Wednesday, April 27, 2016

The Logical Journey of the Zoombinis: A computer game teaching logical thinking skills

When I was a kid, one of my favorite computer games was The Logical Journey of the Zoombinis, which came out in 1996. Players solve puzzles to help guide Zoombinis to safety after they escape imprisonment by the evil Bloats, who have taken over their homeland. The puzzles teach logical and computational thinking skills which are fundamental to mathematics and computer programming. There were two sequels (which I never played) - Zoombinis Mountain Rescue in 2001 and Zombinis Island Odyssey in 2002.

Although the games were made for now outdated operating systems, the original game was recently updated for iOS, Android, Windows, Mac, and Kindle Fire via a Kickstarter campaign (which I excitedly participated in). The National Science Foundation has even awarded a large grant to the creators to study the effects the game has on students' computational thinking skills and how the game could be leveraged in the classroom.  

While new educational materials that compliment the game are still in development as part of the grant, you can find the 1996 guides for parents and teachers here and an awesome article written by the creators entitled Zoombinis and the Art of Mathematical Play here.  The article starts by describing how "play is nature's greatest educational device", but most computer math games are "essentially drill-and-practice programs that focus on a narrow set of skills" and "treat the playful elements as something distinct from the mathematics".  

The game is aimed at elementary and middle school students, although I think many adults will still find it enjoyable and challenging.  I would also recommend that teenagers and adults check out Portal.

iPad Screenshot 2
iPad Screenshot

Friday, April 15, 2016

Curve Stitching and Folding: A Hands on Activity

This weekend, the AMS will be hosting a curve stitching activity at the 2016 USA Science & Engineering Festival held in Washington, DC. The idea is that you can create curves by drawing, folding, or stitching a bunch of straight lines. Below is a quick example I folded (folds are drawn over for visibility), using a Project Origami activity. 

You can prove that the lines I folded are all tangent to a parabola whose focus is the marked point and whose directrix is the bottom edge of the paper. This means that the parabola is the envelope of the family of lines I folded. Yarn also works well to create the lines (hence the name curve stitching), as when you thread yarn through two holes and pull it taut, you get a straight line connecting those points. The AMS website has pictures, pattern sheets with instructions, and further resources to check out. This would make a great math circle activity.  Even elementary school students can do the stitching and marvel at the cool pattern they formed!

Wednesday, April 6, 2016

The Man Who Knew Infinity: Conversation starters about the upcoming film

Two summers ago, my advisor Ken Ono suddenly jetted off to England to help with the filming of the movie The Man Who Knew Infinity (Click here for trailer).  The film, featuring Dev Patel and Jeremy Irons, dramatizes the life of the Indian mathematical genius Ramanujan, focusing on his time at Cambridge working with British mathematician G. H. Hardy in the 1910s.   It is based off of the Robert Kanigel's biography The Man Who Knew Infinity: A Life of the Genius Ramanujan (Amazon affiliate link here). Through Ken, whose role with the film has expanded from math consultant to associate producer, I've gotten to see the movie multiple times already, including at the world premiere in Toronto last September! 

Since the movie is finally coming soon to a theater near you (May 13 is the date I've heard for Atlanta, but other cities may be earlier), the time has come for me to write a post about it. I obviously think it's a great film, but instead of writing a review (I assume you can find many using google), I'm going to give some conversation starters for discussing the film.  Watch it with your kids/students (I'd recommend middle school age and up)!

1. One of the major themes is the relative importance of proof versus intuition in mathematics.  Why are each of them valuable? 

2. Another theme is the importance of reaching out to others and asking for help when you need it.  Ramanujan did this successfully in the beginning of the movie, but struggled once he got to England.  Why? 

3. The film focuses on Ramanujan's work on partitions.  Do you remember the definition? If you need a reminder, the partitions of 4 are 4, 3 + 1,  2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1.  So p(4) = 5.  Try to compute a few partition numbers by yourself and look for patterns.  Partitions makes for a great math circle topic, and I think that Integer Partitions by George Andrews and Kimmo Eriksson (Amazon affiliate link here) is a particularly accessible introduction.  

4. Ramanujan was self-taught.  With only a single book, he was able to rediscover much of modern mathematics and push the field forward. Mark Zuckerberg asked (see the end of this clip): "What would have happened if he had had access to the internet?" Of course, the internet didn't exist when he was alive, but what implications does that have today, when more than half of the world still doesn't have access? 

5. Mathematicians are often inundated by letters and emails from amateurs claiming to prove one of the big unsolved problems in mathematics, many of which are challenging to read because they do not follow the conventions that mathematicians are used to.  How much time and effort should we devote to sifting through all of this for diamonds in the rough? Do we have a duty to look for mathematical talent in unlikely places? 

I also wanted to mention The Spirit of Ramanujan Talent Search.  The first stage of it is powered by Expii, and anyone can take part by solving some math problems on their website.

The Man Who Knew Infinity (film).jpg