In this paper, we propose a potential interactional explanation of tertiary-to-secondary (dis)continuity: that of authority relations. Using secondary mathematics teachers' proof validations across two contexts, we suggest that secondary teachers' conceptions of authority shape their capacity to reconcile their positions as former mathematics…

In this article, we explore the influence of mathematics graduate students' experiences with the teaching assistantships and texts that they encounter in their programs on their development and identity as teachers. We look to von Foerster's notion of trivial and non-trivial machines to interpret the graduate students' experiences and explain how…

There are many ways to generate mathematical problems from a starting point. This author shares some thoughts that led to production of a number of them. The problems contained here range in level from Kindergarten to college. Walter starts by providing the problems so that the reader will have the opportunity to solve them without any hints.…

Explains why mathematics lectures have a special role in stimulating the imagination and why attending lectures has a significant role in inducting students into their university's mathematical community. (KHR)

Investigates the heart of the experience of mathematical engagement and the meaning derived from such activities. Analyzes dialogue between five people, two of whom are professional mathematicians, another two who are graduate students in either engineering or education, and one who lacks advanced mathematical training but maintains a positive…

Presents a dialogue between two mathematics teachers of different nationalities formulated around three points: (1) student role; (2) teacher role; and (3) how dialogue may be understood as a medium for teaching. Offers some conclusions on which this form of teaching may be based. (KHR)

Inspired by the studies of pioneer Raymond, aims to redraw and make obvious the different hypotheses explaining missed devolvement. Supports research on the notions of concept and object in mathematics. (KHR)

Reports on a case study of a student who constructs formalism not from processes of quantification, but from his own visuospatial imagery. Rather than construct new objects from cognitive processes, the student reflects on mental objects already in mind and refines them to build an interpretation of the formal theory. This example leads to…

Explores differences between mathematical definitions and non-mathematical definitions by contrasting three approaches to mathematical reasoning. Examines the consequences of the use of those approaches in a first course in real analysis. Analyzes students' reasoning behavior during analysis and suggests reasons for students' difficulties with the…