Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

Analysis of Belief Types in Mathematics Teachers and their Students by Latent Class Analysis

잠재집단분석(LCA)에 의한 수학교사와 학생들의 신념유형 분석

  • Received : 2019.11.14
  • Accepted : 2020.01.28
  • Published : 2020.02.15
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this study is to analyze the mathematical beliefs of students and teachers by Latent Class Analysis(LCA). This study surveyed 60 teachers about beliefs of 'nature of mathematics', 'mathematic teaching', 'mathematical ability' and also asked 1850 students about beliefs of 'school mathematics', 'mathematic problem solving', 'mathematic learning' and 'mathematical self-concept'. Also, this study classified each student and teacher into a class that are in a similar response, analyzed the belief systems and built a profile of the classes. As a result, teachers were classified into three types of belief classes about 'nature of mathematics' and two types of belief classes about 'teaching mathematics' and 'mathematical ability' respectively. Also, students were classfied into three types of belief classes about 'self concept' and two types of classes about 'School Mathematics', 'Mathematics Problem Solving' and 'Mathematics Learning' respectively. This study classified the mathematics belief systems in which students were categorized into 9 categories and teachers into 7 categories by LCA. The belief categories analyzed through these inductive observations were found to have statistical validity. The latent class analysis(LCA) used in this study is a new way of inductively categorizing the mathematical beliefs of teachers and students. The belief analysis method(LCA) used in this study may be the basis for statistically analyzing the relationship between teachers' and students' beliefs.

본 연구는 수학과 관련된 수학교사와 학생들의 신념을 잠재집단분석(Latent Class Analysis; LCA)을 이용하여 분석하였다. '수학의 본질', '수학의 교수', '수학적 능력'에 대한 고등학교 수학교사 60명의 설문과 '수학교과', '수학문제해결', '수학학습', '자아개념'에 대한 고등학생 1850명의 설문에 대해 유사한 응답을 한 교사와 학생을 각각 소집단으로 분류하고, 그 신념특성을 분석하며 신념프로파일을 작성하였다. 관찰결과, 수학교사들은 '수학의 본질'에 대해 3개, '수학의 교수'와 '수학적 능력'에 대해서는 각각 2개의 신념소집단으로 분류되었다. 또한, 학생들은 '자아개념'에 대해 3개, '수학교과', '수학문제해결', '수학학습'에 대해서는 각각 2개의 신념소집단으로 분류되었다. 이 연구에서 사용된 잠재집단분석은 수학적 신념을 귀납적으로 범주화하는 새로운 방법으로, 교사와 학생의 신념의 상관관계 및 인과관계를 통계적으로 분석하는데 기초가 될 수 있다.

Keywords

References

  1. Kim. R. (2015). A Study on Elementary Teachers" Beliefs about Teaching Mathematics. Journal of Korea Society Educational Studies in Mathematics School Mathematics, 17(4), 593-611.
  2. Kim. B. (2012) Instrument Development and Analysis of Secondary Students' Mathematical Beliefs. Journal of Educational Research in Mathematics, 22(2), 229-259.
  3. Kim. S. (1999). The Effects of Teacher's Beliefs about Mathematics on the Method of Class and the Performance of Problem Solving. Education of Primary School Mathematics, 3(1), 79-88.
  4. Kim, Y. (2014). Mathematical Belief System and Mathematical Problem Solving Activity: a Case Study. Journal of Research in Curriculum Instruction, 18(3), 725-749. https://doi.org/10.24231/rici.2014.18.3.725
  5. Kim. Y. & Ryu. H. (2016). An Analytical Study on the Mathematical Belief of the Elementary School Pre-Service Teachers. School Mathematics, 18(3), 691-709.
  6. Kim. Y. & Ryu. H. (2018). An Analytical Study on the Mathematical Belief of the Elementary School Teachers. Journal of Educational Research in Mathematics, 28(1), 141-157. https://doi.org/10.29275/jerm.2018.02.28.1.141
  7. Kim, Y. & Lee, C. (2014). Analysing High School Students' Mathematical Belief System and Core Belief Factors. School Mathematics, 16(1), 111-133.
  8. Nam, Y., Park, J., Paek, H., Seo, M., Sung, R., Jung, W., Ham, J. & Hwang, J. (1998) Dictionary of education, Seoul: Kyoyookbook.
  9. Nam, Y. & Song, Y. (2008). An Analytic Study of Beliefs about Mathematics and Mathematics Education of High School Students'. School Mathematics, 10(4), 649-669.
  10. Park, B. (2015) Lecture Evaluation Study(LCA) Using The Latent Class Analysis. Master's thesis. Graduate School of Industrial Engineering Sungkyunkwan University. Suwon, Koera.
  11. Jang, I., (2004). The belief and teaching of mathematics in elementary school teachers. Journal of the Elementary Education Society, 5, 55-76.
  12. Cho, C. (2002). Investigation on the belief in mathematics and learning of prospective mathematics teachers. Journal of the Korean Society of Mathematical Education Series E: Communications of Mathematical Education, 14, 371-394.
  13. Ball, D. L., & Wilson, S. M. (1990). Knowing the subject and learning to teach it: Examining assumptions about becoming a mathematics teacher National Center for Research on Teacher Education, Michigan State University.
  14. Cooney, T. J., Shealy, B. E., & Arvold, B. (1998). Conceptualizing belief structures of preservice secondary mathematics teachers. Journal for Research in Mathematics Education, 29(3), 306-333. https://doi.org/10.2307/749792
  15. Gates, P. (2006). Going beyond belief systems: Exploring a model for the social influence on mathematics teacher beliefs. Educational Studies in Mathematics, 63(3), 347-369. https://doi.org/10.1007/s10649-005-9007-z
  16. Jedidi, K., Jagpal, H. S., & DeSarbo, W. S.(1997). Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity. Marketing Science, 16, 39-59. https://doi.org/10.1287/mksc.16.1.39
  17. Lave, J. & Wenger, E. (1991). Situated learning : Legitimate peripheral participation. Cambridge University Press.
  18. Linzer, D. A. & Lewis, J. (2011). poLCA: an R Package for Polytomous Variable Latent Class Analysis. Journal of Statistical Software, 42(10), 1-29
  19. Oh. Y. (2002). Teachers' Mathematical Beliefs and Teaching Practices. 수학교육학연구, 12(2), 247-263.
  20. Raymond, A. M., (1997). Inconsistency between a beginning elementary school teacher's mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550-576. https://doi.org/10.2307/749691
  21. Schoen, R. C., & LaVenia, M. (2019). Teacher beliefs about mathematics teaching and learning: Identifying and clarifying three constructs. Cogent Education, 6(1), 1599488. https://doi.org/10.1080/2331186X.2019.1599488
  22. Schoenfeld, A. H. (2013). 수학수업, 설명을 만나다, 이경화(역) 서울: 경문사. (영어 원작은 2010년 출판)
  23. Smith, A. C. T. (2016). Cognitive mechanisms of belief change. Palgrave MacMillan.
  24. Wang, T., & Hsieh, F. (2014). The cultural notion of teacher education: Comparison of lower-secondary future teachers' and teacher educators' beliefs. International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 255-277) Springer.
  25. Zeichner, K. M., Tabachnick, B. R., & Densmore, K. (1987). Individual, institutional, and cultural influences on the development of teachers' craft knowledge. Exploring Teachers' Thinking, 21-59.