Enhancing Upper Secondary Learners’ Problem-solving Abilities using Problem-based Learning in Mathematics
Keywords:mathematical problem-solving; problem-solving abilities; problem-solving processes; problem-based learning; secondary school learners; Rwandan schools
Developing problem-solving abilities is a major objective of learning mathematics at school. However, learners’ problem-solving abilities are still critical. The main purpose of this study was to investigate how the problem-based learning model could enhance learners’ problem-solving abilities in mathematics. The study used quasi-experimental research with one group pre-test-post-test design. The population in this study consisted of fifty-four grade eleven learners (aged between 16 to 19 years old) from one school in Kayonza District in Rwanda. Data were collected using mathematical problem-solving tests and interviews and were analysed using paired t-tests for dependent sample means and descriptive analysis. The study results indicate that problem-based learning potentially impacts learners’ problem-solving abilities. It is shown from learners’ work in problem-solving that all indicators of problem-solving abilities, namely understanding the problem, planning ways to approach the problem, monitoring the progress while tackling the problem and reviewing the solution process, emerged as being fairly well improved. In addition, based on the interview results from some learners and their teachers, they like the PBL model because embedded tasks helped them to apply the knowledge that can improve their reasoning, creativity and thinking capability. The study recommends that schools encourage teachers to adopt PBL for enhancing learners’ problem-solving abilities. Additionally, researchers are urged to use findings from this study as a reference for further research. Furthermore, researchers could conduct similar research on a large scale using different methodologies.
Aksela, M., & Haatainen, O. (2019). Project-based learning (PBL) in practice : Active teachers’ views of its advantages and challenges. Proceedings of the 5th International STEM in Education Conference, 9–16.
Alise, M. A., & Teddlie, C. (2010). A continuation of the paradigm wars? Prevalence rates of methodological approaches across the social/behavioral sciences. Journal of Mixed Methods Research, 4(2), 103–126. https://doi.org/10.1177/1558689809360805
Astriani, N., Surya, E., & Syahputra, E. (2017). The effect of problem-based learning to students’ mathematical problem-solving ability. International Journal Of Advance Research and Innovative Ideas in Education, 3(2), 3441–3446.
Bostic, J. D. (2011). The effects of teaching mathematics through problem-solving contexts on sixth-grade students' problem-solving performance and representation use [Doctoral dissertation]. University of Florida.
C?prioar?, D. (2015). Problem solving - Purpose and means of learning mathematics in school. Procedia - Social and Behavioral Sciences, 191, 1859–1864. https://doi.org/10.1016/j.sbspro.2015.04.332
Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 119–142. https://doi.org/10.3102/01623737025002119
Craig, T. T., & Marshall, J. (2019). Effect of project-based learning on high school Students ’ state-mandated, standardized math and science exam performance. Journal of Research in Science Teaching, 56(10), 1461–1488. https://doi.org/10.1002/tea.21582
Darma. (2018). Improving mathematical problem-solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic. Proceedings of the 2nd International Joint Conference on Science and Technology (IJCST), 1–11.
Desi, Lesmini, B., & Hidayat, I. (2019). Enhancing student problem solving skills through worksheets-assisted problem-based learning. Journal of Physics: Conference Series, 1166(1). https://doi.org/10.1088/1742-6596/1166/1/012005
Gravemeijer, K., Stephan, M., Julie, C., Lin, F. L., & Ohtani, M. (2017). What mathematics education may prepare students for the society of the future? International Journal of Science and Mathematics Education, 15(1), 105–123. https://doi.org/10.1007/s10763-017-9814-6
Kivunja, C., & Kuyini, A. B. (2017). Understanding and applying research paradigms in educational contexts. International Journal of Higher Education, 6(5), 26. https://doi.org/10.5430/ijhe.v6n5p26
Klegeris, A., & Hurren, H. (2011). Impact of problem-based learning in a large classroom setting : Student perception and problem-solving skills. Advances in Physiology Education, 35, 408–415. https://doi.org/10.1152/advan.00046.2011.
Merritt, J., Lee, M. Y., Rillero, P., & Kinach, B. M. (2017). Problem-based learning in K – 8 mathematics and science education : A literature review. The Interdisciplinary Journal of Problem-Based Learning, 11(2), 5–17.
Mukuka, A., Balimuttajjo, S., & Mutarutinya, V. (2020). Applying the SOLO taxonomy in assessing and fostering students' mathematical problem-solving abilities. Problems of Education in the 21st Century, 77(6), 13.
Novita, R., Zulkardi, & Hartono, Y. (2012). Exploring primary students' problem-solving ability by doing tasks like PISA’s question. IndMS. J.M.E, 3(2), 133–150.
Osman, A., & Kriek, J. (2021). Science teachers’ experiences when implementing problem-based learning in rural schools. African Journal of Research in Mathematics, Science and Technology Education, 0(0), 1–12. https://doi.org/10.1080/18117295.2021.1983307
Padmavathy, R. D., & Mareesh, K. (2013). Effectiveness of problem-based learning in mathematics. International Multidisciplinary E-Journal, II(I), 45–51. www.shreeprakashan.com
Polya, G. (1945). How to solve it mathematical method (2nd ed.). Doubleday Company.
Prastiti, T. D., Dafik, & Azkarahman, A. R. (2020). The application of problem-based learning in mathematics education on several South East Asia high schools. Pancaran, 9(4), 75–89. https://doi.org/10.25037/pancaran.v9i4.317
Purwoko, R. Y., Nugraheni, P., & Instanti, D. (2019). Implementation of pedagogical content knowledge model in mathematics learning for high school. Proceedings of the 1st UPY International Conference on Applied Science and Education 2018, 1–6. https://doi.org/10.1088/1742-6596/1254/1/012079
Razieh, T. N. (2016). Bandura’ s social learning theory & social cognitive learning theory. Journal of Personality and Social Psychology, 1, 589.
Republic of Rwanda. Rwanda Education Board (REB). (2015). Competency-based curriculum -- summary of curriculum framework pre-primary to upper secondary. https://mudarwan.files.wordpress.com/2015/08/curriculum_framework_final_printed-compressed.pdf
Rosli, R., Goldsby, D., & Capraro, M. M. (2013). Assessing students ’ mathematical problem-solving and problem-posing skills. Asian Social Science, 9(16), 54–60. https://doi.org/10.5539/ass.v9n16p54
Savery, J. R. (2019). Comparative pedagogical models of problem-based learning. The Wiley Handbook of Problem-Based Learning, 81–104. https://doi.org/10.1002/9781119173243.ch4
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In D.A. Grouws (Ed.), NCTM Handbook of research on mathematics teaching and learning (pp. 334–370). Macmillan.
Setiana, D. S., Purwoko, Y. R., & Sugiman, S. (2021). The application of mathematics learning model to stimulate mathematical critical thinking skills of senior high school students. European Journal of Educational Research, 10(1), 509–523. https://doi.org/10.12973/eu-jer.10.1.509
Setiawan, B., & Supiandi, M. I. (2018). The contribution of metacognitive skills and reasoning skills on problem-solving ability based on problem-based learning (PBL ) model. Anatolian Journal of Education, 3(2), 75–86.
Sigurdson, S. E., Olson, A. T., & Mason, R. (1994). Problem solving and mathematics learning. Journal of Mathematical Behavior, 13, 361–388.
Simamora, R. E., & Saragih, S. (2019). Improving students’ mathematical problem-solving ability and self-efficacy through guided discovery learning in local culture context. International Electronic Journal of Mathematics Education, 14(1), 61–72. https://doi.org/https://doi.org/10.12973/iejme/3966
Siregar, N. (2017). Problem-solving ability of students mathematics in problem-based learning. Journal of Educational Science and Technology, 3(3), 185–189.
Stacey, K. (2005). The place of problem solving in contemporary mathematics curriculum documents. Journal of Mathematical Behavior, 24(3–4), 341–350.
Surya, E., Putri, F. A., & Mukhtar. (2017). Improving mathematical problem-solving ability and self-confidence of high school students through contextual learning model. Journal on Mathematics Education, 8(1), 85–94. https://doi.org/10.22342/jme.8.1.3324.85-94
Szabo, Z. K., Körtesi, P., Guncaga, J., Szabo, D., & Neag, R. (2020). Examples of problem-solving strategies in mathematics education supporting the sustainability of 21st-century skills. Sustainability Article, 12(10113), 1–28.
Szetala, W., & Nicol, C. (1992). Evaluating problem-solving in mathematics. Educational Leadership, 49(8), 42–45.
Ukobizaba, F., Nizeyimana, G., & Mukuka, A. (2021). Assessment strategies for enhancing students’ mathematical problem-solving skills : A review of literature. Eurasia Journal of Mathematics, Science and Technology Education, 17(3), 2–10.
Valdez, J. E., & Bungihan, M. E. (2019). Problem-based learning approach enhances the problem solving skills in chemistry of high school students. Journal of Technology and Science Education, 9(3), 282–294. https://doi.org/10.3926/JOTSE.631
Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., & Ratinckx, E. (1999). Learning to solve mathematical application problems: A design experiment with fifth graders. Mathematical Thinking and Learning, 1(3), 195–229. https://doi.org/10.1207/s15327833mtl0103_2
Voskoglou, M. G. (2011). Problem-solving from Polya to nowadays : A review and future perspectives. In A.R. Baswell (Ed). Advances in mathematics research, 12(1), 1-18. Nova Publishers.
Vygotsky, L., & Cole, M. (2018). Lev Vygotsky: Learning and social constructivism. Learning theories for early years practice, 58.
Vygotsky, L. S. (1978). Minds in society: The development of higher pschological processes. Harvard University Press. https://doi.org/10.2307/j.ctvjf9vz4
Yu, K.-C., Fan, S.-C., & Lin, K. (2014, November). Enhancing students ’ problem-solving skills through context-based learning. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-014-9567-4
Copyright (c) 2022 Aline Dorimana, Alphonse Uworwabayeho, Gabriel Nizeyimana
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All articles published by IJLTER are licensed under a Creative Commons Attribution Non-Commercial No-Derivatives 4.0 International License (CCBY-NC-ND4.0).