Investigates the basic mechanics of cycling with a simple reckoning of how much effort is needed from the cyclist. The work done by the cyclist is quantified when the ride is on the flat and also when pedaling uphill. Proves that by making use of the available gears on a mountain bike, cycling uphill can be accomplished without pain. (Author/ASK)

Examines the gear system of a mountain bike to discover any redundancy in the many gear settings available to the cyclist. Suggests a best strategy for changing up through the gears on a typical 21-gear system and an adjustment to the available gears that would result in a smoother change. (Author/ASK)

Explains the approach of integrating notions of algebra in problem-solving experiences and the design of instructional activities that integrate nonroutine, nontraditional problems. Presents some problems and students' interpretations, conjectures, and generalizations about the patterns they discovered. (AIM)

Uses math and the power of 10 to understand the intangible concept of magnitude with regard to science. Prefaces the subject of magnitude with a series of activities that check for students' understanding and allows students to explore the dimensions of various objects from the microscopic to the macroscopic level. (SAH)

Documents, compares, and analyzes the nature of spatial reasoning by practitioners (plumbers) in the workplace and students in the school setting while constructing solids, with given specifications, from plane surfaces. Results confirm the power of activity theory and its methodology in explaining and identifying the structural differences…

This study investigated the developmental paths of Japanese Grade 1 students' understanding of quantities through the examination of their addition solution methods over the school year period. The individual students exhibited a wide range of experiences with and knowledge of addition from the beginning to the end of the school year. Students…

This article explores how differences in problem representations change both the performance and underlying cognitive processes of beginning algebra students engaged in quantitative reasoning. Contrary to beliefs held by practitioners and researchers in mathematics education, students were more successful solving simple algebra story problems than…

In this paper, we examine the use of an ordinary differential equation in modelling the SARS outbreak in Singapore. The model provides an excellent example of using mathematics in a real life situation. The mathematical concepts involved are accessible to students with A level Mathematics backgrounds. Data for the SARS epidemic in Singapore are…

This study determines the relative difficulty and associated strategy use of arithmetic (addition and subtraction) story problems when presented in American Sign Language to primary level (K-3) deaf and hard-of-hearing students. Results showed that deaf and hard-of-hearing students may consider and respond to arithmetic story problems differently…

To accurately analyze the problems of students in learning, the composed test sheets must meet multiple assessment criteria, such as the ratio of relevant concepts to be evaluated, the average discrimination degree, difficulty degree and estimated testing time. Furthermore, to precisely evaluate the improvement of student's learning performance…

In higher education today, mathematics has been marginalized: except to a tiny elite, it is either taught as a tool required for the study of other sciences or it is entirely absent. Yet mathematics has been and is an essential ingredient in our understanding and mastery of the physical world, our economic life, our information technology and,…

Teacher should strive to be more than the authority in the classroom identifying right versus wrong relating to problem solving. Identifying and emphasizing what aspects of an answer are mathematically correct improves students' confidence to tackle challenging problems and they view themselves as mathematical problem solvers.

Mathematical knowledge can be categorized in different ways. One commonly used way is to distinguish between procedural mathematical knowledge and conceptual mathematical knowledge. Procedural knowledge of mathematics refers to formal language, symbols, algorithms, and rules. Conceptual knowledge is essential for meaningful understanding of…

Two bibliographies that review 18 books and resource materials that adult educators can use to teach mathematics in adult literacy classes are included. The materials are suggested to help teachers implement an effective, successful mathematics program, using many of the strategies recommended by the National Council of Teachers of Mathematics.…

This book uses a child-initiated, whole language approach to help children have fun while exploring the world of science. The activities are divided into 23 units. Each unit begins with an "Attention Getter," the purpose of which is to introduce the unit to children in a way that grabs their attention, stimulates their interest, and creates…