Communication and interaction: Why talking about mathematics is crucial to student learning
Ewing, Bronwyn F. (2008) Communication and interaction: Why talking about mathematics is crucial to student learning. In Australian Association for Research in Education 2008, 1-4 December 2008, Queensland University of Technology. (In Press)
Recent international comparisons of interactions between teachers and students reported in the Knowledge and Skills for Life: First results from the OECD Programme for International Student Assessment (PISA) 2000 (OECD, 2001) indicate that the type of interactions between teachers and students is statistically significant when associated with student success/failure and performance. It was found that traditional one-way interaction from the teacher to the student did not support student achievement in mathematics because it provided limited opportunities to talk about mathematics.
Indeed, one-way communication appears to be a central aspect in teacher-student interaction across international boundaries. Hiebert et al. (2003), identified that teachers talked more than students "at a ratio of at least 8:1 words" (p. 4) in mathematics classrooms. While the typical intention of teacher talk is to support students with learning mathematics, it can have the opposite effect on students (Begehr, 2006). The consequence is that they are denied opportunities to describe the content to be learned in their own words, to reflect on what they are learning and have learned and what they need to learn in the future (Begehr, 2006). Their efforts to understand the mathematics content are reduced to disjointed fragments without explicit links made while opportunities diminish for them to interact genuinely in and with the overall content. Instead, they are guided along a narrowly defined path that does not grant them time to express their own thoughts about their learning or engage with and use mathematical language (Begehr, 2006).
A study of forty-three early school leavers' accounts of their mathematics learning experiences identified effective communication and interaction as crucial to student learning. The articulation of a social theory of learning and critical discourse theory allowed for an examination of these discursive practices. Together, they provided a way to investigate how students located themselves in discourses relating to their interactions in mathematics classrooms. Critical discourse theory, as methodology and its application in critical discourse analysis [CDA], treated as method, enabled a more extensive examination of communication and interaction as students accounted for their learning experiences in mathematics. Further it allowed for identifying the differing approaches to communication and interactions in secondary and TAFE mathematics classrooms. The accounts allowed for considerations of what constitutes these approaches.
Instructivist approaches that are teacher-centred pedagogies focused on clear didactic communication. In these approaches, "educational effectiveness for all students is crucially dependent on the provision of quality teaching by competent teachers who are equipped with effective, evidence-based teaching strategies that work" (Rowe, 2006, p. 105). The teacher, who possesses sound mathematical content knowledge, is seen to be the expert who passes this knowledge onto students via direct instruction, rehearsal and rote learning. It is the teacher who tells the students what they need to know and learn. Hence classroom interactions are largely initiated by the teacher, they are didactic. Teachers are expected to possess a thorough knowledge of the content and processes of mathematics. They require an understanding of the underlying general principles of mathematics to guide their application effectively and to support student learning. If these requirements are met, it is claimed that instruction will succeed when concepts are conveyed accurately.
A reformist approach to the teaching and learning of mathematics identifies that an interactive classroom is the natural corollary to an interactive teaching style. The nature of classroom relationships--between teacher and students and student and student--is crucial to student learning in the reform classroom. An interactive classroom, then, is one in which, guided by the teacher, students find ways that allow them to interact, inquire and discuss their understandings about mathematics, and relate this to the world beyond the classroom (Cobb, Boufi, McClain & Whitenack, 1997). To address this process in more detail requires defining the teaching and learning of mathematics that reflects finding out why techniques work and justifying assertions.
This approach, learning mathematics through interaction with peers and teachers, has been advocated to encourage student participation and inquiry in mathematics classrooms (Thompson, 2001). From this viewpoint, when students and teachers interact, discuss, and challenge their mathematical ideas, students were found to inquire and participate in their learning. The use of language in this engagement provides teachers with indicators of the students' confidence and competence in mathematics (Bills, 2003). In this process of evaluation, the teacher takes into consideration the language of the context, that is, of mathematics.
The aim of this paper is to foreground the aspects of communication and interaction, situating them in the context of mathematics classrooms. The interactions between teachers and students in mathematics classrooms have been shown to affect significantly the quality of the learning experience for students. In these contexts, students are exposed to mathematics in ways that engage them in inquiry and questioning the mathematics to be learned. Throughout the interactions the teacher supports students in using the language of mathematics and to take risks when doing so. This process enhances the students' conceptual understandings as they articulate their thinking through language in the social context of the classroom.
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