Imagery and visualisation characteristics of undergraduate students' thinking processes in learning selected concepts of mathematical analysis

Abstract

The present study investigated imagery and visualisation characteristics of undergraduate students’ thinking processes in learning selected concepts of mathematical analysis. The aim was to discover the nature of images evoked by these undergraduate students and the role of imagery and visualisations when students were solving some selected problems related to mathematical analysis. The study was guided by the theory of registers of semiotic representations. Psychological notions on imagery were also fused to cater for a cognitive approach to the study. A sample of 50 undergraduate mathematics students participated in the study. The researcher employed both quantitative and qualitative methods. Before the main study, a pilot study was conducted to account for the reliability and validity of the research instruments. The data were collected through use of a cognitive test that was composed of 12 tasks with items selected from mathematical analysis. These tasks were specially designed to capture the variables of imagery and visualisations. A structured interview was also conducted as a follow-up to the results of the cognitive test. The study found that visual images were noticeable in the thinking processes of undergraduate students in solving problems related to mathematical analysis. The nature of the visual images evoked by the students varied from person to person. The nature of these images was also determined by the nature of the task. The most common types of imagery were diagrams, prototypes and symbols. On rare occasions the students also evoked metaphoric images. It was also observed that these images were used for illustrative purposes and to spark the idea for a proof. It was also interesting to note that some images were used to discover the limit of a converging series. The results confirmed the need to use visualisation with caution, especially when treating concepts which involve infinity. The study recommends that instructors of mathematics should encourage visual thinking in the learning and teaching of mathematical analysis. Knowledge of the students’ concept images helped the researcher to understand the nature of the learning difficulties of the students. Further research should focus on the strengths and weaknesses of visual-mediated learning and also on the relationship between creativity and visual thinking.