Argues that basic components of discrete mathematics can be introduced to students through gradual elaboration of experiences with iconic spreadsheet-based simulations of concrete materials. Suggests that the study of homogeneous and heterogeneous patterns of manipulative spreadsheet templates allows for appreciation of the development of…

Provides information on the number sense of Taiwanese students in grades six and eight. Indicates that student performance on questions requiring written computation was significantly better than on similar questions relying on number sense. Supports the need to look beyond correct answers when computational test results are reported. Contains 29…

Presents a brief definition and examples of residue designs while sharing some of the algebraic thought that a student used to form generalizations about the patterns discovered during the investigations of residue designs. (ASK)

Studied number use in language by preschool children and their mothers during cooking experiences. Found that although children used a variety of number words, mothers made greater use of number words than did children. Strong relationship between reciprocal numeracy episodes (between mother and child) and child's number use suggests that adult…

This article describes a series of mathematics activities based on the book "A Grain of Rice," which are designed to help students understand powers of 2. Ideas for activities in other disciplines are also provided. (Contains 3 tables.)

One explanation for the relationship between serial rapid naming (SRN) and reading is that SRN affects the temporal proximity of the phonological activation of the letters in a word, which, in turn, influences the acquisition of orthographic knowledge. To test this hypothesis, a group of Dutch first grade children was trained in the rapid serial…

This study examines one child's use of computational procedures over a period of 3 years in an urban elementary school where teachers were using a standards-based curriculum. From a sociocultural perspective, the use of standard algorithms to solve mathematical problems is viewed as a cultural tool that both enables and constrains particular…

A sequence of number pairs can be used to generate many interesting examples in teaching mathematics subjects at various levels. It is often used in elementary or middle school mathematics classes to illustrate the concept of "patterns." In this paper the authors present a few interesting ways of using this sequence to form examples for high…

In this article, the authors would like to look at a range of solutions submitted by Year 4-5 teams in the 2003 "Naturally Mathematical Challenge" to a question that involves no more than the numbers 1 to 6 and possible arrangements of them. In the context of other competition questions and in their elaboration of mathematical process,…

The Proceedings of PME-XI has been published in three separate volumes because of the large total of 161 individual conference papers reported. Volume I contains four plenary papers, all on the subject of "constructivism," and 44 commented papers arranged under 4 themes. Volume II contains 56 papers (39 commented; 17 uncommented)…

The Proceedings of PME-XVII has been published in three volumes because of the large number of papers presented at the conference. Volume I contains a brief Plenary Panel report, 4 full-scale Plenary Addresses, the brief reports of 10 Working Groups and 4 Discussion Groups, and a total of 23 Research Reports grouped under 4 themes. Volume II…

The Proceedings of PME-XVIII have been published in four separate volumes because of the large number of individual conference papers reported. Volume I contains brief reports for 11 Working Groups and 8 Discussion Groups, 55 "Short Oral Communications," 28 Posters, 5 Plenary Panel reports, and 4 Plenary Session reports. Volume II…

Teaching difficulties often require creative approaches. Difficulties are often compounded when students in class show anxiety toward the material presented and, in particular, in the case of quantitative methods--"fear of numbers." This case presented itself in an advanced course in health behavior theory, where teaching the concepts of validity…

The authors examined developmental and individual differences in pure numerical estimation, the type of estimation that depends solely on knowledge of numbers. Children between kindergarten and 4th grade were asked to solve 4 types of numerical estimation problems: computational, numerosity, measurement, and number line. In Experiment 1,…

This study focuses on the nature of preservice elementary school teachers' understandings of several concepts in elementary number theory that are evoked by a computer-based microworld called "Number Worlds". In particular, the focus is on the concepts of factor, multiple and prime number. The notion of "thickness" is examined with respect to…