Mathematical Modelling of Social Issues in School Mathematics in South Africa

Understanding Prospective Teachers’ Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

“…Likewise, in investigating prospective teachers' professional knowledge of modeling competencies, Kaiser, Schwarz, and Tiedemann (2010) found that although prospective teachers (PTs) had knowledge of modeling to different degrees, most of them did not consider applying the validation phase. Similar findings reported by Julie and Mudaly (2007) who pointed out an absence of the processes of returning to the real problem situation and checking for the appropriateness of the proposed solution. Such research findings indicate that it is not only the students, but also the in-service and pre-service teachers who had difficulties with certain stages of the modeling process (i.e., understanding the problem, structuring and simplifying the problem, making appropriate assumptions, making connections between real-world problem situation and mathematical representation, interpreting the model in terms of reallife problem situations, and validating the obtained model).…”

“…It is important and yet hard to maintain a balance between the students' independence, as emphasized in the modeling perspective, and the teacher's support and guidance (Borromeo-Ferri & Blum, 2010). Various studies document in-service and PTs' difficulties in solving modeling tasks (Biembengut & Faria, 2011;Julie & Mudaly, 2007;Kaiser, 2007), understanding different approaches to modeling (Borromeo-Ferri & Blum, 2010), and teaching (through) modeling (Lingefjärd & Holmquist, 2005;Stillman & Brown, 2011). Thus, various researchers have emphasized that teacher education programs should provide opportunities to learn and experience various dimensions of the modeling process (Biembengut & Faria, 2011;Blum et al, 2002;Borromeo-Ferri & Blum, 2010;Burkhardt, 2011;Kuntze 2011;Maaß, 2006;Niss et al, 2007).…”

“Why do I have to learn this?” A case study on students’ experiences of the relevance of mathematical modelling activities

“…3). This pragmatic perspective is also known as 'mathematical modelling as content' as opposed to using modelling activities following the scientific-humanitarian perspective, also indicated by 'modelling as a vehicle' to learn mathematics (Julie and Mudaly 2007). In the latter perspective modelling activities are used to introduce abstract mathematical concepts or to foster motivation towards (pure) mathematics.…”

Mathematical Modeling: A Bridge to STEM Education

“…At first glance, the appearance of different perspectives of mathematical modeling can be found in the literature (Erbas et al, 2014;Kaiser & Sriraman, 2006). According to Julie and Mudaly (2007) and Erbaş et al (2014), there are two perspectives about the usage of mathematical modeling in teaching and learning mathematics that are seeing modeling as content in its own right and modeling as vehicle to teach mathematics. The researchers seeing mathematical modeling as a content in its own right focuses on describing and teaching the modeling cycle, the phases in modeling cycle, modeling abilities and competencies.…”