Students' Accounts of Their Experiences of Learning Mathematics

Abstract

This research identifies important features of mathematics learning from the accounts of early school leavers. These students were enrolled in a Youth Reconnected Program at a Technical and Further Education [TAFE] college. Specifically, it examines the relationship between their experiences of mathematics learning in two different social contexts, the program and secondary school classrooms, the discourses and associated discursive practices of these two contexts, and the forms of identities of participation that are constructed in them. Drawing on a social theory of learning and critical discourse theory, the research identifies the processes by which membership in communities of learning is achieved and identities discursively constructed. It draws on the accounts of forty-three early school leavers and six staff members located in a Youth Reconnected Program, a program designed to re-engage early school leavers in education and or training, about their prior experiences of secondary school and their current experiences of TAFE. From these accounts, the thesis seeks to explicate their experiences of learning mathematics in both contexts and to consider the implications of different student experiences of learning for mathematics education. Critical discourse analysis provides the means for applying this framework to examine the discourses, discursive practices, identities, and forms of participation constructed in the accounts. It views the accounts as constituted by their social context. It shows how the language of the accounts works to construct particular versions of reality and how relations of power construct particular identities. It allows a richer qualitative exploration of the reported practices of mathematics classrooms with particular regard to linking the theoretical and practical concerns of this study. It makes transparent the relations between the social (including relations of power and domination), discourse, and discursive practice, thus enabling a more in-depth reading of the participants‘ accounts. Discourses about two different experiences of mathematics learning were identified—one about mathematics learning in the Youth Reconnected Program (TAFE) and the other about mathematics learning in secondary schools. The discourses and their associated discursive practices—differing application of instructional style, communication and interaction, source of authority, pace of instruction, grouping of students and assessment— were found to contribute significantly to the construction of particular student identities and forms of participation. Student experiences emphasised the importance of four characteristics for membership in a community of learners—mutual engagement, joint enterprise, shared repertoire and access. These characteristics and practices were shown to contribute substantially to the construction of identities of participation in mathematics learning for most of the students who participated in this study. There was strong evidence to indicate that small class sizes impacted significantly on student engagement and participation in learning. A crucial factor here rests with the role of the teachers and tutors and how, given the opportunities for reduced class size, they implement, sustain and maintain interactions with the students for effective teaching and learning to occur. If in this context, consistent interactions are provided that also includes clear and explicit explanations, discussion, and negotiation, students are more likely to maintain their interest and actively participate in mathematics learning. This study‘s significance is twofold. It lies in the critical importance of the issue it addresses—student participation in mathematics learning—and the articulation of a social theory of learning with critical discourse theory to enable a different and more effective understanding of the significance of discourses, identities and communities of participation in mathematics learning. Although the study cannot claim generalisability across other populations of learners or across all mathematics and TAFE classrooms because of the small select sample of early school leavers drawn upon, by highlighting these accounts of students‘ learning experiences in some mathematics classrooms and the TAFE program, and their associated experiences of them, it draws attention to a different perspective on mathematics learning. In this alternative framing, learning as a social process is contingent on access to the discourse of mathematics learning and the discursive practices that support learning, participation, and membership in a community of mathematics learners. An attention to the social processes of mathematics learning infers a significant role for mathematics teachers in enabling student access to certain discourses and communities of learning. Such a role is often neglected in current contexts of accountability that specify a focus on achieving syllabus outcomes.