Ernest P. (1991) Constructivism, the psychology of learning, and the nature of mathematics. In: Furinghetti F. (ed.) Proceedings of the 15th PME International Conference 2. PUBLISHER, PLACE: 25–32.

Two dichotomies in the philosophy of mathematics are discussed: the prescriptive – descriptive distinction, and the process – product distinction. By focusing on prescriptive matters, and on mathematics as a product, standard philosophy of mathematics has overlooked legitimate and pedagogically rewarding questions that highlight mathematics as a process of knowing which has social dimensions. In contrast the social-constructivist view introduced here can affect the aims, content, teaching approaches, implicit values, and assessment of the mathematics curriculum, and above all else, the beliefs and practices of the mathematics teacher.

Ernest P. (1993) Constructivism, the psychology of learning, and the nature of mathematics: Some critical issues. Science & Education 2: 87–93. https://cepa.info/2948

Constructivism is one of the central philosophies of research in the psychology of mathematics education. However, there is a danger in the ambiguous and at times uncritical references to it. This paper critically reviews the constructivism of Piaget and Glasersfeld, and attempts to distinguish some of the psychological, educational and epistemological consequences of their theories, including their implications for the philosophy of mathematics. Finally, the notion of ‘cognizing subject’ and its relation to the social context is examined critically.

Ernest P. (1994) Social constructivism and the psychology of mathematics education. In: Ernest E. (ed.) Constructing mathematical knowledge: Epistemology and mathematics education. Falmer Press, London: 68–79. https://cepa.info/3655

Excerpt: It is widely recognized that a variety of different forms of constructivism exist, both radical and otherwise (Ernest, 1991b). However it is the radical version which most strongly prioritizes the individual aspects of learning. It thus regards other aspects, such as the social, to be merely a part of, or reducible to, the individual. A number of authors have criticized this approach for its neglect of the social (Ernest 1991b, 1993d; Goldin 1991; Lerman, 1992, 1994). Thus in claiming to solve one of the problems of the psychology of mathematics education, radical constructivism has raised another: how to account for the social aspects of learning mathematics? This is not a trivial problem, because the social domain includes linguistic factors, cultural factors, interpersonal interactions such as peer interaction, and teaching and the role of the teacher. Thus another of the fundamental problems faced by the psychology of mathematics education is: how to reconcile the private mathematical knowledge, |69| skills, learning, and conceptual development of the individual with the social nature of school mathematics and its context, influences and teaching? In other words: how to reconcile the private and the public, the individual and the collective or social, the psychological and the sociological aspects of the learning (and teaching) of mathematics?

Ernest P. (1995) The one and the many. In: Steffe L. & Gale J. (eds.) Constructivism in Education. Lawrence Erlbaum, New York: 459–486. https://cepa.info/4160

Excerpt: I use the pre-Socratics’ contrast of the one and the many as my organizing theme. It fits well with the aim of this chapter: to offer both an analysis and synthesis of half of the preceding contributions. Synthesis constructs unity (the one), whereas analysis turns out to suggest diversity (the many). Starting with “the one,” I consider what different positions in constructivism have in common. Then I consider “the many” – analyzing some salient differences between different constructivist positions (and a few others). Finally, I offer a synthesis, “the one” again, identifying what seem to be deeply shared themes, problems and points of growth for constructivism, and alternative epistemologies in education.

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. Lawrence Erlbaum, Hillsdale: 315–350. 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?

Ernest P. (2010) Reflections on theories of learning. In: Sriraman B. & English L. (eds.) Theories of mathematics education. Springer, Berlin: 39–47. https://cepa.info/5843

Four philosophies of learning are contrasted, namely ‘simple’ constructivism, radical constructivism, enactivism and social constructivism. Their underlying explanatory metaphors and some of their strengths and weaknesses are contrasted, as well as their implications for teaching and research. However, it is made clear that none of these ‘implications’ is incompatible with any of the learning philosophies, even if they sit more comfortably with one of them.