For the last several years teachers have been using counters and connected cube "trains" and creating base-10 block models to help students develop number sense and understand number concepts. It is described how ten-frame tiles could be more useful tool for building number understanding for many students.

Many assertions about the occurrence of the golden ratio phi in art, architecture, and nature have been shown to be false, unsupported, or misleading. For instance, we show that the spirals found in sea shells, in particular the "Nautilus pompilius," are not in the shape of the golden ratio, as is often claimed. Some of the most interesting…

Within the set of points in the plane with integer coordinates, one point is said to be visible from another if no other point in the set lies between them. This study of visibility draws in topics from a wide variety of mathematical areas, including geometry, number theory, probability, and combinatorics.

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.

"Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…

To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…

Few studies investigating the impacts of teacher characteristics and beliefs about the importance of early skill learning have included measures of children's learning outcomes. This study investigated how teachers' educational attainment, experience, and beliefs impact the development of letter identification and number concepts (enumeration,…

This book's activities probe rational and irrational numbers and investigate properties of integers and complex numbers. They explore numbers and operations embedded in physical objects and show how simple problems can lead to sophisticated considerations. Students examine the usefulness of irrational numbers in designing musical scales and of…

Through the importance of the number three in our culture and the strange preference for a ternary pattern of our nature one can perceive how and why number theory degraded to numerology. The strong preference of our minds for simple patterns can be read as the key to understanding not only the development of numerology, but also why scientists…

This paper discusses the use of Stern teaching materials with children with Down syndrome. The theory underlying the design of the materials is discussed, the teaching approach and methodology are described and evidence supporting effectiveness is outlined. (Contains 2 figures.)

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)

Several excerpts from Euclid's "Elements" are cited, and their applications to the natural, positive rational, and positive real number systems are discussed. (SD)