics curriculum for the promotion of statistical education. Kofac Research Report 2014A039.
Kim, W. K., Moon, S. Y., Byun, J. Y. (2006). Mathematics teachers' knowledge and belief on the high school probability and statistics. The Mathematical Education, 45(4), 381-406.
Kim, J. H., Kang, E. K., Kim, S. M., Kwon, S. Y., Park, M. G., Cho, S. Y. (2019). A Study on Pre-service Elementary Teachers' Mathematical Beliefs about the Nature of Mathematics and the Mathematics Learning. Education of Primary School Mathematics, 22(1), 49-64.

원문보기 상세보기
Ko, E. S., Park, M. S. (2017). Pre-Service Elementary School Teachers Statistical Literacy Related To Statistical Problem Solving. School Mathematics, 19(3), 443-459.
Kwon, D. S. (2019). Effects of Thinking related to Statistical Variability on the Understanding of Population Mean Estimation. Graduate school of Education Ewha Womans University, Seoul.
Lee, E. J., Park. M. S. (2019). Statistical Reasoning of Preservice Elementary School Teachers Engaged in Statistical Problem Solving: Focused on Question Posing Stage. J. Korea Soc. Math. Ed. Ser. C: Education of Primary School Mathematics, 22(4), 205-221.
Lee, J. M. (2020). Analysis of problem statements in poster presentations of statistical investigation. Graduate School Seoul National University, Seoul.
Lee, J. Y. (2016). An Analysis on the Mathematics Teachers' Subject Matter Knowledge of Normal Distribution. Graduate School of Education Korea National University of Education, Chung-Buk.
Lee, K. H. (2016). A journey for statistics, statistics education, and statistics education research. Proceeding of the conference of the mathematics education, 49, 41-56.
Lee, S. J., Kim, G. Y. (2019). How middle-school mathematics textbooks of Korea and the US support to develop students' statistical reasoning. J. Korea Soc. Math. Ed. Ser. A: The Mathematical Education 58(1), 139-160.
Lee, Y. K. (2009). The Effect of Project Classes on Statistical Teaching for First-Year Middle School Students. Graduate School of Education Korea National University of Education, Chung-Buk.
Mackay, R. J., & Oldford, R. W. (1994). Stat 231 Course Notes Fall 1994. Waterloo: University of Waterloo.
Mackay, R. J., & Oldford, R. W. (2000). Scientific Method, Statistical Method and the Speed of Light. Statistical Science, 15(3), 254-278.

상세보기
Makar, K. & Fielding-Wells, J. (2011). Teaching teachers to teach statistical investigations. In C. Batenero, G. Burill, & C. Reading (Eds.), Teaching statistics in school mathematics challenges for teaching and teacher education (pp. 9-13). New York: Springer.
Marriott, J., Davies, N., & Gibson, L. (2009). Teaching, learning and assessing statistical problem solving. Journal of Statistics Education [Online], 17(1), www.amstat.org/publications/jse/v17n1/marriott.html
Ministry of Education (2015). The 2015 Revised Mathematics Curriculum. The Ministry of Education, 2015-74 [Separate volum 8].
National Council of Teachers of Mathematics (2000). Principles and standards for mathematics. Reston, VA: The author.
Park, B. Y. (2020). An Analysis on Secondary Mathematics Teachers' Statistical Knowledge about Statistical Problem Solving. Graduate School of Education Korea National University of Education, Chung-Buk.
Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula, T. J. Buttery & E. Guyton (Eds.), Handbook of research on teacher education. (2nd ed, pp. 102-119). New York: Macmillan.
Ryu, K. U., Jung, J. W., Kim, Y. S., Kim, H. B. (2018). Understanding qualitative research methods. Seoul: PYMATE.
Shulman, Lee S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher. 4-14.
Stake, R. (1995). The art of case study research. Thousand Oaks. CA: Sage.
Watson, J. & English, L. (2017). Statistical problem posing, problem refining, and further reflection in grade 6. Canadian Journal of Science, Mathematics and Technology Education, 17(4), 347-365.

상세보기
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-265.

상세보기
Woo, J. H. (2017). The educational foundation of school mathematics(revised). Seoul: Seoul National University Press.

저자의 다른 논문 :

표제어: PCR

동의어: Packet Collision Rate

용어 설명 출처 목록 (6)

용어 설명: PCR은 세균 특이성이 있는 primer를 이용하여 적은 수의 세균이 있을지라도 쉽게 검출할 수 있는 유용한 방법이며, 이를 이용하여 구강 내 치면세균막이나 타액에서 직접 세균을 검출할 수 있게 되었다[8].

내보내기 구분	파일저장 인쇄 메일전송
구성항목	기본정보 상세정보 관리번호, 논문명, 저널/프로시딩명, 저자 , 발행년, 권, 호, 시작페이지, 끝페이지, 발행기관 관리번호, 논문명, 대등논문명, 저자 , 저널/프로시딩명, 발행기관, 발행년, 발행언어, 권, 호, 시작페이지, 끝페이지, ISBN, ISSN, 주제분야, 키워드, 초록(한글), 초록(영문), 저자(소속기관)
저장형식	Text(ASCII format) Excel format RefWorks Direct Export RIS format (for Reference Manager, ProCite, EndNote), Scholar's Aids, Mendeley
메일정보	받는사람 (필수) @ 보내는사람 (선택) @ 제목 내용 KISTI 검색결과 이메일 서비스
안내	총 건의 자료가 검색되었습니다. 다운받으실 자료의 인덱스를 입력하세요. (1-10,000) 검색결과의 순서대로 최대 10,000건 까지 다운로드가 가능합니다. 데이타가 많을 경우 속도가 느려질 수 있습니다.(최대 2~3분 소요) 다운로드 파일은 UTF-8 형태로 저장됩니다. 파일의 내용이 제대로 보이지 않을실 때는 웹브라우저 상단의 보기 -> 인코딩 -> 자동선택 여부를 확인하십시오. ~ Text(ASCII format) Excel format

연합인증