Are abstract representations of number--representations that are independent of the particular type of entities that are enumerated--a product of human language or culture, or do they trace back to human infancy? To address this question, four experiments investigated whether human infants discriminate between sequences of actions (jumps of a…

The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…

This article presents some wonderful books that reinforce math concepts with young children. In "I Spy Two Eyes: Numbers in Art," children see reproductions of the work of famous artists and count elements in the pictures. A list of math books that reinforce math concepts is included.

Certain definitions introduce appropriate concepts, among which are the definitions of the counting functions of the primes and twin primes, along with definitions of the correlation coefficient in a bivariate sample space. It is argued conjecturally that the characteristic functions of the prime "p" and of the quantity "p"+2 are highly…

This article describes an exploration activity involving Mayan numerals, which can be adapted by teachers at various levels to help students better understand the concept of place value and appreciate contributions to mathematics made by an indigenous Central American culture.

STARS (Secondary Training for Alaskan Rural Students) materials resulted from extensive rewriting of the Vocational Adult Secondary Training (VAST) materials produced by the British Columbia Department of Education, after those materials had been used with the 9th and 10th graders on Kodiak Island. Revision was done by teachers who had been using…

Experienced traders in furs, blankets, and other goods, the Haidas of the 1700's had a well-developed decimal system for counting and calculating. Their units of linear measure included the foot, yard, and fathom, or six feet. This booklet lists the numbers from 1 to 20 in English and Haida; explains the Haida use of ten, hundred, and thousand…

Research addressing the effectiveness of feedback for learning has focused on many dimensions of feedback, including the timing (Kulik & Kulik, 1988), type (Mory, 2004), and amount of available information (Dempsey et. al, 1993). Much of the feedback research in education has tacitly assumed that the available information is perceived, and any…

Learning about mathematics begins in the early years. Through their everyday activities, young children build important foundational knowledge and understanding of mathematics, especially when adults provide specific opportunities to learn and practice concepts and skills. Young children develop early on an informal understanding of important…

Human cognition is founded, in part, on four systems for representing objects, actions, number, and space. It may be based, as well, on a fifth system for representing social partners. Each system has deep roots in human phylogeny and ontogeny, and it guides and shapes the mental lives of adults. Converging research on human infants, non-human…

For mathematics teachers who are continually looking for ways in which to engage their students in the learning process, the capabilities offered by technology answer the call. Whether the technology comprises computer based applications or graphics calculators, often boring aspects can be bypassed so that students can work on the "good…

This paper discusses the use of Numicon number 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 4 figures.)

These materials were designed to help remedial students increase mathematics proficiency on topics found in the Regents Competency Testing Program. The activities developed come complete with questions, "cards," and/or sample game boards. Included in each activity is a list of materials needed. Several different activities often use the…

This is one of a series of 20 booklets designed for participants in an in-service course for teachers of elementary mathematics. The course, developed by the University of Illinois Arithmetic Project, is designed to be conducted by local school personnel. In addition to these booklets, a course package includes films showing mathematics being…

This booklet is a teacher's guide for a lesson, appropriate for grades 3-9, to strengthen students' mathematics skills while increasing their knowledge of energy. It consists of a game in which teams of students solve mathematics problems about energy units. The booklet contains 24 challenging mathematics word problems and 1 mega-question. (MKR)