Constructing mathematics in an interactive classroom context

Abstract

This paper investigates the nature of the interaction between the teacher and students as they worked on different mathematics activities in a single classroom over a 10-month period. Sociocultural theories and the Vygotskian zone of proximal development provide the main framework for examining the teaching and learning processes and explaining the incorporation of a four-phase lesson plan as increasing participation of the teacher and students in the teaching and learning process. Drawing on the analyses of discourse from videotaped lessons and the interviews with the teacher and students, five different types of interactions that emphasized mathematical sense-making and justification of ideas and arguments were identified. Excerpts from transcriptions of such interactions are provided to illustrate the learning practices, either academic or non-academic, that students developed in response to these interactions.

The Effects of Cooperative Learning on Students' Mathematics Achievement and Attitude towards Mathematics

“…Learning will be more successful if they are given the opportunity to explain or clarify ideas (Burns, 1990). Lau et al (2009) explains that "the mathematics skills required for youth of today's and adults of tomorrow to function in the workplace are different from that for youth and adults of yesterday". In terms of pedagogy, the development of education now requires teaching strategies that emphasize student involvement.…”

Before and after Lightfoot/León. Using rich pictures to illustrate an educational journey through the world of opera and ballet

“…He suggested that individual and social processes of learning and development are interdependent, and that individuals acquire knowledge through participating in collaborative activities and working with others (Wertsch, 1985;1991;). Vygotsky's proposition provided a framework that has found much resonance in educational research (Tappan, 1998;Mills, 2010;Lau, Singh & Hwa, 2009;Eun, 2010;Rassaei, 2014). His ideas have been further developed in a large number of influential scholarly works that argue for an understanding of learning as socially situated (e.g.…”

Cross‐Cultural Study of Cognitive and Metacognitive Processes During Math Problem Solving

“…The environment of small group problem solving provides a natural setting "to supply explanations and elaborate [one's] reasoning" (Kramarski, Mevarech, & Arami, 2002, p. 228); it encourages interpersonal monitoring and reflection (Artzt & Armour-Thomas, 1992); and, it makes students negotiate with each other on viable solutions (Ben-Ari & Kedem-Friedrich, 2000;Lambert, 2002). Past studies have described how the patterns of classroom interactions may facilitate or impede learning (Goos, 2004;Goos & Galbraith, 1996;Goos, Galbraith, & Renshaw, 2002;Lau, Singh, & Hwa, 2009;Truxaw & DeFranco, 2008;Zolkower & Shreyar, 2007).…”