Three years ago, the Mathematical Sciences Research Institute at UC Berkeley in California decided to do a little outreach, to share the wonders of math with the public. Little did they know that 20,000 people would show up at the Smithsonian Institute in Washington DC for the first National Math Festival. Yes, there's that much interest.
Now, two years later, interest has only grown, with movies like Hidden Figures, and snowballing interest in STEM (Science, Technology, Engineering, Math) for education. On Saturday, Apr 22, 2017, another 20,000 people descended on the DC Convention Center (and dozens of affiliate science museums across the country) for the second National Math Festival. There were balloon polyhedra, talks by mathematicians profiled in the movie Hidden Figures, mathematical magicians, and mathematical art from all over the world. It's all the fun stuff about math that you never learned in school.
I hosted an all-day hands-on workshop showing kids of all ages (that includes adults) how to make your own versions of Sudoku and Pentominoes — two of the most popular mathematical puzzles. If you didn't make it to the event, or you attended and want more, here are the downloadable handouts so you can try them at home, plus the twelve 11"x17" play mats, and instructions for printing the mats and making the accompanying manipulatives. If you want more, check out the links at the end of this article to math puzzle books and web sites.
Puzzles are the literature of mathematics. Puzzles are where the ideas in math class come alive, and dance off the page into our imagination. Traditional math education is full of worksheets that are boring to fill out (word problems are third-rate puzzles), and train kids in very narrow ways of thinking. Puzzle, in contrast, are exciting to solve, memorable, and require resourceful think-on-your-feet problem solving.
Puzzles are not just entertaining, they have a deeper purpose. As every scientist, engineer and mathematician knows, puzzles are the play version of problem solving. When kids solve puzzles, they wrestle with the elements of problem solving that they will encounter later in life, just as lion cubs wrestle with each other to build fighting skills they will use later in life. And problem solving is one of the most important skills that every child needs to succeed in life.
Playing puzzles and games is as important for a well-rounded math education as reading books is to language education. In an ideal world, math students would spend much time playing puzzles and games, doing art projects, building things, and reading math stories.
If that sounds strange, imagine an English class without books. If English class consisted entirely of spelling, grammar and verb conjugation, then students would become proficient at the mechanics of language, but never fall in love with the subject. They would ask "when are we ever going to use this?" And they would not be able to read anything but sentences written in the forms that appear on their worksheets. Language education without books sounds absurd. But sadly, that is exactly how conventional math education works.
WHY PUZZLE MAKING?
If solving puzzles is like reading, then, making puzzles is like writing. Making a puzzle is harder than solving a puzzle, because you don't have the safety net of knowing what the solution is, or even if there is a solution. It's like a writer facing a blank page, or an artist facing a blank canvas. The challenge is higher, but so are the rewards.
Making your first puzzle is an important experience that everyone should have — it changes mathematics from a utilitarian chore into a creative activity that you can make your own. Making a puzzle is like writing a story or composing a song. Doing it well takes years of practice, but anyone can try it if they start with small steps. In my puzzle making handout, I start simple — make a 4 by 4 Sudoku puzzle, or a 5-piece Pentomino puzzle. For those who want to go deeper, I offer suggestions for customizing your puzzle or changing the rules.
Having taught dozens of puzzle making classes to kids, I have found that I don't have to do much instruction — once I tell kids that we are going to make puzzles, most kids know immediately what they want to do. Some kids focus on art and story, creating a narrative frame around a familiar puzzle. Other kids go deep into the math, making difficult puzzles with original rules. Besides Sudoku and geometric puzzles like Pentominoes, logic puzzles are particularly popular among young puzzle makers, because they are easy to construct, and easy to adapt to a particular theme.
I invite you to try making your own puzzles, and find your puzzle making style. Be sure to have someone else try your puzzle, to make sure it is solvable and that the instructions are clear. As with creative writing, your first draft is rarely your final draft. Send me photos of your creations and I'll add them to this site. Happy puzzle making!
WHAT MORE CAN I DO?
Kids. Play lots of different kinds of puzzles. Play with friends. Find out which kinds you like.
Parents. Read math stories and play puzzles and games with your kids. See this bibliography for suggestions.
Teachers. Have a puzzle corner in your classroom. Start the day with puzzles. Don't just give puzzles to advanced students to do when they are done with their work; puzzles are for everyone. Have kids invent test questions — the best way to learn is to teach. Here are other ideas for using puzzles in your classroom.
Will Shortz Presents The Monster Book of Sudoku for Kids: 150 Fun Puzzles. St. Martin’s Griffin, 2006.
The Art of Sudoku, by Thomas Snyder. Grandmaster Puzzles, 2012. Superior artful puzzles.
Mutant Sudoku, by Thomas Snyder and Wei-Hwa Huang, Puzzlewright, 2009. Imaginative variations.
Taking Sudoku Seriously, the math behind the world's most popular pencil puzzle. By Jason Rosenhouse and Laura Taalman, Oxford U. Press 2012.
Pentomino Puzzles: 365 Teasers to Keep Your Brain in Shape. By Eric Harshbarger, Puzzlewright, 2011. Beautful and challenging. Comes with a set of Pentominoes.
Polyominoes: Puzzles, Patterns, Problems, and Packings. By Sol Golomb, Princeton U Press 1996. The math of pentominoes and related puzzles, written by the mathematician who coined the term Pentominoes.
Rainbow Premier Pentominoes. By Learning Resources. Six plastic sets, in rainbow colors.
Quintillions, Gamepuzzles.com. Not cheap. A sublimely pleasurable laser-cut set of wooden Pentominoes, lovingly designed by Kate Jones, whose site gamepuzzles is a treasure trove of artistically crafted mathematical puzzles.
PUZZLES & RECREATIONAL MATH
BedtimeMath.org. Brief daily stories and questions for elementary-aged kids and their parents. Web site and app.
The Little Book of Big Mind Benders. By Scott Kim, Workman Publishing, 2014. Over 450 puzzles of all sorts: visual, word, spatial and mathematical.
The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. By Martin Gardner, W. W. Norton, 2001. The ultimate recreational math book. For high schoolers and adults.
ThinkFun.com. Makers of Rush Hour and other superbly entertaining physical math puzzles for kids and adults.
Mathfair.com. How to stage a math fair in your school where every child makes and hosts a puzzle.
Puzzlecraft: The Ultimate Guide on How to Construct Every Kind of Puzzle, by Mike Selinker and Thomas Snyder. A superb practical book with detailed advice on how to create nearly every type of paper and pencil puzzle, from crosswords and Sudoku, to logic puzzles and word puzzles. The only book of its kind.
Flatlandthemovie.com. The best math fable ever written is now a wonderful animated 30-minute movie.
Mathical. This annual prize for the best math books for kids and teens is an excellent place to find out about math books you can share with your kids.