The use of the computer, and specifically the mathematics software package Maple, has played a central role in the authors' abstract algebra course because it provides their students with a way to see realistic examples of the topics they discuss without having to struggle with extensive computations. However, Maple does not provide the computer…

The subject matter presented in this article can be used in the classroom to enrich the learning experience of students taking a course that includes a unit on combinatorics, such as discrete mathematics, graph theory, or probability. In order to provide such students with the background needed to appreciate the significance of the generalization…

In this paper, the author aims to offer an elaboration of simple, yet powerful, mathematical patterns through mathematical games. Mathematical games may serve as colorful instructional tools for teachers and textbooks, and may raise students' motivation and intuition. Patterns are fundamental in mathematics and computer science. In the case of…

The purpose of this article is to present an interdisciplinary project, developed as a collaborative effort by the authors, involving the design of a telescope mirror as it was given to second semester calculus students. The goals of the project are to provide an applied setting for the topics typically covered in this type of course including the…

The authors discuss mass as one of the three fundamental measurements (the others being length and time), noting that estimation of mass is little taught and assessed in primary schools. This article briefly explores the reasons for this in terms of culture, practice, and the difficulty of assessing estimation of mass. An activity using the…

The authors propose that word problems can serve as a context in which to learn mathematics concepts for elementary school students, providing a bridge for connecting classroom mathematics with real-world mathematics. This article focuses on the potential barrier to success that students may encounter because of the words, and subsequent contexts,…

In this article, the authors explain how curriculum-based measurement (CBM) differs from other forms of classroom-based assessment. The development of CBM is traced from computation to concepts and applications to real-life problem solving, with examples of the assessments and illustrations of research to document technical features and utility…

Math is about the relationship between numbers. Right answers are not the only thing to look for when examining students' work in mathematics. Looking at how children solve computation problems can give teachers insight into their thinking and help determine what math skills they already know and what they still need to learn. The author contends…

Although equal sharing problems appear to support the development of fractions as multiplicative structures, very little work has examined how children's informal solutions reflect this possibility. The primary goal of this study was to analyze children's coordination of two quantities (number of people sharing and number of things being shared)…

This article describes how third-grade students developed an understanding of the equals sign and began to use relational thinking as they discussed true/false and open-number sentences. The sequence of instructional activities and children's responses to them are provided.

Teaching teachers to become observers and inquirers into mathematics will help change how they teach math to students. Essential to all professional development in mathematics is the idea that making sense of mathematics is key to learning. Just as learning to read calls for bringing meaning to the printed page, learning math calls for bringing…

The Country Data Project was developed for eighth-grade students of Milwaukee public schools to make them understand the importance of numbers by making them interpret the full descriptions of people of various countries by analyzing the numbers summarizing the population distribution of the respective country. The results prove that the project…

Literacy has been studied extensively in the context of children's play, but few studies exist of numeracy development through play. The purpose of this study was to investigate the frequency and type of numeracy exchanges that occurred spontaneously during parent-child play. Twenty-six 4-year-olds and their mothers played with a variety of toys,…

This paper discusses the curriculum and students' and teachers' conceptions of proof. It goes on to discuss university students' difficulties with proving related to understanding and using definitions and theorems, understanding the structure of a proof, knowing how to read and check proofs, knowing and using relevant concepts, bringing…

"Progress in Mathematics[C] 2006" is a new core curriculum for students in kindergarten through grade 6. "Progress in Mathematics[C] 2006" differs substantively from "Progress in Mathematics[C] 2000" in both content and assessment material. "Progress in Mathematics[C] 2006" uses a sequence of systematic…