Transforming sociomathematical norms in a South African grade 11 classroom to enhance learners’ mathematical proficiency

Abstract

In this paper we use parts of qualitative data from the first author’s doctoral study to explore how transforming existing sociomathematical norms enhance learners’ mathematical proficiency. The study was conducted in a grade 11 mathematics classroom comprising of 23 learners, facilitated by the first author as learners engaged in a mathematical discourse on analytical geometry. Data were gathered through video recording, documents and researcher journal. We adopted Yackel and Cobb’s (1996) interpretive framework and Kilpatrick et al.’s (2001) notion of mathematical proficiency as lenses, which guided the data analysis. We analyzed the data following Polkinghorne’s (1995) narrative analysis method. We found that transforming existing sociomathematical norms to enhance learners’ mathematical proficiency involved a three-stages process: negotiating entry into learners’ existing sociomathematical norms, disrupting learners’ existing sociomathematical norms and constituting ‘new’ sociomathematical norms. As learners developed new taken-as-shared meanings regarding acceptable mathematics explanations, justifications and mathematically different solutions they enhanced their <i>conceptual understanding, procedural fluency, adaptive reasoning</i>,<i> </i>and<i> strategic competence</i>.