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, D. S."
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Item Open Access The level of metacognitive awareness of pre-service mathematics teachers at a higher education institutions(University of the Free State, 2017) Du Toit, Henriette; Junqueira, K. E.; Du Toit, D. S.; Mahlomaholo, S.𝑬𝒏𝒈𝒍𝒊𝒔𝒉 There are ongoing concerns about educational institutions not empowering learners with the knowledge, skills, and dispositions needed for school achievement, lifelong learning, and the workplace of the new millennium. In particular, South African learners have performed poorly in recent national and international assessments of mathematical proficiency. As a result, the Department of Basic Education has asserted the importance of enhancing the quality of Mathematics teaching and learning. Enhancing the ability to teach Mathematics has the potential to improve educational outcomes, as well as increase future employment and higher education opportunities for young South Africans. The poor Mathematics results point to the need to enhance, among other things, learners’ metacognitive awareness. Metacognitive awareness entails the knowledge and regulation of one’s cognitive processes. Enhancing metacognition could not only support learners in solving mathematical problems, and so improve mathematical achievement, but could also enhance productive and lifelong learning in learners. Fostering metacognitive awareness within Mathematics learners involves first fostering metacognitive awareness in Mathematics teachers, who are responsible for facilitating quality Mathematics teaching and learning. However, research suggests that teachers generally do not teach or model metacognitive awareness to their learners, or display metacognitive adaptive competence in their own teaching practice. The purpose of the study was to determine the level of metacognitive awareness of Mathematics pre-service teachers at a Higher Education Institution. Framed within a post-positivist/interpretivist paradigm, a mainly quantitative research approach with a minor qualitative enquiry informed the study. The Metacognitive Awareness Inventory (MAI) was distributed to fourth-year Mathematics pre-service teachers at a South African Higher Education Institution in order to determine their metacognitive awareness regarding Knowledge of cognition (comprising of Declarative knowledge, Procedural knowledge, and Conditional knowledge) and Regulation of cognition (comprising of Planning, Information management, Monitoring, Debugging, and Evaluation). To enrich the findings of the quantitative analysis, the qualitative data generated from a think-aloud problem-solving session—where the pre-service teachers recorded their thought processes whilst solving a problem—was analysed to determine the extent to which their reported metacognitive awareness translated into successfully solving a Mathematics problem. In the quantitative findings on the MAI, the pre-service teachers reported a moderately high level of metacognitive awareness; in addition, they reported a higher level of metacognitive knowledge (Knowledge of cognition) than of metacognitive skills (Regulation of cognition). Findings from the think-aloud problem-solving session, meanwhile, point to an inadequate level of metacognitive awareness, indicating a gap between what the pre-service teachers report to do in the learning and problem solving of Mathematics and what they can actually do in a problem-solving context. There is historical precedent for this gap, as noted in the scholarship. The close of the study highlights the need to enhance the metacognitive awareness and reflective practice of these Mathematics pre-service teachers by enhancing their metacognitive skills—Monitoring, Debugging, and Evaluation—and enhancing their problem-solving skills. It is further recommended that reflective problem-solving opportunities built around complex, novel problems be incorporated into Mathematics modules in teacher training, to facilitate prolonged and deliberate reflection. More broadly, it recommends that metacognitive reflective and problem-solving opportunities are provided for novice and underqualified teachers. Such opportunities will aid prospective and current Mathematics teachers to become mathematically proficient and metacognitively aware themselves, to deal with novel scenarios in Mathematics and their teaching practice and to translate this metacognitive adaptive competence for their learners.Item Open Access Obstacles that hamper learners from successfully translating mathematical word problems into number sentences(University of the Free State, 2014) Reynders, Amaria; Junqueira, K. E.; Du Toit, D. S.Various research studies show that the language ability and Mathematics performance of primary school learners are closely related. In South Africa, as is elsewhere, the language issue at schools has always been shifted from the academic battlefield into the political battlefield. The Minister of Education has always been a politician and therefore the current curriculum in SA is politically inspired and do not always address the needs of learners, according to Sedibe (2003). Many primary school learners with an African background are taught in a second language and not in their mother tongue due to the policy of the National Education Department. It is mostly these learners who find it difficult to relate to the language of instruction and the meaning-making of that language in a Mathematical context. The Annual National Assessment (ANA), an initiative of the National Education Department, shows that most of the primary school learners in South Africa are still not on track concerning Numeracy and Literacy skills. Language barriers for learners who are not taught in their mother tongue lead to misunderstanding regarding Mathematical word problems. The interpretation of word problems has throughout the years been a concern of Mathematics teachers, even if the learners were taught in their mother tongue. The purpose of this study was to investigate, by means of a case study, the barriers primary school learners experience with the translation of mathematical word sums into number sentences. Qualitative research was conducted. The study was grounded in the interpretivist paradigm, hence the reasons for the learners’ problems in converting word problems into number sentences and perations were investigated in real-life situations. Data was collected through observations. Audio-visual material was used. Activities of Grade four learners, from a primary school in the Motheo teaching district of the Free State Province, was recorded audio visually, while being busy with group work. The group work was done in the form of a worksheet, which contained two word problems. The learners had to discuss the word problems in order to compile number sentences. The learners could use any language during their discussions. A Sotho translator translated the discussions into English for analysis purposes. The research findings support the research problem, as it was clear that although learners were presented with word problems in a language other than their mother tongue, they preferred to discuss the content of the word problems in their mother tongue. The main recommendations emerging from this study is that teachers should become more aware of the linguistic issues in learning and teaching Mathematics and must develop tools for talking about language in ways that enable them to engage productively with learners in constructing mathematical knowledge. Teachers in culturally diverse school settings need to develop “tools” to enable learners to understand the mathematical vocabulary better via the language of instruction. The following recommendations regarding these tools can be made. Teachers who teach Mathematics in the foundation phase should compile a Mathematics dictionary as part of their literature studies. These teachers must consult language interpreters in order to find mother tongue words for words that explain mathematical concepts. These words should be repeated regularly throughout their contact time with the learners, even if it is not the Mathematics period. The Mathematical concepts and content must be carried over to non-mother tongue learners in such a way that they can identify the context of their everyday lives in it. Only then will the learners make meaning of word problems and will they be able to compile numbers sentences from the word problem in order to carry out the correct Mathematical operations.