Puzzle Theory

| | Comments (0)

Last week at the Gaming Brownbag, I gave a PuzzleTheory.pptx for education (a completely made up name) which is an exploration of how the principles of entertainment puzzles (Sudoku, solitaire, word games, math and logic games, etc) can be implemented in different courses, specifically those which assign lots of "problem sets" as homework.

I got interested in puzzles partly because I like them, but also because they structurally overlap with exercises I give out as homework, yet are actually considered fun. A question I have is what are the makers of Soduko and online solitaire doing that we're not to make these addictive.

Puzzles/Problem Sets vs. Design vs. Games

When considering learning objectives, it's important to consider the properties of entertainment puzzles versus a game or a "design". Puzzles are game-like in that there are formal rules, but different in that there is generally a limited solution set (sometimes just one). Also, games have competitors and generally have a winner, but a puzzle can be a solo activity.

Another distinction is design versus puzzles. There are lots of open-ended problems which can be solved with any number of creative solutions from architectural problems (environmentally friendly yet tasteful) to social engineering (getting people to eat vegetables) to optimization. You can (and should) build learning activities around these design issues, but I also think that puzzles with limited solutions are also valid.

Puzzles in Real Life

There are actually lots of puzzles in real life with few solutions....but it's not the case that we can find an answer (yet). Some recent examples

  • What do those weird Egyptian heiroglyphic symbols mean? (solved!)
  • Which crazy Unicode font is making Elizabeth's Photoshop crash? (unsolved)
  • Why does the patient sufffer back pain?
  • How many people are employeed by Penn State in each county?
  • Where do you plug things in to set up Adobe Connect audio?
  • Which route to a particular Washington DC suburb is the fastest?

Entertainment Puzzles vs. Problem Sets

In the discussion we had, we compared puzzles vs. problem sets. One issue we discussed was whether "bells and whistles" would add to the experience. Online puzzles generally have interesting graphics/sound effects (e.g. Mahjong for iPad) not found in problem sets.

Another feature of both modern puzzles and games is a wacky sense of humor. Each round of the iPad game Angry Birds presents the ballistic challenge of efficiently destroying a structure with a missile - yet few engineering classes will ask you how to launch an avian projectile to destroy building built by villainous pork.

A third issue was context - why should students care about the problem? In engineering, solving a problem correctly could prevent a major disaster. In linguistics or foreign language, it might mean being able to buy some groceries. Yet most problem sets present exercises out of context. It can be hard to write good word problems, but maybe we need some humor too!

Finally, a lesson I have to keep re-learning is to NOT make your problem sets too difficult. Addictive puzzles are those which are tricky, but not impossible to solve. A successful series of puzzles can you ramp you up from simple to easy so that you learn the easy puzzles quickly, then work your way towards more challenging puzzles. But once a puzzle becomes too hard, players quit.

As a general note, a puzzle that is fun or challenging for an instructor will likely be too hard for students, especially in intro courses. The students will probably be more frustrated by a challenge rather than being inspired by it (unless they happen to "get it").

Learning Through Failure

I think the most important insight I had was that part of solving a puzzle is going through a series of repeated failures until you get it right. That is, puzzles are somewhat low-stakes where you are rewarded more making an effort rather than perfection. Problem sets, on the other hand...generally high stakes.

Entertainment Puzzles Problem Sets
  • Fun!
  • Can reset/do over
  • Can look at answer key/cheat code
  • Can ask for help
  • OK to fail multiple timnes before solving
  • Not Fun ;(
  • No do over
  • No answer key (until grading)
  • No outside help
  • Turn in once and hope for the best

This does make me think about how traditional education works. In the worst case scenario, we may show simple problems, but then assign students for homework (or show hard problems in class then assign very easy problems in homework to bewildered students).

What we rarely do is ask students to re-do a problem again so that they can learn from it. We just hope our answer key is clear enough for them to understand what went wrong. Nor do we ask students to work through a simple problem on their own, which could allow students to figure out the strategies. It is no wonder that they are passively waiting for us to tell them what to do - it's how instructors roll.

I know I am re-inventing problem based learning (PBL), but puzzles are a way to show how it can work successfully, when you start tossing birds at pigs.

Leave a comment