The role of visual literacy on grade 11 learners' conceptual understanding of graphical functional relationships.

Abstract

This study intends to foreground visual literacy within the wider context of visualisation and visual thinking in mathematics teaching and learning. Visualisation in general has been receiving attention in mathematics education research. I distinguish visual literacy from visualisation by referring to visual literacy as the combination of visualisation and logical thought. Visual literacy emphasises construction of meaning through the process of decomposition, comprehension and analysis of visual representations. The section on functional relationships is located in the National Curriculum Statement (NCS) for mathematics in the Further Education and Training (FET) phase for Grades 10-12 (Department of Education, 2003). Graphical functional relationships, which form an integral part of functions and algebra in the FET phase for Grades 10-12, demand visual literacy, which includes graphical interpretation and comprehension skills. Therefore, the conceptual understanding associated with graphs is dependent on the way graphs are presented. This study examines learners‟ and educators‟ procedural and conceptual understanding of the graphs they sketch and interpret in the FET curriculum. The data analysis contributes towards the fast growing body of knowledge on visualisation in mathematics with the significant impact visual literacy has on the conceptual understanding of mathematical graphs. The analysis reveals that the overarching theoretical framework of constructivism embracing the Process-Object, Visualizer-Analyzer and Semiotic models are useful in illustrating and justifying the link between visual literacy and the conceptual understanding of learners. In examining the visual understanding of graphical representations of ten Grade 11 learners and the two mathematics educators that teach them, the data reveals that learners display a somewhat skewed understanding of the nature of the Cartesian plane, the characteristics of graphs, functional notation and graphical terminology. In fact their educators, in some instances, displayed similar understandings. Learners display procedural understanding of graphical representations to a large extent. The educators‟ visual understanding does suggest that learners‟ interpretation of graphs is in some way influenced by the way they teach. The overriding contribution of the research study is that visual literacy plays a significant role in the conceptual understanding of functional graphical relationships. The relationship between graphical representations and logical thought is central to visual literacy. Key concepts: visual literacy, conceptual understanding, graphical representations, visualisation, analytical thinking, constructivism, process-object, Visualizer / Analyzer, semiotics and vehicles of reasoning.