When teaching primary mathematics, story problems with themes that are special to children (such as anything to do with animals) work well to develop their numerical reasoning. Children benefit from problem-solving experiences that help develop their number sense. The paper presents an activity for practicing numerical reasoning and offers three…

Presents a problem for students in grades 4-6 on Venn diagrams with or without manipulatives. Lists questions for teachers to reflect upon during the problem-solving process concerning student understanding of problems, problem-solving strategies, assessment, and reasoning skills. (ASK)

First of three experiments compared third graders who had studied worked, two-step arithmetic word problems to those learning through conventional problem solving. The former grouped showed superior test performance. In experiments two and three, children presented with integrated worked examples outperformed those presented with split-source…

This article describes the authors' experiences using clock arithmetic to help students understand key structural properties in algebra, such as identities and inverses. (Contains 10 figures.)

In 1750, the Swiss mathematician Gabriel Cramer published a well-written algebra book entitled "Introduction a l'Analyse des Lignes Courbes Algebriques." In the appendix to this book, Cramer gave, without proof, the rule named after him for solving a linear system of equations using determinants (Kosinki, 2001). Since then several derivations of…

This study presents problem solving strategies and processes of thinking of mathematically gifted elementary children with respect to non-routine word problems. The data stem from a university-based course, especially designed to foster gifted children, ages 6-10 years, through the enrichment of the elementary mathematics curriculum. Videotapes of…

Despite general agreement that students should consider more than one way to solve a complex mathematics problem, this practice is rarely observed in U.S. classrooms. In this paper, we examine data that trace the year-long professional development experience of 12 veteran teachers of middle grades mathematics--experienced users of a…

Results of a 10-item mathematical word problem test taken by 80 preservice elementary teachers showed that those receiving accurate pictures accompanying each problem scored significantly higher than both those receiving no pictures and those having inaccurate diagrams; the "no picture" group scored significantly higher than the "inaccurate…

A logical analysis of word problems provides an hypothesis about the kinds of knowledge that may be necessary for solving multi-step word problems. This hypothesis is that knowledge of the overall pattern of relations in a problem may function in problem-solving apart from knowledge of the particular entities and the local relations in which they…

Using license plates and telephone numbers for teaching probability ideas involving counting rules is suggested. How each is useful is illustrated in some detail. (MNS)

In this paper we put forward a theoretical position that, in cognitive terms, a differentiation should be made between a correspondence and a function. Important in understanding this difference is the role of an assignation rule; the correspondence acts as a way to identify a rule in context, whilst the function accommodates the rule in a more…

Three forms of a problem-solving test were given randomly to 322 tenth graders. Performance on the form containing accurate pictorial representations of items was significantly higher than on the form with only prose descriptions, which was in turn significantly higher than on the form with distorted pictorial representations. (DT)

The importance of teaching mathematics as a body of strategies and methods of inquiry is stressed; examples of situations which emphasize skills in classification, generalization, using symbols, and proof are given. (DT)