Interaction or intersubjectivity? A reply to Lerman

Lerman, in his challenge to radical constructivism, presented Vygotsky as an irreconcilable opponent to Piaget's genetic epistemology and thus to von Glasersfeld's radical constructivism. We argue that Lerman's stance does not reflect von Glasersfeld' s opinion of Vygotsky's work, nor does it reflect Vygotsky's opinion of Piaget's work. We question Lerman's interpretation of radical constructivism and explain how the ideas of interaction, intersubjectivity, and social goals make sense in it. We then establish compatibility between the analytic units in Vygotsky's and von Glasersfeld's models and contrast them with Lerman's analytic unit. Consequently, we question Lerman's interpretation of Vygotsky. Finally, we question Lerman's use of Vygotsky's work in mathematics education, and we contrast that use with how we use von Glasersfeld's radical constructivism.

[1]  Peter M. Hejl,et al.  Autopoiesis, communication, and society : the theory of autopoietic systems in the social sciences , 1980 .

[2]  E. Glasersfeld.  Radical constructivism in mathematics education , 2002 .

[3]  W. T. Powers.  Behavior, the control of perception , 1973 .

[4]  Norbert Wiener,et al.  Cybernetics. , 1948, Scientific American.

[5]  Massimo Piattelli-Palmarini,et al.  Language and Learning: The Debate Between Jean Piaget and Noam Chomsky , 1980 .

[6]  E. Glasersfeld.  Radical Constructivism: A Way of Knowing and Learning. Studies in Mathematics Education Series: 6. , 1995 .

[7]  L. Vygotsky,et al.  The Development of Scientific Concepts in Childhood. , 1962 .

[8]  G. Miller,et al.  Psychology and Biology of Language and Thought: Essays in Honor of Eric Lenneberg , 1979 .

[9]  Donald M MacKay.  The Place of ‘Meaning’ in the Theory of Information , 1969 .

[10]  P. Watzlawick.  The invented reality : how do we know what we believe we know? Contributions to constructivism , 1984 .

[11]  Leslie P. Steffe,et al.  The Constructivist Teaching Experiment: Illustrations and Implications , 1991 .

[12]  Heinz von Foerster,et al.  On Constructing a Reality , 2015, Environmental Design Research.

[13]  H. Maturana.  Reality: The Search for Objectivity or the Quest for a Compelling Argument , 1988 .

[14]  Susan E. B. Pirie,et al.  Growth in mathematical understanding: How can we characterise it and how can we represent it? , 1994 .

[15]  Paul Cobb,et al.  Learning mathematics : constructivist and interactionist theories of mathematical development , 1994 .

[16]  Stephen Lerman,et al.  Articulating Theories of Mathematics Learning , 1994 .

[17]  Stephen Lerman,et al.  Intersubjectivity in Mathematics Learning: A Challenge to the Radical Constructivist Paradigm?. , 1996 .

[18]  Leslie P. Steffe,et al.  Children's counting types: Philosophy, theory, and application , 1983 .

[19]  N. Minick,et al.  The Development of Vygotsky’s Thought: An Introduction , 1987 .

[20]  E. Glasersfeld.  THE DEVELOPMENT OF LANGUAGE AS PURPOSIVE BEHAVIOR , 1976 .

[21]  J. Plamenatz,et al.  Man and Society , 1965 .

[22]  Leslie P. Steffe,et al.  Radical constructivism in action : building on the pioneering work of Ernst von Glasersfeld , 2002 .

[23]  Piaget and the Solitary Knower , 1982 .

[24]  Donald M. MacKay,et al.  The nomenclature of information theory , 1953, Trans. IRE Prof. Group Inf. Theory.

[25]  Paul Cobb,et al.  Construction of Arithmetical Meanings and Strategies , 1987 .