Using Sociocultural Theory to Teach Mathematics: A Vygotskian Perspective

Abstract

This study describes an elementary teacher's implementation of sociocultural theory in practice. Communication is central to teaching with a sociocultural approach and to the understanding of students; teachers who use this theory involve students in explaining and justifying their thinking. In this study ethnographic research methods were used to collect data for 4 1/2 months in order to understand the mathematical culture of this fourth‐grade class and to portray how the teacher used a sociocultural approach to teach mathematics. To portray this teaching approach, teaching episodes from the teacher's mathematics lessons are described, and these episodes are analyzed to demonstrate how students created taken‐as‐shared meanings of mathematics. Excerpts from interviews with the teacher are also used to describe this teacher's thinking about her teaching.

Semantic Structure of Classroom Discourse Concerning Proof and Proving in High School Mathematics

“…Sierpinska (2005) stated that during the last 20 years, research about language in mathematics education involves at least three common theoretical approaches with language as a code, representation, and discourse. Hiebert, Carpenter, Fennema, Fuson Wearne, Murray, Oliver and Human (1998) claimed that students accomplish mathematical understanding only when they form connections between knowledge and the relations/links of their knowledge; so that communication is the key component to providing the associational understanding (cited in Steele, 2001). Methods of investigation about communication and its theoretical source is offered in the disciplines of language, psychology, and sociology.…”

An evaluation of the supplemental instruction program implemented in a first-year calculus course.

“…Educators have moved beyond Piaget's emphasis on cognition and discovery processes, and now are also concerned with the cultural context as proposed by Vygotsky (Bunch, 1995;Daniels, 1995;Gee, 1996;Steele, 2001;Wells, 2001a;Zack & Graves, 2001). …”

“…Martin (1973) petitioned for a program that integrated reasoning and study skills with course content; not isolated from it (Martin & Arendale, 1992 It is these practices that are currently forefront on theories of learning and reflect theory by creating opportunity for discourse in the language of the discipline (Chapman, 1995;Gee, 1996;Kenney & Kallsion, 1994;Linn & Kessel, 1996;Steele, 2001;Wells, 2001b). Many of the guiding principles of SI, although arising out of practice, have a solid theoretical grounding.…”

“…The search for effective methods of teaching mathematics, so that students are better able to master the concepts, ideas, and the language of the discipline, continues to challenge professional educators and researchers alike (Steele, 2001;Sfard, 2000;Chapman, 1995;Wells, 2001a). Attempts to improve mathematics achievement have fallen short of desired outcomes.…”

“…The need to improve mathematical competency in students has led to extensive research in recent years and an examination of existing practices (Gee, 1996;Sfard, 2000;Steele, 2001;Wells, 2001a). Current trends in educational research point to the need to create discourse through social interaction as a means for improving mathematical knowing (Forman & Ansell, 2001;Gee, 1996;Steele, 2001;Wells, 2001b;Zack & Graves, 2001). In this paper 1 examine current theory on how mathematics may best be acquired and learned within a sociocultural context, through the use of "dialogue" (Gee, 1996;Vygotsky, 1978), program.…”