Sociomathematical norms constituted for promoting learners' proficiency in mathematics

Abstract

The qualitative study reported here sought to explore constitution of sociomathematical norms in a class where teaching was undertaken to promote learners’ proficiency in mathematics. A case study research design in which I served as a teacher-researcher was adopted and focused on a Grade 11 mathematics class in which all learners were participants. The study was guided by three interrelated research questions and these questions were: (i) what are the sociomathematical norms constituted for promoting learners’ proficiency in mathematics? (ii) how are the sociomathematical norms for promoting learners’ proficiency in mathematics constituted and enacted in the classroom? (iii) how does the enactment of the constituted sociomathematical norms promote learners’ proficiency in mathematics? Three theories were employed during this study, namely: (i) sociocultural theory as a referent for classroom practice (Vygotsky, 1978). (ii) theoretical constructs of socio and sociomathematical norms found in the emergent approach by Cobb and Yackel (1996) as a lens through which data were analysed; and, (iii) the five interwoven strands of mathematical proficiency (Kilpatrick, Swafford & Findell, 2001) as standards for learners’ mathematical development. The interplay of these three theories gave rise to the conceptualisation of a framework which best accounts for how the study unfolded. Data were generated through video recording and participant observation. Data also emerged from classroom discussions when learners, in their pairs or small groups, worked through learning activities. These interactions, were audio and video recorded. Meanwhile, observation data were recorded in a researcher journal in which entries were made after each lesson. Data were analysed following Polkinghorne’s (1995) narrative analysis of eventful data, followed by an analysis of narratives as the final step. During the analysis I listened to and watched the audio and video recordings a number of times, and then selected the excerpts which were to be used for analysis. This was followed by the transcription of the selected audio and video data into text. It was found that learners constituted and enacted the sociomathematical norms concerned with acceptable mathematical explanations, mathematical justifications and mathematically different solutions. The constitution and enactment of these sociomathematical norms provided learners with multiple opportunities to engage in classroom discourse which promoted their proficiency in mathematics. Furthermore, it became apparent that teachers’ ability to foster productive sociomathematical norms is imperative for mathematics learning. As a result, I proposed a model for fostering the constitution of sociomathematical norms as teaching and learning unfolds in the natural setting of a classroom. The model consists of four major constructs, namely, identifying productive sociomathematical norms, knowing learners’ existing sociomathematical norms, disrupting and deconstructing learners’ sociomathematical norms and negotiating and authoring new sociomathematical norms. Enactment of sociomathematical norms, on the other hand, emerged as learners engaged in mathematical classroom discourse and experienced the situation for challenges and justifications. The enactment of these sociomathematical norms reflected the unification of social norms and mathematical norms, as learners engaged in mathematical activity. In order to orchestrate the enactment of sociomathematical norms, teachers should first adopt social learning theories (sociocultural theory) as a referent for classroom practice. These social learning theories, if adopted, will ensure that learning is taking place within environments, which allows for social interactions to take place.