Confrey J. (1998) Voice and perspective: hearing epistemological innovation in students’ words. In: Larochelle M., Bednarz N. & Garrison J. (eds.) Constructivism and education. Cambridge University Press, New York NY: 104–120.

Excerpt: In this chapter, I have argued that radical constructivist interpretations of constructivism differ from other interpretations in that radical constructivism is an epistemological theory based in viability. It is suggested that viability commits one to the expectation of and support for diversity in the classroom. Moreover, it obliges the radical constructivist to also reinterpret the mathematical meaning of concepts in light of the students’ inventions. To do this effectively, the radical constructivist must learn techniques of close listening and follow these by the articulation of student voice and the examination of the changes in his or her own perspective. It is the “voice-perspective” relationship which makes radical constructivism capable of deep reform in mathematics instruction.

Confrey J. (2000) Constructivism revisited and revised. Nordisk Mathematik Didaktik 8(3): 7–30.

I will first review a set of central principles of constructivism, describe their modification when applied in the setting of urban education and then describe how we have revised them further to engage in whole school and district level change.

Confrey J. (2011) The Transformational Epistemology of Radical Constructivism: A Tribute to Ernst von Glasersfeld. Constructivist Foundations 6(2): 177–182. https://cepa.info/196

Problem: What is it that Ernst von Glasersfeld brought to mathematics education with radical constructivism? Method: Key ideas in the author’s early thinking are related to ideas that are central in constructivism, with the aim of showing their importance in math education. Results: The author’s initial thinking about constructivism began with Toulmin’s view of thinking as evolving. Ernst showed how Piaget’s genetic epistemology implied an epistemology that was not about ontology. Continuing with an analysis of the way radical and trivial constructivism were received by the mathematics education community, implications of Ernst’s ideas are considered. Implications: These include the need to consider major changes in ways content is introduced to children, to consider carefully the language used to describe children’s emerging mathematical ideas, and to consider new conjectures and also how we think about the foundations of mathematics. Ultimately the value of RC is the way it reinspires belief in the possibility and importance of human growth.

Confrey J. & Kazak S. (2006) A thirty-year reflection on constructivism in mathematics education in PME. In: Gutierrez A. & Boero P. (eds.) Handbook of research on the psychology of mathematics education: Past, present and future. Sense Publications, Rotterdam: 305–345. https://cepa.info/2973

Introduction:As the International Group for the Psychology of Mathematics Education (IG PME) grew up, so did constructivism. Reflecting over the role of constructivism in the history of mathematics education is a daunting task, but one which provides an opportunity to reflect on what has been accomplished, honor the contributions of scholars around the world, and identify what remains unfinished or unexplained. In undertaking this task, we divide our treatment into five major sections: (1) The historical precedents of constructivism during the first ten years (1976–85); (2) The debates surrounding the ascendancy of constructivism during the next ten years (1986–95); (3) Our own articulation of key principles of constructivism; (4) Thematic developments over the last ten years (1996-present); and (5) An assessment of and projection towards future work. Looking back, we hope we can share the excitement of this epoch period in mathematics education and the contributions to it which came from across the globe. Since its inception at the 1976 International Congress on Mathematical Education (ICME) in Karlsruhe, PME has addressed three major goals all addressing the need to integrate mathematics education and psychology. While PME clearly has welcomed and thrived on multiple theories of psychology, beginning with Skemp’s (1978) The Psychology of Learning Mathematics, it has preferred those with a cognitive, and to some extent, an affective orientation. Two major theories of intellectual development have been dominant, namely constructivism and socio-cultural perspectives. In recent years, these two theories have intermingled, but in this volume, they are separated as we trace their paths, overlapping and distinctive. We will not give in to the frequent temptation to cast constructivism and socio-cultural perspectives as a diametrically opposed where one is personal/individual and the other social; but rather track the evolution of the theory via the theorists and the perspectives that they assign to their work.

Confrey J. & Maloney A. (2006) From constructivism to modeling. In: Stewart S. M., Olearski J. E. & and Thompson D. (eds.) Proceedings of the Second Annual Conference for Middle East Teachers of Science, Mathematics and Computing (METSMaC). Middle East Teachers of Science, Mathematics and Computing, Abu Dhabi: 3–28. https://cepa.info/3880

This paper traces the development of constructivism as a theory of epistemology and learning, and identies ten key principles of this “grand theory.” It identies the need to further develop bridging theories that more closely link to empirical evidence. Within these bridging theories, it identies primary themes: grounding in action, activity and tools, alternative perspectives, student reasoning patterns and developmental sequences, student-invented representations, socioconstructivist norms, etc., that are useful in linking theory and practice. Finally, it discusses how these ideas have been evolving into a view of modelling as an orientation to mathematics and science instruction, and identies this approach as a successor to constructivist theories.

Confrey J., Mundy J. & Waxman B. (1983) Educating mathematics teachers: The cognitive/constructivist perspective. In: Bergeron J. & Herscovics N. (eds.) , Proceedings of the Fifth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education Volume 2. University of Quebec-Montreal, Montreal: 196–204.