In this paper, the author gives a further simple generalization of a power series evaluation of an integral using Taylor series to derive the result. The author encourages readers to consider numerical methods to evaluate the integrals and sums. Such methods are suitable for use in courses in advanced calculus and numerical analysis.

This study examined the generality of the logarithmic to linear transition in children's representations of numerical magnitudes and the role of subjective categorization of numbers in the acquisition of more advanced understanding. Experiment 1 (49 girls and 41 boys, ages 5-8 years) suggested parallel transitions from kindergarten to second grade…

The course described in this article, "Multicultural Mathematics," aims to strengthen and expand students' understanding of fundamental mathematics--number systems, arithmetic, geometry, elementary number theory, and mathematical reasoning--through study of the mathematics of world cultures. In addition, the course is designed to explore the…

Numbers can be represented in a variety of ways--through pictures, diagrams, symbols. Each representation highlights different features of the number and the number system. This study aims to explore pupil understanding of number both within and across representations. A computer environment (suite of programmes) was created within which…

We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

This paper focuses on the kinds of notations young children make for fractional numbers. The extant literature in the area of fractional numbers acknowledges children's difficulties in conceptualizing fractional numbers. Some of the research suggests possibly delaying an introduction to conventional notations for algorithms and fractions until…

This study explores pupils' performance and processes in tasks involving equations and inequalities of complex numbers requiring conversions from a geometric representation to an algebraic representation and conversions in the reverse direction, and also in complex numbers problem solving. Data were collected from 95 pupils of the final grade from…

A solid understanding of equivalent fractions is considered a steppingstone towards a better understanding of operations with fractions. In this article, 55 rural Australian students' conceptions of equivalent fractions are presented. Data collected included students' responses to a short written test and follow-up interviews with three students…

Wishing to explore the complexity of the conceptual, didactic and institutional aspects of learning a scientifically defined object of knowledge, we chose to study the link between the personal relation to numeration developed by six-year-old pupils in first grade ("cours preparatoire" the first level of primary school in France), and…

A sense of number is now generally recognised as a central factor in learning, and later applying, mathematics. Consequently, number sense is increasingly emphasised in curriculum documentation related to mathematics. The "Primary School Curriculum: Mathematics," published by the Government of Ireland in 1999, is no exception. It…

The name of Zoltan P. Dienes (1916- ) stands with those of Jean Piaget, Jerome Bruner, Edward Begle, and Robert Davis as a legendary figure whose work left a lasting impression on the field of mathematics education. Dienes' name is synonymous with the multibase blocks that he invented for the teaching of place value. Among numerous other things,…

Investigations into children's number learning have been a feature of recent mathematics education research in Australasia. This book is a compilation of the major results of this research with the aim of making them more accessible to researchers, teachers, and others who may be able to use the findings to improve classroom practice. The…

The paper describes evolution of an approach to teaching mathematically disabled and slow learning students through a Piagetian framework. It is explained that a step-by-step procedure is used to internalize material actions into mental actions via perception and verbalization. Formulae are introduced early, and emphasis is placed on promoting…

When comparing rows of dots in length or number, some children used number strategies and some length strategies. After training to correct missed items, errors were made on previously correct items. These findings are interpreted with reference to the distinction between having a dimensional strategy and attaching it to appropriate situations.…

The life of Fibonacci is summarized, and his importance in the development of mathematics is assessed. Several problems first solved by Fibonacci are posed. (SD)