In this article, the authors present an approach to developing open-ended problems through capturing contextualised mathematics in photographs. They draw upon their research with the Problem Posing Research Project, a collaborative venture between an Australian and a Canadian university to broaden pre-service teachers pedagogical practices in the…

Highlights in the history of the axiomatic method are described, and Hilbert's and Godel's contributions are discussed. (DT)

The decline in enrollment in mathematics courses at universities is used as evidence of the increasing irrelevance of the mathematics done and taught at that level. (MP)

This paper discusses ways of discussing limits in the secondary classroom. Particular attention is paid to showing that hypothesized answers are not limits to given sequences. (SD)

This article is the first of two parts of a paper based on a collection of lectures dealing with the possible use of history of mathematics in mathematics education. A lecture course in the history of mathematics for teachers is described in detail and then more general points are discussed. (Author/MN)

A Keller-plan, mathematics laboratory-based review program initiated in response to the problem of forgotten relevant mathematical skills, new and different terminology and gaps in mathematics backgrounds, is described. (MN)

Functions with a variety of properties (sets of discontinuities, unbounded derivations, etc.) are discussed. (SD)

The use of flow charts in the teaching of college mathematics enhances students' understanding of mathematical processes. Used appropriately in elementary and secondary schools they could also nurture understanding of algorithms. (SD)

The fundamental results of integration theory are shown to follow from an axiomatic definition of the integral as a real valued function whose domain is a subset of the set of real valued functions of a real variable. (SD)

An approach to the calculus beginning with calculations of speeds was suggested by Morris Kline. This approach is developed and metricated. (SD)

A game is presented in which computation by a stepping-stone method is used to solve minimax problems. An additional application of this game is used for finding the Pearson correlation coefficient by non-parametric techniques. The game provides considerable computational practice as well as a motivational problem solving situation. (JP)

Components of a computer studies course are discussed, goals for 15 topics to be covered in a first-year course are specified, and sample evaluation items are included. (DT)

Recent developments are explained which use the concepts and methods of mathematical logic to provide a suitable framework for the development of the differential and integral calculus. (DT)

The effect of different secondary school mathematics syllabi on first-year performance in college-level mathematics was studied in an attempt to evaluate the syllabus change. Students with a modern mathematics background performed sigficantly better on most first-year units. A topic-by-topic analysis of results is included. (DT)

Attention is called to the apparent widespread misunderstanding of algebraic notation by secondary school students, and how this may arise from some common approaches to teaching algebra to beginners is discussed. (MNS)