Overviews and materials from the Sketchpad User Group and other featured conference presentations, held at the 2008 NCTM Annual Meeting in Salt Lake City, Utah.

Featured Sketchpad Presentations

Constructing Regular Pentagons: Exploring the Geometry of the Golden Ratio with Sketchpad
Abstract: 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.
Presenter: Andres Marti, Key Curriculum Press, Emeryville, California

Do the Wave: Trigonometry Comes Alive with Sketchpad
Abstract: 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.
Presenter: Scott Steketee, Key Curriculum Press, Oakland, California

Using Sketchpad Activities to Enrich Textbook Lessons, with Examples from Math Trailblazers
Abstract: 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.
Presenters: Rhea Irvine, Key Curriculum Press, Emeryville, California; and Philip Wagreich, University of Illinois at Chicago, Chicago, Illinois

Nontypical Investigations in Geometry for 2008
Abstract: 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.
Presenter: Michael Serra, Key Curriculum Press, San Francisco, California

Other Sketchpad Presentations

Transform, Iterate, and Create! Iterate a Tiger? Why Not? Megan Did!
Abstract: Sketchpad gives students chances to preview major mathematical concepts. We will look at big ideas hidden in the Transform menu, take a bug walk, and design with iterations. Projects that foster the emergence of students' creativity will be shared.
Presenter: Virginia Highstone, York Community High School, Elmhurst, Illinois

Meaning through Motion: Improving Calculus Understanding through Interactive Computer Animations
Abstract: Explore interactive computer animations (Sketchpad 4) that greatly improve calculus understanding and literally bring it to life as the study of motion and change. Topics include limits, derivatives, integrals, related rates, volumes, and much more.
Presenter: Audrey Weeks, Calculus In Motion, Burbank, California

Spinning Around: Using Sketchpad and a Ferris Wheel to Facilitate an Entire Trigonometry Unit
Abstract: By modeling the motion of a Ferris wheel in Sketchpad, an entire unit of trigonometry can be faciltated. Students can discover and develop trigonometry concepts from graphing, the unit circle, and even polar coordinates. Sketches will be shared.
Presenter: Kevin Thompson, University High School, Normal, Illinois

Tour de Pythagoras, Archimedes, and Euclid with The Geometer's Sketchpad, Powerpoint, and a Digital Camera
Abstract: We revisit antique (but current) Greek mathematics with modern technology for state-of-the-art teaching and learning of geometry.
Presenters: Armando M. Martinez-Cruz, California State University-Fullerton, Fullerton, California; Paul Sexton, Buena Park High School, Buena Park, California; and Greg Love, Buena Park High School, Buena Park, California

Using Technology-Based Projects to Foster Geometric Thinking in the Middle Grades
Abstract: Join us to discuss classroom-tested projects that engage students using The Geometer's Sketchpad. Topics will include transformations, quadrilaterals, angle relationships, and more. Activities are aligned with the NCTM Standards and include assessments.
Presenters: Jennifer Nickell, Lakota Local Schools, Liberty Township, Ohio; Suzanne Rushton, Harper Miami University, Oxford, Ohio; and Shannon Driskell, University of Dayton, Dayton, Ohio

On the Shoulders of Technology Your Students Can See Farther
Abstract: Let the power of technology bring mathematical insights to your students. The visual capabilities of computers, digital images, and software make your classroom come alive for 21st-century kids.
Presenter: Frank Sobierajski, North Rose-Wolcott Central School District, Wolcott, New York

Technology-Enhanced Mathematics Instruction: Effects of Visualization on Learning Trigonometry
Abstract: Hear details of a research study that found a positive effect for technology use on students' learning of trigonometry. Wholeclass, technology-intensive instruction emphasizing visualization produced superior results over traditional instruction.
Presenter: Jeffrey John Steckroth, Old Dominion University, Norfolk, Virginia Room

Sketchpad User Group

Key Curriculum Press and KCP Technologies hosted the NCTM Sketchpad User Group. Several Sketchpad users gave fantastic informal presentations.

Keynote Presentation
Abstract: 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.
Presenters: Daniel Scher and Steven Rasmussen, Key Curriculum Press, Emeryville, CA

Geometry Course Project
Abstract: 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.
Presenter: Michael J. Bosse, East Carolina University, Greenville, NC
Presentation Materials: Bosse_NCTM2008.zip

Sketchpad LessonLink
Abstract: 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 Sketchpad LessonLink, which helps teachers easily incorporate Sketchpad activities into classroom planning.
Presenter: Bridget Foster, Key Curriculum Press, Emeryville, CA

Line Design Introduction
Abstract: 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.
Presenter: Karen Greenhaus, Key Curriculum Press, Emeryville, CA
Presentation Materials: The_Dot_and_The_Line.gsp

Physics and Sketchpad
Abstract: Construction and use of Sketchpad models for physics phenomena allows students to think through basic ideas of mechanics and explore their consequences.
Presenter: Paul J. Karafiol, Walter Payton College Prep H.S., Chicago, IL
Presentation Materials: PJKs_Physics_NCTM2008.zip

Shadow Functions
Abstract: 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.
Presenter: Ralph Pantozzi, Mount Olive Public Schools, New Jersey
Presentation Sketch: Shadow_Functions_NCTM2008.gsp

Color Around the Pool
Abstract: 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.
Presenter: Frank Sobierajski, North Rose Wolcott CSD, Cato, NY

Sketchpad and Some Calculus Activities
Abstract: Andy used Sketchpad to verify interesting conjectures about functions and their derivatives.
Presenter: Andy Ventress, Marist High School, Chicago, IL