Pre-service Teachers’ Perception of the Benefits of Problem-solving and Strategies Used to Solve Mathematical Problems: A Case from some Colleges of Education in Ghana
DOI:
https://doi.org/10.26740/jomp.v6n2.p113-125Keywords:
Problem-solving, Pre-service teachers, Benefits, Mathematical problemsAbstract
The quality of pre-service mathematics teacher education depends greatly on their understanding of mathematical problem-solving and its pedagogy. This study investigates pre-service teachers’ perceptions of the benefits of problem-solving in mathematics and the strategies they employ to solve problems. A qualitative design was adopted, involving 30 randomly selected participants from three Colleges of Education in Ghana. Data were collected through semi-structured interviews, transcribed, and analyzed thematically. Findings reveal that participants possess substantial knowledge of the benefits of problem-solving, including developing critical thinking and understanding, fostering intellectual challenge, enhancing real-life application skills, achieving set goals, overcoming difficulties, and selecting appropriate strategies. The study also highlights the range of strategies used by pre-service teachers, such as visual representation, logical reasoning, and varied heuristic approaches. These insights underscore the need to strengthen problem-solving pedagogy in teacher preparation programs to enhance both mathematical understanding and teaching practice.
References
Ahmed, F., & Aziz, J. (2009). Students’ perception of their teachers’ teaching of literature: Communicating and understanding through the eyes of the audience. European Journal of Social Sciences, 7(3), 17–26.
Archibald, S. (2006). Narrowing in on educational resources that do affect student achievement. Peabody Journal of Education, 81(4), 23–42. https://doi.org/10.1207/s15327930pje8104_2
Baker, K., Jessup, N. A., Jacobs, V. R., Empson, S. B., & Case, J. (2020). Productive struggle in action. Mathematics Teacher: Learning and Teaching PK–12, 113(5), 361–367. https://doi.org/10.5951/MTLT.2019.0060
Berenger, A. (2018). Pre-service teachers' difficulties with problem solving. Mathematics Education Research Group of Australasia. https://eric.ed.gov/?id=ED592470
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
Bogdan, R. C., & Biklen, S. K. (1998). Foundations of qualitative research in education: An introduction to theory and methods (1st ed.). Allyn & Bacon.
Buabeng, I., Ntow, F. D., & Otami, C. D. (2020). Teacher education in Ghana: Policies and practices. Journal of Curriculum and Teaching, 9(1), 86–95. https://doi.org/10.5430/jct.v9n1p86
Cahyani, N. P. I., Suarsana, I. M., & Mahayukti, G. A. (2021). Improving students’ mathematical problem-solving skills through relating–experiencing–applying–cooperating–transferring learning strategy and graphic organizer. In First International Conference on Science, Technology, Engineering and Industrial Revolution (ICSTEIR 2020) (pp. 337–344). Atlantis Press. http://creativecommons.org/licenses/by-nc/4.0/
Chambel, T., & Guimarães, N. (2005). Learning styles and multiple intelligences. In Encyclopedia of Distance Learning (pp. 1237–1247). IGI Global.
Cooney, T. J., & Shealy, B. E. (1997). On understanding the structure of teachers' beliefs and their relationship to change. In E. Fennema & B. Nelson (Eds.), Mathematics teachers in transition (pp. 87–109). Lawrence Erlbaum Associates.
Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). Sage Publications.
Darling-Hammond, L., & Baratz-Snowden, J. (2005). A good teacher in every classroom: Preparing the highly qualified teachers our children deserve. Jossey-Bass.
Doorman, M., Drijvers, P., Dekker, T., van den Heuvel-Panhuizen, M., de Lange, J., & Wijers, M. (2007). Problem solving as a challenge for mathematics education in The Netherlands. ZDM, 39, 405–418. https://doi.org/10.1007/s11858-007-0043-2
Elia, I., & Philippou, G. (2004). The functions of pictures in problem solving. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 327–334). Bergen University College.
Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp. 249–253). Falmer Press.
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, 105–123. https://doi.org/10.1007/s10763-017-9814-6
Handal, B., & Herrington, A. (2003). Mathematics teachers’ beliefs and curriculum reform. Mathematics Education Research Journal, 15(1), 59–69. https://doi.org/10.1007/BF03217369
Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202. https://doi.org/10.5951/jresematheduc.41.2.0169
Jurdak, M. E. (1991). Teachers' conceptions of math education and the foundations of mathematics. In Proceedings of the 15th International Conference for the Psychology of Mathematics Education (pp. 137–144). PME.
Kalmykova, Z. I. (1975). Processes of analysis and synthesis in the solution of arithmetic problems. Soviet Studies in the Psychology of Learning and Teaching Mathematics, 11, 1–171.
Lester Jr, F. K., & Cai, J. (2016). Can mathematical problem solving be taught? Preliminary answers from 30 years of research. In F. K. Lester Jr. & J. Cai (Eds.), Posing and solving mathematical problems: Advances and new perspectives (pp. 117–135). Springer. https://doi.org/10.1007/978-3-319-28023-3_8
Mudaly, V. (2021). Constructing mental diagrams during problem-solving in mathematics. Pythagoras, 42(1), a633. https://doi.org/10.4102/pythagoras.v42i1.633
Mutodi, P., & Ngirande, H. (2014). The influence of students’ perceptions on mathematics performance: A case of a selected high school in South Africa. Mediterranean Journal of Social Sciences, 5(3), 431–434. https://doi.org/10.5901/mjss.2014.v5n3p431
Nisbet, S., & Warren, E. (2000). Primary school teachers’ beliefs relating to mathematics, teaching and assessing mathematics and factors that influence these beliefs. Mathematics Teacher Education and Development, 2, 34–47.
Novita, R., Zulkardi, Z., & Hartono, Y. (2012). Exploring primary students' problem-solving ability by doing tasks like PISA's question. Indonesian Mathematical Society Journal on Mathematics Education, 3(2), 133–150. https://doi.org/10.22342/jme.3.2.571.133-150
Perkilla, P. (2003). Primary school teachers’ mathematics belief and teaching practice. In Proceedings of the 3rd Conference of the European Society for Research in Mathematics Education.
Polit, D. F., & Hungler, B. P. (1999). Nursing research: Principles and method (6th ed.). Lippincott.
Polya, G. (1962). Mathematical discovery: On understanding, learning, and teaching problem solving (Vol. 1). Wiley.
Royster, D. C., Harris, M. K., & Schoeps, N. (1999). Dispositions of college mathematics students. International Journal of Mathematical Education in Science and Technology, 30(3), 317–333. https://doi.org/10.1080/002073999287851
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004
Simon, H. A. (1973). The structure of ill-structured problems. Artificial Intelligence, 4(3–4), 181–201. https://doi.org/10.1016/0004-3702(73)90011-8
Skemp, R. R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26(3), 9–15. http://www.jstor.org/stable/41187667
Sullivan, P., & Mousley, J. (2001). Thinking teaching: Seeing mathematics teachers as active decision makers. In F.-L. Lin & T. J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 147–163). Kluwer Academic Publishers. https://doi.org/10.1007/978-94-010-0828-0_7
Teo, W. L. (1997). Espoused beliefs of Singapore teachers about mathematics and its teaching and learning (Master’s thesis). Ontario Institute for Studies in Education, University of Toronto.
Thompson, A. G. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). Macmillan Publishing.
Tolsberg, K., Põldre, S., & Kikas, E. (2022). Learner-generated drawing as a learning strategy: The effect of teacher-guided intervention program “Learning with Understanding” on composing drawings in math word problems in the primary grades. Frontiers in Education, 7, 962067. https://doi.org/10.3389/feduc.2022.962067
Vygotsky, L. S., & Cole, M. (1978). Mind in society: Development of higher psychological processes. Harvard University Press.
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