Exploring the Conceptual Understanding of the Quadratic Function Concept in Teachers’ Colleges in Zimbabwe
More details
Hide details
Bindura University of Science Education, ZIMBABWE
Mutare Teachers College, ZIMBABWE
Online publication date: 2019-10-28
Publication date: 2019-10-28
EURASIA J. Math., Sci Tech. Ed 2020;16(2):em1817
This paper reports on an exploration of preservice teachers’ understanding of the quadratic function concept in Zimbabwe. These concepts were taught to preservice teachers studying for a diploma in Education wishing to specialize in the teaching of Ordinary level mathematics. Concerns about high Mathematics failure rate in Zimbabwean Secondary Schools have prompted this investigation into finding out if teachers’ understanding of quadratic function concept could be the cause. The study adopted the APOS (action-process-object-schema) to investigate their conceptual understanding of the concepts. Data were generated from students’ responses to a written task and follow up interviews were used to solicit information from the preservice teachers. A designed genetic decomposition for quadratic concepts was used as an analysis tool. The findings of the study also revealed majority of the pre-service teachers seemed to be operating at the action level of understanding, with very few teachers who have reached the object level. It was noted that the preliminary genetic decomposition failed to accommodate all students’ responses which lead to the development of a modified genetic decomposition.
Akpan, A. A. (1987). Correlation of mathematical problem–solving ability among secondary school students in the Cross River State of Nigeria. Thesis, University of Ibadan.
Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E., Matthews, D., & Thomas, K. (1996). A framework for Research and Development in Undergraduate Mathematics Education, 2, 1-32.
Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics, (pp. 83-104). Westport, CT: Ablex.
Borgen, K. L., & Manu, S. S. (2002). What do students really understand? Journal of Mathematical Behaviour, 21(2), 151-165.
Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23(3), 194-222.
Bourdieu, P., Chamboredon, J. C., & Passeron, J. C. (2000). The Craft of Sociology: Epistemological Preliminaries. New York: Walter de Grayter.
Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process of conception of function. Educational studies in Mathematics, 23, 247-285.
Burke, M., Erickson, D., Lott, J. W., & Obert, M. (2001). Navigating through Algebra in Grades 9-12. Reston, VA: National Council of Teachers of Mathematics.
Burns, S. N., & Grove, S. K. (2003). Understanding nursing research (3rd ed.). Philadelphia: Saunders. Cape Town: AMESA.
Chazan, N. (1992). Africa’s democratic challenge. World Policy Journal, 9(2), 279-307.
Cooney, T. J., & Wilson, M. R. (1993). Teachers’ thinking about fractions; Historical and Research perspectives. In T. Romberg, E. Fennema, & T. Carpenter (Eds.), Integrating research on the graphical representation of functions, (pp. 131-151). Hillsdale, NJ: Lawrence Erlbaum Associates.
Donevska-Todorova, A. (2016, March). Procedural and Conceptual Understanding in Undergraduate Linear Algebra. In First conference of International Network for Didactic Research in University Mathematics.
Dubinsky, E. (1991). Reflective Abstraction. In D. O. Tall (Ed), Advanced Mathematical.
Dubinsky, E., & Harel, G. (1992). The concept of function, aspects of epistemology & pedagogy. MAA Notes, 25, 85-106.
Dubinsky, E., & Mcdonald, M. A. (2001). APOS: A Constructivist Theory of Learning in Undergraduate Mathematics Education Research. In: D. Holton, M. Artigue, U. Kirchgräber, J. Hillel, M. Niss, A. Schoenfeld (Eds.), The Teaching and Learning of Mathematics at University Level. New ICMI Study Series, vol 7. Springer, Dordrecht.
Ellis, A. B., & Grinstead, P. (2008). Hidden lessons: How a focus on slope-like properties of quadratic functions encouraged unexpected generalizations. The Journal of Mathematical Behavior, 27(4), 277-296.
Fajemidagba, M. O. (1986). Mathematical word problem solving: An analysis of errors committed by students. The Nigerian Journal of Guidance and Counseling, 2(i), 23-30.
Grossman, P. L., Wilson, S. M., & Shulman, L. S. (1989). Teachers of substance: Subject matter knowledge for teaching. Profesorado, Revista de Currículum y Formación del Profesorado, 9(2), 1-25.
Hartley, J. (2004). Case study research. In C. Cassell & G. Symon (Eds.), Essential guide to qualitative methods in organizational research (pp. 323-333). London: Sage.
Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development institutes. Journal for research in mathematics education, 330-351.
Ibeawuchi, E. O. (2010). The role of pedagogical content knowledge in the learning of quadratic functions. Pretoria.
Jojo, Z. M. M. (2011). An APOS exploration of the conceptual understanding of the chain rule in calculus b first year engineering students (Unpublished Doctoral Thesis), University of KwaZulu-Natal, South Africa.
Kotsopoulos, D. (2007). Unravelling student challenges with quadratics. Australian Mathematics Teacher, 63(2), 19-24.
Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning and teaching. Review of Educational Research, 60, 1-64.
Maharaj, A. (2013). An APOS analysis of natural science students’ understanding of mathematics at University level: An ICMI study. South African Journal of Education, 33(1).
Ndlovu, D., & Brijlall, D. (2015). Pre-service Teachers mental constructions of concepts in Matrix Algebra. African Journal of Research in Mathematics Science and Technology Education, 19(2), 1-16.
Owens, J. E. (1992). Families of parabola. The Mathematics Teacher, 85(6), 477-479.
Parameswaran, R. (2007). On Understanding the Notion of Limits and Infinitesimal Quantities, International Journal of Science and mathematics Education, 5(2), 193-216.
Parent, J. S. S. (2015). Students’ understanding of quadratic functions: Learning from students’ voices. Doctor of Education. University of Vermont.
Romberg, T. A., & Fredric W. T. (1992). Mathematics Curriculum Engineering: Some Suggestions from Cognitive Science, The Monitoring of School mathematics: Background Papers, (2).
Shulman, L. (1986). Knowledge and teaching: Foundations of the new reform. Harvard educational review, 57(1), 1-23.
Siyepu, S. W. (2013). Students’ interpretations in learning derivatives in a university Thinking, (pp. 95–123), Dordrecht: Kluwer Academic Publishers.
Zaslavsky, O. (1997). Conceptual obstacles in the learning of quadratic functions. Focus on Learning Problems in Mathematics, 19(1), 20-44.