EXAMINING MATHEMATICAL DISCOURSE PRACTICES

What are the features of Discourse practices? Are there characteristic mathematical Discourse practices? Can we distinguish everyday and academic mathematical Discourse practices? This article [1] considers these questions from a socio-cultural and situated perspective of mathematical Discourse practices (Moschkovich, 2002a, 2004) [2]. To ground that discussion, I first present an excerpt of a classroom discussion about quadrilaterals. The excerpt comes from a lesson in a third grade (students are 8-9 years old) bilingual classroom in an urban California school. The students have been working on a unit on two-dimensional geometric figures. During the past weeks, instruction had included technical vocabulary such as the names and definitions for different quadrilaterals. Students had been talking about shapes and the teacher had asked them to point to, touch, and identify different quadrilaterals. In this lesson, students were describing quadrilaterals as they folded and cut paper to form Tangram pieces (see Figure 1).

[1]  S. Stodolsky.  The Subject Matters: Classroom Activity in Math and Social Studies , 1988 .

[2]  Philip J. Davis,et al.  The Mathematical Experience , 1982 .

[3]  L. Radford.  Signs and meanings in students' emergent algebraic thinking: A semiotic analysis , 2000 .

[4]  Judit N. Moschkovich,et al.  A Situated and Sociocultural Perspective on Bilingual Mathematics Learners , 2002 .

[5]  Paul Cobb,et al.  Participating in Classroom Mathematical Practices , 2001 .

[6]  J. Greeno.  THE SITUATIVITY OF KNOWING, LEARNING, AND RESEARCH , 1998 .

[7]  David W. Carraher,et al.  Mathematics in the streets and in schools , 1985 .

[8]  S. Scribner.  Studying working intelligence. , 1984 .

[9]  Judit N. Moschkovich,et al.  Appropriating Mathematical Practices: A Case Study of Learning to Use and Explore Functions Through Interaction with a Tutor , 2004 .

[10]  David W. Carraher,et al.  Street mathematics and school mathematics , 1993 .

[11]  N. Nasir,et al.  Identity, Goals, and Learning: Mathematics in Cultural Practice , 2002 .

[12]  Judit N. Moschkovich,et al.  Moving Up and Getting Steeper: Negotiating Shared Descriptions of Linear Graphs , 1996 .

[13]  Michael Tomasello.  CURRENT DIRECTIONS IN PSYCHOLOGICAL SCIENCE Culture and Cognitive Development , 2022 .

[14]  B. Rogoff.  Apprenticeship in Thinking: Cognitive Development in Social Context , 1990 .

[15]  P. V. Bendegem.  Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics , 1993 .

[16]  A. Paton.  WAYS WITH WORDS , 1995 .

[17]  D. Pimm,et al.  Speaking Mathematically: Communication in Mathematics Classrooms , 1987 .

[18]  A. Schoenfeld.  Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics (Reprint) , 2009 .

[19]  James Paul Gee,et al.  话语分析入门 : 理论与方法 = An introduction to discourse analysis : theory and method , 1999 .

[20]  Edwin W. Schreiber.  The National Council of Teachers of Mathematics , 1936 .

[21]  L. Quéré.  Cognition in Practice , 1996 .

[22]  Jens Høyrup,et al.  In Measure, Number, and Weight: Studies in Mathematics and Culture , 1994 .

[23]  Leone Burton,et al.  The Practices of Mathematicians: What do They Tell us About Coming to Know Mathematics? , 1998 .

[24]  H. Mehan,et al.  Learning Lessons, Social Organization in the Classroom , 1979 .

[25]  A. Collins,et al.  Situated Cognition and the Culture of Learning , 1989 .

[26]  Robin C. Scarcella,et al.  Academic English: A Conceptual Framework , 2003 .

[27]  J. Gee.  Social Linguistics And Literacies: Ideology in Discourse , 1996 .

[28]  Ubiratan D’ambrosio.  Socio-Cultural Bases for Mathematical Education , 1986 .

[29]  J. Gee.  Social Linguistics and Literacies : Ideology in Discourses , 2008 .

[30]  E. Forman,et al.  Learning what counts as a mathematical explanation , 1997 .

[31]  Judit N. Moschkovich.  Chapter 1: An Introduction to Examining Everyday and Academic Mathematical Practices , 2002 .

[32]  P. Cobb,et al.  Discourse, mathematical thinking, and classroom practice. , 1993 .

[33]  Etienne Wenger,et al.  Situated Learning: Legitimate Peripheral Participation , 1991 .