Development in the ability of 11-year-olds to solve numerical problems of addition, multiplication, and proportion was analysed by means of three Rasch models of change. The students, who had participated in a New Zealand numeracy project in 2002, comprised two groups that differed in socio-economic status: 1,274 students came from low…

The purpose of the present article is to give an account of the emergence of knowledge pertaining to the transition from arithmetic to algebra in the course of a debate in a grade 7 classroom. This debate follows two other instances of work: (1) the adidactic interaction between each student and a given problem, (2) the adidactic interaction of…

This article features the life and accomplishments of Stuart Appleton Courtis. As a teacher, a developer of tests in a variety of subjects, a member of several school surveys, a student of educational measurement, and a director of a bureau of educational research, Courtis participated in the twentieth-century transformation of public education.…

One of the most difficult questions facing any enterprise, including colleges and universities, is where to invest limited information technology resources for the maximum benefit of customers, constituents, and institutional mission. Now, compounding this difficulty, constrained and shrinking IT budgets are colliding with increasing demand for…

This article classifies and describes a selection of mathematical fiction. It also provides some practical activities teachers or parents can use to help make the mathematics more explicit and engaging for their children. Not many people, apart from primary teachers, are aware of mathematical fiction or mathematical picture storybooks, although…

This study was conducted to obtain information related to mental computation from students in Years 3, 5, 7, and 9 in Western Australia. The numbers of subjects were 163, 163, 163 and 152 in years 3, 5, 7, and 9, respectively. The research was designed to provide three different perspectives of mental computation: (1) a survey of the kinds of…

This study investigated the effect on teachers of observing or implementing an alternative form of instruction in a primary-grade arithmetic class. Under consideration were the relationships between the beliefs teachers held about mathematics and about teaching mathematics, and their recognition and internalization of the principles of the…

The Calculators in Primary Mathematics Project in Australia was a long-term investigation into the effects of the introduction of calculators on the learning and teaching of primary mathematics. The Australian project commenced with children who were in kindergarten and grade 1 in 1990, moving up through the schools to grade 4 level by 1993.…

Drawing from research and observations at Lansing Community College (Michigan) (LCC), this paper argues that typical arithmetic courses do little to prepare students to master algebra, and proposes an alternative set of arithmetic skills as actual prerequisites to algebra. The first section offers a description of the algebra sequence at LCC,…

Elementary school activities designed for celebraing the significant dates of each school month, excluding December, are described in this compilation. The collection covers birthdays of well-known people, historical events, mathematics, writing, reading, science, history, social studies, art, and cooking. (JW)

G. L. Anderson reported finding an interaction between drill and meaningful methods of instruction with fourth grade student ability and achievement. The reanalysis overturns Anderson's conclusion that there is an aptitude treatment interaction within classes. (BJG)

The author finds that students who have not previously mastered arithmetic skills do not benefit from an individualized review course. He describes such a course and presents four case studies in support of his position. (SD)

This booklet describes basic counting principles and provides activities designed to develop basic skills in: (l) stable ordering; (2) one-to-one matching; (3) total number; (4) different objects; and (5) different order. These are extended to more advanced strategies aimed at building counting skills strong enough to provide a basis for adding,…

Chapters 5 through 10 of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter…

The problem of sex bias in mathematics word problems is discussed, with references to the appropriate literature. Word problems are assessed via cognitive science analysis of word problem solving. It has been suggested that five basic semantic relations are adequate to classify nearly all story problems, namely, change, combine, compare, vary, and…