In this minicourse we will look at the basic concepts in fractal generation. The topics will include fractal curves such as the Koch, Hilbert, and Peano curves, "Mandelbrot" sets, Julia sets, fractal dimension, iterated function systems, chaos and others. An emphasis will be placed on creating fractals by repeating simple sets of instructions. The activities will be hands-on and include stamping, folding strips of paper, cutting pop-up fractals, building 3-dimensional models, creating computer generations of fractals, and others. Materials for this fractal course are on the web at Will Webber's website.
A new version 4.0 of The Geometer's Sketchpad has appeared with new possibilities for authoring and graphing. This software is a powerful tool in any course named "Geometry", but this minicourse will focus how Sketchpad can be used in other math courses as well, including Integrated Math courses. Sketchpad can be used for visualization, experiment, modeling, and dynamic graphing. This course will demonstrate how Sketchpad can be used to study such topics as trigonometry, conics and projectile motion, centers of mass, complex numbers, max-min problems, nets for polyhedra, dynamic graphs linked to models, simulation of physical devices.
The minicourse will highlight the new graphing and tool features in Sketchpad 4.0. This is an Intermediate Sketchpad course; participants will be expected to know basic Sketchpad operations. (If there are questions about the level of Sketchpad knowledge needed and/or how to acquire this knowledge, please inquire of the instructors.)
How can you express "six degrees of separation" in mathematical terms? Is Kevin Bacon the center of the Hollywood universe? How many colors does a mapmaker need? Can you schedule all your school's finals in two days? How many ways can you walk around a dodecahedron? All this and much more can be addressed with the accessible and relatively young area of mathematics called graph theory. We'll look at the subject's history and modern applications, using web resources and lots of collaborative work.
Explore the world of data. Collect real data with technology and simulation. Investigate patterns in data and chance. Make those patterns come to life for your students with the help of the calculator and the software Fathom. Data analysis and probability are woven into our everyday lives. The course is designed to strenght the skills of teachers being asked to ready their students for the WASL standard.
Experience manipulative madness across the math curriculum! We'll engage in a series of hands-on approaches to help your students meet each of the standards for geometry, probability and statistics, measurement, number sense, and algebra.
Transformations become tangible with the use of mirrors, models and technology, including The Geometer's Sketchpad and calculators. Transformational geometry will be connected with other geometry through constructions, coordinates and problem solving. The basic properties of transformations will be investigated visually. Transformations will be used to create and analyze symmetric patterns and to analyze and simulate physical devices.