How Does Working Memory Capacity Affect Prospective Mathematics Teachers' Creative Reasoning in Problem Solving?
Keywords:
working memory capacity, creative reasoning, problem solvingAbstract
The mixed methods research reported in this article examined the relationship between differences in working memory capacity (WMC) and problem-solving and creative reasoning of 30 prospective mathematics teachers. WMC data were obtained using an OSPAN test instrument, and creative reasoning data were obtained using a problem-solving test. Quantitative data were analysed using linear regression. The qualitative data analysis process was conducted through data condensation, which involved selecting and presenting simpler data, labelling transcriptions, and coding. The validity of the findings was validated through data triangulation, which assessed data consistency. The research showed that WMC influences mathematical problem-solving, which obtained a significant positive correlation between the two variables. The prospective mathematic teachers with high WMC were more creative and flexible in creating problem-solving strategies compared to prospective mathematic teachers with low WMC. They also remembered more information and had better management in solving problems, using advanced strategies and finding appropriate problem solutions. In contrast, prospective mathematic teachers with low WMC were not as good at remembering and managing information, identifying missing vital information from problems, and using imperfect problem-solving strategies. In addition, they experience decreased cognitive performance when solving more complex problems, resulting in less appropriate problem-solving solutions.
References
Alloway, T. P., & Passolunghi, M. C. (2011). The relationship between working memory, IQ, and mathematical skills in children. Learning and Individual Differences, 21(1), 133–137. https://doi.org/10.1016/j.lindif.2010.09.013
Ball, D. L., Ferrini-Mundy, J., Kilpatrick, J., Milgram, R. J., Schmid, W., & Schaar, R. (2005). Reaching for common ground in K-12 mathematics education. Notices of the American Mathematical Society, 52(9), 1055–1058.
Beilock, S. L., & Carr, T. H. (2005). When high-powered people fail: Working memory and “Choking under pressure” in math. Psychological Science, 16(2), 101–105. https://doi.org/10.1111/j.0956-7976.2005.00789.x
Bergqvist, E. (2007). Types of reasoning required in university exams in mathematics. 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
Bryman, A. (2004). Qualitative research on leadership: A critical but appreciative review. Leadership Quarterly, 15(6), 729–769. https://doi.org/10.1016/j.leaqua.2004.09.007
Céspedes, N., Aquije, M. E., Sánchez, A., & Vera Tudela, R. (2016). Productividad y apertura comercial en el Perú. In Productividad en el Perú: medición, determinantes e implicancias. https://doi.org/10.21678/978-9972-57-356-9-5
Chang, F.-R. (2010). Stochastic optimization in continuous time. Cambridge University Press. https://doi.org/10.1017/cbo9780511616747.007
Chapman, O. (2005). Constructing pedagogical knowledge of problem solving: preservice mathematics teachers. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 225–232). http://ftp.ict.nsc.ru/mirrors/ftp.emis.de/EMIS/proceedings/PME29/pme29completeproc/pme29vol2adl_fre.pdf#page=231
Conway, A. R. A., Kane, M. J., & Al, C. E. T. (1942). Preview and Guide. Chemical & Engineering News Archive, 20(21), 1399. https://doi.org/10.1021/cen-v020n021.p1399
Cowan, N., Chen, Z., & Rouder, J. N. (2004). Constant capacity in an immediate serial-recall task: A logical sequel to Miller (1956). Psychological Science, 15(9), 634–640. https://doi.org/10.1111/j.0956-7976.2004.00732.x
Friso-Van Den Bos, I., Van Der Ven, S. H. G., Kroesbergen, E. H., & Van Luit, J. E. H. (2013). Working memory and mathematics in primary school children: A meta-analysis. Educational Research Review, 10(October 2017), 29–44. https://doi.org/10.1016/j.edurev.2013.05.003
Fu, Y., & Kartal, O. (2023). Developing Preservice Teachers ’ Self -efficacy and Growth Mindset for Teaching Mathematics : Practices from a Mathematics Methods Course. 25(2), 1–19.
Gathercole, S. E., & Pickering, S. J. (2000). Working memory deficits in children with low achievements in the national curriculum at 7 years of age. British Journal of Educational Psychology, 70(2), 177–194. https://doi.org/10.1348/000709900158047
Hasan, B., Juniati, D., & Masriyah. (2024). Gender and analogical reasoning in mathematics problem solving. AIP Conference Proceedings, 3046(1). https://doi.org/10.1063/5.0195145
Holyoak, H. J., & R. G. Morrison, R. G. (Eds.) (2005).The Cambridge handbook of thinking and reasoning. Cambridge University Press.
Ivankova, N. V., Creswell, J. W., & Stick, S. L. (2006). Using mixed-methods sequential explanatory design: From theory to practice. Field Methods, 18(1), 3–20. https://doi.org/10.1177/1525822X05282260
Jonsson, B., Mossegård, J., Lithner, J., & Karlsson Wirebring, L. (2022). Creative mathematical reasoning: Does need for cognition matter? Frontiers in Psychology, 12(January), 1–10. https://doi.org/10.3389/fpsyg.2021.797807
Juniati, D., & Budayasa, I. K. (2020). Working memory capacity and mathematics anxiety of mathematics undergraduate 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
Juniati, D., & Budayasa, I. K. (2022). The influence of cognitive and affective factors on the performance of prospective mathematics teachers. European Journal of Educational Research, 11(3), 1379–1391. https://doi.org/10.12973/eu-jer.11.3.1379
Kane, M. J., Conway, A. R. A., Miura, T. K., & Colflesh, G. J. H. (2007). Working memory, attention control, and the N-back task: A question of construct validity. Journal of Experimental Psychology: Learning Memory and Cognition, 33(3), 615–622. https://doi.org/10.1037/0278-7393.33.3.615
King, B. (2019). Using teaching through problem solving to transform in-service teachers’ thinking about instruction. Mathematics Teacher Education and Development, 21(1), 169–189.
Kılıçoglu, A. (2018). Qualitative research for educational science researchers: A review of an introduction to qualitative research. The Qualitative Report, 23(4), 949–951. https://doi.org/10.46743/2160-3715/2018.3352
Lerik, M. D. C., Hastjarjo, T. D., & Dharmastiti, R. (2020). Situation awareness viewed from sense of direction and choice of navigation direction. In Proceedings of the 1st International Conference on Psychology (ICPsy):Volume 1 (pp. 352-362), Banda Aceh, Indonesia. https://doi.org/10.5220/0009820503520362
Lithner, J. (2003). Students’ mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52(1), 29–55. https://doi.org/10.1023/A:1023683716659
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. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM Mathematics Education, 49(6), 937–949. https://doi.org/10.1007/s11858-017-0867-3
Mac an Bhaird, C., Nolan, B. C., O’Shea, A., & Pfeiffer, K. (2017). A study of creative reasoning opportunities in assessments in undergraduate calculus courses. Research in Mathematics Education, 19(2), 147–162. https://doi.org/10.1080/14794802.2017.1318084
Marchisio, M., Remogna, S., Roman, F., & Sacchet, M. (2022). Teaching mathematics to non-mathematics majors through problem solving and new technologies. Education Sciences, 12(1). https://doi.org/10.3390/educsci12010034
Miller, H., & Bichsel, J. (2004). Anxiety, working memory, gender, and math performance. Personality and Individual Differences, 37(3), 591–606. https://doi.org/10.1016/j.paid.2003.09.029
Öztürk, M., Akkan, Y., & Kaplan, A. (2020). Reading comprehension, Mathematics self-efficacy perception, and Mathematics attitude as correlates of students’ non-routine Mathematics problem-solving skills in Turkey. International Journal of Mathematical Education in Science and Technology, 51(7). https://doi.org/10.1080/0020739X.2019.1648893
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). https://doi.org/10.1088/1742-6596/1417/1/012055
Polya, G. (1945/2004). How to solve it: A new aspect of mathematical method. Princeton University Press.
Russo, J., & Hopkins, S. (2019). Teachers’ perceptions of students when observing lessons involving challenging tasks. International Journal of Science and Mathematics Education, 17(4), 759–779. https://doi.org/10.1007/s10763-018-9888-9
Schoenfeld, A. H. (1985). Making sense of “out loud” problem-solving protocols. The Journal of Mathematical Behavior, 4(2), 171–191.
Schoenfeld, A. H. (1992). On paradigms and methods: What do you do when the ones you know don’t do what you want them to? Issues in the analysis of data in the form of videotapes. Journal of the Learning Sciences, 2(2), 179–214. https://doi.org/10.1207/s15327809jls0202_3
Shodiq, L. J., Juniati, D., & Susanah. (2023). Influence of personal background on lateral thinking skill of prospective mathematics teachers. AIP Conference Proceedings, 2886(1), 1–8. https://doi.org/10.1063/5.0154628
Steen, L. A. (1999). Twenty questions about mathematical reasoning. In L. V. Stiff & F. R. Curcio (Eds.), Developing mathematical reasoning in grades K–12: Yearbook 1999 (pp. 270–285). NCTM.
Stillman, G. (1996). Mathematical processing and cognitive demand in problem solving. Mathematics Education Research Journal, 8(2), 174–197. https://doi.org/10.1007/BF03217296
Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: a survey. ZDM Mathematics Education, 52(1), 1–16. https://doi.org/10.1007/s11858-020-01130-4
Wang, Y., & Chiew, V. (2010). On the cognitive process of human problem solving. Cognitive Systems Research, 11(1), 81–92. https://doi.org/10.1016/j.cogsys.2008.08.003
White, J., Johnson, P., & Goos, M. (2021). Pre-service teachers as agents of change in the mathematics classroom: A case study. Mathematics Teacher Education and Development, 23(1), 54–73. https://mted.merga.net.au/index.php/mted/article/view/477
Wiley, J., & Jarosz, A. F. (2012). Working memory capacity, attentional focus, and problem solving. Current Directions in Psychological Science, 21(4), 258–262. https://doi.org/10.1177/0963721412447622
