An analysis of the 1990 National Assessment of Educational Progress (NAEP) found that only 46 percent of all high school seniors demonstrated success with a grasp of decimals, percentages, fractions and simple algebra. This article investigates error patterns that emerge as students attempt to answer questions involving the ability to apply…

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 present study examined performance on an arithmetic task of increasing difficulty and a frustrating puzzle task for children with ADHD and comparison children. Emotional competence also was investigated in the two groups. Sixty-four children, 21 previously diagnosed with ADHD, participated. Performance on the arithmetic task was measured in…

The development of conceptual understanding in arithmetic is a gradual process and children may make use of a concept in some situations before others. Previous research has demonstrated that when children are given arithmetic problems with an inverse relationship they can infer that the initial and final quantities are the same. However, we do…

In this article, the author describes a week of "timely" open-ended lessons with a high ability Y9 group of boys. He gives lessons that would give the students some sense of purpose, as they try to generate a mathematical entity to represent something they used regularly. He states that understanding metric time is something his students…

Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…

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…

Through her work as a consultant, Burns has found that a handful of students in all classes lack an adequate foundation in basic math concepts and lag far behind their peers in both understanding and skills. Students who lack a foundation on which to build new learning are generally not well served even by well-planned, differentiated instruction;…

Can the salience of gender identity affect the math performance of 7-8 year old girls? Third-grade girls and boys were required to solve arithmetical problems of varied difficulty. Prior to the test, one half of the participants had their gender identity activated. Results showed that activation of gender identity affected girls' performance but…