Browsing by Author "Gow, Melanie"
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- ItemA case study of mental mathematics lessons : analysing early grade teachers’ perceptions of their practice(Stellenbosch : Stellenbosch University, 2021-03) Gow, Melanie; Lampen, C. Erna; Stellenbosch University. Faculty of Education. Curriculum Studies.ENGLISH SUMMARY : Research has shown that South African primary school students are performing below international and national grade level expectations for mathematics. It can be argued that a root cause is students’ reliance on inefficient counting-based versus reasoning-based strategies for calculating. Personal experience with supporting teachers in a wide range of classrooms resonates with the literature, which reveals that the reliance on counting-based strategies hinders the development of more efficient, number range appropriate strategies in the later years. Teaching approaches that favour learning through the memorisation of facts, rules and procedures in the early grades encourage the use of learnt procedures over the development of reasoning-based strategies. Alternatively, teaching for understanding and reasoning negates the need for memorisation and supports the development of reasoning-based calculating strategies. In ‘Adding it up: Helping children learn mathematics’, Kilpatrick, Swafford and Findell (2002) refer to mathematical proficiency to convey what they think it means to be successful in mathematics. Mathematical proficiency describes success in mathematics as the ability not only to calculate accurately, but also to understand, apply, reason and engage with mathematics. Mathematical proficiency consists of an interrelated set of actions that are equally important in contributing to success in mathematics. These actions, or strands of mathematical proficiency, are comprised of a combination of calculating, understanding, applying, reasoning and engaging. Mental mathematics forms an integral part of the development of number sense in the early years and can mean so much more than the recall of facts. If taught for understanding and reasoning, mental mathematics can support the development of mathematical proficiency, and result in the development of reasoning-based calculating strategies. This is a qualitative case study that analyses how early grade teachers perceive their mental mathematics teaching practice. Using Activity Theory as the analytical framework, the study considers the interrelated dimensions that contribute to the activity of teaching. Two Grade 3 teachers participated in the study. Data were collected through introductory interviews (semi-structured), lesson observation video recordings, self-reflection checklists and reflective interviews (unstructured). There was a workshop session where mathematical proficiency and the resultant implications for teaching mental mathematics were discussed. The teachers then reflected on their own practice via video recordings using the lens of mathematical proficiency. The reflections were for both of their lesson observations: one that took place before the workshop session (pre-workshop lesson) and one that took place after (post-workshop lesson). The analysis explored how the teachers perceived their own teaching through self-reflection. Using Activity Theory as the analytical framework allowed for the analysis of relationships within the activity of teaching that described the teachers’ perceptions of practice. The analysis revealed that both teachers have an awareness of where and how they should adapt their practice, and their perceptions of practice revealed similar themes, namely: 1. Object (lesson objective) Move beyond the constraints of ‘knowing’ and ‘calculating’ during mental mathematics lessons: to create opportunities to develop understanding, application and reasoning. 2. Tools Move beyond the ‘knowing’ level of mental mathematics task items: to elicit application and reasoning through the use of more cognitively demanding tasks that are purposefully utilised to allow noticing of patterns relationships. 3. Division of labour Move beyond ‘answer only’ questioning in mental mathematics lessons: to facilitate student discussion and reflection through more deliberate planning. The findings of this study highlighted tensions between existing practice and desired practice as reflected on through the lens of mathematical proficiency. These tensions, if further explored and supported with ongoing reflection, may lead to professional learning opportunities that enable transformative teacher practice.