This paper examines how a person's gesture space can become endowed with mathematical meaning associated with mathematical spaces and how the resulting mathematical gesture space can be used to communicate and interpret mathematical features of gestures. We use the theory of grounded blends to analyse a case study of two teachers who used gestures…

Considers examples of aspects of the infinitely small and large as they unfolded in the history of calculus from the 17th through the 20th centuries. Presents didactic observations at relevant places in the historical account. (Author/MM)

Compares two groups of students, one of which used writing to learn mathematics and the other which engaged thinking about mathematical ideas without writing. Indicates no significant differences between the two groups and emphasizes the importance of discussing and communicating mathematical ideas. (Contains 29 references.) (Author/ASK)

Examines the possibility that at times imagery might be a disadvantage in certain tasks. For example, the notion of a persistent image may be so vivid as to actually block other creative thought. Describes one calculus student's images supporting high levels of mathematical functioning which occasionally became so powerful as to obscure more than…

Examines the views of proof held by university-level mathematics students and teachers. Develops a framework for characterizing people's views of proof based on a distinction between public and private aspects of proof and the key ideas that link these two domains. (Author/KHR)

A number of general ideas intended to be helpful in analyzing differences in concept images among individuals are formulated. These ideas are applied to the specific concepts of continuity and limits, as taught in the secondary school and university. (MP)

Divided into two parts, this article analyzes why some pupils feel reserve about instantaneous velocities and instantaneous flows. The second part relates reactions of pupils facing a problem that implicates the instantaneous rate of change. Describes some characteristics of this problem that enables the authors to explain its instructional…