School of Mathematics, Natural Sciences and Technology Education

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Browsing School of Mathematics, Natural Sciences and Technology Education by Author "Du Toit, G. F."

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    The effect of metacognitive intervention on learner metacognition and achievement in mathematics
    (University of the Free State, 2013-02) Du Toit, Daniël Stephanus; Du Toit, G. F.; Wilkinson, A. C.
    English: International and national measures point to the poor mathematics achievement of South African learners. The enhancement of the quality of mathematics education is a key priority of the Department of Basic Education in South Africa. Several studies have found a correlation between learner metacognition and mathematics achievement. Metacognition entails knowledge and regulation of one’s cognitive processes. Previous studies point to the positive effect of metacognitive interventions on learner metacognition and mathematics achievement. The purpose of this study was to investigate the effect of a metacognitive intervention (MI) on learner metacognition and the mathematics achievement of Grade 11 learners in the Free State from a predominantly pragmatic perspective. The MI was developed by combining aspects of a mathematical perspective on De Corte’s (1996) educational learning theory with aspects of previous metacognitive intervention studies in mathematics. A mixed methods research design was employed where qualitative data were embedded within a quasi-experiment. Data were collected from an experimental group (N=25) and a control group (N=24). Quantitative data on learner metacognition were obtained from the Metacognitive Awareness Inventory (MAI), while quantitative data on mathematics achievement were obtained from the learners’ Terms 1 and 4 report marks. Qualitative data were acquired by means of teacher interviews, problem-solving sessions, and learner and teacher perspectives on the MI process. The mixed methods research question investigated the extent to which the findings from the qualitative phase of the study support the findings from the quantitative phase regarding the effect of MI on learner metacognition and mathematics achievement. The quantitative findings indicated that MI had a statistically significant impact on learner metacognition in respect of the MAI total score, the Knowledge of cognition (KC) factor, the Regulation of cognition (RC) factor, and the subscales Declarative knowledge, Planning, and Monitoring. The impact of MI on mathematics achievement was less pronounced, as inferences had to be drawn from the correlation between learner metacognition and mathematics achievement. The quantitative findings showed a statistically significant correlation between KC and mathematics achievement, as well as between Declarative knowledge and mathematics achievement. Since MI had a statistically significant impact on KC and Declarative knowledge, it is concluded that MI also had a positive impact on mathematics achievement. The qualitative findings strongly support the quantitative findings regarding the positive impact of MI on learner metacognition. The quantitative findings in respect of the correlation between learner metacognition and mathematics achievement were only partially supported by the qualitative data. Main recommendations emerging from this study relate to the improvement of learners’ mathematics achievement by enhancing their Declarative knowledge, the enhancement of learners’ problem-solving skills, and the need to implement metacognitive interventions in mathematics particularly in schools where the teachers are inexperienced or underqualified.
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    Teaching and learning of fractions in primary schools in Maseru
    (University of the Free State, 2013-01) Marake, ‘Maphole Georgina; Du Toit, G. F.
    Throughout the world governments and other education stakeholders advocate quality education and education for all. Among others, mathematics education is seen by governments as essential in the advancement of the development of countries. Lesotho is no exception in this regard hence mathematics is one of the core subjects in Lesotho’s education system. Though Mathematics education is seen as pivotal to the development of countries, analysis of mathematics Junior Certificate (JC) examination results in Lesotho indicates that performance in mathematics is not good. This study therefore aspired to investigate teaching strategies predominantly employed by primary mathematics teachers and assess their effect on learners’ meaningful learning of fractions. In order to meet this aim the study attempted to determine what literature said about effective learning and teaching of fractions, the level of training given to mathematics teachers and determine whether effective learning and teaching materialised in the three classrooms that were studied. The existing literature proposed different teaching strategies that resulted in significant learning of fractions. To investigate dominant teaching strategies that teachers used in the teaching of fractions, class observations of three teachers were conducted. Teachers were observed in their classrooms over a period of time and follow-up interviews were conducted. Samples of the teachers’ documents and the learners’ work were analysed to evaluate the extent to which effective learning and teaching of fractions were taking place in these respective classes. Literature indicates that effective learning, of fractions, entails meaningful construction of the concept through handling of concrete materials and formation of relationship between concepts. Effective teaching on the other hand entails the ability to create situations in which learning is facilitated. Teachers are said to possess both mathematical knowledge for teaching (MKT) and Pedagogical content knowledge (PCK) in order to be able to teach effectively. In order to fully understand the level of training that the teachers received teacher trainers were interviewed. It was found that teachers did not engage learners in high order reasoning and problem solving, instead they gave close-ended questions which learners answered by practising rules and procedures that teachers taught. Learners therefore did not use their own strategies when writing solutions to questions. It was recommended that teachers should use readily available materials like paper and papers and when planning lessons they should think of possible errors, misconceptions and difficulties that learners were likely to have.