Describes how the use of an area model manipulative can help students learn fractions and related concepts. Uses several illustrated examples. (MM)

A mathematics activity is presented which is a lesson frequently taught to upper elementary school students. It helps the students to see the connection of mathematics with a real-world activity, appreciate the mathematical knowledge required of quilt makers, reinforce their knowledge of the geometrical properties of different shapes and bring…

In this paper, we describe the skeleton of two teaching units, based on a Model for teaching mathematics, Context Orientated Teaching (COT). The first teaching unit concerns the proof of a mathematical proposition, while the second one concerns the solution of an open problem. Both are taught in the 10th grade, under the specific conditions of the…

This paper reflects on the use of didactic material in mathematics classes. It focuses on the mathematical activities of students and the didactical activities of teachers. Its point of departure is a critique of technical-managerial approaches to teaching, learning, and innovation. Based on this critique, fundamental tensions between the…

The design of technology tools has the potential to dramatically influence how students interact with tools, and these interactions, in turn, may influence students' mathematical problem solving. To better understand these interactions, we analyzed eighth grade students' problem solving as they used a java applet designed to specifically accompany…

What is a routine question? The focus of this paper is routine questions and time (in years) since a hitherto routine question was last attempted by the solver. The data comes from undergraduate students' work on solving two calculus questions. The data was selected for reporting purposes because it is well documented and because it threw up…

Sometimes simple ideas are more productive than complex and over-prepared lessons; perhaps because of the flexibility afforded both teachers and students. This article provides a description of the basic activity and the potential mathematics associated with it. It also gives examples of how the basic activity could be implemented with students of…

There is ample evidence that positive involvement of families in children's learning can be a major contribution. Where to start is often a challenge, however, especially in the numeracy area. As part of the Australian Government's "Numeracy Research and Development Initiative" a team led by Beth Powell in Western Australia has developed…

Recent changes in mathematics curricula, both in South Africa and elsewhere, have begun to change the overwhelmingly symbolic nature of mathematics in schools (in the sense of use of mathematical symbolism), promoting more use of the oral and written language. Engaging students in "Writing-to-Learn" activities in mathematics classrooms…

This nonexperimental, longitudinal field study examines the extent to which variation in observed classroom supports (quality of emotional and instructional interactions and amount of exposure to literacy and math activities) predicts trajectories of achievement in reading and math from 54 months to fifth grade. Growth mixture modeling detected…

This article discusses how math teachers at San Marcos High School turned to an online curriculum and in-class assessments to increase student achievement. Setting aside their 7-year-old textbooks, teachers filled the void largely with an online math curriculum, called Agile Mind, that comes equipped with an array of assessment tools. The idea was…

Several researchers have noted how children's whole number schemes can interfere with their efforts to learn fractions. An Australian study found that children who were successful with the solution of rational number tasks exhibited greater whole number knowledge and more flexible solution strategies. Behr and Post (1988) indicated that children…

This book presents a numerical problem-solving environment for middle grade students using the computerized spreadsheet. It offers a package of spreadsheet models and suggested activities that promote student thinking with numbers. (ASK)

The purpose of this paper is to investigate how drawings can contribute to generating new information when solvers use drawings in solving mathematical problems. For this purpose, two episodes, in which drawings enabled a solver to find ideas useful for his solutions, were qualitatively and closely analyzed, especially focusing on what roles…

Written for all teachers of young children, this book illustrates activities that promote early mathematics development for children ages three to five and "showcases" mathematics for the young child. The thirty-five activities in this book are distributed into five content areas: number and operations, geometry, algebra, measurement, and data…