A variety of applications of logarithms are presented along with suggestions about how this topic might be made more interesting and relevant in a secondary classroom. In most cases, the treatment is multi-modal using numerical, graphical and algebraic approaches.

In this work, we present an algorithm for computing logarithms of positive real numbers, that bears structural resemblance to the elementary school algorithm of long division. Using this algorithm, we can compute successive digits of a logarithm using a 4-operation pocket calculator. The algorithm makes no use of Taylor series or calculus, but…

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 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.

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…

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…

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.)

This article discusses Pythagoras' theorem, typically, it is introduce to students in the junior years of secondary school. Students consolidate their understanding of the theorem by using it for finding missing sides of triangles and for checking whether a given triangle has a right angle. But the topic often seems to dry up rapidly once these…

A hundreds chart is a simple 10 x 10 grid with the numbers 1-100. Here, the author discusses several activities for different grade levels using the hundreds chart. The activities are: (1) Chart tour (Grades K-2); (2) Mystery number (Grades 1-3); (3) Missing numbers (Grades 1-3); (4) Multiple patterns (Grades 3-5); and (5) Least common multiples…

Two experiments investigated 5-month-old infants' amodal sensitivity to numerical correspondences between sets of objects presented in the tactile and visual modes. A classical cross-modal transfer task from touch to vision was adopted. Infants were first tactually familiarized with two or three different objects presented one by one in their…