One of the aims of mathematics instruction is to achieve the understanding of mathematical concepts through the development of rich and well organized cognitive representations (Goldin, 1998; NCTM, 2000; DeWindt-King, & Goldin, 2003). In this study the term representation is interpreted as the tool used for representing mathematical ideas such…

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in algebra from the Moebius strip to the googol. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally on concerns for curriculum…

The focus of these worksheets is on problem solving. Verbal problems involving number concepts are presented for primary levels; worksheets for the intermediate grades draw on geometric concepts, measurement, and elementary logic. (DT)

The problem of determining the number of squares on a checkerboard is extended to finding the number of rectangles on an n x n board and finding the total numbers of cubes and rectangular solids in an n x n x n cube. (DT)

A series of problems is presented that (1) focus on certain kinds of numbers or (2) emphasize a specific concept of number theory. Several are appropriate for extensive investigation with a computer. (MNS)

Five problems on the generation and study of prime and related numbers are discussed. Solutions to the problems posed will be in next month's presentation. (MP)

Activities designed to aid pupils explore the Fibonacci sequence are presented in worksheets. (MP)

Determining which whole numbers can be expressed as the difference of two squares and which as the sum of two squares forms the basis of two discovery exercises. (DT)

Discusses a problem that appeared in the September, 1999 issue of this journal and presents solutions from students in grades 2-6. The question involved using colored cubes rearranged to make different stacked towers. (KHR)

Investigates problems called "cranium crackers" and focuses on number sense, logical reasoning, data analysis, geometry, measurement, and algebraic thinking. (Author/NB)

The importance of establishing a problem-solving atmosphere is stressed. Children asking "why" are on their way to strengthening their number sense. Curiosity should be promoted, encouraging children to test their own hypotheses and pursue their own predictions. An example with an eight-year-old girl is given to illustrate these points.…