A Geometrical Map to Discovering Number Theory
*This course is intended for upper elementary students
Class Schedule
June 29th-July 3rd
11:00 am-11:50 am PST
OR
July 27th-July 31st
11:00-11:50 am PST
Note: Classes are listed in PST, click below to convert time to your time zone.
Course Overview
Small Group Advanced Math
These weeklong courses will be a maximum of 3 students in this amazing opportunity to work with Master Teacher, Dr. Peter Koehler.
Going back to the ancient Greeks we will turn the numbers in the times tables into geometric shapes. While they used small stones, we will use colored interlocking blocks. Our students can make shapes and structures, hold them in their hands, move them around, take them apart and put them together again in different ways. This unleashes their creativity and imagination necessary for making their own discoveries in math. Number Theory is the investigation of the properties of numbers and their interconnectedness.
We begin creating the geometric map by making a 16 piece jigsaw puzzle with the blocks which consists of rectangles and squares. Embedded in these multiplication squares are hidden
the early discoveries of the Pythagoreans in number theory, which are surprisingly accessible to our students to be creative and inventive with. One of the most important discoveries in elementary geometry is the Theorem of Pythagoras. We will look at the whole number solutions of the Pythagorean triangle A^2+B^2=C^2, which mathematicians call ‘Pythagorean Triples‘. When they do not have a common factor they are called ‘Primitive Pythagorean Triples’ and are a fascinating chapter of Number Theory.
*Materials Required:
- 1cm graph paper
- blank paper
- colored pencils
- cm/inch ruler
- scissors
- scotch tape
- colored markers
- 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.
