Seeing is Believing An Exeter Retrospective Jonathan Choate

Seeing is Believing An Exeter Retrospective Jonathan Choate jchoate@groton. org www. zebragraph. com

A Long Time Ago We Had

And Produced This

How did I get here? • I bought my first Apple 2 in the late 70’s for three reasons. – i) My handwriting was awful – ii) I’m a geometer at heart – iii) I was doing the school schedule

What did I do with it? • Discovered the power of a spreadsheet. • Created a Dynamo simulator. • Wrote simple graphics programs. • Helped produce Bank Street Writer.

• April 1985, I met Anja Greer at a conference in Sturbridge, MA.

25 Years Ago we had

And The Much Beloved Trash 80

Visi. Calc

Green Globs

The First Phillips Exeter Math and Technology Conference MAJOR SPEAKERS: Zalman Usiskin, University of Chicago Judah Schwartz, Harvard University Michal Yerushalmy, Harvard University John Kemeny, Dartmouth College Stephen Maurer, Swarthmore College

And here is what we taught Algebra/Getting Started This seminar is for those who have yet to make much use of the computer in their teaching. Participants will develop worksheets which explore mathematical ideas using simple BASIC programs. Tehh objective will be to integrate this material into the participant's own curricular structure. Topics from algebra and precalculus will be used. Leader: Bill Campbell (Phillips Exeter Academy)

Geometry/LOGO The use of LOGO with young children is well known; it is being used increasingly often with high school students for exploring geometry and teaching a structured approach to problem solving. This seminar will present materials appropriate for a standard high school geometry course. Leader: Joseph Aieta (Weston High School)

Geometry/"Geometric Supposer“ "The Geometric Supposer" is a commercially available software item, co-developed by guest speakers Judah Schwartz and Michal Yersushalmy, which offers exciting opportunities for conjecturing. This seminar will present one teacher's approach to incorporating "The Geometric Supposer" into a standard high school geometry course. Leader: Richard Houde (Weston High School)

Pre-Calculus/Elementary Functions The computer will be used to develop many topics from the standard algebra and precalculus curriculum: solutions to equations, graphing elementary functions, sequences, series, trigonometry, limits, matrices, and so forth. Teacher-designed programs will be demonstrated as well as commercial software such as mu. Math, TK-Solver, Green Globs, and Graph Guesser. Leader: Jon Choate (Groton School)

Potpourri Offered primarily for those teachers who would rather write their own software, this seminar will present one teacher's attempts to stimulate his students mathematically using the computer as a natural resource. Example will be provided at all levels, and it is hoped that participants will bring ideas to share. Leader: Richard Parris (Phillips Exeter Academy)

Calculus This seminar will focus on the use of the computer as a tool for conceptual development of introductory calculus. Participants will explore strategies for using tool-kit and symbolmanipulation programs (mu. Math) in the teaching of the subject. Leader: Kathleen Heid (Penn State University)

Mathematical Modeling The power of mathematics to describe and explain the real world is vividly demonstrated through the use of computer simulation models, in which discrete approximations to continuous functions permit realism without the use of calculus. Participants will learn to build models as well as to use existing models in their teaching. Models will be selected to demonstrate the wide variety of application areas appropriate for simulation. Leaders: Jennifer Kemeny (M. I. T) and David Myers (The Winsor School)

Contemporary Algorithmic Mathematics A contemporary emphasis in mathematics, both in research and in college teaching, is on algorithmic thinking - not only to compute answers, but also to suggest problems and even to do proofs. This theme will be illustrated with material appropriate at the secondary level, such as sequences and series, linear equations, and graph theory. Leader: Stephen Maurer (Swarthmore College)

Statistics This seminar will explore the use of the computer to crunch numbers and to facilitate statistical computations. Topics will include measures of central tendency, standard deviation, confidence intervals, line of best fit, and chi-square tests. Leader: To be determined

What was the focus? -The use of a limited number of available Softwares such as Green Globs and Visi-Calc. - The use of programming languages such as BASIC and LOGO to create programs for classroom use.

What We Didn’t Have -The ability to share files and information. -The ability to project from a computer. -The ability to stay in touch after a course was over. - Graphing Calculators !!!!! - Sophisticated Computer Graphics - The Internet

What We Do Have Now The GUI Interface

Easy To Use Operating Systems

Superior Graphing Calculators

Lots and Lots of Softwares

Statistics Packages

Function Plotters

Geometric Construction Programs

Computer Algebra Systems

Internet Resources

Great Reads

Some Examples of The Power of Computer Graphics • My Favorite Problem Visualized - Geometric Construction Programs • Natural Forms - Creating Fractals • 3 D Geometry - Google’s Free Sketch. Up - Mathematica 3 D • Interactive Demos - Mathematica’s Manipulate Command

The Art Gallery Problem

Some Examples of The Power of Computer Graphics • My Favorite Problem Visualized - Geometric Construction Programs • Natural Forms - Creating Fractals • 3 D Geometry - Google’s Free Sketch. Up - Mathematica 3 D • Interactive Demos - Mathematica’s Manipulate Command

Making A Fern http: //ecademy. agnesscott. edu/~lriddle/ifskit/

Some Examples of The Power of Computer Graphics • My Favorite Problem Visualized - Geometric Construction Programs • Natural Forms - Creating Fractals • 3 D Geometry - Google’s Free Sketch. Up - Mathematica 3 D • Interactive Demos - Mathematica’s Manipulate Command

Visualizing 3 D Geometry exeter tetra. gsp

Some Examples of The Power of Computer Graphics • My Favorite Problem Visualized - Geometric Construction Programs • Natural Forms - Creating Fractals • 3 D Geometry - Google’s Free Sketch. Up - Mathematica 3 D • Interactive Demos - Mathematica’s Manipulate Command

Tetrahedra and Spheres

Some Examples of The Power of Computer Graphics • My Favorite Problem Visualized - Geometric Construction Programs • Natural Forms - Creating Fractals • 3 D Geometry - Google’s Free Sketch. Up - Mathematica 3 D • Interactive Demos - Mathematica’s Manipulate Command

Mathematica’s Manipulate Command

Demos for The Math and Science Classroom

Some Closing Thoughts Impact of graphing calculators Google vs. Facebook What is Next?

The Future? ?

A Final Question In the information age, what does it mean to be mathematically literate?