Mathematical reasoning of prospective mathematics teachers in solving problems based on working memory capacity differences

Inelsi Palengka; Dwi Juniati; Abadi

doi:10.29333/ejmste/12670

Full Text (PDF)

Inelsi Palengka ¹ ² , Dwi Juniati ¹ ^* , Abadi ³

More Detail

¹ Mathematics Education, Universitas Negeri Surabaya, Jawa Timur, INDONESIA² Mathematics Education, Universitas Kristen Indonesia Toraja, Tana Toraja, INDONESIA³ Universitas Negeri Surabaya^* Corresponding Author

Abstract

This study aims to investigate algorithmic reasoning and creative reasoning of prospective mathematics teachers in solving problems. This research is a qualitative research. The research subjects are prospective mathematics teachers with high working memory capacity (HWMC) and low working memory capacity (LWMC). Based on the results on algorithmic reasoning, it is known that for subjects with HWMC using algorithms to solve the given problems. While subjects with LWMC using sum and multiplication rules to solve the given problems. On creative mathematical reasoning it is known that for subjects with HWMC using a novel strategy, providing predictive and verification reasons for the selection of strategies, and providing convincing reasons accordance with the intrinsic mathematical properties. While subjects with low memory capacity had difficulty providing a verification reason and the reason that the way of solving was in accordance with the intrinsic mathematical properties.

Keywords

mathematical reasoning
open ended
problem-solving
working memory capacity

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 18, Issue 12, December 2022, Article No: em2193

https://doi.org/10.29333/ejmste/12670

Publication date: 25 Nov 2022

Article Views: 1646

Article Downloads: 995

Open Access References How to cite this article

References

Aineamani, B. (2018). How learners communicate their mathematics reasoning in mathematics discourse. In J. Moschkovich, D. Wagner, A. Bose, J. Rodrigues Mendes, & M. Schütte (Eds.), Language and communication in mathematics education (pp. 65-74). Springer. https://doi.org/10.1007/978-3-319-75055-2_6
Anjariyah, D., Juniati, D., & Eko, T. Y. (2022). How does working memory capacity affect students’ mathematical problem solving? European Journal of Educational Research, 11(3), 1427-1439. https://doi.org/10.12973/eu-jer.11.3.1427
Baddeley, A. (2000). The episodic buffer: A new component of working memory? Trends in Cognitive Sciences, 4(11), 417-423. https://doi.org/10.1016/s1364-6613(00)01538-2
Bergqvist, E. (2007). Types of reasoning required in university exams in mathematics. The Journal of Mathematical Behavior, 26(4), 348-370. https://doi.org/10.1016/j.jmathb.2007.11.001
Boesen, J., Lithner, J., & Palm, T. (2010). The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics, 75(1), 89-105. https://doi.org/10.1007/s10649-010-9242-9
de Fockert, J. W., Rees, G., Frith, C. D., & Lavie, N. (2001). The role of working memory in visual selective attention. Science, 291(5509), 1803-1806. https://doi.org/10.1126/science.1056496
de Ron, A., Christiansen, I., & Skog, K. (2022). Configuring the landscape of research on problem-solving in mathematics teacher education. International Electronic Journal of Mathematics Education, 17(4), em0712. https://doi.org/10.29333/iejme/12457
Dröse, J., Prediger, S., Neugebauer, P., Delucchi Danhier, R., & Mertins, B. (2021). Investigating students’ processes of noticing and interpreting syntactic language features in word problem solving through eye-tracking. International Electronic Journal of Mathematics Education, 16(1), em0625. https://doi.org/10.29333/iejme/9674
Fan, L., & Bokhove, C. (2014). Rethinking the role of algorithms in school mathematics: A conceptual model with focus on cognitive development. ZDM, 46(3), 481-492. https://doi.org/10.1007/s11858-014-0590-2
Fatmanissa, N., Kusnandi, K., & Usdiyana, D. (2020). Effect of schema use in solving word problems: Emphasis on linguistic difficulties. Contemporary Mathematics and Science Education, 1(2), ep20006. https://doi.org/10.30935/conmaths/8495
Fyfe, E. R., Matz, L. E., Hunt, K. M., & Alibali, M. W. (2019). Mathematical thinking in children with developmental language disorder: The roles of pattern skills and verbal working memory. Journal of Communication Disorders, 77, 17-30. https://doi.org/10.1016/j.jcomdis.2018.11.001
Habtamu, S. B., Mulugeta, A. A., & Mulugeta, W. G. (2022). The effect of cooperative problem-solving method on students’ motivation towards learning algebra. Pedagogical Research, 7(2), em0123. https://doi.org/10.29333/pr/11906
Hershkowitz, R., Tabach, M., & Dreyfus, T. (2016). Creative reasoning and shifts of knowledge in the mathematics classroom. ZDM, 49(1), 25-36. https://doi.org/10.1007/s11858-016-0816-6
Hokor, E. K., Apawu, J., Owusu-Ansah, N. A., & Agormor, S. (2022). Preservice teachers’ misconceptions in solving probabilistic problems. Pedagogical Research, 7(1), em0112. https://doi.org/10.29333/pr/11441
Jonsson, B., Kulaksiz, Y. C., & Lithner, J. (2016). Creative and algorithmic mathematical reasoning: Effects of transfer-appropriate processing and effortful struggle. International Journal of Mathematical Education in Science and Technology, 47(8), 1206-1225. https://doi.org/10.1080/0020739x.2016.1192232
Jonsson, B., Norqvist, M., Liljekvist, Y., & Lithner, J. (2014). Learning mathematics through algorithmic and creative reasoning. The Journal of Mathematical Behavior, 36, 20-32. https://doi.org/10.1016/j.jmathb.2014.08.003
Julius, E. (2022). The relationship between self-concept and problem-solving skills on students’ attitude towards solving algebraic problems. Contemporary Mathematics and Science Education, 3(2), ep22020. https://doi.org/10.30935/conmaths/12509
Juniati, D., & Budayasa, I. K. (2020). Working memory capacity and mathematics anxiety of mathematics students and its effect on mathematics achievement. Journal for the Education of Gifted Young Scientists, 8(1), 279-291. https://doi.org/10.17478/jegys.653518
Kane, M. J., Bleckley, M. K., Conway, A. R., & Engle, R. W. (2001). A controlled-attention view of working-memory capacity. Journal of Experimental Psychology: General, 130(2), 169-183. https://doi.org/10.1037/0096-3445.130.2.169
Langi, E. L., Juniati, D., & Abadi. (2021). Understanding definite integral concepts of prospective teachers through actions and processes based on gender difference. Journal of Physics: Conference Series, 1747(1), 012026. https://doi.org/10.1088/1742-6596/1747/1/012026
Lester, F. K., & Cai, J. (2016). Can mathematical problem solving be taught? Preliminary answers from 30 years of research. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Posing and solving mathematical problems (pp. 117-135). Springer. https://doi.org/10.1007/978-3-319-28023-3_8
Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255-276. https://doi.org/10.1007/s10649-007-9104-2
Lithner, J. (2015). Learning mathematics by creative or imitative reasoning. In S. J. Cho (Ed.), Selected regular lectures from the 12^th International Congress on Mathematical Education (pp. 487-506). Springer. https://doi.org/10.1007/978-3-319-17187-6_28
Muzaini, M., Juniati, D., & Siswono, T. Y. (2019). Exploration of student’s quantitative reasoning in solving mathematical problem: Case study of field-dependent cognitive style. Journal of Physics: Conference Series, 1157, 032093. https://doi.org/10.1088/1742-6596/1157/3/032093
Norqvist, M. (2017). The effect of explanations on mathematical reasoning tasks. International Journal of Mathematical Education in Science and Technology, 49(1), 15-30. https://doi.org/10.1080/0020739x.2017.1340679
Norqvist, M., Jonsson, B., Lithner, J., Qwillbard, T., & Holm, L. (2019). Investigating algorithmic and creative reasoning strategies by eye tracking. The Journal of Mathematical Behavior, 55, 100701. https://doi.org/10.1016/j.jmathb.2019.03.008
Øystein, H. P. (2011). What characterizes high achieving students’ mathematical reasoning? In B. Sriraman, & K. H. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 193-215). Springer. https://doi.org/10.1007/978-94-6091-439-3_13
Palengka, I., Juniati, D., & Abadi. (2019). Creative mathematical reasoning of prospective teachers in solving problems reviewed based on working memory capacity. Journal of Physics: Conference Series, 1417(1), 012055. https://doi.org/10.1088/1742-6596/1417/1/012055
Palengka, I., Juniati, D., & Abadi. (2021). Mathematical reasoning structure of junior high school students in solving problems based on their working memory capacity. Journal of Physics: Conference Series, 1747(1), 012023. https://doi.org/10.1088/1742-6596/1747/1/012023
Portaankorva-Koivisto, P. M., Laine, A. T., & Ahtee, M. (2021). Two primary teachers developing their teaching problem-solving during three-year in-service training. International Electronic Journal of Mathematics Education, 16(1), em0624. https://doi.org/10.29333/iejme/9617
Ramdani, R., Syamsuddin, A., & Sirajuddin, S. (2019). Development of mathematical module-problem solving approach to train student’s reflective thinking. Pedagogical Research, 4(4), em0040. https://doi.org/10.29333/pr/5861
Schoenfeld, A. H. (2014). What makes for powerful classrooms, and how can we support teachers in creating them? A story of research and practice productively intertwined. Educational Researcher, 43(8), 404-412. https://doi.org/10.3102/0013189x14554450
Sidenvall, J., Lithner, J., & Jäder, J. (2014). Students’ reasoning in mathematics textbook task-solving. International Journal of Mathematical Education in Science and Technology, 46(4), 533-552. https://doi.org/10.1080/0020739x.2014.992986
Sumpter, L. (2015). Investigating upper secondary school teachers’ conceptions: Is mathematical reasoning considered gendered? International Journal of Science and Mathematics Education, 14(S2), 347-362. https://doi.org/10.1007/s10763-015-9634-5
Swanson, H. L. (2017). Verbal and visual-spatial working memory: What develops over a life span? Developmental Psychology, 53(5), 971-995. https://doi.org/10.1037/dev0000291
Wiley, J., & Jarosz, A. F. (2012). How working memory capacity affects problem solving. In B. H. Ross (Ed.), Psychology of learning and motivation (pp. 185-227). Academic Press. https://doi.org/10.1016/b978-0-12-394393-4.00006-6
Wirebring, L. K., Lithner, J., Jonsson, B., Liljekvist, Y., Norqvist, M., & Nyberg, L. (2015). Learning mathematics without a suggested solution method: Durable effects on performance and brain activity. Trends in Neuroscience and Education, 4(1-2), 6-14. https://doi.org/10.1016/j.tine.2015.03.002

How to cite this article

APA

Palengka, I., Juniati, D., & Abadi (2022). Mathematical reasoning of prospective mathematics teachers in solving problems based on working memory capacity differences. Eurasia Journal of Mathematics, Science and Technology Education, 18(12), em2193. https://doi.org/10.29333/ejmste/12670

Vancouver

Palengka I, Juniati D, Abadi. Mathematical reasoning of prospective mathematics teachers in solving problems based on working memory capacity differences. EURASIA J Math Sci Tech Ed. 2022;18(12):em2193. https://doi.org/10.29333/ejmste/12670

AMA

Palengka I, Juniati D, Abadi. Mathematical reasoning of prospective mathematics teachers in solving problems based on working memory capacity differences. EURASIA J Math Sci Tech Ed. 2022;18(12), em2193. https://doi.org/10.29333/ejmste/12670

Chicago

Palengka, Inelsi, Dwi Juniati, and Abadi. "Mathematical reasoning of prospective mathematics teachers in solving problems based on working memory capacity differences". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 12 (2022): em2193. https://doi.org/10.29333/ejmste/12670

Harvard

Palengka, I., Juniati, D., and Abadi (2022). Mathematical reasoning of prospective mathematics teachers in solving problems based on working memory capacity differences. Eurasia Journal of Mathematics, Science and Technology Education, 18(12), em2193. https://doi.org/10.29333/ejmste/12670

MLA

Palengka, Inelsi et al. "Mathematical reasoning of prospective mathematics teachers in solving problems based on working memory capacity differences". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 12, 2022, em2193. https://doi.org/10.29333/ejmste/12670