Abstract
In this investigation the level of learner metacognition as well as the level of mathematics achievement during problem-solving in a mathematics classroom was investigated. Learner metacognition plays a pivotal role during the problem-solving process and when the problem-solving is successful it can be viewed as evidence of high achievement in mathematics. Data were collected from one intact Grade 11 class of 25 girls. A word problem was given to the learners to solve individually. The learners recorded their thoughts relating to the problem as well as the calculations that corresponded to their thoughts. The level of achievement of the learners were analysed by noting calculation and conceptual errors in the solving of the problem. The learners’ level of metacognition was determined by analysing the written account of their thoughts and comparing it to the items on an adapted Metacognitive Awareness Inventory (MAI). Strong evidence was obtained from the recorded thoughts of learners that their metacognitive behaviours corresponded to the first three phases of Polya’s problem-solving model, but there was no evidence of metacognitive behaviours that corresponded with Polya’s fourth phase (Looking back) of problem-solving. It was further determined that the learners’ metacognitive awareness during the problem-solving session did not relate to the subscale Evaluation of the MAI. It was thus evident that the learners were not reflecting on the validity and correctness of their own solution. In this study a qualitative one- phase approach was used to examine the process of intervention, as well as a two-phase approach on the qualitative data which was also embedded in the quantitative methodology prior to and after the intervention phase (two-phase approach).
Highlights
Governments of most countries regard quality education as a top priority (Barber & Mourshed, 2007: 3)
Item 17 (“I am good at remembering mathematics facts and principles”) was very prominent as it relates to knowledge of the correct formulas for the areas of the different shapes
Of the six items that featured strongly in the problem-solving session, Item 22 (“I ask myself questions about the problem before I begin to solve a mathematics problem”), Item 13 (“I consciously focus my attention on important information in a mathematics question”), and Item 30 (“When I receive new information about a familiar topic or a new topic in mathematics, I focus on the meaning and significance of the new information”) relate to Polya’s first phase, namely Understanding the problem
Summary
Governments of most countries regard quality education as a top priority (Barber & Mourshed, 2007: 3). Du Toit & Du Toit government’s acknowledgement of the importance of education, there are national and international concerns about the quality of the South African education system as 60% to 80% of schools are considered to be dysfunctional (Bloch, 2009: 17). In an effort to improve the quality of education, the Department of Basic Education (DBE) introduced a draft education sector plan in 2010, entitled “Action Plan to 2014: Towards the Realisation of Schooling 2025” (DBE, 2010a). This Action Plan sets out 27 goals to address deficiencies in the following areas: teachers; learner resources; whole school improvement; school funding; school infrastructure, and support services
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