Abstract
M.Ed.
This study is an investigation into cognitive mapping as strategy in the constructivistic approach to mathematics education to learners with a visual disability with the view to describe the change in pupils' thoughts on mathematical concepts, as well as their experiences during the process of cognitive mapping.
The rationale for the investigation was derived from the shift in South African Mathematics teaching from traditional teaching to constructivistic (or problem-centered) teaching. As this implies a shift in paradigm, teachers will be in need of relevant constructivistic training to equip them with effective teaching strategies. The objective of this study is to examine cognitive mapping as a possible supportive strategy to constructivism .
The study commences with a theoretical framework in which constructivism is clearly explicated. The principles of radical and social constructivism, the roots of which can be traced back to the epistemological theories of Piaget and Vygotsky, are explored. The constructivistic view of knowledge, with the relationship between public knowledge and the forming of personal knowledge, is discussed and extended to include the formation of mathematical knowledge. The focus then shifts to the concepts of instruction and learning and the role they play in the constructivistic paradigm. In the constructivistic view, learning implies cognitive restructuring, which is facilitated by assimilation and accommodation. The implications of this view of learning for instruction, and in particular mathematics instruction, is then discussed. This chapter concludes with the working definition the
researcher has used to conduct the remainder of the study.
The theoretical framework is structured furthermore to give background regarding cognitive mapping. According to the constructivistic approach, learning implies conceptual change. Cognitive maps externalise conceptual change by means of visual representations, and therefore it was decided to investigate them as a teaching strategy. Some definitions, as found in the literature, are given, and three types of maps are illustrated as examples. The different uses of cognitive maps, among which study strategy, lesson planning and means of evaluation, are discussed. A discussion on the different methods of constructing a map follows, with specific focus on how to include the whole class in the activity. The advantage of social interaction while constructing knowledge, is highlighted. Lastly, the advantages and disadvantages connected to cognitive mapping as teaching strategy, are discussed.
The theoretical framework is complemented by a chapter on the design of the research,
substantiating the choice of format and methods of data collection and analysis. The data is reported in the succeeding chapter, and examples of raw data from transcriptions, journals of the pupils and cognitive maps are presented. Finally, the consolidated data is interpreted.
In the concluding chapter the findings of the study are discussed. The most significant findings of this study are: cognitive mapping, as mathematical teaching strategy, improved the understanding of grade nine learners, with a visual disability, of real numbers; the learners experienced the teaching strategy of cognitive mapping positively;
the number of group members involved in the construction of a cognitive map, influenced.