External Representation Flexibility of Domain and Range of Function

Abstract

This study attempts to analyze pre-service secondary mathematics teachers’ flexibility of external representations of domain and range of functions. To reach the purpose, a task consisted of thirty question items were designed. Participants of the study were thirty-eight Indonesian pre-service secondary mathematics teachers attending mathematics education department at one private university in Jakarta, Indonesia. Based on the analysis participants written responses, this paper revealed participants’ difficulties in providing a proper and consistent definition of the concept of domain and range of functions. We also disclosed the participants’ lack of flexibility in doing translation among representations under the concept of domain and range of function. In general, participants written responses to the task did not provide evidence of a solid understanding of domain and range. There are several implications of these findings offered for secondary mathematics teacher education’s program.

Pre-Service Secondary Mathematics Teachers’ Understanding of Absolute Value

“…Therefore, it is important for mathematics teachers to have their students make sense of various external representations of absolute value by integrating it and its formal definition or meaning. Aziz & Kurniasih (2019) also emphasized the importance of flexibility of external representation in an effort to grasp the mathematical concept. When attempting to solve the absolute value task, typical mistakes made by participants are removal of absolute value bars, focus on rules of strategies, conversion of the absolute value bars to parentheses, taking out the number inside absolute value bars, poor performance in algebraic manipulation, and a lack proficiency in drawing absolute value function.…”

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.…”

“…Participants of that study exhibited deficiencies in ways in which they described and interpreted such differences. Later, Aziz and Kurniasih (2019) analyzed preservice secondary mathematics teachers' knowledge of representations of domain and range of functions. Results revealed a lack of understanding of both concepts and difficulties in defining or using basic facts related to them.…”

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

“…Pre-service teachers have been reported in previous studies of having difficulties with the concept of domain and range of a function (Arnold, 2004;Aziz & Kurniasih, 2019;Dorko & Weber, 2014). They exhibited misconceptions and could hardly define domain and range.…”

“…One of the most researched aspects of the function concept in relation to preservice teachers is their knowledge of different representations of the concept of a function (Aziz & Kurniasih, 2019;Dorko & Weber, 2014;Gagatsis & Shiakalli, 2004;Martinez-Planell et al, 2015). Different representations of the function concept usually take the form of tables, algebraic symbols, ordered pairs and graphical representations.…”