Dysfunctional Functions: The Case of Zambian Mathematics Education Students

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.

Pre-service mathematics teachers’ knowledge of functions: a mixed methods sequential explanatory study

“…This implied that 61 percent of the pre-service teachers who participated in this study exhibited poor common content knowledge, specialized content knowledge and knowledge of content and students related to the function concept. These findings coincide with other prior research findings which noted poor subject-matter knowledge and pedagogical content knowledge of pre-service and inservice mathematics teachers related to the concept of a function (Sajka, 2003;Hatisaru & Erbas, 2017;Even, 1993;Aksu & Kul, 2016;Nyikahadzoyi, 2015;Malambo, 2016Malambo, , 2019Karahasan, 2010;Tasdan & Koyunkaya, 2017). However, some previous studies revealed contrary results (Steele et al, 2013) by observing positive development of teacher knowledge related to teaching the function concept.…”

“…In recent years, research exclusively or mainly focusing on the mathematical knowledge that is necessary for teaching the concept of a function has been on the increase (Aziz et al, 2018;Aziz & Kurniassih, 2019;Even, 1992;Kontorovich, 2017;Malambo et al, 2019;McCulloch et al, 2019;Karahasan, 2010;Paoletti et al, 2018;Paoletti, 2020;Taşdan, 2019;Ubah & Bansilal, 2018;Wasserman, 2017). In spite of the volume of research related to knowledge of the concept of functions, research on pre-service teachers" knowledge of the concept of function, on the one hand, and how their corresponding subject-matter knowledge and their knowledge of content and students interrelate to achieve effective learning goals, on the other hand, is still in its infancy in Zambia, as it is also the case in many other similar international educational contexts.…”

“…Similarly, Malambo et al (2019) investigated pre-service mathematics teachers" understanding of secondary school level function concepts. By examining pre-service teachers" depth of knowledge related to the function concept, they argued that studying university level advanced mathematics was not a guarantee for comprehending school level function concepts.…”

Pre-service secondary teachers’ knowledge of the function concept: A cluster analysis approach

“…Research exclusively -or mainly-focusing on the mathematical knowledge that is necessary for teaching the concept of function has been on the increase in recent years (Aziz, Pramudiani, & Purnomo, 2018;Aziz & Kurniasih, 2019;Malambo, Van Putten, Botha, & Stols, 2019;McCulloch, Lovett, & Edgington, 2019;Lovett & Edgington, 2019;Paoletti, Stevens, Hobson, Moore, & LaForest, 2018;Sintema, Phiri, &Marbán, 2018;Taşdan, 2019;Ubah & Bansilal, 2018). In the paper by Aziz et al(2018), the authors examined prospective secondary teachers' views regarding their knowledge of differences between functions and quadratic equations.…”

“…Results revealed a lack of understanding of both concepts and difficulties in defining or using basic facts related to them. Similarly, Malambo et al (2019) investigated pre-service mathematics teachers' understanding of secondary school level function concepts. By examining pre-service teachers' depth of knowledge related to the function concept, they argued that studying university level advanced mathematics was not a guarantee for comprehending school level function concepts.…”