Browsing by Author "Luwango, Luiya"
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- ItemThe development of pre-service teachers mathematical knowledge for teaching flexible mental computation(Stellenbosch : Stellenbosch University, 2020-03) Luwango, Luiya; Lampen, Erna; Stellenbosch University. Faculty of Education. Curriculum Studies.ENGLISH SUMMARY : This empirical study explored an approach to develop elementary pre-service teachers’ mathematical knowledge for teaching flexible mental computation skills in school. The study began by determining pre-service teachers’ existing knowledge, beliefs and experience pertaining to how they learned flexible mental computation skills at school. Ways pre-service teachers learned flexible mental computation skills in school shape their beliefs about learning and teaching. Currently, research indicates that pre-service teachers continue to graduate with inadequate skills to do flexible mental computation, and overreliance on calculators and the standard method is prevalent among pre-service teachers. Since teacher knowledge affects learning directly, developing pre-service teachers’ mathematical knowledge for teaching flexible mental computation of whole numbers would break the cycle of innumeracy. Whole number computation forms the basis of learning different mathematical topics at school, and most professions and activities in society involve the calculation of whole numbers. To achieve the objective of this study, a purposive sample of 51 pre-service elementary mathematics teachers participated in the study. Both quantitative and qualitative research methods were used to collect data using questionnaires, pre- and post-intervention tests, intervention cycles and interviews. This study used the realistic mathematics education (RME) instructional theory with the backing of design-based research (DBR) to design problems that translated into a hypothetical learning trajectory (HLT) to contribute to the knowledge of how to prepare teachers to teach flexible mental computation. The nature of the HLT makes it suitable for teacher educators to adopt it to develop pre-service teachers for effective teaching. This study found that most pre-service teachers believe that flexible mental computation is important and that concrete objects and the use of the pencil-and-paper method underpins its development. Pre-intervention interviews indicated that PSTs developed flexible mental computation skills through problem solving or memorisation of the multiplication table. Pre-service teachers also indicated that at school they had done mental calculations using strategies prescribed by their teacher. Consequently, during the intervention some PSTs expected a prescription of strategies and had to be persuaded to develop the necessary habits of mind to invent strategies. In the pre-intervention test, 49% of the PSTs’ scored above 50% whereas in the post-intervention test 53% scored above 50%. Pre-intervention interviews revealed that although correct answers were provided for specific items, not all answers were calculated in a flexible manner. Interviews revealed the use of fingers and standard algorithms to compute mentally. This occurred during and after the intervention process, and these existing methods were hard to change. Findings confirmed that the invention of flexible strategies demanded considerable effort on the part of the pre-service teachers to solve context-rich problems, discuss, think, imagine reason and justify invented strategies. It was, however, demonstrated that all pre-service teachers could develop fluency and flexibility with mental calculation, provided their knowledge of numbers and operations, ability to generalise patterns, and knowledge of relationships between numbers had improved through practice. Ultimately, a problem solving approach is recommended as it fosters critical and strategic thinking to re-invent calculation strategies and develop the desire to teach constructively.