The relationship between problem solving and self-directed learning in grade 7 mathematics classrooms

Abstract

The learners in the South African school system did not perform well in international assessments such as the Trends in Mathematics and Science Studies (TIMSS) in 1995, 1999 and 2003, respectively. Because of these below par achievements, problem areas were identified in terms of literacy and numeracy. In 2011 the Department of Basic Education implemented the Annual National Assessments in an attempt to achieve the goals set by the Department. These goals included, amongst others, to improve learners' reading and writing skills, equip them to think critically and to solve mathematical problems, in order for learners to become productive and meaningful citizens (DBE, 2011:8). The primary goal of this study was to investigate the relationship between problem solving and self-directed learning in Grade 7 Mathematics classrooms. In this study a sequential explanatory mixed-method research design was used (Ivankova et al., 2006:4) in order to determine the influence of problem solving activities on Grade 7 learners' self-directed learning abilities, and to determine whether self-directed learning, through problem solving, has an influence on learners' mathematical achievement. During the quantitative investigation, learners from the experimental as well as the control groups completed questionnaires to determine their self-directed learning ability. A self-directed learning instrument (SDLI) and selected fields of the LASSI(HS) were used in both pre- and post-tests. In addition, learners' March as well as their November report results were also taken into consideration. The qualitative investigation included task-based activities conducted with selected learners from the experimental group. These learners had to solve mathematical problems with respect to topics from each learning content area in grade 7 Mathematics. The qualitative investigation was based on Polya's model of problem-solving, where learners had to implement the four suggested phases, namely; (1) understand the problem, (2) make a plan to solve the problem, (3) carry out the plan and (4) look back or reflect on the solution. The learners had to make predictions regarding the solutions to given mathematical problems. However, the learners in general over-estimated their problem-solving abilities, and their predictions were lower than their actual abilities. The findings did not give a clear indication with respect to whether or not a relationship exists between self-directed learning, problem-solving and mathematical achievement. Although it is not clear whether self-directed learning or problem-solving activities or both had an influence on learners' mathematical achievement, there was an improvement in the experimental group's average mathematical achievement after the intervention through problem-solving activities.