The European Educational Researcher

Teacher Interventions using Guided Discovery and Mathematical Modelling in Grade 10 Financial Mathematics

The European Educational Researcher, Volume 6, Issue 2, June 2023, pp. 35-53
OPEN ACCESS VIEWS: 549 DOWNLOADS: 401 Publication date: 15 Jun 2023
ABSTRACT
Minimal guidance or maximal independence? How can teachers achieve that complex balance when teaching mathematics? This pre-and post-test quasi-experimental research study explored the above questions in Grade 10 Financial Mathematics following guided discovery and mathematical modelling frameworks. Fifty-four (54) Grade 10 students at a Government High School in Johannesburg, South Africa, participated in the study. One group of students was taught following guided discovery and modelling learning principles and another group was taught following direct instruction. Students mean scores were compared at the end of the intervention. The main findings revealed that although the overall performance in the post-test was similar in both groups, there was a significant difference in understanding the concept of compound interest in the guided discovery learning group. The research highlights the promise of guided discovery learning and modelling approach over direct instruction, especially on supporting the understanding of difficult concepts in financial mathematics.
KEYWORDS
Guided discovery, mathematical modelling, financial mathematics, direct instruction, compound interest, quasi-experimental, Grade 10
CITATION (APA)
Ekol, G., & Greenop, S. (2023). Teacher Interventions using Guided Discovery and Mathematical Modelling in Grade 10 Financial Mathematics. The European Educational Researcher, 6(2), 35-53. https://doi.org/10.31757/euer.623
REFERENCES
  1. Alfieri, L., Brooks, P.J., Aldrich, N.J. & Tenenbaum, H.R. (2011). Does discovery-based instruction enhance learning? Journal of Educational Psychology, 103, 1-18. https://doi.org/10.1037/a0021017
  2. Asempapa, R. S. & Sturgill, D. J. (2019). Mathematical Modeling: Issues and Challenges in Mathematics Education and Teaching. Journal of Mathematics Research, 11(5), 71-78. https://doi.org/10.5539/jmr.v11n5p71
  3. Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp.73 -96). Cham: Springer. https://doi.org/10.1007/978-3-319-12688-3
  4. Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt? Journal of mathematical modelling and applications, 1(1), 45-58. https://proxy.furb.br/ojs/index.php/modelling/index
  5. Blum, W., Galbraith, P. L., Henn, H-W., & Niss, M. (2007). Modelling and applications in mathematics education. The 14th ICMI Study. New York: Springer. https://doi.org/10.1007/978-0-387-29822-1_59
  6. Blum, W. & Leiβ, D. (2007). In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering, and economics: Proceedings from the twelfth International Conference on the Teaching of Mathematical Modelling and Applications (pp. 222-231). Chichester: Horwood. ISBN-13: 978-1-904275-20-6):
  7. De Jong, T. & Lazonder, A. W. (2014). The guided discovery learning principle in multimedia learning. In R. Mayer (Ed), The Cambridge handbook of multimedia learning (2nd edition) (pp. 371 - 390). Cambridge: Cambridge University Press. ISBN 978-1-107-03520-1 (Hardback); ISBN 978-1-107-61031-6 (paperback).
  8. Dekker, R. & Elshout-Mohr, M. (2004). Teacher interventions aimed at mathematical level raising during collaborative learning. Educational Studies in Mathematics, 56, 39-65. https://www.jstor.org/stable/pdf/4150263.pdf
  9. Department of Basic Education (2011). Curriculum and Assessment Policy Statement Grades 10 - 12 Mathematics. Pretoria, South Africa. https://www.jstor.org/stable/pdf/4150263.pdf
  10. Durandt, R., Blum, W., & Lindl, A. (2022). Fostering mathematical modelling competency of South African engineering students: which influence does the teaching design have? Educational Studies in Mathematics, 109(2), 361-381. https://doi.org/10.1007/s10649-021-10068-7
  11. Ellis, R., Loewen, S., & Erlam, R. (2006). Implicit and explicit corrective feedback and the acquisition of L2 grammar. Studies in second language acquisition, 28(2), 339-368.https://doi.org/10.1017/S0272263106060141
  12. Furtak, E. M., Seidel, T., Iverson, H. & Briggs, D. C. (2012). Experimental and quasi-experimental studies of inquiry-based science teaching. Review of Educational Research, 82, 300-329. https://doi.org/10.3102/0034654312457206
  13. Geiger, V., Galbraith, P., Niss, M., & Delzoppo, C. (2022a). Developing a task design and implementation framework for fostering mathematical modelling competencies. Educational Studies in Mathematics, 109(2), 313-336. https://doi.org/10.1007/s10649-021-10039-y
  14. Geiger, V., Galbraith, P., Niss, M., & Holland-Twining, B. (2022b). A Typology for Instructional Enablers of Mathematical Modelling. Mathematics Education Research Group of Australasia. https://files.eric.ed.gov/fulltext/ED623748.pdf
  15. Hmelo-Silver, C. E., Duncan, R. G. & Chinn, C. A. (2007). Scaffolding and achievement in problem-based and inquiry learning: A response to Kirschner, Sweller, and Clark. Educational Psychologist, 42, 99-107. https://doi.org/10.1080/00461520701263368
  16. Lazonder, A. W. & Kamp, E. (2012). Bit by bit or all at once? Splitting up the inquiry task to promote children's scientific reasoning. Learning and Instruction, 22, 458-464. https://doi.org/10.1016/j.learninstruc.2012.05.005
  17. Lazonder, A. W. & Harmsen, R. (2016). Meta-analysis of inquiry-based learning: Effects of guidance. Review of Educational Research, 86(3), 681-718. https://doi.org/10.3102/0034654315627366
  18. Leiβ, D. &. Wiegand, B. (2005). A classification of teacher interventions in mathematics teaching. ZDM, 37 (3), 240-245. https://link.springer.com/content/pdf/10.1007/s11858-005-0015-3.pdf
  19. Mayer, R. E. (2004). Should there be a three-strikes rule against pure discovery learning? American Psychologist, 59, 14-19. https://doi.org/10.1037/0003-066X.59.1.14
  20. Meyer, H. (1999). UnterrichtsMethoden. Teil II: Praxisband. Frankfurt: Cornelsen Scriptor. ISBN: 3-9806975-9-2
  21. Osborne, J. & Dilon, J. (2008). Science Education in Europe: Critical Refelctions. London: Nuffield Foundation. http://efepereth.wdfiles.com/local--files/science-education/Sci_Ed_in_Europe_Report_Final.pdf
  22. Pournara, C. (2015). Talking Time, Seeing Time: The Importance of Attending to Time in Financial Mathematics. African Journal of Research in Mathematics, Science and Technology Education, 19(1), 82-94. https://doi.org/10.1080/10288457.2015.1014235
  23. Wess, R. K., Klock, H., Siller, H. S. & Greefrath, G. (2021). Measuring professional competence for teaching of mathematical modelling: A test instrument. Cham: Springer Nature. https://doi.org/10.1007/978-3-030-78071-5
  24. Zulkarnaen, R. (2018). Why is mathematical modeling so difficult for students? In AIP Conference Proceedings (Vol. 2021, No. 1, p. 060026). AIP Publishing LLC. https://doi.org/10.1063/1.5062790
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