Fred Goodman (University of Michigan)

School grades may be misleading because the problems students learn to solve in school may not be the kind of problems they face after they graduate.

Solving a puzzle brings closure to a problematic situation. The creator of a puzzle must not pose a problem that does not have a solution. Success at puzzle solving can be measured by comparing the speed, completeness and elegance of different solvers' performance and by assessing the relative difficulty of the puzzle.

Closure in a game is defined by the game rules not by a problem being solved the way the creator specified. The creator of a game constructs a situation in which players are both the posers and solvers of one another's problems. Success at games is measured in a startlingly surprising variety of ways, not just in terms of whether a player's team wins or loses. These characterizations lead me to the following points.

First, an analogy: Games are to puzzles as mysteries are to secrets.

Second, a claim: The more you know about a mystery, the more mysterious it becomes. The more you know about a secret, the less secret it becomes.

Third, a comparison: A puzzle creator is "God-like" in that the creator constructs both the problem and the correct solution to it. A game creator is "God-like" in that the creator constructs the rules that enable participants to make choices that affect each other, provide a criterion by which to compare the participants' overall success, and specify when the activity ends.

Fourth, an observation: Schools tend to pose problems to students in the form of puzzles far more than in the form of games. This can result in students being taught to think that there is an answer to every question, a solution to every problem. There is an endless array of secrets that others know and you don't. When students leave school they frequently find that problems in the "real world" tend not to have "once and for all" solutions. Many problems seem to have no solution at all. People create problems themselves and solve problems created by others. They begin to think in terms of strategies for coping with their problems, strategies that serve their ends but can be expected to conflict with other people's goals. Therefore a puzzle-based education might not prepare people for life after school as well as a game-based education might.

These four points call into question the importance that our society assigns to school grades. In many contemporary upwardly mobile families getting good grades is right up there with "Godliness." (In some families good grades are probably ranked even higher than "Godliness.") Grading is intended not only to give feedback to students in a manner that might help them learn better in the future, grading is intended to sort people out in terms of their future value to others. If pernicious grade inflation is to be avoided, some students must learn to adjust to the fact that they just aren't as good at solving certain kinds of problems as others are. Further, they learn that some kinds of problems are more important than others. But what if the problems that are the basis for such conclusions aren't the kind of problems that people need to solve when they get out of school?

The answer to that question might well have economic implications but there could be even more serious consequences. As the world moves closer and closer to a world where Gods collide and their followers depend with greater and greater certainty on the correctness of their God's solution, we need to look more closely at the relations that might exist between games, Gods and grades. If learning is conceived primarily as a matter of finding the one correct answer according to the teacher who already knows the answer, and students' sense of worth is tied to their ability to discover, understand and accept that correct answer, we may be encouraging, even in our secular schools, a tendency towards sectarian thinking.

There are practical alternatives to the puzzle approach, alternatives that encourage people to reflect upon, cope with, and even enjoy mysteries. That games are analogous to mysteries does seem to be the case insofar as progress towards higher and higher levels of game playing proves to bring greater and more confusing challenges. "Solutions" that worked at one level are exposed quickly as solutions that were only relevant to the prior situation. This follows whether the game is bridge, chess, football ... or to move closer to the topic at hand ... Equations: The Game of Creative Mathematics.

The examples of Equations and Queries ‘n Theories are offered to demonstrate that the points being argued are not solely theoretical. There is a great deal of experience with the use of soundly constructed educational games that manage competition constructively. The example, however, might also serve as "the exception that proves the rule." That is, even the best of educational games tend to be marginalized and channeled in the direction of extra-curricular activities. Schools pose problems in the form of puzzles, almost to the complete exclusion of problems posed in the form of games. That observation deserves serious attention because how a problem is structured makes all the difference in the world.