The Theorem by Pythagoras
*This course is intended for upper elementary students
Class Schedule
Mondays 5:30-6:20 pm PST
October 21st, October 28th,
November 4th, November 11th, and November 18th
Note: Classes are listed in PST, click below to convert time to your time zone.
Course Overview
Small Group Advanced Math
This 5-week course will be a maximum of 3 students in this amazing opportunity to work with Master Teacher, Dr. Peter Koehler.
A problem that you may have encountered before is The Pythagorean Equation: A^2+B^2=C^2. The ancients of every culture before Pythagoras knew a few examples of the 3 numbers: A, B, and C. Everyone knew 3^2+4^2=5^2 and some more. Others were not easy to find and students, if they do not know them already, can try to solve this equation even before coming to this session. No one understood what was going on or knew how to predict more of the triples of numbers that would work. It is believed that Pythagoras and followers found why and how it worked and they could predict many more triples. Euclid, too, showed it in his own way. Pythagoras did it with pebbles Euclid on papyrus. We will focus on using the pebble method or rather blocks, but if we have enough time we will try to link both.
Not unlike the Pythagoreans, we will experiment with blocks. We will wonder and ask questions. Instead of writing A^2+B^2=C^2 we build the squares by hand, just as Pythagoras did. And, we will discover surprise after surprise. Pebbles or blocks let us get an understanding of the most important theorem in all of elementary math. Every student will at one point encounter it at school, learn it, and remember it. In this course, engaged in mathematical and spatial thinking we will find how and why it all works-a lesson in math, a lesson for life.
Materials Required:
- Interlocking blocks sold as Omnifix blocks that Peter recommends. Please let us know if you have trouble accessing the materials!
Student Experience
Pattern Seeker
Mathematician
Researcher
Inventor
Your Teacher: Dr. Peter Koehler
Peter Koehler holds a PhD in theoretical and elementary particle physics from Royal Holloway College, University of London; a master’s degree from Imperial College of Science, Technology and Medicine, London; and carried out post-doc studies in the theory group at Stanford Linear Accelerator Center before becoming a math enrichment teacher at Nueva, where he has been teaching for over 20 years. At Nueva, Peter has become particularly interested in encouraging and fostering mathematical creativity in his students and was awarded a fellowship from Johns Hopkins University for excellence in teaching in 2012. He enjoys showing his students the surprising ways in which math can be used to describe aspects of the natural world. Inspired by the work of the Pythagoreans, he has developed an approach to elementary math teaching where the students use colored interlinking blocks and follow a few simple rules to visualize numbers; look for patterns, shapes, and sequences; make their own mathematical creations; and develop a sense of the more general principles of mathematics. He has found that this approach stimulates interest and enthusiasm for math, is a great motivator, and can spark mathematical creativity, originality, and a joy in the subject, and can lead to more intriguing and advanced aspects of math.
Peter has been a regular presenter at the Nueva ILC conferences and will be presenting a paper at the 11th International Conference on Mathematical Creativity and Giftedness in Hamburg, Germany, in 2019. He has taught independent enrichment programs at several Bay Area schools and the University of Santa Cruz extension. A painter in his spare time, Peter has run visual arts summer camps throughout the Bay Area for the past 25 years. He has also written plays for children.
