Prospective Mathematics Teachers’ Beliefs and Representations

Sadrack Luden Pagiling(1*), Irmawaty Natsir(2), Markus Palobo(3), Dian Mayasari(4)

(1) Universitas Musamus
(2) Universitas Musamus
(3) Universitas Musamus
(4) Universitas Musamus
(*) Corresponding Author

Abstract


Beliefs have been identified as an affect on the psychology of mathematics education. Additionally, representations play a paramount role in mathematics teaching and learning. However, few studies have examined prospective teachers' beliefs and their relationship to representations in problem-solving. The purpose of this study is to examine prospective mathematics teachers' beliefs and representations in solving word problems review from gender differences. This study involves 103 college students from the mathematics education department at a public university in Merauke Regency. The data were gathered using a questionnaire, a test, and in-depth interviews. A questionnaire was utilized to elicit the belief of prospective teachers. A test and interview were conducted to evoke data about participants' representations when solving word problems. The male student was found to be capable of arriving at a solution employing multiple representations. Due to the inaccurate representation constructed, the female student was unable to find the correct solution. This work implies that lecturers should heed prospective teachers' beliefs and generate representations of the focal point of classroom learning practice.

Keywords


Belief, Gender, Prospective Teacher, Representations.

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References


Andhani, R. A. (2016). Representasi Eksternal Siswa dalam Pemecahan Masalah SPLDV Ditinjau dari Kemampuan Matematika. Kreano, Jurnal Matematika Kreatif-Inovatif, 7(2), 179–186. https://doi.org/10.15294/kreano.v7i2.6615

Aziz, T. A., & Kurniasih, M. D. (2019). External representation flexibility of domain and range of function. Journal on Mathematics Education, 10(1), 143–155. https://doi.org/10.22342/jme.10.1.5257.143-156

Beswick, K. (2005). The beliefs/practice connection in broadly defined contexts. Mathematics Education Research Journal, 17(2), 39–68. https://doi.org/10.1007/BF03217415

Beswick, K. (2012). Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice. Educational Studies in Mathematics, 79(1), 127–147. https://doi.org/10.1007/s10649-011-9333-2

Beswick, K., & Chick, H. (2019). Beliefs and Pedagogical Content Knowledge for Teachers of Mathematics. International Handbook of Mathematics Teacher Education: Volume 1, 185–209. https://doi.org/10.1163/9789004418875_008

Boonen, A. J. H., van der Schoot, M., van Wesel, F., de Vries, M. H., & Jolles, J. (2013). What underlies successful word problem solving? A path analysis in sixth grade students. Contemporary Educational Psychology, 38(3), 271–279. https://doi.org/10.1016/j.cedpsych.2013.05.001

Boonen, A. J. H., Van Wesel, F., Jolles, J., & Van der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15–26. https://doi.org/10.1016/j.ijer.2014.08.001

Brizuela, B. M., Blanton, M., Sawrey, K., Newman-Owens, A., & Murphy Gardiner, A. (2015). Children's Use of Variables and Variable Notation to Represent Their Algebraic Ideas. Mathematical Thinking and Learning, 17(1), 34–63. https://doi.org/10.1080/10986065.2015.981939

Creswell, J. W. (2015). Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research (Fourth). Pearson.

Dreher, A., Kuntze, S., & Lerman, S. (2016). Why Use Multiple Representations in the Mathematics Classroom? Views of English and German Preservice Teachers. International Journal of Science and Mathematics Education, 14, 363–382. https://doi.org/10.1007/s10763-015-9633-6

Ernest, P. (1989). The Knowledge, Beliefs and Attitudes of the Mathematics Teacher: a model. Journal of Education for Teaching:International Research and Pedagogy, 15(1), 13–33. https://doi.org/10.1080/0260747890150102

Fonger, N. L. (2019). Meaningfulness in representational fluency: An analytic lens for students' creations, interpretations, and connections. Journal of Mathematical Behavior, 54(March 2018), 100678. https://doi.org/10.1016/j.jmathb.2018.10.003

Giardino, V., & Wöpking, J. (2019). Aspect seeing and mathematical representations. Avant, 10(2), 1–19. https://doi.org/10.26913/AVANT.2019.02.27

Goldin, G. A., & Shteingold, N. (2001). System of mathematical representations and development of mathematical concepts. In A. A. Cuoco (Ed.), The Roles of Representation in School Mathematics (pp. 1–23). National Council of Teachers of Mathematics.

Hoogland, K., de Koning, J., Bakker, A., Pepin, B. E. U., & Gravemeijer, K. (2018). Changing representation in contextual mathematical problems from descriptive to depictive: The effect on students' performance. Studies in Educational Evaluation, 58(November 2017), 122–131. https://doi.org/10.1016/j.stueduc.2018.06.004

Hwang, W.-Y., Chen, N.-S., Dung, J., & Yang, Y.-L. (2007). Multiple Representation Skills and Creativity Effects on Mathematical Problem Solving using a Multimedia Whiteboard System Jian-Jie Dung Yi-Lun Yang. Educational Technology & Society, 10(2), 191–212.

Jupri, A., Usdiyana, D., & Sispiyati, R. (2020). Peran Representasi Matematis dalam Pembelajaran Perkalian Bentuk Aljabar melalui Pendekatan Matematika Realistik. Jurnal Elemen, 6(1), 89–98. https://doi.org/10.29408/jel.v6i1.1716

Lee, M. Y., & Lee, J. E. (2019). Pre-service teachers' perceptions of the use of representations and suggestions for students' incorrect use. Eurasia Journal of Mathematics, Science and Technology Education, 15(9). https://doi.org/10.29333/ejmste/103055

Mitchell, R., Charalambous, C. Y., & Hill, H. C. (2014). Examining the task and knowledge demands needed to teach with representations. Journal of Mathematics Teacher Education, 17(1), 37–60. https://doi.org/10.1007/s10857-013-9253-4

NCTM. (2000). Principles and Standards for School Mathematics. National Council of Teachers of Mathematics.

Nugroho, A. A., Nizaruddin, N., Dwijayanti, I., & Tristianti, A. (2020). Exploring students' creative thinking in the use of representations in solving mathematical problems based on cognitive style. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 5(2), 202–217. https://doi.org/10.23917/jramathedu.v5i2.9983

Pagiling, S. L. (2019). Exploration of students' representation in solving pythagorean theorem problems based on cognitive style. Journal of Physics: Conference Series, 1321(3), 1–6. https://doi.org/10.1088/1742-6596/1321/3/032004

Pagiling, S. L., & Munfarikhatin, A. (2020). BAGAIMANA KONSEPSI GURU SEKOLAH MENENGAH PERTAMA TENTANG REPRESENTASI DALAM PEMBELAJARAN MATEMATIKA? AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 9(4), 1005–1017. https://doi.org/10.24127/ajpm.v9i4.3199

Panasuk, R. M., & Beyranevand, M. L. (2010). Algebra Students' Ability to Recognize Multiple Representations and Achievement. International Journal for Mathematics Teaching and Learning. http://www.eric.ed.gov/ERICWebPortal/detail?accno=EJ904885

Philipp, R. A. (2007). Mathematics teachers' beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–315). Information Age Publishing.

Rosli, R., Han, S., Capraro, R. M., & Capraro, M. M. (2013). Exploring Preservice Teachers' Computational and Representational Knowledge of Content and Teaching Fractions. Research in Mathematical Education, 17(4), 221–241. https://doi.org/10.7468/jksmed.2013.17.4.221

Rothbaeur, P. M. (2008). Triangulation. In L. M. Given (Ed.), The SAGE Encyclopedia of Qualitative Research Methods (pp. 892–894). SAGE Publications, Inc. https://books.google.com/books?id=y_0nAQAAMAAJ&pgis=1

Safrudiannur, Labulan, P. M., Suriaty, & Rott, B. (2021). Beliefs about school mathematics vs. university mathematics and beliefs about teaching and learning in different contexts of students' Achievement. Beta Jurnal Tadris Matematika, 14(1), 1–14. https://doi.org/10.20414/betajtm.v14i1.493

Safrudiannur, & Rott, B. (2020). Offering an Approach to Measure Beliefs Quantitatively: Capturing the Influence of Students' Abilities on Teachers' Beliefs. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-020-10063-z

Safrudiannur, S., & Rott, B. (2019). Measuring Teachers' Beliefs: A Comparison of Three Different Approaches. EURASIA Journal of Mathematics, Science and Technology Education, 16(1), 1–16. https://doi.org/10.29333/ejmste/110058

Santia, I., Purwanto, Sutawidjadja, A., Sudirman, & Subanji. (2019). Exploring mathematical representations in solving ill-structured problems: The case of quadratic function. Journal on Mathematics Education, 10(3), 365–378. https://doi.org/10.22342/jme.10.3.7600.365-378

Selling, S. K. (2016). Learning to represent, representing to learn. Journal of Mathematical Behavior, 41, 191–209. https://doi.org/10.1016/j.jmathb.2015.10.003

Siswono, T. Y. E., Kohar, A. W., & Hartono, S. (2017). Secondary Teachers' Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving. Journal of Physics: Conference Series, 812. https://doi.org/10.1088/1742-6596/755/1/011001

Stylianou, D. A. (2010). Teachers' conceptions of representation in middle school mathematics. Journal of Mathematics Teacher Education, 13(4), 325–343. https://doi.org/10.1007/s10857-010-9143-y

Stylianou, D. A. (2011). An examination of middle school students' representation practices in mathematical problem solving through the lens of expert work: Towards an organizing scheme. Educational Studies in Mathematics, 76(3), 265–280. https://doi.org/10.1007/s10649-010-9273-2

Viholainen, A., Asikainen, M., & Hirvonen, P. E. (2014). Mathematics student teachers' epistemological beliefs about the nature of mathematics and the goals of mathematics teaching and learning in the beginning of their studies. Eurasia Journal of Mathematics, Science and Technology Education, 10(2), 159–171. https://doi.org/10.12973/eurasia.2014.1028a

Wibawa, K. A., Payadnya, I. P. A. A., Atmaja, I. M. D., & Simons, M. D. (2020). Defragmenting structures of students' translational thinking in solving mathematical modeling problems based on CRA framework. Beta: Jurnal Tadris Matematika, 13(2), 130–151. https://doi.org/10.20414/betajtm.v13i2.327

Yee, S. P., & Bostic, J. D. (2014). Developing a contextualization of students' mathematical problem solving. Journal of Mathematical Behavior, 36, 1–19. https://doi.org/10.1016/j.jmathb.2014.08.002

Yeo, K. (2009). Secondary 2 Students' Difficulties in Solving Non-Routine Problems. International Journal for Mathematics Teaching and Learning, 1–30. http://eric.ed.gov/?id=EJ904874




DOI: http://dx.doi.org/10.30998/formatif.v12i1.10067

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