Schoenfeld A. H. (1992) Radical Constructivism and the Pragmatics of Instruction: Review of Radical Constructivism in Mathematics Education. Journal for Research in Mathematics Education 23(3): 290–295. https://cepa.info/5419

Simon M. A. (1995) Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education 26(2): 114–145. https://cepa.info/3671

Constructivist theory has been prominent in recent research on mathematics learning and has provided a basis for recent mathematics education reform efforts. Although constructivism has the potential to inform changes in mathematics teaching, it offers no particular vision of how mathematics should be taught; models of teaching based on constructivism are needed. Data are presented from a whole-class, constructivist teaching experiment in which problems of teaching practice required the teacher/researcher to explore the pedagogical implications of his theoretical (constructivist) perspectives. The analysis of the data led to the development of a model of teacher decision making with respect to mathematical tasks. Central to this model is the creative tension between the teacher’s goals with regard to student learning and his responsibility to be sensitive and responsive to the mathematical thinking of the students.

Steffe L. P. & D’Ambrosio B. (1995) Toward a working model of constructivist teaching: A reaction to Simon. Journal for Research in Mathematics Education 26(2): 146–159. https://cepa.info/2105

Steffe L. P. & Kieren T. (1994) Radical constructivism and mathematics education. Journal for Research in Mathematics Education 25(6): 711–733. https://cepa.info/2102

intention in this mticle is to provide an interpretation of the influence of constructivist thought on mathematics educators starting around 1960 and proceeding on up to the present time. First, we indicate how the initial influence of constructivist thought stemmed mainly from Piaget’s cognitive development psychology rather than from his epistemology. In this, we point to what in retrospect appears to be ineTitable distmtions in the interpretations of Piaget’s psychology due primarily to its interpretation in the framework of Cartesian epistemology. Second) we identify a preconstructivist revolution in research in mathematics education beginning in 1970 and proceeding on up to 1980. There were two subperiods in this decade separated by Ernst von Glasersfeld’s presentation of radical constructiTism to the Jean Piaget Society in Philadelphia in 1975. Third, we rnark the beginning of the constructivist revolution in mathematics education research by the publication of two important papers in the JRME (Richards & van Glasersfeld, 1980; van Glasersfeld, 1981). Fomth, we indicate how the constructivist revolution in mathematics education research served as a period of preparation for the reform movement that is currently underway in school mathematics.

Steffe L. P. & Thompson P. W. (2000) Interaction or intersubjectivity? A reply to Lerman. Journal for Research in Mathematics Education 31(2): 191–209. https://cepa.info/2109

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.