The authors provide a dynamic Ferris wheel computer activity that teachers can use as an instructional tool to help students investigate functions. They use a student's work to illustrate how students can use relationships between quantities to further their thinking about functions.

Mathematics teachers continually look for ways to make the learning of mathematics more active and engaging. Hands-on activities, in particular, have been demonstrated to improve student engagement and understanding in mathematics classes. Likewise, many scholars have emphasized the growing importance of giving students experience with the…

Geometry students need challenges. They need to apply what they already know to new contexts. As a result, high school teacher Wayne Nirode is always looking for groups of related problems of theorems to challenge his geometry students. He came across one such group or problems when reading Jun's (2012) one-page abstract posted online for the 12th…

How can the key concept of equivalent expressions be addressed so that students strengthen their representational fluency with symbols, graphs, and numbers? How can research inform the synergistic use of both paper-and-pencil analysis and computer algebra systems (CAS) in a classroom learning environment? These and other related questions have…

Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…

All teachers, especially high school teachers, face the challenge of ensuring that students have opportunities to relate and connect the various representations and notions of mathematics concepts developed over the course of the pre-K-12 mathematics curriculum. NCTM's (2000) Representation Standard emphasizes the importance of students being…

A fundamental component of mathematical learning is spatial visualization. To improve their spatial visualization skills, students should be given opportunities to work with two- and three-dimensional objects. The authors describe two activities that use tetrahedra nested within cubes to help improve students' visualization of two- and…

The use of data is critical to the teaching of probability and statistics. At the very least, data should be provided within a meaningful context rather than presented as a generic, meaningless collection of numbers. Students often respond better, however, when working with data that they have gathered themselves. Having students collect data is a…

Mathematics teachers can use a broad range of technologies--calculators, computers, display systems, and others--as teaching and learning tools. Simply using technology is not enough; well-intentioned activities can fall flat or pose roadblocks to student understanding, and practical issues can interfere with student success and lasting concept…

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…

Technology impacts students' learning experiences. The increased use of calculators, computer algebra systems, and computer-based and Web-based assessments opens up new opportunities and challenges for teaching and learning mathematics. Students' lives are becoming busier, and they have less time to dedicate to homework outside the classroom.…

Today's classrooms are much different from those of yesterday. The increased diversity of learners, students' familiarity and attraction to technology, and the improved availability of technology in education have made it increasingly possible for teachers to use various forms of technology in instruction. The responsibility for addressing these…

Students are more likely to develop a deep conceptual understanding of mathematics when they interact with and discuss their thoughts with others. The National Council of Teachers of Mathematics (NCTM) (1989, 2000) has recommended that students be active learners--communicating with one another, conjecturing, exploring, and justifying claims by…

Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…

Technology use in mathematics often involves either exploratory or expressive modeling. When using exploratory models, students use technology to investigate a premade expert model of some phenomena. When creating expressive models, students have greater flexibility for constructing their own model for investigation using objects and mechanisms…