We need to make up for the gap: University student teachers’ difficulties associated with basic algebraic manipulations

Year 2021, Volume: 9 Issue: 4, 351 - 358, 15.12.2021

Hlamulo Mbhiza , Dimakatjo Muthelo , Kabelo Chuene

https://doi.org/10.17478/jegys.1015993

Abstract

With the increasing number of students enrolling in South African Higher Education institutions, it is essential to determine what level of mathematical knowledge gaps and understanding they bring from secondary school level. This was the context for a study of first year undergraduate mathematics education students at the University of Limpopo. In this paper, we present our autoethnographical experiences of lecturing calculus courses for a teacher preparation programme. The patterns that emerged from our interactions with students revealed that they experienced difficulties in understanding basic algebraic procedures and recognising structure to solve algebraic problems in the context of differentiation. This made us aware that we needed to configure effective strategies to make up for the identified elementary mathematics knowledge gaps, which we assumed students brought with from Grade 12. Our quest to make up for the algebraic knowledge gaps does not only serve the purpose of enabling our student teachers’ mathematical knowledge, but to ensure that they develop good knowledge base needed to teach the subject during their training as well as once they qualify as teachers.

Keywords

Algebraic manipulation, Prospective teachers, Differentiation, Structure, Mathematics education

References

• Adams, T. E., Ellis, C., & Jones, S. H. (2017). Autoethnography. The international encyclopedia of communication research methods, 1-11.
• Adendorff, S. A., Jooste, Z., Mosimege, M., & Govender, R. (2019). Ascertaining and understanding primary pre-service teachers’knowledge of transformation and tessellation in Geometry. Association For Mathematics Education Of South Africa, 1, 279.
• Amador, J. M., Estapa, A., de Araujo, Z., Kosko, K. W., & Weston, T. L. (2017). Eliciting and analyzing preservice teachers' mathematical noticing. Mathematics Teacher Educator, 5(2), 158-177.
• Anthony, G., Beswick, K., & Ell, F. (2012). The professional education and development of prospective teachers of mathematics. In Research in Mathematics Education in Australasia 2008-2011 (pp. 289-312). Brill Sense.
• Askew, M., Bowie, L., & Venkat, H. (2019). Pre-service primary teachers’ mathematical content knowledge: An exploratory study. African Journal of Research in Mathematics, Science and Technology Education, 23(3), 286-297.
• Bell, P., Tzou, C., Bricker, L., & Baines, A. D. (2012). Learning in diversities of structures of social practice: Accounting for how, why and where people learn science. Human Development, 55(5-6), 269-284.
• Boylorn, R. M. (2011). Gray or for colored girls who are tired of chasing rainbows: Race and reflexivity. Cultural Studies? Critical Methodologies, 11(2), 178-186.
• Brodie, K. (2014). Learning about learner errors in professional learning communities. Educational studies in mathematics, 85(2), 221-239.
• Cooper, B., Morris, S., & Boylorn, R. (2017). The Crunk Feminist Collection. New York: The Feminist Press.
• Ellis, C. (2009). Telling tales on neighbors: Ethics in two voices. International Review of Qualitative Research, 2(1), 3-27.
• Ellis, C., & Patti, C. (2014). With heart: Compassionate interviewing and storytelling with Holocaust survivors. Storytelling, Self, Society, 10(1), 93-118.
• Ellis, C., & Rawicki, J. (2013). Collaborative witnessing of survival during the Holocaust: An exemplar of relational autoethnography. Qualitative Inquiry, 19(5), 366-380.
• Hawthorne, C., & Druken, B. K. (2019). Looking for and using structural reasoning. The Mathematics Teacher, 112(4), 294-301.
• Hoch, M., & Dreyfus, T. (2005). Structure Sense in High School Algebra: The Effect of Brackets. International Group for the Psychology of Mathematics Education. Holland, D., & Lave, J. (2009). Social practice theory and the historical production of persons. Actio: An International Journal of Human Activity Theory, 2(1), 1-15.
• Koç, Y., & Bozkurt, A. (2011). Evaluating pre-service mathematics teachers’ comprehension level of geometric concepts. In The Proceedings of the 35th annual meeting of the international group for the psychology of mathematics education (Vol. 1, p. 335). Ankara: PME.
• Lesh, R., Post, T. R., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In Problems of representations in the teaching and learning of mathematics (pp. 33-40). Lawrence Erlbaum.
• Maharaj, A. (2010). An APOS analysis of students' understanding of the concept of a limit of a function. Pythagoras, 2010(71), 41-52.
• Masinire, A. (2015). Recruiting and retaining teachers in rural schools in South Africa: Insights from a rural teaching experience programme. Australian and International Journal of Rural Education, 2-14.
• Mbhiza, H. (2021). Rural Teachers’ Teaching of Algebraic Functions Through a Commognitive Lens. Interdisciplinary Journal of Rural and Community Studies, 3(1), 10-20.
• Ndlovu, Z., Amin, N., & Samuel, M. A. (2017). Examining pre-service teachers' subject matter knowledge of school mathematics concepts. Journal of Education (University of KwaZulu-Natal), (70), 46-72.
• Patti, C. J. (2021). A ROSE BY ANOTHER NAME. Advances in Autoethnography and Narrative Inquiry: Reflections on the Legacy of Carolyn Ellis and Arthur Bochner, 95.
• Pillay, A. (2008). Forking in the free group. Journal of the Institute of Mathematics of Jussieu, 7(2), 375-389.
• Putra, Z. H., & Winsløw, C. (2018, September). Teachers’ collective knowledge: the case of equivalent fractions. In Journal of Physics: Conference Series (Vol. 1088, No. 1, p. 012003). IOP Publishing.
• Rittle-Johnson, B., Matthews, P. G., Taylor, R. S., & McEldoon, K. L. (2011). Assessing knowledge of mathematical equivalence: A construct-modeling approach. Journal of Educational Psychology, 103(1), 85.
• Ryan, J., & Williams, J. (2011). Teachers’ stories of mathematical subject knowledge: Accounting for the unexpected. In Mathematical knowledge in teaching (pp. 251-271). Springer, Dordrecht.
• Sebsibe, A. S., & Feza, N. N. (2019). Assessment of students’ conceptual knowledge in limit of functions. International Electronic Journal of Mathematics Education, 15(2), em0574.
• Siyepu, S. W. (2015). Analysis of errors in derivatives of trigonometric functions. International Journal of STEM Education, 2(1), 1-16.
• Spaull, N. (2013). South Africa’s education crisis: The quality of education in South Africa 1994-2011. Johannesburg: Centre for Development and Enterprise, 1-65.
• Speer, N. M., King, K. D., & Howell, H. (2015). Definitions of mathematical knowledge for teaching: Using these constructs in research on secondary and college mathematics teachers. Journal of Mathematics Teacher Education, 18(2), 105-122.
• Tullis, J.A. (2013) Self and others: Ethics in autoethnographic research. In S. H. Jones, T. E. Adams & C. Ellis (Hrsg.), Handbook of autoethnography (S. 244–261). Walnut Creek: Left Coast Press.
• Tunc, M. P., & Durmus, S. (2012). Pre-service elementary school classroom and mathematics teachers' interpretations about the definition of angle concept. Energy education science and technology part b-social and educational studies, 4(1), 131-140.
• Wasserman, N. H. (Ed.). (2018). Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers. Springer.
• Wood, L., & Solomonides, I. (2008). Different disciplines, different transitions. Mathematics Education Research Journal, 20(2), 117-134.
• Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for research in mathematics education, 27(4), 458-477.