Report from the 2008 NCTM Annual Meeting
Salt Lake City, Utah
April 9-12, 2008
The Geometer's Sketchpad featured prominently at the National Council of Teachers of Mathematics 86th Annual Meeting in Salt Lake City. Talk abstracts and User Group details are given below.
Featured Sketchpad Presentations
Constructing Regular Pentagons: Exploring the Geometry of the Golden Ratio with SketchpadAbstract: Learn how to construct a regular pentagon and see where the golden ratio appears in a regular pentagram. Examine why the golden cut construction results in the value of the golden ratio and how this value is related to Fibonacci numbers and spirals. |
Do the Wave: Trigonometry Comes Alive with SketchpadAbstract: Trig makes sense and is more fun when students make sinusoids actually wave, combine the waves, and explore real-world applications. See several activities, examine how they improve students' understanding, and receive copies to use with your class. |
Using Sketchpad Activities to Enrich Textbook Lessons, with Examples from Math TrailblazersAbstract: Explore how dynamic representations help students find patterns and make predictions in both exact and uncertain contexts while laying foundations for multiplicative and algebraic reasoning. Examples will come from Math Trailblazers. |
Nontypical Investigations in Geometry for 2008Abstract: Can you tile the plane with pentominoes? What is Polya's problem? What are all the Archimedean tilings? What is Pick's formula? If any of these are new to you, come join us as we explore some not-so- typical, cool investigations in geometry. |
Other Sketchpad Presentations
Sketchpad User Group
Key Curriculum Press and KCP Technologies hosted the NCTM Sketchpad User Group. Several Sketchpad users gave fantastic informal presentations.
Keynote PresentationAbstract: Key Curriculum Press and KCP Technologies have, over the past several years, been doing extensive research into how Sketchpad can be used effectively to teach mathematics in younger grades, as well as how it can be even more effective in secondary school math. Out of this research came a collection of hundreds of Sketchpad activities, for grades 3–12, along with a way to search, organize, and assign the activities to students. In the closing presentation, Steve and Daniel introduced the new Sketchpad LessonLink™. Sign up for updates about Sketchpad LessonLink, so you can know when it becomes available. |
Geometry Course ProjectAbstract: My geometry course for preservice teachers uses no textbook, only a list of geometric theorems and terms for which students must create their own entire geometry textbook in GSP. This textbook includes static sketches and definitions, demonstrations of theorems, real world examples of theorems, and proofs. Generally, the project results in an average of 450 pages in GSP! All students report to learning far more in geometry than ever expected and a readiness to teach geometry in high school and middle school. |
Sketchpad LessonLinkAbstract: Using Sketchpad in the classroom is even better when you can easily find activities that are directly aligned to your curriculum and assign activties to your students. Bridget shared the soon-to-be-launched Sketchpad LessonLink that will help teachers to easily incorporate Sketchpad activities into classroom planning. |
Line Design IntroductionAbstract: An introductory activity to get geometry students (middle and/or high school) excited about beginning and creating a line design project using GSP. This activity is based on a story by Norton Juster. The teacher reads the story and uses this GSP document to illustrate various sections of the story, which includes sketches and animations that correlate to the story. |
Physics and SketchpadAbstract: Construction and use of Sketchpad models for physics phenomena allows students to think through basic ideas of mechanics and explore their consequences. |
Shadow FunctionsAbstract: Ralph presented a sketch that allows one to investigate the length of the shadow of an object. In the sketch, the height of a light, the position of an object, and the height of an object can be varied, and the length of the shadow formed is shown and plotted in the xy-plane. The shadow is cast either entirely on the ground, or upon the ground and a wall that can also be re-positioned. Important mathematics from Algebra, Geometry, and beyond can be found lurking in these shadows. |
Color Around the PoolAbstract: Frank showed the swimming pool problem with max & mins shown using parametric color, both on the edge of the pool and also in a graph of degrees/radians vs distance. See an online video of this demonstration. |
Sketchpad and Some Calculus ActivitiesAbstract: Andy used Sketchpad to verify interesting conjectures about functions and their derivatives. |