In this article, the author reports findings from a project designed to explore approaches for improving students' mathematical learning outcomes in relation to the base ten number system. The project explored the role of a commonly used teaching activity, referred to in the project as the "base ten game," in developing children's…

A widely recognized concern in elementary school mathematics education is that teachers' understanding of the mathematical curricular content generally appears quite fragmented, sparsely connected, and procedurally oriented. This pilot study applies methods of educational neuroscience to investigate and improve preservice teachers' learning and…

This article offers some ideas about creating mathematical art based on number patterns. It includes a process for students that integrates number and geometry and results in attractive and useful patterned squares. Students may pursue the activity with paper and pencil or they may use computer software like The Geometer's Sketchpad to achieve…

In this paper we explore the influence of students' personalized notion of "small" numbers based on real life experiences on their understanding of limits. Tests were conducted on two samples of students. The first sample, consisting of students in the XII grade, had been taught limits using an informal approach (i.e., without recourse to the…

Here we explore the educational implications of classroom activities related to the backgrounds and motivations of talented Hollywood comedy writers and the mathematical moments they created for the Emmy Award-winning animated sitcom "Futurama." (Contains 6 figures.)

Katrina is 10 years old and has Down syndrome. She is making good progress with learning numbers and mathematics. We describe how Katrina has learned number concepts and arithmetic skills over several years. We highlight the influence of early learning habits, visual supports, motivation and practice, and the uses made of different number…

Research has established that children's development of addition and subtraction skills progresses through a hierarchy of strategies that begin with counting-by-one methods through to flexible mental strategies using a combination of knowledge of basic facts and understanding of place value. An important transition point is the shift from the…

This book is intended for supplementary reading in the elementary school. It is written in non-technical language, and the effort has been made to connect with the history enough of the human element to make it more interesting than any mere recital of facts. With it there is also joined something of the history of writing materials, this being…

ATTITUDES OF STUDENTS TOWARD ARABIC NUMBERALS AND THEIR ASSOCIATIONS WITH THE NUMBERS FROM 1 TO 9 WERE INVESTIGATED IN A SERIES OF FIVE STUDIES ON (1) NONQUANTITATIVE ASSOCIATIONS TO NUMERALS AS A FUNCTION OF AGE, ABILITY LEVEL, AND SEX AMONG AMERICAN CHILDREN, (2) COLOR ASSOCIATIONS WITH NUMERALS AMONG MALE COLLEGE STUDENTS, (3) PERSONALITY…

This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

A concept-by-concept approach to Jean Piaget's ideas and findings about the intellectual growth of children is presented in simplified form for the lay reader. It first reviews the theoretical rationale behind Piaget's work and sets forth his basic principles of development. Then comes an overview of developmental stages of intellectual growth…