This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in…

Both virtual and physical manipulatives are reported as effective learning tools when used with different groups of students in a variety of contexts to learn mathematical content. The use of multiple representations and the flexibility to translate among those representational forms facilitates students' learning and has the potential to deepen…

This brochure is part of NAEPFACTS, a new series that briefly summarizes findings from the National Assessment of Educational Progress (NAEP). Course-taking is generally a powerful indicator of mathematics achievement. This occurs partially because students who are more proficient tend to take more mathematics classes and, at the eighth grade, the…

This book takes the position that the teaching of elementary linear algebra can be made more effective by emphasizing applications, exposition, and pedagogy. It includes the recommendations of the Linear Algebra Curriculum Study Group with their core syllabus for the first course, and the thoughts of mathematics faculty who have taught linear…

This article reports the results of a questionnaire applied to secondary school students (n=35) to explore efficiency in the resolution of equations in the domain of whole numbers and the spontaneous responses to problems leading to negative solutions. The most significant results obtained with the questionnaire are the lack of knowledge of the…

This book aims to present helpful, practical ideas and suggestions for mathematics teaching. Focus is on how teaching can be developed in a Rudolf Steiner (Waldorf) School and includes treatment of mathematical topics applicable to the 7-14 age group. Suggestions for curriculum and examples for children to work on are presented with a very wide…

Research indicates that students have great difficulty solving algebra word problems and that few high school seniors have mastered the fundamentals of algebra, let alone algebra problem-solving skills. Improving students' algebra problem solving skills is considered to be critically important by those who have worked on reforming mathematics…

In the United States female and male students supposedly have the same educational opportunities. Females continue to score below male students on the mathematics portions of standardized tests and less frequently choose mathematics-oriented careers. In this experimental study (n=95), 47 first-year algebra students participated in a month-long…

Use of the computer programs provided here in APL programming language can help students understand computational algorithms. (SD)

Some theorems concerning factorization of Pythagorean triples are presented. (SD)

Activities in which the claims of psychics are evaluated can be used in probability classes. (SD)

The author argues that the "least number principle" (well-ordering for positive integers) is more intuitively acceptable to high school students than mathematical induction which can be derived from it. (SD)

An approach to solving equations is presented. (SD)

Enrichment topics dealing with solutions of polynomials over modular systems are described. (SD)

The inequality involving the arithmetic and geometric means is a powerful tool in dealing with applications of mathematics. It is very important in geometric programming. The article discusses this inequality and demonstrates two real world applications accessible to secondary teachers and students. (Author/KM)