The Book That Made Me Love Math Again (And The Class It Inspired)

For the final quarter of school, a colleague and I decided to teach a 50 minute, twice-a-week elective course called "Advanced Math and Logic". Several students had approached us, some looking for something different and others looking to challenge themselves before attempting college math next year, so we set off to design something that would introduce them to high-level concepts while focusing on logic and problem solving that they could use in any course.

I wasn't sure exactly what shape the course was going to take, but then I started reading What's Math Got to Do with It? by Jo Boaler over my April vacation two weeks ago. Boaler, a math professor at Stanford, tries to get to the bottom of what's wrong (and right) with math education in America (a topic dear to my heart). It was the project-based, problem solving approach used by successful schools she profiled that set me off on the task of creating the most exciting math class possible.

One problem she observed a school using was the Four-Color Theorem, which became one of the first concepts we explored in my class. It set me off on a search for more books with interesting math challenges that connected to theories and ideas we normally didn't cover in high school.

When I hosted the Math Teachers at Play carnival recently, I mentioned how a book I read over my April vacation had me rethinking everything from my classroom structure to my future. The more I think about it, the more I realize that this book has made me love math again. I can't remember the last time I could say that.

The book is Professor Stewart's Cabinet of Mathematical Curiosities by Ian Stewart, prolific math and science author and Professor of Mathematics at the University of Warwick in England. With deadpan humor and dead simple prose, Professor Stewart breaks down exciting areas of mathematics that we rarely get to touch in algebra, geometry or even calculus.

A portion of the book deals with classic and original math puzzles, while the rest is split between interesting anecdotes about famous mathematicians and stories behind solved and unsolved problems. After reading the book, I decided to divide each class in half: the first part working on logic puzzles and problems, and the second connecting those problems to the theories behind them. This would keep the class engaging and set it distinctly apart from our regular math classes.

In the last two weeks we've had four successful classes, covering different areas of topology, including knot theory (and its important uses), Mobius strips, and the Konigsberg Bridge Problem. This week we'll start discussing cellular automata, such as Conway's Game of Life.

This whole process is probably more exciting for me than even the students (who seem to be very engaged in what we're doing), mostly because I've never really been able to teach any of these topics in my Algebra I or II classes. More importantly, I'm imagining an entirely new first day of school, where we start the year off with mind-blowing Mobius strip activities or classic math puzzles. I'm imagining ways to integrate pretty much everything we're doing into my classes on a regular basis, which would help me get closer to the kind of can't-miss, what-are-we-going-to-learn-today anticipation that I've always wanted my classroom to have.

These are some of the topics we've covered or will cover for these last few weeks of school:

• Topology (Mobius strips, Klein bottles, knot theory, etc)
• Cellular automata and complex systems
  
• Chaos Theory
• Game Theory
• Probability and statistics
• Maybe economics (from the Freakonomics point of view) or cryptography
  

The list of topics is still evolving as I study more and gauge what the students are most interested in. Stewart's book, as well as a personal interest in creating educational games, inspired me to seek out a book on game theory. I've been thoroughly enthralled with Len Fisher's Rock, Paper, Scissors: Game Theory in Everyday Life, which breaks down the essential dilemmas in a way that I think my students will appreciate when we start to explore it. I also have realized that game theory is the reason many of the strategies and systems in my classroom work, because I was applying the principles without even knowing it!

Stewart's book is the best starting point for teachers looking to keep students interested as the school year winds down, as it has many ready-to-use puzzles you can start with. I think the other ideas he covers will then get you off and running, as it did for me, into other areas you can explore with your kids.

Remember, the best benefit of all of this is investing your students in the idea that math is fun, everywhere around us, and encompasses so much more than preparing for multiple-choice tests!

Stay tuned over the next few weeks for more specific lesson ideas and resources to make these concepts come to life in the classroom! I also look forward to seeing what others have to share in the comments.