Shares some explorations of Fibonacci sequences with a special focus on problem-solving and posing processes. (ASK)

Provides examples of the uses of proportions from the fields of mathematics and science. (ASK)

Features a brief description of fractals and their characteristics, some example activities, and an argument for including fractals in the mathematics curriculum. (ASK)

Produces algebraic solutions by reducing the problems to equations and arithmetic solutions that do not use variables. Investigates how the arithmetic solution helps students better understand the problem before they approach it algebraically and how logic used in solving the problem arithmetically can be directly linked to the algebraic…

Presents six examples illustrating both the way in which the level of mathematical demand has been raised, and ways in which the response has sometimes been inadequate with the use of graphing calculator technology. (ASK)

Presents activities to cultivate the tendency to see special qualities in numbers that can be played on certain calendar days. Includes games on the constant of the day, Fibonacci and golden ratio dates, primes, powers, December 25, and the day of the year. (ASK)

Illustrates two ways of exploring the properties of cubic polynomials. The first exploration uses a Computer Algebra System (CAS) to help students understand an important part of mathematical history, the discovery of an algorithm to find the roots of a cubic equation. The second exploration states some conditions required for a curve and finds a…

Presents and discusses examples that can be used to develop the concept of slope as a rate of change through three modes of learning: (1) visualization, (2) verbalization, and (3) symbolization. (ASK)

Computer algebra systems have great potential uses, but learning the basic concepts of algebra is itself a mathematical activity. Explores theoretical concepts that may be seen as essential enabling skills for computer algebra systems users. (Author/ASK)

One of the biggest hurdles in teaching statistics is convincing students that the area under curves has anything to do with all the samples, histograms, and various other indicators to which they have been exposed. Presents two examples to illustrate this phenomenon. (ASK)

Presents an activity that uses square-foot tiles as a coordinate system on which human geometric models are constructed. (ASK)

Discusses the benefits of learning the history of mathematics and how it can be useful in teaching as well as interesting. Provides information on how to put mathematics in its historical context, show the interaction of mathematics with cultures, and shed light on the teaching and learning of mathematics. (Contains 25 references.) (ASK)

Active involvement and infusion of mathematics into familiar, everyday experiences are essential elements in challenging students to engage in true thinking. Presents an investigation on graphing that touches on all representations including tables of values, graphs, and verbal descriptions. (ASK)

Describes students' investigative work that resulted from playing the game Set in an attempt to show how such games can be used to develop mathematical reasoning. (ASK)

Geometrical representations can help students generalize arithmetic to algebra. Includes several examples including triangle numbers and models of cubes. (Author/MM)