The activities of a research working group are described. The investigators from several institutions coordinate their work on space and geometry. Underlying assumptions of the group and issues faced by it are described. (SD)

Three degrees of cognitive processing were tapped by four problem types when 60 children between four and eight years were administered a set of geometry tasks differing in complexity. Analysis revealed that the tasks differed in difficulty, task success was related to age, and a hierarchical sequence existed among the skills. (SKC)

Discusses: (1) how complex roots can be made visible; (2) a proof which supplies a fresh example of mathematical induction; (3) proving Heron's formula tangentially; and (4) income tax averaging and convexity. (JN)

How to determine when there is a unique solution when two sides and an angle of a triangle are known, using simple algebra and the law of cosines, is described. (MNS)

A twenty-week course was designed around investigating many properties of the torus. Topology, differential geometry, and topics from both real and complex analysis were included. (SD)

The author argues that sine, secant, and tangent should be taught as the three basic trigonometric functions rather than sine, cosine, and tangent. (SD)

A method is presented for finding an asymptote which is not parallel to the x or y axis in a graph. (DT)

A Mascheroni construction for obtaining the length of a line segment which is the square root of a natural number is explained. (DT)

This article presents, in the context of solving a specific mathematical problem, an argument to indicate how problem posing can lead to a deeper understanding of what is involved in the act of problem solving. (DT)

Four problems concerning the maximum number of regions determined by circles and polygons are explored. (DT)

This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…

In a longitudinal study of children in grades 0-4, gender differences are developing very early in some number domains, but there do not appear to be similar differences showing in the measurement and geometry domains studied. The Early Numeracy Research Project collected data at the beginning and end of each year from over 11,000 children in…

In this paper we report on a research aimed to identify and characterize secondary school students' reasoning and proof abilities when working with 3-dimensional geometric solids. We analyze students' answers to two problems asking them to prove certain properties of prisms. As results of this analysis, we get, on the one side, a characterization…

This book demonstrates how K-2 students deepen their mathematical ideas when encouraged to represent and communicate their thinking. Numerous vignettes from actual classrooms and reflective comments from teachers provide a model for how show and tell can enhance classroom teaching and improve children's learning. Examples of students' work and…