Pixie S. & Kieren T. (1992) Creating constructivist environments and constructing creative mathematics. Educational Studies in Mathematics 23: 505–528.

Simmt E. & Kieren T. (2015) Three “moves” in enactivist research: A reflection. ZDM Mathematics Education 47: 307–317. Fulltext at https://cepa.info/4481

In this paper the authors reflect on the contents of this current issue of ZDM and ask why focus an entire issue on enactivism as a research methodology in mathematics education. In their synthesis of the papers they distinguish and explicate what they observe as three moves in the enactivist research discussed. The first move (and the one that receives much of the attention in the papers) is that of the observer. Enactivism proposes the observer is one who arises in the act of observing and whose knowing is explained through the mechanism she describes. The second move is an understanding that all knowing is perceptually guided action that brings forth a world of significance. The third is a consequence of the first two: All knowing has implications. Hence that third move is towards ethics. The observer is not neutral; her observations bring forth worlds of significance that intersect with the worlds of others. They conclude, that the strength of enactivism as a methodological frame for mathematics education research is that it is a form of research that is incomplete. Incomplete in that from this framework there is necessarily always more to be said and different grounds for the saying about the phenomena under investigation in mathematics education.

Steffe L. P. & Kieren T. (1994) Radical constructivism and mathematics education. Journal for Research in Mathematics Education 25(6): 711–733. Fulltext at 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.