Simon M. A. (1995) Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education 26(2): 114–145. Fulltext at 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.

Simon M. A. (2014) Models of Students’ Mathematics and their Relationship to Mathematics Pedagogy. Constructivist Foundations 9(3): 348–350. Fulltext at https://cepa.info/1089

Open peer commentary on the article “Constructivist Model Building: Empirical Examples From Mathematics Education” by Catherine Ulrich, Erik S. Tillema, Amy J. Hackenberg & Anderson Norton. Upshot: I comment on the nature and exemplification of second-order models in Ulrich et. al. I discuss what I see as the theoretical gap between second-order models and mathematics pedagogy. Finally, I share work we are doing to contribute towards filling that theoretical gap.