I transformed my PhD work into a 5-day mini course for Grade 10s through The Brilliant Club. I am making the course material available here. Contact me or write in the comments for more resources and help using them!
Below is an excerpt of a case study that I wrote for The Brilliant Club:
My Scholars Programme, “How to Make a Mathematical Discovery,” is designed to introduce the idea that maths is much bigger than practicing algebra and arithmetic, or applying such concepts to solve real-life problems. Research mathematics is also about exploring ideas, identifying patterns, and connecting concepts through mathematical abstraction. Why do mathematicians see a teacup and a donut as being the same thing? (Hint: consider the handle). My course gives pupils the opportunity to rediscover the main theorem of my PhD thesis by playing with a set of 3D-Printed tiles, specially designed for the programme. Not a single equation is solved and not a single expression is evaluated.
The outcome of the course was generally positive, in spite of it being conceptually challenging. All 12 of my pupils submitted their final illustrated essay assignment and passed the course, six of them with 1sts, two with distinction, and a third pupil will have her assignment published in The Scholar. I am extremely proud of them! These quotes speak for themselves: “I’ve never got maths before, but I get this!” “I thoroughly enjoyed the program and I miss it already :)” “I loved this programme and the programme has definitely solidified my dream to carry on with maths in the future. From a parent, “May I just thank Alejandro for working with _ throughout the programme. The marking comments were very positive and were a real boost to _’s confidence, and I feel she gained a lot from the programme.
Congratulations to Katie Hancock. Her work on tatami tilings were published in The Brilliant Club’s journal, The Scholar!
K. Hancock, supervised by A. Erickson. How to make a mathematical discovery: The tatami restriction at large, The Scholar, Vol. 1, No. 3, pp. 20-22, July 2015. (Alternate links hosted on my website: Whole issue Just the article)
Tatami Mini Course Resources
There are a few other handouts that I can locate upon request. Below is an excerpt from the last activity before the final project (i.e., Katie Hancock’s work, above), showing how far the students go in just a short time.