This paper was prepared in response to the Conference Board of Mathematical Sciences recommendations for the preparation of secondary teachers. It shows how using trigonometry as a conceptual tool in spreadsheet-based applications enables one to develop mathematical understanding in the context of constructing geometric representations of unit…

This paper was developed with the goal of enhancing the mathematical preparation of secondary school teachers in the technological paradigm. It shows how two-variable inequalities can be utilized as models for the construction of geometric objects using the software Graphing Calculator 3.5 (produced by Pacific Tech) as a relation grapher. An…

Inequalities are considered among the most useful tools of investigation in pure and applied mathematics; yet their didactical aspects have not received much attention in mathematics education research until recently. An important aspect of teaching problem solving at the secondary level deals with the notion of equivalence of algebraic…

This paper introduces technology-based teaching ideas that facilitate the development of qualitative reasoning techniques in the context of quadratic equations with parameters. It reflects on activities designed for and used with prospective secondary mathematics teachers in accord with standards for teaching and recommendations for teachers in…

This article attempts to extend current research and development activities related to the use of technology in problem posing, to early grades mathematics. It is motivated by the authors' work with elementary preservice teachers toward this goal, both at the graduate and undergraduate levels. New York State Learning Standards for K-4 mathematics…

This paper suggests that knowledge of the school mathematics curriculum, as one of the key components of teachers' education, can be extended to include concepts and structures that generally belong to hidden domains of the curriculum. Motivated by work done with elementary pre-service teachers in a mathematics course employing a hidden…

Shows how the joint use of a dynamic geometry program and a spreadsheet can provide a computational environment for exploring geometry on plane lattices that lessens the risk of developing the false empiricist view of mathematics often associated with the use of information technology. Contains 17 references. (Author/ASK)

Suggests that using the iconic and computing features of a spreadsheet enhances the transition from natural language sentences to pictorial and numerical representations of algebraic word problems. Presents work performed in a lab setting with preservice and inservice teachers enrolled in contemporary general mathematics and problem-solving…

Describes how a software package that includes a spreadsheet, a relation grapher, and a dynamic geometry can contribute to teacher training through an exploratory problem-solving course. Discusses the ways in which technology-rich environments enhance and extend traditional topics. Contains 17 references. (DDR)

Examines the use of spreadsheets for solving equations by the method of iterations. The combination of the spreadsheets and graphical representation is shown to be appropriate both for teaching and learning the method of iterations and for investigating properties of equations. (Author)