Secondary Mathematics Teachers' Content Knowledge for Teaching the Concept of Function

Abstract

This study examined secondary mathematics teachers' content knowledge for teaching the concept of function. Content knowledge, for the purpose of this study, includes the common content knowledge and specialized content knowledge domains of Ball and her colleagues' Mathematical Knowledge for Teaching (MKT) framework. Data were collected through a 10-item questionnaire from 42 teachers practicing at fifteen different industrial vocational high schools in Ankara, Turkey. Findings revealed that most of the teachers placed a strong emphasis on the set correspondence and algebraic representations; found the uniqueness condition of functions very important for students to understand; and had a wide repertoire of examples of functions which constitute the uniqueness condition. The teachers' choice of examples mostly included giving set correspondence relations and checking whether they define a function. Additionally, a strong focus on the computational aspects associated with functions was evident. The teachers' understanding of the function concept might be influenced by the curricular materials, contextual factors, and high-stakes testing. The methodological and practical implications of these findings are discussed, and directions for future studies are offered.

Enhancing pre-service mathematics teachers’ understanding of function ideas

“…For instance, many mathematics teachers and PMTs ignored the univalence characteristic of functions or thought that each input always entails different outputs. Hence, they could not define the function correctly (Even, 1993;Hatisaru, 2020;Huang & Kulm, 2012;Steele et al, 2013;Zazkis & Marmur, 2018). Also, they often have limited concept images (e.g.…”

“…Also, they often have limited concept images (e.g. overemphasis on the rule or single formula, only one graph could go through two points (for details see Dubinsky & Wilson, 2013) that would result in either an incorrect or limited conceptualization of function (Dede & Soybas, 2011;Elia & Spyrou, 2006;Hatisaru, 2020;Zazkis & Marmur, 2018). Teachers' limited understanding of the function or even correct conceptualizations of them may not reflect different ideas about function.…”

“…Teachers' limited understanding of the function or even correct conceptualizations of them may not reflect different ideas about function. One particular idea might be dominant in teachers' or PMTs' concept images, generated function examples and personal concept definitions (Hatisaru, 2020;Viirman et al, 2010;Vinner & Dreyfus, 1989).…”