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…

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)

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…

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…

Presents a study to describe and understand the thinking processes of students in a computer environment while undertaking mathematical tasks related to the differentiation of functions defined on real numbers. Describes two different approaches, the visual and the algebraic approach, in the thinking processes of calculus students. (Contains 19…

Explores some of the issues behind mathematical modeling for technology with reference to undergraduate teaching and professional practice. Discusses theory and practice in mathematical modeling and its place and uses of modeling in engineering. (ASK)

Interviews students majoring in mathematics who had passed a required introductory course on algebraic structures on students' difficulties with basic concepts in group theory as part of a research project. Reports data concerning cyclic groups. (ASK)

Reflects on four years of teaching a course called Principle of Major Teachers for pre-service elementary school teachers. Identifies and describes the discord between their formal mathematical knowledge and their informal language used in the context of elementary number theory. Presents encouraging results from a code-switching experiment.…

Examines how components of the concept of function (variable, domain, and range) and the process-object duality in its nature emerge as highly relevant to student learning in various mathematical contexts related to linear and abstract algebra. (Contains 22 references.) (ASK)

Presents an exploratory study with expert university students to determine how students could reseal the rupture and restore a sense of unity between the figural and conceptual components of conic sections. Suggests certain tools of semiotic mediation which could be introduced to enable students to achieve the conceptual oversight that is possibly…

Reflects on some aspects of learning mathematics that emerged along the way in creating a turtle-based exploratory tool for non-Euclidean geometry. Contains 14 references. (ASK)

Argues for the use of multiple approaches to instruction as a way to encourage students to be active critics instead of passive recipients. Presents six classroom scenes in historical sequence that review both the mathematical story and the art of teaching. (DDR)