From the equality of the ratios of the surface areas and volumes of a sphere and its circumscribed cylinder, the exploration of theorems relating the ratios of surface areas and volumes of a sphere and other circumscribed solids in three dimensions, and analogous questions relating two-dimensional concepts of perimeter and area is recounted. (MDH)

Presents an activity in which students develop their own theorem involving the relationship between the triangles determined by the squares constructed on the sides of any triangle. Provides a set of four reproducible worksheets, directions on their use, worksheet answers, and suggestions for follow-up activities. (MDH)

This paper describes the use of cooperative groups in teaching calculus. It discusses benefits and drawbacks of group techniques and presents reactions from both students and the author. (Author)

Discusses the problem of finding the amount of fence it would require for the outfield fence of a baseball field of given dimensions. Presents different solution methods for each of the levels from grades 9-12. The different methods incorporate geometry, trigonometry, analytic geometry, and calculus. (MDH)

Following a brief historical review of the mechanism of mathematical modeling, examples are included that associate a mathematical model with given data (changes in sea level) and that model a real-life situation (process of parallel parking). Also provided is the rationale for the curricular implementation of mathematical modeling. (JJK)

Video cameras can be used to gather data, record the development of a project, document learning, aid in problem solving, or create a class archive. Short clips can be laced together with dialog or music without extensive editing. (SW)

Investigates different approaches of students from different cultures to problems and problem-solving strategies. Suggests ways to encourage students to use algebraic strategies. Provides some action research ideas for teachers to try in their classrooms. Contains 11 references. (ASK)

Describes a unit of study for gifted fifth graders that connects architecture to the content areas of history, mathematics, and science. Emphasis was on problem solving of real-world problems as recommended in major reports on mathematics instruction. The unit also used technology in innovative ways, including computer-drawn images and digital…

Provides suggestions for decreasing gender-related differences in mathematics and questions for teachers to ask themselves regarding gender equity in mathematics. Teachers are urged to highlight the contributions of female and male mathematicians, to create a classroom climate that values problem solving, and to hold high expectations for all…

Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for…

Reports on a pilot study that examined use by sixth-grade students in Costa Rica of a mathematical microworld written in LOGO. The investigation had three phases: (1) open exploration of the microworld; (2) group discussion and sharing of hypotheses; and (3) guided discovery and problem solving. (Contains 11 references.) (SLW)

Compares two experimental programs for teaching mental addition and subtraction in the Dutch second grade (N=275). Discusses realistic program design (RPD) and gradual program design (GPD). Concludes that RPD pupils show a more varied use of solution procedures than GPD pupils. Contains 46 references. (Author/ASK)

This article describes a teacher's techniques and strategies for promoting productive discourse and supporting active learning in the mathematics classroom. The lesson excerpts included are from two days of a workshop with primarily middle-grades teachers. These excerpts demonstrate the teacher's typical progression through defining a problem,…

This article explores how students learned to measure tall objects using a clinometer and some basic calculations. Such activities provide opportunities for students and teachers to learn the usefulness of linking mathematics content and science content to real-world problem-solving situations. (Contains 7 figures.)

This article elaborates on the basics of problem-based learning units and tips for implementation. The problem-based learning unit described focuses on the course of action involved in purchasing a new car. (Contains 2 figures.)