Early approach to theoretical thinking: gears in primary school

Gears are part of everyday experience from very early childhood. This paper analyses a teaching experiment conducted with 4th graders in the field of experience of gears. The aim is to identify the characteristics which, given a suitable sequence of tasks and proper teacher guidance, have enabled the pupils to approach theoretical thinking, and in particular mathematical theorems. We have focused on the relationships between the epistemological analysis of some pieces of mathematical knowledge brought into play in tasks concerning gears, cognitive analysis of pupil construction of those pieces of mathematical knowledge, and didactic analysis of the teacher's role in designing tasks and in offering cultural mediation. This paper presents the early findings of the teaching experiments, both at the external level of interpersonal classroom processes and at the inner level of individual mental processes.

[1]  Paolo Boero,et al.  Challenging the traditional school approach to theorems: a hypothesis about the cognitive unity of theorems , 1996 .

[2]  Paolo Boero,et al.  Some dynamic mental processes underlying producing and proving conjectures , 1996 .

[3]  The principle of operative concept formation in geometry teaching , 1980 .

[4]  J. Wertsch.  Voices of the Mind: A Sociocultural Approach to Mediated Action , 1992 .

[5]  André Leroi-Gourhan,et al.  L'homme et la matière , 1971 .

[6]  H. Freudenthal.  Didactical Phenomenology of Mathematical Structures , 1983 .

[7]  Maria G. Bartolini Bussi,et al.  Mathematical discussion and perspective drawing in primary school: to Giovanni Prodi on occasion of his 70th birthday , 1996 .

[8]  Brian Rotman,et al.  Signifying Nothing: The Semiotics of Zero , 1987 .

[9]  G. Lakoff.  The Metaphorical Structure of Mathematics: Sketching Out Cognitive Foundations For a Mind-Based Mathematics , 1997 .

[10]  Paolo Boero,et al.  Approaching geometry theorems in contexts: from history and epistemology to cognition , 1997 .

[11]  G. Longo.  Géométrie, mouvement, espace : cognition et mathématiques , 1997 .

[12]  L. Vygotsky.  Mind in Society: The Development of Higher Psychological Processes: Harvard University Press , 1978 .

[13]  A. Treffers.  Three Dimensions: A Model of Goal and Theory Description in Mathematics Instruction ― The Wiskobas Project , 1986 .

[14]  Mathematics: "In Context,""Pure," or "with Applications"?. , 1995 .

[15]  Maria Giuseppina Bartolini,et al.  Theoretical and Empirical Approaches To Classroom Interaction , 1994 .

[16]  Guy Brousseau,et al.  Rôle de la mémoire didactique de l'enseignant , 1991 .