Principle of duality and numerical calculation of income and substitution effects under Hicksian Compensation are often left out of intermediate microeconomics courses because they require a rigorous calculus based analysis. But these topics are critically important for understanding consumer behavior. In this paper we use excel solver--a…

A large body of literature reports that there are gender differences in mathematical problem solving favouring males. Strategy use, as a reflection of different patterns in mathematical problem solving between genders, is found to be related to cognitive abilities, together with psychological characteristics and mediated by experience and…

This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

In this article, the author presents an innovative approach to teaching multiplication facts for children in middle school or younger. After introducing the dangers of some contradictions that persist, relating a brief summary of related research and guidelines regarding math facts and their relation to strategic approaches to more complex math,…

This study extends the debate concerning the mathematical skills deficit of bioscience undergraduates towards a deeper understanding of their mathematics learning, since only through the latter can appropriate and effective explicit teaching be implemented. Three hundred and twenty-six first-year bioscience undergraduates, from three pre- and four…

Describes the method to solve problems called T-E-M-T-T: trial, error, and modified trial through technology. The method integrates students' skills of estimation, mental computation, and appropriate choice of calculator use. Includes 2 activities for each of grades K-4 and 5-8 that illustrate the method. (MDH)

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

This article explores the origins and potential benefits of the empty number line for the development of mental computation. It also provides a learner's perspective of its use through the reflections of nine-year-old Emily. (Contains 3 figures.)

This article explores how counting collections of objects helps elementary-age children develop number sense and number relations. The authors provide evidence that counting collections offers multiple entry points for children at different places on the counting trajectory. It is suggested that the teacher's role is one of noticing, questioning,…

This article investigates several methods of identifying individual guessers from their response data. Both the posterior probability method and the likelihood ratio method are based on the two-state mixture modeling approach to response times. The accuracy method is based on response accuracy data. Results from the simulation study showed that…

Different computational tools may offer teachers and students distinct opportunities in representing, exploring and solving mathematical tasks. In this context, we illustrate that the use of dynamic software (Cabri Geometry) helped high school teachers to think of and represent a particular task dynamically. In this process, the teachers had the…

The purpose of this descriptive study was to create and test questions on stoichiometry with number ratios for quick mental calculations and to identify students' problem-solving strategies. The present study was a component of a more comprehensive investigation in which 7,441 German senior high school students were asked to work on 154 test items…

Presents five activities focusing on mental computation and estimation for the K-3, 3-5, 4-6, and 6-8 grade levels that require the student, acting as a judge, to review solutions to problems and to pronounce and justify a verdict. Provides suggested materials, questions, possible extensions, answers, and worksheets for each activity. (MDH)

This book addresses different types of thinking, including critical, creative, and analytical, and presents a variety of problem-solving strategies, along with specific ways they can be taught to students. The main emphases of the book are thinking and mathematics, problem solving, and the application of computational skills. The problem-solving…