Double-entry bookkeeping (DEB) implicitly uses a specific mathematical construction, the group of differences using pairs of unsigned numbers ("T-accounts"). That construction was only formulated abstractly in mathematics in the nineteenth century, even though DEB had been used in the business world for over five centuries. Yet the…

This paper reports on results of a targeted and extended (two school terms) program for building Grade 3 and Grade 4 students' facility with number facts and application for mental computation. As part of a larger project, this paper reports results from two schools. Results indicated strong gains in number fact recall and mental computation for…

The aim of this study was to model the most crucial numerical factors to the development of mathematical skills among children aged five to eight years (i.e. kindergarten, preschool, first and second graders). We categorised numerical skills into four main groups based on the results of longitudinal studies. A series of analyses of test batteries…

The representation of numbers is commonly viewed as an ordered continuum of magnitudes, referred to as the "mental number line." Previous work has repeatedly shown that number representations evoked by a given task can be easily altered, yielding an ongoing discussion about the basic properties of the mental number line and how malleable…

Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

Proposes a framework that identifies the components of number sense and the attributes of students who possess it. Discusses various aspects of three areas where number sense plays a key role: number concepts, operations with numbers, and applications of number and operation. (MDH)

This activity guide is a supplement to the November 1996 issue of the National Council of Teachers of Mathematics Student Math Notes. It contains a series of problems based on one main story problem. Using this problem and the other problems contained in the guide based on it, students explore different mathematical concepts such as graph theory,…

Describes five basic understandings involved in rational counting: (1) groupings of same or different items may be counted; (2) there is a stable order of the counting numbers; (3) one-to-one correspondence; (4) it does not matter which item is counted first; and (5) the cardinal principle. Discusses the importance of rational counting ability and…

An appeal is made for a more formal treatment of the topics of estimation and reasonableness of answers in the school mathematics curriculum. (MP)

Describes six key practices vital to a problem-centered instructional approach to number sense and computational strategies. Also presents actual classroom examples of strategies. (AIM)

Presents three traditional problems from discrete mathematics with alternative solutions and discussion of those solutions. (PK)

Presents activities utilized with primary teachers to alleviate instructional concerns about using calculators and provide reasons for using calculators in their mathematics instruction. Activities address the topics of estimation, number sense, numeration, whole number and fraction operations, probability, and problem solving. (MDH)

This is a condensed report of a study commissioned by the Minister's Advisory Committee on Student Achievement (MACOSA). The study was designed to provide information about current levels of achievement in mathematics among students in Alberta schools and to provide a data base for future assessments. The test was given to third-, sixth-, ninth-,…

The first of four quins intended to develop computational skills with non-negative rational numbers through applications to business and industry, this guidebook on minimum course content is designed for the student who has acquired basic computational skills with non-negative rational numbers. Overall course goals are specified, a course outline…