Educational forms of initiation in mathematical culture

A review of literature shows that during the history of mathematics education at school the answer of what counts as ‘real mathematics’ varies. An argument will be given here that defines as ‘real mathematics’ any activity of participating in a mathematical practice. The acknowledgement of the discursive nature of school practices requires an indepth analysis of the notion of classroom discourse. For a further analysis of this problem Bakhtin’s notion of speech genre is used. The genre particularly functions as a means for the interlocutors for evaluating utterances as a legitimate part of an ongoing mathematical discourse. The notion of speech genre brings a cultural historical dimension in the discourse that is supposed to be acted out by the teacher who demonstrates the tools, rules, and norms that are passed on by a mathematical community. This has several consequences for the role of the teacher. His or her mathematical attitude acts out tendencies emerging from the history of the mathematical community (like systemacy, non-contradiction etc.) that subsequently can be imitated and appropriated by pupils in a discourse. Mathematical attitude is the link between the cultural historical dimension of mathematical practices and individual mathematical thinking.

[1]  P. Cobb,et al.  Mathematizing and Symbolizing: The Emergence of Chains of Signification in One First-Grade Classroom , 2021, Situated Cognition.

[2]  G. Wells,et al.  "Dialogic Inquiry. Towards a Sociocultural Practice and Theory of Education", Gordon Wells, Cambridge 1999 : [recenzja] / Marta Marchow. , 2001 .

[3]  Geoffrey B. Saxe,et al.  Studying mathematics learning in collective activity , 1998 .

[4]  L. Vygotsky.  Thinking and Speech , 1987 .

[5]  Hans Freudenthal,et al.  Revisiting mathematics education : China lectures , 1991 .

[6]  J. Lave.  Cognition in Practice: Outdoors: a social anthropology of cognition in practice , 1988 .

[7]  K.P.E. Gravemeijer,et al.  Developing realistic mathematics education , 1994 .

[8]  M. Bakhtin,et al.  The Bakhtin Reader , 1994 .

[9]  Michael Billig,et al.  Arguing and Thinking: A Rhetorical Approach to Social Psychology , 1987 .

[10]  K.P.E. Gravemeijer.  Mediating between concrete and abstract , 1997 .

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

[12]  P. Bourdieu.  Leçon sur la leçon , 1982 .

[13]  Pam Morris,et al.  The Bakhtin reader : selected writings of Bakhtin, Medvedev and Voloshinov , 1997 .

[14]  V. Voloshinov.  Marxism and the philosophy of language , 1973 .

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

[16]  Paul Cobb,et al.  Individual and Collective Mathematical Development: The Case of Statistical Data Analysis. , 1999 .

[17]  H. Freudenthal.  Mathematics as an Educational Task , 1972 .

[18]  Anna Sfard,et al.  On Reform Movement and the Limits of Mathematical Discourse , 2000 .

[19]  James G. Greeno,et al.  Response: On Claims That Answer the Wrong Questions , 1997 .

[20]  Heinz Steinbring.  Mathematical understanding in classroom interaction – the interrelation of social and epistemological constraints , 1993 .

[21]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[22]  Jean Piaget,et al.  Psychologie et pédagogie , 1969 .

[23]  R. Harré,et al.  The Discursive Mind , 1994 .

[24]  Hans Freudenthal,et al.  Weeding and Sowing: Preface to a Science of Mathematical Education , 1977 .

[25]  Bert Van Oers,et al.  Didactic Models and the problem of intertextuality and polyphony , 1999 .

[26]  G. Wells.  Dialogic Inquiry: Towards a Socio-cultural Practice and Theory of Education , 1999 .

[27]  Bert van Oers,et al.  From context to contextualizing , 1998 .

[28]  H.J.M. van Oers,et al.  Contextualisation for abstraction , 2001 .

[29]  Brian Rotman,et al.  Towards a Semiotics of Mathematics , 1988 .

[30]  N. Minick,et al.  Contexts for learning , 1997 .

[31]  Peter Auer,et al.  From Context to Contextualization , 1996 .

[32]  Jorge Larreamendy-Joerns,et al.  “You're going to want to find out which and prove it”: collective argumentation in a mathematics classroom , 1998 .

[33]  A. Bishop.  Mathematical Enculturation: A Cultural Perspective on Mathematics Education , 1988 .

[34]  Falk Seeger,et al.  The culture of the mathematics classroom , 1998 .

[35]  Koeno Gravemeijer,et al.  The role of contexts and models in the development of mathematical strategies and procedures , 1997 .

[36]  K. Bruffee.  Collaborative Learning: Higher Education, Interdependence, and the Authority of Knowledge , 1995 .

[37]  Jorge Larreamendy-Joerns,et al.  Making Explicit the Implicit: Classroom Explanations and Conversational Implicatures , 1998 .

[38]  Geoffrey B. Saxe,et al.  Culture and cognitive development , 1990 .

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

[40]  Sarah Michaels,et al.  Discourse, learning, and schooling: Shifting participant frameworks: orchestrating thinking practices in group discussion , 1996 .

[41]  H. Freudenthal,et al.  Revisiting mathematics education , 1992, The Mathematical Gazette.

[42]  J. Lave.  Cognition in practice , 1988 .

[43]  L. Darling-Hammond.  Teachers and Teaching: Testing Policy Hypotheses From a National Commission Report , 1998 .

[44]  James Paul Gee.  The social mind , 1992 .

[45]  J. Terwel,et al.  Strategic Learning in Primary Mathematics Education: Effects of an Experimental Program in Modelling , 2003 .

[46]  Y. Engeström,et al.  Perspectives on activity theory: Play, learning, and instruction , 1999 .

[47]  Are you sure? Stimulating mathematical thinking during young children's play , 1996 .

[48]  E. Wenger,et al.  Legitimate Peripheral Participation , 1991 .

[49]  Edwin W. Schreiber.  The National Council of Teachers of Mathematics , 1936, The Mathematical Gazette.

[50]  H.J.M. van Oers.  The appropriation of mathematical symbols. A psychosemiotic approach to mathematics learning. , 1999 .

[51]  Leslie P. Steffe,et al.  Theories of Mathematical Learning , 1996 .

[52]  Paul W. Richardson.  The culture of education , 1996 .

[53]  R. Veer,et al.  The Social Mind: Construction of the Idea , 2000 .