Dysfunctional Functions: The Case of Zambian Mathematics Education Students

Priestly Malambo; Sonja van Putten; Hanlie Botha; Gerrit Stols

doi:10.29333/ejmste/99510

Full Text (PDF)

Priestly Malambo ¹, Sonja van Putten ² ^* , Hanlie Botha ², Gerrit Stols ²

More Detail

¹ University of Zambia, Lusaka, ZAMBIA² University of Pretoria, Pretoria, Gauteng, SOUTH AFRICA^* Corresponding Author

Abstract

This study investigated student mathematics teachers’ ability to recognise and explain their understanding of school level functions. We challenged the assumption that studying advanced mathematics automatically develops an understanding of school mathematics that is sufficient to explain concepts and justify reasoning. This case study tested this assumption by exploring the depth of pre-service mathematics student teachers’ understanding of school function concepts at the University of Zambia. The test items required calculation, as well as justification of the answers, and an explanation of the concepts. Of the 22 participants, all final year mathematics education students, 18 student teachers scored below the 50% pass mark. The average mark was 8 out of a possible 28 (27%). The majority of the participants found it difficult to explain and justify their reasoning. This study resulted in the development of a new school mathematics module for prospective mathematics teachers at the University of Zambia.

Keywords

mathematics education students
secondary school functions
mathematical knowledge for teaching

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2019, Volume 15, Issue 1, Article No: em1651

https://doi.org/10.29333/ejmste/99510

Publication date: 01 Nov 2018

Article Views: 3242

Article Downloads: 3577

Open Access References How to cite this article

References

Akkoc, H. (2008). Pre-service mathematics teachers’ concept images of radian. International Journal of Mathematical Education in Science & Technology, 39(7), 857-878. https://doi.org/10.1080/00207390802054458.
Bair, S. L., & Rich, B. S. (2011). Characterizing the Development of Specialized Mathematical Content Knowledge for Teaching in Algebraic Reasoning and Number Theory. Mathematical Thinking & Learning, 13(4), 292-321. https://doi.org/10.1080/10986065.2011.608345.
Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144. https://doi.org/10.2307/749140.
Bayazit, I. (2011). Prospective Teachers’ Inclination to Single Representation and Their Development of the Function Concept. Educational Research and Reviews, 6(5), 436-446. Retrieved from https://academicjournals.org/journal/ERR/article-abstract/6C23F115280.
Bayazit, I., & Gray, E. (2004). Understanding inverse functions: the relationship between teaching practice and student learning. Paper presented at the Proceedings of the 28th Conference of the International.
Bell, J. (2014). Doing Your Research Project: A guide for first-time researchers. UK: McGraw-Hill Education.
Bromme, R. (1994). Beyond subject matter: A psychological topology of teachers’ professional knowledge. In R. Biehler, W. R. Scholz, R. StraBer, R., & B. Winkelmann (Eds.), Didactics of mathematics as a scientific discipline (pp. 73-88). The Netherlands: Kluwer Academic Publishers.
Bryan, T. J. (1999). The conceptual knowledge of preservice secondary mathematics teachers: How well do they know the subject matter they will teach. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal. Volume 1: Content Knowledge.
Chesler, J. (2012). Pre-service Secondary Mathematics Teachers Making Sense of Definitions of Functions. Mathematics Teacher Education and Development, 14(1), 27-40.
Clement, L. (2001). What do students really know about functions. MatheMaticS teacher, 94(9), 745-748.
Cooney, T. J., & Wiegel, H. G. (2003). Examining the mathematics in mathematics teacher education. In A. J. C. M. A. K., C. Bishop; J. Kilpatrick, & F.K.S. Leung (Ed.), Second International Handbook of Mathematics Education (pp. 795). Netherlands: Kluwer Academic Publishers.
Dede, Y., & Soybaş, D. (2011). Preservice mathematics teachers’ experiences about function and equation concepts. Eurasia Journal of Mathematics, Science & Technology Education, 7(2), 89-102. https://doi.org/10.12973/ejmste/75183.
Dubinsky, E., & Harel, G. (1992). The nature of the process conception of function. The concept of function: Aspects of epistemology and pedagogy, 25, 85-106.
Dubinsky, E., & Wilson, R. T. (2013). High school students’ understanding of the function concept. The Journal of Mathematical Behavior, 32(1), 83-101. https://doi.org/10.1016/j.jmathb.2012.12.001.
Evangelidou, A., Spyrou, P., Elia, I., & Gagatsis, A. (2004). University students’ conceptions of function. Paper presented at the Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education.
Even, R. (1990). Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21(6), 521-544. https://doi.org/10.1007/BF00315943.
Even, R. (1993). Subject-Matter Knowledge and Pedagogical Content Knowledge: Prospective Secondary Teachers and the Function Concept. Journal for Research in Mathematics Education, 24(2), 94-116. https://doi.org/10.2307/749215.
Fi, C. (2003). Preservice secondary school mathematics teachers’ knowledge of trigonometry: subject matter content knowledge, pedagogical content knowledge, & envisioned pedagogy (PhD thesis). University of Iowa.
Fi, C. (2006). Pre-service secondary school mathematics mathematics teachers’ knowledge of trigonometry: Cofunctions Paper presented at the Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Mérida, México.
Gerson, H. (2008). David’s Understanding of Functions and Periodicity. School Science and Mathematics, 108(1), 28-38. https://doi.org/10.1111/j.1949-8594.2008.tb17937.x.
Haambokoma, C., Nkhata, B., Kostyuk, V. S., Chabalengula, V., Mbewe, S., Tabakamulamu, M., Ndhlovu, Z. B., Mushanga, R., & Nthani, D. (2002). Strengthening of Mathematics and Science Education in Zambian Secondary schools. Lusaka: Ministry of Education.
Henning, E. (2014). Matric begins in Grade 1. The Con, 13th January 2014.
Hiebert, J. (2013). Conceptual and procedural knowledge: The case of mathematics. UK: Routledge. https://doi.org/10.4324/9780203063538.
Jojo, Z., Brijlall, D., & Maharaj, A. (2011). The reliability of a research instrument used to measure mental constructs in the learning of the chain rule in calculus. Paper presented at the Proceedings of the 16th Annual Congress of the Association of Mathematics Education of South Africa.
Kambilombilo, D., & Sakal, W. (2015). An Investigation into the Challenges In-Service Student Teachers Encounter in Transformational Geometry, “Reflection and Rotation”: The Case of Mufulira College of Education. Journal of Education and Practice, 6(2), 139-149.
Lee, J., & Zuilowski, S. S. (2015). ‘Making do’: Teachers’ coping strategies for dealing with textbook shortages in urban Zambia. Teaching and Teacher Education, (48), 117-128. https://doi.org/10.1016/j.tate.2015.02.008.
Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of educational research, 60(1), 1-64. https://doi.org/10.3102/00346543060001001.
Lloyd, G., Beckmann, S., Zbiek, R. M., & Cooney, T. (2010). Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9-12. ERIC.
Malambo, P. (2015). Exploring Zambian Mathematics student teachers’ content knowledge of functions and trigonometry for secondary schools (PhD thesis). University of Pretoria, South Africa.
Markovits, Z., Eylon, B. S., & Bruckheimer, M. (1986). Functions today and yesterday. For the learning of mathematics, 18-28. Retrieved from https://www.jstor.org/stable/40247808.
Ministry of Education. (2013a). “O” Level Mathematics Syllabus (Grades 10 to 12) Lusaka, Zambia: Zambia Curriculum Development Centre.
Ministry of Education. (2013b). Zambia Education Curriculum Framework. Lusaka: Zambia Curriculum Development Centre.
Nyikahadzoyi, M. R. (2013). Teachers’ Knowledge of the concept of a function: A theoretical framework. International Journal of Science and Mathematics Education, 1-23. https://doi.org/10.1007/s10763-013-9486-9.
Spyrou, P., & Zagorianakos, A. (2010). Greek students’ understandings of the distinction between function and relation. Research in Mathematics Education, 12(2), 163-164. https://doi.org/10.1080/14794802.2010.496988.
Steele, M. D., Hillen, A. F., & Smith, M. S. (2013). Developing mathematical knowledge for teaching in a methods course: the case of function. Journal of Mathematics Teacher Education, 16(6), 451-482. https://doi.org/10.1007/s10857-013-9243-6.
Thames, M. H., Ball, D. L., & Phelps, G. (2008). Content Knowledge for Teaching What Makes It Special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554.
Watson, A., & Harel, G. (2013). The role of teachers’ knowledge of functions in their teaching: A conceptual approach with illustrations from two cases. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 154-168. https://doi.org/10.1080/14926156.2013.784826.
Wilburne, J. M., & Long, M. (2010). Secondary Pre-Service Teachers’ Content Knowledge for State Assessments: Implications for Mathematics Education Programs. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1. Retrieved from https://eric.ed.gov/?id=EJ872484.
Wilson, M. R. (1994). One preservice secondary teacher’s understanding of function: The impact of a course integrating mathematical content and pedagogy. Journal for Research in Mathematics Education, 346-370. https://doi.org/10.2307/749238.
Wood, E. (1993). Making the connections: The mathematical understandings of prospective secondary teachers (PhD thesis). Michigan State University East Lansing, MI.

How to cite this article

APA

Malambo, P., van Putten, S., Botha, H., & Stols, G. (2019). Dysfunctional Functions: The Case of Zambian Mathematics Education Students. Eurasia Journal of Mathematics, Science and Technology Education, 15(1), em1651. https://doi.org/10.29333/ejmste/99510

Vancouver

Malambo P, van Putten S, Botha H, Stols G. Dysfunctional Functions: The Case of Zambian Mathematics Education Students. EURASIA J Math Sci Tech Ed. 2019;15(1):em1651. https://doi.org/10.29333/ejmste/99510

AMA

Malambo P, van Putten S, Botha H, Stols G. Dysfunctional Functions: The Case of Zambian Mathematics Education Students. EURASIA J Math Sci Tech Ed. 2019;15(1), em1651. https://doi.org/10.29333/ejmste/99510

Chicago

Malambo, Priestly, Sonja van Putten, Hanlie Botha, and Gerrit Stols. "Dysfunctional Functions: The Case of Zambian Mathematics Education Students". Eurasia Journal of Mathematics, Science and Technology Education 2019 15 no. 1 (2019): em1651. https://doi.org/10.29333/ejmste/99510

Harvard

Malambo, P., van Putten, S., Botha, H., and Stols, G. (2019). Dysfunctional Functions: The Case of Zambian Mathematics Education Students. Eurasia Journal of Mathematics, Science and Technology Education, 15(1), em1651. https://doi.org/10.29333/ejmste/99510

MLA

Malambo, Priestly et al. "Dysfunctional Functions: The Case of Zambian Mathematics Education Students". Eurasia Journal of Mathematics, Science and Technology Education, vol. 15, no. 1, 2019, em1651. https://doi.org/10.29333/ejmste/99510