Primary students solve "oversized" story problems using drawings, equations, and written responses, helping them understand the links between the language of story problems and the numerical representations of matching equations. The activity also includes oral language and reflective writing, thus bringing together a variety of language…

This article summarizes research conducted in Gifted Algebra I and Gifted Precalculus classes in a public, suburban high school in spring 2002, which investigated the importance of reading and writing in understanding mathematical principles. The classroom teacher supplemented traditional numerical problem solving with vocabulary quizzes, reading…

The broad aim of this research is to characterize the views of proof held by college calculus students and their two types of teachers mathematics graduate students and professors. The analysis is based on an examination of the ways in which people in all three groups produce and evaluate different types of solutions to a proof-based problem from…

This book draws on the analysis of national curriculum test data from more than 600 children of 10-11 and 13-14 years of age, as well as in-depth interviews with 250 of these students, as they attempt to solve test problems, in order to explore the nature of the difficulties children experience with realistic items. It is shown, by comparing test…

Multibase arithmetic blocks are used to investigate the minimum number of blocks of each size to make a square of a given size in a given base. Generalizations are made to any size and any base through pattern recognition. The problem is extended to rectangles, cubes, and rectangular solids. (LS)

Since problem solving is recommended as the focus of school mathematics, it should be given emphasis in programs for teacher preparation. A course should focus on strategies for solving problems, rather than simply using problem-solving techniques as other content is studied. (MNS)

This exercise in mathematical modelling requires understanding of geometric progressions, inequalities, and absolutes. It presents a problem on credit creation in the banking system. (MNS)

The first nationwide effort of industry, education, and government to promote excellence in mathematics through a junior high school mathematics competition is described. The rationale for MATHCOUNTS, the organizational structure, the format, and mathematics content are described. Contains some sample items. (MNS)

Brief articles on a linguistic approach to learning mathematics vocabulary, designing cross-figure puzzles, an activity with probability, and a problem with an erroneous solution are included in this section. (MNS)

The material examines areas generated by combinations of: (1) Circles and Triangles; (2) Closely Packed Circles; and (3) Overlapping Circles. The presentation looks at examples of certain areas and at logical ways to generate the necessary algebra to clarify the problems and solve general cases. Ideas for extension are provided. (MP)

People are noted as intrigued for centuries by interplay between algebra and geometry with many important advances viewed to have come down through some sort of linking of the two. Examples are given of advantages to learning and discovery that can be found in an investigative approach combining them. (Author/MP)

Three probability problems designed to challenge students are presented: Liars and Diamonds, Heads Wins, and Random Walks. Other statistic problems are suggested that could involve computer simulations. (MNS)

Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…

The mathematical nature of the product barcode that now appears on many supermarket goods is discussed. Particular attention is given to the nature and formula of a "check digit" used to verify that product numbers are correctly scanned. Several possible student activities related to this code and others are suggested. (MP)