The query "When are we ever going to use this?" is easily answered when discussing the slope of a line. The pitch of a roof, the grade of a road, and stair stringers are three applications of slope that are used extensively. The concept of slope, which is introduced fairly early in the mathematics curriculum has hands-on applications…

Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…

In this article, the author describes the development and implementation of a measurement-based group activity designed to support students in understanding the connection between angle magnitude and the shape of the sine function. She explains that the benefit of this activity is that it allows students to build their trigonometric knowledge…

Learning to reason spatially is increasingly recognized as an essential component of geometry education. Generally taken to be the "ability to represent, generate, transform, communicate, document, and reflect on visual information," "spatial reasoning" uses the spatial relationships between objects to form ideas. Spatial thinking takes a variety…

Many students at all levels--from middle school to graduate programs for in-service teachers--struggle with visualizing three-dimensional shapes. Many also are challenged to locate appropriate centers of rotation, placement of lines of symmetry, and translation vectors for transformations on the plane. Hands-on experience helps with these…

Early in their introductory college linear algebra class, the author's students learn to use a matrix to represent and solve systems of linear equations. Indeed, this simple idea is perhaps the foundational idea of the course. Nevertheless, the author was delighted to find that the study of linear systems can lead to surprisingly deep mathematics.…

The author and his first-year algebra students explored the quadratic behavior behind the parabolic shape of fountains at the local family splash park. This hands-on discovery project has three main parts: (1) gathering data by experimenting with and photographing the fountains; (2) analyzing the photographs to obtain numerical data; and (3)…

The triangle congruence conditions are a central focus to nearly any course in Euclidean geometry. The author presents a hands-on activity that uses straws and pipe cleaners to explore and justify the triangle congruence conditions. (Contains 4 figures.)

In mathematics, developing a conceptual understanding and observing properly modeled methods rarely lead to successful student performance. The student must participate. As with bike riding, participation with monitoring and guidance makes initial efforts meaningful and beneficial. In this article, the authors share a bike riding experience and…

A WebQuest is an inquiry-based lesson plan that uses the Internet. This article explains what a WebQuest is, shows how to create one, and provides an example. When engaged in a WebQuest, students use technology to experience cooperative learning and discovery learning while honing their research, writing, and presentation skills. It has been found…

This article describes a hands-on project in which unusual fractal images are produced using only a photocopy machine and office supplies. The resulting images are an example of the contraction mapping principle.

The central limit theorem is demonstrated in a simple, unsophisticated manner through three experiments. (JT)

Introduces service learning and explores how it can be used in mathematics education. Relates experiences of using service learning in mathematics classes. (ASK)