This article describes an activity that, on the surface, engages the students in basic skill review. Its ultimate goal is to cause students to make conjectures, seek to justify those conjectures, and to think mathematically. (Contains 3 figures.)

Cross-cultural studies on mathematical cognition and education have suggested that curriculum and teaching have contributed to U.S. versus Asian differences in student performance; however, previous discussions of curriculum and teaching practices have been very general and have not focused on a detailed analysis of how mathematics concepts are…

The United States Military Academy (USMA) has a four course core mathematics curriculum that is studied by all students. The third course is MA205, Calculus II; a multivariate calculus course filled with practical applications. During a Problem Solving Lab (PSL), students participated in a hands-on exercise with multiple vector operations,…

This article focuses on the kinds of conceptual changes that occur when students have to deal with negative numbers in elementary algebraic operations. Interviews were carried out with twelve 8th-grade level students who were selected on the basis of their results in a test where they were required to reduce polynomials. The questions applied to…

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…

The aim of this study was to ascertain the nature of the interaction between the affective value of musical distraction, personality type and performance on the cognitive tasks of reading comprehension, free recall, mental arithmetic and verbal reasoning in children aged 11-12 years. It was hypothesized that the cognitive performance of extraverts…

Many people believe that the 1989 National Council for Teachers of Mathematics (NCTM) standards heralded the biggest mathematics reform of the 20th century. Despite all reform efforts, recent studies indicate that mathematics taught in primary and middle school mainly consists of basic arithmetic tasks that use memorization and repetition. Today…

This study investigated the effects of second language (L2) proficiency and task-induced cognitive workload on participants' speech production and retention of information in an environment designed to simulate the demands faced by pilots receiving instructions from air-traffic controllers. Three groups of 20 participants (one…

This article discusses a comparative study, funded by the European Union, of the teaching of mathematics in five European countries, (Flanders, England, Finland, Hungary and Spain) to students in the upper primary (ages 10-12) and lower secondary (12-14) years. These ages were chosen as they represent a time when many students' experiences of…

In this study, we examine whether preventive enrichment of pre-math skills has an influence on number knowledge in preschool children from low income families. Our data analyses use two methods to examine the influence of two independent programs implemented during junior kindergarten and kindergarten. The first implies the traditional approach…

Teachers who believe "practice makes perfect" may engage students in repetitive, perhaps timed, computational exercises. If educators teach students to understand the procedures they practice, however, they will not need as much drill and they will have more flexible use of the computations they perform. Three-quarters of a century ago,…