Presents three investigations that extend the problem of counting the number of squares on a grid in two dimensions to an analogous problem of counting the number of cubes in a three-dimensional cubic array. (MDH)

Using the notion of the difference between a number and its cube as a starting point, this article presents a wide range of mathematical activities at varying levels of sophistication utilizing numerical, intuitive, and graphical approaches. (JJK)

Presents a problem that requires solving a card problem by exploring patterns that will lead to a logical solution. Involves students in developing and analyzing their own algorithms as well as discussing their reasoning with peers. (ASK)

A study examined understanding of number line concepts by 4th grade culturally and linguistically diverse (CLD) students (n=30), students with learning disabilities (n=23), and 21 controls. CLD students with disabilities demonstrated difficulty due to several factors beyond lack of language competence, including failure to apply number lines to…

The author advocates for writing as an essential communication skill for learning mathematics. Mathematical diary writing is cited as a good way for students to privately represent their thinking through pictures, language, or symbols, and also as a channel for children to communicate with themselves and with their teachers. Cited research…

A major goal of instruction is for students to develop competence with numbers. This study attempts to determine the effect of instructional materials that develop number concepts and connect these concepts to mental computation procedures. The study used 16 classes of eighth-grade students and a pretest-posttest design with two treatment groups.…

This guide is organized around a list of skills that all students should know and be able to do at each grade level from kindergarten through sixth grade. It provides parents, teachers, and students with knowledge of what is being taught in a logical scope and sequence by grade level. The purpose of this guide is to help build a basis for…

The purpose of the project was to develop computer games that could be used by students in grades 1-4 as part of their mathematics instruction. Eight games were developed, covering a wide variety of mathematical topics, including number/numeration, computation, geometry, measurement, statistics, and probability. The games were field tested in 20…

This booklet is designed to show teachers the many things children in preschool through grade 2 can learn about and do with numbers. Included is information on preparing to teach counting skills, getting the classroom ready, activities to do with children, projects for children and teachers, lists of materials, and computer background information.…

This booklet designed for students in grades 4-8 provides 52 activities, including puzzles and problems. Activities range from simple to complex, giving learners practice in finding patterns, numeration, permutation, and problem solving. Calculators should be available, and students should be encouraged to discuss solutions with classmates,…

Pascal's Triangle is an important numerical table; with its help, a number of computation problems may be solved. Some of these problems are examined and the question of what"solving a problem" can mean is generally considered. (Author/MK)

The title of this mathematics text for preservice elementary teachers is intended to suggest the book's theme of mathematics as an abstraction from human experience with sticks (lines, segments), stones (sets, counting) and other objects. An introductory chapter which describes the objectives of the author and discusses learning and attitudes…

Suggests that good number sense is fundamental for success in estimation, approximation, and problem solving. Further, large-number concepts are appropriate for development in upper elementary school, high school, and beyond. Presents examples to enhance a sense of large numbers in middle and high school students. (PK)

Presented are six problems from diverse areas of mathematics that are appropriate for students of differing age and ability levels. (PK)

Ten activities that give learners in grades 5-8 a chance to explore mathematics with calculators are provided. The activity cards involve such topics as odd addends, magic squares, strange projects, and conjecturing rules. (MNS)