Investigating the nature of grade six after school mathematics club learners' shifts in mathematical number sense and procedural fluency - Baart, Noluntu Via (Rhodes University, Faculty of Education, Department of Education, 2019)
A wide range of research locally points to intermediate phase learners having extremely weak basic number sense resulting in the dominance of inefficient strategies for calculations with the four operations, irrespective of the number range. The grade six Annual National Assessments (ANA) diagnostic reports for 2012 to 2014 also point to errors and misconceptions that tend to dominate learners' computations in the four basic operations; such errors are often attributed to the use of either tallies or incorrectly applied mathematical procedures. Having the above context in mind and following informal conversations with teachers in the Uitenhage Education District, five teachers expressed an interest in running the afterschool mathematics clubs based on the South African Numeracy Chair (SANC) project model. The SANC project team ran workshops in April, May and June 2016 with nine teachers (five as facilitators and four others as co-facilitators in five different club sites) in which teachers were provided with key resources for use in their clubs. Fifteen club sessions ran in each club with grade six learners across the 2nd and 3rd terms. These clubs form the empirical field for this research, which aims to investigate the nature of learners' evolving number sense, procedural fluency and teachers' experiences of working with learners in the club space. The unit of analysis in this study is both the shifts evident in learners' number sense and procedural fluency as a result of participating in the clubs and the teacher's experiences of working with learners in those clubs as club facilitators. A social constructivist perspective of learning guides this study. Especially Vygotsky's (1978) notion that cognitive development stems from social interactions and guided learning within the Zone of Proximal Development (ZPD) of children, guided by more knowledgeable others. Furthermore, Kilpatrick et al.'s (2001) strands of mathematical proficiency provide the conceptual frame with a particular focus on procedural fluency and number sense. A mixed method approach to data collection was used. Quantitative data has been drawn from learner's scores on pre- and post- assessments on four basic operations. Visual progression spectra have been adopted from the Pushing for Progression (PfP) Programme which is an intervention Programme developed by the SANC project for club facilitators. They provide explanations of learner progression trajectories and how to analyse learner methods. Qualitative narratives were drawn from learner progression data, as well as teacher post club questionnaires and one-to-one teacher interviews. The findings of this research suggest that learner workings when used in conjunction with visual progression spectra can provide important clues to researchers and teachers. This in turn contributes to an understanding of where learners are in their mathematical learning and gives ideas for how to support learners to progress using more flexible methods of calculation, particularly for poor performing learners. Included, is the discussion of the effectiveness of the club space to enable such shifts and improve learner flexibility, fluency and performance as displayed in learner methods and scores of the pre- and post- assessments. The teachers' observations about the relaxed atmosphere in the club space, small sized groups, learning through play with co-members may have enabled the shifts in procedural fluency and number sense in club learners. Additionally, implications of the study are discussed, and tentative recommendations are made for the DBE to consider.
Keywords: Mathematics -- Study and teaching (Elementary) -- South Africa; Mathematics -- Study and teaching (Elementary) -- South Africa -- Case studies; Numeracy -- South Africa