Mathematical symbolisation: challenges and instructional strategies for Limpopo Province secondary school learners

Abstract

This study reports on an investigation into the manner in which mathematical symbols influence learners’ understanding of mathematical concepts. The study was conducted in Greater Sekhukhune and Capricorn districts of Limpopo Province, South Africa. Multistage sampling (for the district), simple random sampling (for the schools), purposive sampling (for the teachers) and stratified random sampling with proportional allocation (for the learners) were used. The study was conducted in six schools randomly selected from rural, semi-urban and urban settings. A sample of 565 FET learners and 15 FET band mathematics teachers participated in the study. This study is guided by four interrelated constructivist theories: symbol sense, algebraic insight, APOS and procept theories. The research instruments for the study consist of questionnaires and interviews. A mixed method approach that was predominantly qualitative was employed. An analysis of learners’ difficulties with mathematical symbols produced three (3) clusters. The main cluster consists of 236 (41.6%) learners who indicate that they experience severe challenges with mathematical symbols compared to 108 (19.1%) learners who indicated that they could confidently handle and manipulate mathematical symbols with understanding. Six (6) categories of challenges with mathematical symbols emerged from learners’ encounters with mathematical symbols: reading mathematical text and symbols, prior knowledge, time allocated for mathematical classes and activities, lack of symbol sense and problem contexts and pedagogical approaches to mathematical symbolisation. Two sets of theme classes related to learners’ difficulties with mathematical symbols and instructional strategies emerged. Learners lack symbol sense for mathematical concepts and algebraic insight for problem solving. Learners stick to procedurally driven symbols at the expense of conceptual and contextual understanding. From a pedagogical perspective teachers indicated that they face the following difficulties when teaching: the challenge of introducing unfamiliar notation in a new topic; reading, writing and verbalising symbols; signifier and signified connections; and teaching both symbolisation and conceptual understanding simultaneously. The study recommends teachers to use strategies such as informed choice of subject matter and a pedagogical approach in which concepts are understood before they are symbolised.