Ernest P. (1996) Varieties of constructivism: A framework for comparison. In: Steffe L. P., Nesher P., Cobb P., Goldin G. A. & Greer B. (eds.) Theories of mathematical learning\>Theories of mathematical learning. Lawrence Erlbaum, Hillsdale: 315–350. Fulltext at https://cepa.info/5282

Excerpt: Following the seminal influence of Jean Piaget, constructivism is emerging as perhaps the major research paradigm in mathematics education. This is particularly the case for psychological research in mathematics education, However, rather than solving all of the problems for our field, this raises a number of new ones. Elsewhere 1 have explored the differences between the constructivism of Piaget and that of von Glasersfeld (Ernest, 1991b) and have suggested how social constructivism can be developed, and how it differs in its assumptions from radical constructivism (Ernest, 1990, 1991a). Here I wish to begin to consider further questions, including the following: What is constructivism, and what different varieties are there? In addition to the explicit principles on which its varieties are based, what underlying metaphors and epistemologies do they assume? What are the strengths and weaknesses of the different varieties? What do they offer as tools for researching the teaching and learning of mathematics? In particular, what does radical constructivism offer that is unique? And last but not least: What are the implications for the teaching of mathematics?

Glasersfeld E. von (1996) Aspects of radical constructivism and its educational recommendations. In: Steffe L. P., Nesher P., Cobb P., Goldin G. A. & Greer B. (eds.) Theories of mathematical learning\>Theories of mathematical learning. Lawrence Erlbaum, Hillsdale: 307–314. Fulltext at https://cepa.info/1473

In the context of theories of knowledge, the name “radical constructivism” refers to an orientation that breaks with the Western epistemological tradition. It is an unconventional way of looking and therefore requires conceptual change. In particular, radical constructivism requires the change of several deeply rooted notions, such as knowledge, truth, representation, and reality. Because the dismantling of traditional ideas is never popular, proponents of radical constructivism are sometimes considered to be dangerous heretics. Some of the critics persist in disregarding conceptual differences that have been explicitly stated and point to contradictions that arise from their attempt to assimilate the constructivist view to traditional epistemological assumptions. This is analogous to interpreting a quantum-theoretical physics text with the concepts of a 19th-century corpuscular theory. It may be useful, therefore, to reiterate some points of our “post-epistemological” approach,1 so that our discussion might have a better chance to start without misinterpretations.

Goldin G. A. (1996) Theory of mathematics education: The contributions of constructivism. In: Steffe L. P., Nesher P., Cobb P., Goldin G. A. & Greer B. (eds.) Theories of mathematical learning\>Theories of mathematical learning. Lawrence Erlbaum, Hillsdale: 303–306.

Janvier C. (1996) Constructivism and its consequences for training teachers. In: Steffe L. P., Nesher P., Cobb P., Goldin G. A. & Greer B. (eds.) Theories of mathematical learning\>Theories of mathematical learning. Lawrence Erlbaum, Hillsdale NJ: 449–463.

The aim of this chapter is to examine the consequences of constructivism for the training of secondary level mathematics teachers, In the first section, 1 expose my understanding of what constructivism is. This enables me to draw inferences for teaching. It is argued that constructivism is only concerned with learning and not with teaching. As a consequence, it is only possible to specify constructivist conditions that must be respected in order to make “good” learning happen. These conditions lead us, in the next section, to the objectives that constructivism suggests for teachers’ training. At this point, the stage is set to proceed to a fair description of the intricate web of cognitive processes underlying the training of teachers who, in short, are taught to learn about learning and teaching. In the final section, I present and analyze the constructivist content and objectives of a few training/learning activities that my colleagues and I, at Université du Quebec a Montreal (UQAM), have been developing over the last few years in our pro-gram.