Learning mathematics with mathematical software.

Abstract

The study took the form of action research situated in a case study. The participants consisted of sixteen Grade 11 learners who attend a non-profit tutoring organisation called Ikamva Youth on Saturday mornings and who volunteered to learn mathematics with mathematical software. Data were collected from the learners using a structured questionnaire, journals in which learners were encouraged to record their daily experiences and by studying the learners’ own written work during the research period. Moreover, the research closed with a focus group session. The study primarily described three aspects, viz. the degree to which learners are able to work with the strands of strategic competence and adaptive reasoning with particular emphasis on interpretation and application, knowledge production and justification and social collaboration; barriers in terms of working with these strands in a digital environment that may interfere with the learning process; and, the personal (affective) response of the students to the availability of technology. Findings suggest that the participants experienced difficulties in accessing these particular strands of mathematical knowledge, and subsequently expressed the desire to revert back to a place where the teacher assumes a more direct teaching style and where the focus of mathematical learning is on technique. In other words, learners preferred routine expertise, whilst appearing to lack in adaptive expertise. With respect to the second aspect of the research, it is suggested that one of the most prominent barriers to integrating technology into mathematics does not necessarily relate to adjustments in terms of the instrumental use of software and the computer environment, but seems to stem from the learners’ own epistemologies and beliefs about the nature of what constitutes effective mathematical teaching and learning. In paying attention to the voice of the learners it surfaced that the learners tend to associate computers more strongly with a cultural tool for entertainment than with mathematical learning. Although the study points out that implementing an interactive curriculum integrated with technology into a classroom with learners from low socio-economic backgrounds is not necessarily straightforward, it does suggest that with more frequent exposure certain learners can develop a propensity for working within a cognitively rich problem-solving context and effectively employ the mathematical software as an extension of their own thinking. This study adds to broader research on the role of technology in learning by reporting that the learners felt that the contextualisation of mathematics, followed by the ability to manipulate the graph themselves were the main contributors to their mathematical learning. The learners disregarded the visualisation effect of the computer as they felt that it had very little impact on their mathematical learning.