The way teachers understand mathematics strongly influences their teaching and what pupils learn. Describes the influence of two variables on preservice teachers' performance: (1) the presence of a formal definition; and (2) previous classroom activities that addressed the concept of the altitude of a triangle. (Contains 30 references.)…

Describes two activities that led students to contradictions between conjectures and findings. Analyzes the conjectures, working methods, and explanations given by students when faced with the contradictions that arose. (Author/MM)

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

A new study on the link between high school coursework and postsecondary success paints a challenging picture for education advocates: African Americans can succeed in rigorous courses, but too few get the opportunity. The report from Achieve Inc., finds that few states set high curricula and content standards that prepare students for college.…

The National Council of Teachers of Mathematics (1989) proposes using everyday objects, such as paper, to enable students to explore geometric relationships and vocabulary. Paper-folding and other types of hands-on activities have been found to increase students' ability to communicate mathematically and foster their understanding of mathematical…

Three pieces of literature are used to launch mathematical investigations. The tasks provide opportunities for students to apply proportional reasoning skills, explore linear relationships, calculate a unit rate, and find the relationship between the volume of a cylinder and a cone. A poem, a short story, and a young adult novel are discussed.…

This article describes a joint effort between a mathematics educator and a middle school art teacher who wanted their students to experience first hand how construction works in the real world. It starts with students designing and building scale models for a large inflatable item in which they display their art and extends to building the…

This paper addresses a central issue in secondary school geometry, namely the role of proof. In an integrated mathematics and science curriculum, the role of proof as a process of conjecturing, explaining, and justifying within a small-group setting is analyzed. Particular attention is given to the students' use of empirical evidence and algebraic…

This study investigated whether the van Hiele model accurately describes the geometric thinking of gifted students in the 6th through 8th grades prior to a formal course in geometry and made comparisons with what has been found with other populations. The results from 120 students who completed a 25-item multiple choice paper-and-pencil test,…

In this unit of the Seeing and Thinking Mathematically series, students use geometry to analyze buildings from around the world, design and build their own house models, create plans for their designs, and build from each other's plans. Students start out the unit building with cubes and later move to other geometric shapes. As they learn to…

This yearbook focuses on the role of technology in school mathematics. Chapters are replete with classroom-tested ideas for using technology to teach new mathematical ideas and to teach familiar mathematical ideas better. Chapters included: (1) "Using the Graphing Calculator in the Classroom: Helping Students Solve the "Unsolvable" (Eric Milou,…

The Colorado Model Content Standards for Mathematics were designed to serve as a guide for school districts as they define standards that will enable every Colorado student to develop the mathematical literacy needed for citizenship and employment in the 21st century. A new vision is provided of the content students should study in order to…

Finding the number of cubes in rectangular solids provides a cognitive framework for understanding the measurement of volume. This study reveals whether the activities provided in the context of equal investing and equal sharing that emphasize both numerical and spatial aspects of cube configurations cause any improvement in student strategies…

This volume attempts to bring together a collection of reports on the Geometric Supposer, a series of computer software environments which can be a tool for exploring particulars and generalizations in geometry. The book contains the following chapters: (1) "A Personal View of the Supposer: Reflections on Particularities and Generalities in…

In the attempt to improve the quality of geometry instruction in schools, researchers and teachers alike have given considerable attention to the van Hiele theory of geometry learning and development, which proposes a series of cognitive levels through which every geometry student passes. This paper reports a study to determine the extent to which…