Instructors: Peg Cagle and Philip Mallinson
I have up my sleeve a regular polygon all of whose angles are right angles. Question: how many sides does it have? Four? Correct! But after this two-day minicourse you will see why 0, 1, 2, 3, …, 2006, … are all correct answers. And we will make models to prove it. Our goal for this course is to explore geometries where Euclid’s rules don’t always hold and by doing so to fit the traditional geometry course into a wider geometrical context. We hope that you will develop a better sense of what Euclidean geometry is by exploring examples of what Euclidean geometry isn’t. These explorations are valuable in their own right but they also deepen a student’s understanding of Euclid’s world. We will make models of surfaces which may be unfamiliar to you, explore them with paper, scissors and Scotch tape and also on the computer. Each of us has used these activities and models to teach our students in regular classes. Students love the challenges of solving problems in non-Euclidean geometry. Communicating their conjectures about the exciting and unfamiliar results they unearth is yet another challenge. You want a triangle whose angles add up to 100 degrees? 200 degrees? No problem. Just sign up for two mind-expanding days of Geometry Other Than Euclid’s.
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 or Tinker Plots. Data analysis and probability are woven into our everyday lives. The course is designed to strengthen the skills of teachers being asked to ready their students for the WASL standard.
In this minicourse, we'll take an in-depth look at mathematics' most famous theorem. Following Frank Swetz's "Was Pythagoras Chinese?", our historical study will start before the Greek philosopher. We'll work through many, many proofs of the theorem, prompting a discussion of why more than one proof of a result can be both interesting and helpful. Special attention will be given to "Pythagorean triples," integers that arise as side lengths of right triangles. This is the subject of a classic book by Sierpinski, a gem for understanding and writing good proofs. We'll even see how matrices contribute to understanding these triples. So come explore some of the rich mathematics behind the theorem that almost every student knows.
Experience the dynamic power of The Geometer’s Sketchpad to energize your math classes. From Sierpinski's triangle, kaleidoscopes, and graphing linear functions in Algebra I to modeling functions and solids of revolutions in Calculus, Sketchpad has something to offer all levels of math. Expand your repertoire of Sketchpad features to share. This course will benefit intermediate and advanced users, but beginners are welcome as well.