Two questions about certainty in mathematics are asked. First, is mathematical knowledge known with certainty? Second, why is the belief in the certainty of mathematical knowledge so widespread and where does it come from? This question is little addressed in the literature. In explaining the reasons for these beliefs, both cultural-historical and…

In this paper, we look at what engaging with psychoanalysis, through psychosocial accounts of subjectivity, has contributed to our struggles for legitimacy and security within our ways of knowing. The psychosocial, with its insistence on the unconscious and the irrational, features as both a source of security and of insecurity. We use three…

What are the theoretical foundations of mathematics education? Recently disciplines other than mathematics and psychology have grown in importance, including philosophy. But which branch of philosophy is the most fundamental for mathematics education? In this article, I consider the claims of five branches of philosophy to be our "first…

Explores and compares the assumptions and nature of four constructivist-related positions in mathematics education: information processing theory, trivial constructivism, radical constructivism, and social constructivism. (19 references) (Author/MKR)

Discusses two dichotomies in the philosophy of mathematics: the prescriptive-descriptive distinction, and the process-product distinction. Introduces the social-constructivist view that can affect the aims, content, teaching approaches, implicit values, assessment of the mathematics curriculum, and the beliefs and practices of mathematics…