## From Playability to Learning Target

### The Problem

So, you've built a simulation that embodies important information about a useful learning domain. Then you've built a game on top of the simulation, and you've found ways to make that game playable, and fun, or at least engaging. Can you declare success?

Not necessarily. It may be possible for people to play your game a lot, and play it successfully, without learning what you want them to learn.

Let's use Shuxin Nie's very nice minimum spanning tree game as an example. In this game the player has to navigate along the edges of a graph whose edges have numeric weights. The goal is to mark out a connected collection of edges that visits all of the nodes while minimizing the total weight of the edges used (such a collection is called a minimum spanning tree ot the graph.) It's a fun game, with a good built-in sense of progress towards the goal, and the feedback Shuxin provides enhances it by telling you when you can do better, keeping you at work.

The learning goal for the game is that players should learn the greedy algorithm for the problem. You can form a minimum spanning tree by choosing the cheapest edge that joins the path you have created to a node you haven't yet visited. Once you realize that, it is fairly easy to play perfectly, though you have to be careful to check all of the appropriate edges. The question is, can Shuxin be sure that people who play her game will learn this method? I think it is doubtful that anyone could learn to play perfectly for arbitrary graphs without getting the concept of the greedy algorithm. BUT (a) it is possible for someone to play perfectly for any finite collection of graphs, such as Shuxin's levels might offer, without learning the algorithm: they could just learn an adequate sequence of moves for each level, by trial and error; and (b) it may be that most people will not play the game long enough or carefully to attain perfect play, even for the levels Shuxin provides.

What can Shuxin do to make it more likely that players will reach her learning goal?

### Solutions

Shuxin's learning goal requires developing concepts at a more abstract level than the play of the game intrinsically requires. She needs to do something to push players to bring these abstract concepts into their thinking. Here are some approaches.
• Place the game in a larger context
• The goal of play within the game is just to find a minimum spanning tree. Shuxin could provide context for the game, say by creating a classroom activity that includes the game, or by adding material to the introduction to game itself, in which the added goal of finding an optimal strategy is explicitly stated. This could be done up front, on the way into the game, or this added goal could be presented after the player has attained an optimal solution for the first level, or some later level.

Depending on how difficult players find it to find and state an optimal strategy, Shuxin may want to provide some hints or cues in the presentation of the game, to help players see what factors they should be considering in choosing their moves. For example, she could highlight all the edges the player should be comparing at a given stage. Shuxin could use fading, an approach in which these extra cues are gradually eliminated, so that the player has to internalize them to continue to play well.

• Shuxin could make the game part of an activity in which players discuss what they have learned about playing the game. This would be easy to do in a classroom setting. Because discussion requires players to describe how to play, rather than just playing, this discussion might lead some players to articulate the greedy algorithm, especially if sessions of play and discussion were alternated.

• Shuxin could make the game part of an activity in which telling someone else how to play is required. A team competition could be set up between two (or more) teams of n players. One player from each team would leave the room while the other n-1 players played the game and discussed strategy. After an agreed period of time, the n-1 players would be permitted to brief the 1 player who had been set aside, and these briefed players would then compete in the game, using levels that the n-1 players had not seen (so that describing specific levels or moves would do no good).

• Shuxin could raise the conceptual level even further by asking players to prove that their strategy is optimal.

• Promote abstract conceptualization within the play of the game
• Having a very rich set of levels will make it more likely that successful players will have to formulate an optimal strategy. Note that this will do no good if the game isn't engaging enough to make players persist to the point of mastery. Hints, as described above, could be used to make finding the strategy less demanding, so that the game would not have to be as engaging to work.

• Shuxin could escalate the penalty of making a wrong move, to move players from "just playing" to being careful on each move. Again, hints could be used to control the difficulty of succeeding in this form of the game, if needed to maintain player interest.

• Shuxin could consider creating a sequel to her game in which players must instruct a robot within the game how it should choose edges. This would make the goal of finding a strategy a part of the game itself, rather than part of the context.

### Generalizing these Ideas

These approaches can be applied to many other games. The key idea is to find ways to promote thinking or talking about how to play, and not just playing. A subtheme is, if you raise the demand of the game so as to promote more thoughtful play, you may need to provide some hints or cues to keep the game from becoming too difficult to be engaging for some players. You may then need to use fading to keep players from relying on the cues, rather than on the ideas the cues are intended to suggest.

Not all games require these approaches. If your game is such that playing the game actually requires mastering the ideas targeted in your learning goals, you don't have to worry that people can play the game without learning what you want them to learn. We're assuming here that your game is already playable and fun, so you don't have more to do.