Describes an experimental approach to determining the speed of light in water using some simple observations and Fermat's principle. Enables students to integrate mathematical techniques and encourages mathematical exploration in which the students have control over what mathematics and technology to use and when to use them. Presents extensions…

Discusses how the National Science Foundation (NSF)-funded curricula stack up against the National Council of Teachers of Mathematics (NCTM)'s "Principles and Standards". Identifies distinctive features of the five textbook series and includes an example that shows some of these features for each series. (KHR)

Describes how the concept of similar triangles was taught using an optical method of estimating large distances as a corresponding activity. Includes the derivation of a formula to calculate one source of measurement error and is a nice exercise in the use of the properties of similar triangles. (Author/NB)

Explains how conic sections can be approximated by paper-folding activities and proves why they work. (Author/NB)

Presents an active way for students to learn about SAS, SSS, ASA, AAS, and HL in determining congruent triangles. (Author/NB)

Discusses ratio analysis by which investments may be evaluated. Requires the use of fundamental mathematics, problem solving, and a comparison of the mathematical results within the framework of industry. (Author/NB)

Demonstrates how to use graphing calculators to explore rational number approximations to irrational numbers. (Author/NB)

Suggests an alternative proof by analytic methods, which is more accessible than rigorous proof based on Euclid's Elements, in which students need only apply standard methods of trigonometry to the data without introducing new points or lines. (KHR)

Presents a lesson to teach matrices that emphasizes conceptual understanding and allows students to extend their investigations into important and relevant situations by using graphing calculators after important conceptual understanding has been developed. (KHR)

A beginning solution and generalization are given to a problem on area and perimeter presented in a previous article. Various figures are used to illustrate how posing problems and identifying increasingly general methods promotes problem-solving maturity. (MNS)

Presents an activity that involves drawing pictures to collect data, conjecturing a recurrence relation, and solving the relation using geometric series and partial fractions. (MKR)

Uses rectangular models for illustrating products of numbers to solve mixture word problems. (MKR)

Presents mathematics problems which use technology for exploring and verifying relationships among data sets; comparing and analyzing effects of changes in parameters of mathematical models; simulating complex, expensive, or dangerous events using probability models based on random outcomes; and graphically or numerically zooming in on apparent…

Demonstrates the application of spreadsheet analysis in solving equations beyond quadratics. Considers the costs of interest, gasoline, and maintenance in deciding how long it pays to keep a car. (MKR)

Portfolios inform teachers and students of progress toward established goals. Offers tips for helping students create their own portfolios and suggests criteria for assessment and self-assessment. (MKR/SW)