TURKISH PRE-SERVICE MATHEMATICS TEACHERS’ BELIEFS IN MULTIPLICATION
Abstract
Mathematics teachers’ beliefs play an important role in the mathematics teaching practices. However, the instruments used to measure the mathematics on certain contents are still limited. Thus, this study was conducted to develop a Multiplication Beliefs Questionnaire (MBQ) to identify and examine the profile of Turkish pre-service mathematics teachers’ beliefs. The samples of this study consisted of 414 four-year pre-service primary mathematics teachers from 18 different universities in Turkey collected using a convenience sampling technique. The validity of the questionnaire was analyzed using an exploratory factor analysis (EFA). We obtained four components of beliefs in multiplication covering, remote belief in multiplication (C1), multiplication operation belief in mathematics textbooks (C2), dynamic belief in multiplication learning (C3), and self-efficacy belief in multiplication problems (C4). The results showed that the pre-service mathematics teachers’ beliefs in components C1, C3, and C4 were positive, while component C2 was neutral. This study had an essential contribution to the mathematics literature since developing a questionnaire on multiplication distributed to the pre-service teachers. The previous studies showed that belief was subjective yet objectively influenced knowledge. Thus, identifying the pre-service teachers’ beliefs in teacher education may provide various benefits in reforming mathematics teaching.
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Ayd?n, E., Sevimli, E., & Abed, S. (2019). Statistical self-efficacy beliefs among pre-service mathematics teachers: The case of Palestine. Journal of Theoretical Educational Science, 12(4), 1209-1222. https://doi.org/10.30831/akukeg.451395
Ball, D. L. (1991). Research on teaching mathematics: Making subject-matter knowledge part of the equation. Research on Teaching Mathematics, 2, 1-48. https://doi.org/10.1.1.118.4400
Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Englewood Cliffs, NJ: Prentice-Hall.
Bar-Tal, D. (1990). Group beliefs. A conception for analyzing group structure, processes, and behavior. New York: Springer. https://doi.org/10.1007/978-1-4612-3298-8
Beaton, D. E., Bombardier, C., Guillemin, F., & Ferraz, M. B. (2000). Guidelines for the process of cross-cultural adaptation of self-report measures. Spine, 25, 3186-3191.
https://doi.org/10.1097/00007632-200012150-00014
Beavers, A. S., Lounsbury, J. W., Richards, J. K., Huck, S. W., Skolits, G. J., & Esquivel, S. L. (2013). Practical considerations for using exploratory factor analysis in educational research. Practical Assessment, Research, and Evaluation, 18, 6. https://doi.org/10.7275/qv2q-rk76
Beswick, K. (2012). Teachers’ beliefs about school mathematics and mathematicians’ mathematics and their relationship to practice. Educational Studies in Mathematics, 79, 127–147. https://doi.org/ 10.1007/s10649-011-9333-2
Callejo, M., & Vila, A. (2009). Approach to mathematical problem solving and students’ belief systems: two case studies. Educational Studies in Mathematics, 72, 111-126. https://doi.org/10.1007/sl0649-009-9195-z
Cobb, P. (1986). Contexts, goals, beliefs, and learning mathematics. For the Learning of Mathematics, 6(2), 2-9. https://www.jstor.org/stable/40247805
Cormas, P. C. (2020). Preservice teachers’ beliefs in a mathematics/science course. Research in Science & Technological Education, 1-17. https://doi.org/10.1080/02635143.2020.1784126
Costello, A. B., & Osborne, J. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research, and Evaluation, 10, 7. https://doi.org/10.7275/jyj1-4868
Cross, D. (2009). Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their in?uence on instructional practices. Journal of Mathematics Teacher Education, 12, 325–346. https://doi.org/10.1007/s10857-009-9120-5
Dede, Y. (2006). Values in Turkish middle school mathematics textbooks. Quality and Quantity, 40(3), 331–359. https://doi.org/10.1007/s11135-005-6133-8
Dede, Y. (2012). Why is mathematics valuable? A comparison of Turkish and German mathematics teachers. Bolema: Boletim de Educação Matemática, 26(44), 1171–1206. https://doi.org/10.1590/S0103-636X2012000400005
Dede, Y., & Uysal, F. (2012). Examining Turkish preservice elementary teachers’ beliefs about the nature and the teaching of mathematics. International Journal of Humanities and Social Science, 2(12), 125-135. http://www.ijhssnet.com/journals/Vol_2_No_12_Special_ Issue_June _2012/17.pdf
Ernest, P. (1989). The knowledge, beliefs, and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–34. https://doi.org/10.1080/0260747890150102
Ernest, P. (1994). The impact of beliefs on the teaching of mathematics. In A. Bloomfield & T. Harries (Eds.), Teaching and Learning Mathematics. Derby: Association of Teachers of Mathematics.
Geisler, S., & Rolka, K. (2021). That wasn’t the math I wanted to do! Students’ beliefs during the transition from school to university mathematics. International Journal of Science and Mathematics Education, 19, 599–618. https://doi.org/10.1007/s10763-020-10072-y
Gómezescobar, A., & Fernández, R. (2018). Los maestros y sus actitudes hacia las Matemáticas: un estudio sobre Educación Infantil y Primaria en España. UNIÓN-Revista Iberoamericana de Educación Matemática, 52, 186–200. https://dialnet.unirioja.es/servlet/articulo?codigo=6392999
Gravetter, F., & Forzano, L. (2009). Research methods for the behavioral sciences. Belmont, CA: Wadsworth Cengage Learning.
Grootenboer, P. (2008). Mathematical belief changes in prospective primary teachers. Journal Mathematics Teacher Education, 11, 479–497. https://doi.org/10.1007/s10857-008-9084-x
Grootenboer, P., & Marshman, M. (2016). Mathematics, affect and learning: Middle school students’ beliefs and attitudes about mathematics education. Singapore: Springer. https://doi.org/10.1007/978-981-287-679-9
Hailikari, T., Nevgi, A, & Komulainen, E. (2008). Academic self?beliefs and prior knowledge as predictors of student achievement in Mathematics: A structural model. Educational Psychology, 1, 59-71. https://doi.org/10.1080/01443410701413753
Hair, J. F., Anderson, R. E., Tatham, R. L., & Black, W. C. (1998). Multivariate Data Analysis (5th ed.). New Jersey: Prentice-Hall.
Hamukwaya, S. T., & Haser, Ç. (2021). “It does not mean that they cannot do mathematics”: Beliefs about mathematics learning difficulties. International Electronic Journal of Mathematics Education, 16(1), em0622. https://doi.org/10.29333/iejme/9569
Howard, M. C. (2016). A review of exploratory factor analysis decisions and overview of current practices: What we are doing and how can we improve? International Journal of Human-Computer Interaction, 32, 51–62. https://doi.org/10.1080/10447318.2015.1087664
Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187-200. https://doi.org/10.1007/BF02289233
Kaiser, H. F. (1974). An index of factorial simplicity. Psychometrika, 39(1), 31-36. https://doi.org/10.1007/BF02291575
Kennedy, L. M., & Tipps, S. (1997). Guiding children’s learning of mathematics. Belmont: Thomson Wadsworth.
K?l?ç, H. (2011). Preservice secondary mathematics teachers’ knowledge of students. Turkish Online Journal of Qualitative Inquiry, 2(2), 17-35. https://doi.org/10.17569/TOJQI.93311
Liljedahl, P., Rolka, K., & Rösken, B. (2007). Affecting affect: The reeducation of preservice teachers’ beliefs about mathematics and mathematics teaching and learning. In W. G. Martin, M. E. Strutchens, & P. C. Elliott (Eds.), The learning of mathematics. Sixty-ninth yearbook of the National Council of Teachers of Mathematics (pp. 319–330). Reston, VA: National Council of Teachers of Mathematics.
Liljedahl, P., Rösken, B., & Rolka, K. (2021). Changes to preservice elementary teachers’ beliefs about mathematics and the teaching and learning of mathematics: How and why? Journal of Adult Learning, Knowledge, and Innovation, 4(1), 20–30. https://doi.org/10.1556/2059.03.2019.09
McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York: Macmillan.
Merenda, P. (1997). A guide to the proper use of factor analysis in the conduct and reporting of research: Pitfalls to avoid. Measurement and Evaluation in Counseling and Development, 30, 156-164. https://doi.org/10.1080/07481756.1997.12068936
Muhtarom, Juniati, D., & Siswono, T. Y. E. (2019). Examining prospective teacher beliefs and pedagogical content knowledge towards teaching practice in mathematics class: A case study. Journal on Mathematics Education, 10(2), 185-202. https://doi.org/10.22342/jme.10.2.7326.185-202
Nicol, C. C., & Crespo, S. M. (2006). Learning to teach with mathematics textbooks: How preservice teachers interpret and use curriculum materials. Educational Studies in Mathematics, 62(3), 331-355. https://doi.org/10.1007/s10649-006-5423-y
Op 'T Eynde, P., De Corte, E., & Verschaffelg, L. (2002). Framing students' mathematics-related beliefs. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A Hidden Variable in Mathematics Education? (pp. 13-37). Dordrecht: Kluwer. https://doi.org/10.1007/0-306-47958-3
Polly, D., McGee, J. R., Wang, C., Lambert, R. G., Pugalee, D. K., & Johnson, S. (2013). The association between teachers’ beliefs, enacted practices, and student learning in mathematics. The Mathematics Educator, 22(2), 11–30. http://citeseerx.ist.psu.edu/viewdoc/download? doi=10.1.1.1000.1775&rep=rep1&type=pdf
Reigeluth, C. M. (1999). Instructional design theories and models: A new paradigm of instructional theory (Vol. II). Mahwah, NJ: Lawrence Erlbaum.
Ren, L., & Smith, W. M. (2018). Teacher characteristics and contextual factors: links to early primary teachers’ mathematical beliefs and attitudes. Journal Mathematics Teacher Education, 21, 321–350. https://doi.org/10.1007/s10857-017-9365-3
Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula (Ed.), Handbook of research on teacher education (pp. 102–119). New York: Macmillan.
Robb, M. (2019). Potential advantages and disadvantages digital textbooks. Nurse Author & Editor, 29(4), 1-9. https://doi.org/10.1111/j.1750-4910.2019.tb00054.x
?ahin, I. (2009). Curriculum assessment: Constructivist primary mathematics curriculum in Turkey. International Journal of Science and Mathematics Education, 8, 51-72. https://doi.org/10.1007/s10763-009-9162-2
Sevgi, S., Berkeroglu, G., Cobb, P., & Smith, T. M. (2021). A cross-cultural comparison of the self-efficacy of middle-school mathematics teachers across Turkey and the United States. International Journal of Mathematical Education in Science and Technology, 1-18. https://doi.org/10.1080/0020739X.2020.1861348
Simon, M. A., Kara, M., Norton, A., & Placa, N. (2018). Fostering construction of a meaning for multiplication that subsumes whole-number and fraction multiplication: A study of the Learning Through Activity research program. Journal of Mathematical Behavior, 52, 151-173. https://doi.org/ 10.1016/j.jmathb.2018.03.002
Staub, F. C., & Stern, E. (2002). The nature of teachers' pedagogical content beliefs matters for students' achievement gains: Quasi-experimental evidence from elementary mathematics. Journal of Educational Psychology, 94(2), 344-355. https://doi.org/10.1037/0022-0663.94.2.344
Szydlik, J. E., Szydlik, S. D., & Benson, S. R. (2003). Exploring changes in pre-service elementary teachers' mathematical beliefs. Journal of Mathematics Teacher Education, 6(3), 253-279. https://doi.org/10.1023/A:1025155328511
Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Boston: Pearson.
Thompson, B. (2004). Exploratory and confirmatory factor analysis: Understanding concepts and applications. Washington, DC: American Psychological Association. https://doi.org/10.1037/10694-000
Törner, G. (2002). Mathematical beliefs – a search for common ground: Some theoretical considerations on structuring beliefs, some research questions, and some phenomenological observations. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A Hidden Variable in Mathematics Education? (pp. 73-94). Dordrecht: Kluwer. https://doi.org/10.1007/0-306-47958-3
Uysal, F., & Dede, Y. (2016). Mathematics anxiety and beliefs of Turkish pre-service elementary teachers. EURASIA Journal of Mathematics, Science and Technology Education, 12(8), 2171-2186. https://doi.org/10.12973/eurasia.2016.1418a
Wilson, M., & Cooney, T. (2002). Mathematics teacher change and development: The role of beliefs. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 127–148). Dordrecht, The Netherlands: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47958-3
Zhang, Q., & Morselli. (2016). Teacher beliefs. In G. Kaiser (Ed), Attitudes, beliefs, motivation and identity in mathematics education: An overview of the field and future directions. Hamburg, ICME-13 Topical Surveys, (pp. 11-13). https://link.springer.com/content/pdf/10.1007%2F978-3-319-32811-9.pdf
Zuljan, D., Valen?i?, Z. M., & Peji?, P. P. (2021). Cognitive constructivist way of teaching scientific and technical contents. International Journal of Cognitive Research in Science, Engineering and Education, 9(1), 23–36. https://doi.org/10.23947/2334-8496-2021-9-1-23-36
Yang, X., Kaiser, G., König, J., & Blömeke, S. (2020). Relationship between pre-service mathematics teachers’ knowledge, beliefs, and instructional practices in China. ZDM, 52, 281–294. https://doi.org/10.1007/s11858-020-01145-x
Y?lmaz, D., & Turan, H. (2020). Self-efficacy beliefs of pre-service teachers in teaching first reading and writing and mathematics. Participatory Educational Research, 7(1), 257-270. https://doi.org /10.17275/per.20.15.7.1
DOI: https://doi.org/10.22342/jme.12.3.14440.469-486
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