Vimolan Mudaly

Mathematical Modelling of Social Issues in School Mathematics in South Africa

Learners’ and teachers’ engagement with the mathematical modelling of social issues is the focus of this chapter. It is contended that the mathematical modelling behaviour of both learners and teachers is dominated by mathematical modelling as a vehicle for “entry into mathematics”. This, it is suggested mitigates against the development of a “mathematical temper”. It is recommended that more emphasis be placed on mathematical modelling “as content” which would open windows of opportunity to deal with social issues in school mathematics.

The role of visualisation in learners' conceptual understanding of graphical functional relationships

Abstract This paper is based on a study which explored the conceptual understanding of Grade 11 mathematics learners of graphical functional relationships, in particular their understanding of the Cartesian plane, notation, symbols and graphical terminology. The National Curriculum Statement (NCS) for Grades 10–12 in mathematics stipulates functional relationships as a key learning outcome, emphasising a variety of graphical skills. The study highlights visualisation skills in graphical interpretation, and explores the relationship between the way graphs are presented and learners understanding of graphs. Learners understanding of graphical representations is analysed using the procedural-conceptual dichotomy. Grade 11 learners, who had engaged with graphical representations in Grade 10, were interviewed in two schools. This research indicated a strong tendency of these learners to use procedural knowledge to explain simple concepts and, further showed that the learners visual understanding was weak and dependent on the diagrams that educators use in the classroom.

Pre-service Teacher Knowledge: Thinking About Conceptual Understanding

Abstract This paper reports on research conducted with pre-service teachers in a university in South Africa. Two groups of students, those who were doing a four-year teacher education degree and those who had completed a pure science and mathematics degree, were respondents in this research. The research reported in this paper is part of a larger study conducted. The data was analyzed using teacher knowledge, the Three Dimensions of Knowledge model and the commognitive process in mathematical thinking. The findings indicate that both groups lacked a deep conceptual understanding of gradients of straight lines, despite their being trained to practice as mathematics teachers the following year. Moreover, the data also showed that despite passing many university level mathematics modules, some of these pre-service teachers were uncertain about their understanding of the concept of gradient.

Mathematics Learning in the Midst of School Transition from Primary to Secondary School

Abstract This paper is based on a research study, which explored six primary school learners’ transition to secondary school and the influences that this may have had on their mathematical learning and performances. The study was carried out over a seven-month period, from the latter part of their final primary school year until the end of the first term of high school. The study documented detailed descriptions of various stakeholders in the transition process as well as the factors that affect mathematics learning. The data reflects the findings of the study and discusses some of the implications regarding mathematics teaching and learning that should be considered during the transitional period from primary school to secondary school.

A visualisation-based semiotic analysis of learners' conceptual understanding of graphical functional relationships

Within the South African school curriculum, the section on graphical functional relationships consists of signs which include symbols, notation and imagery. In a previous article we explored the role visualisation played in the way learners understood mathematical concepts. That paper reported on the learners fixation with the physical features of graphs with little understanding of the actual mathematics concepts involved. We recommended then that visual strategies must be used to improve learner conceptual understanding. This study extends that exploration to investigate the role of visualisation in the learners conceptual understanding of graphical relationships from the perspective of Peircean semiotics. Semiotics is a key element of mathematical understanding and construction of meaning. The role of semiotics incorporates Vygotskys semiotic mediation as this influences learners understanding of graphs and serves as a useful foundation to make sense of learners responses. This qualitative study is embedded in the interpretivist paradigm and meaning is extracted from a deep analysis of the empirical data in order to explain learners understanding of graphical functional relationships.