The American obsession with egalitarianism (or equality, or whatever one wishes to call it) tends to suffer from a certain fuzziness about exactly what we are supposed to be equating (or equalizing). For all I know, the same thing happens in other countries. I don't know so much about it, though, so I will focus on the situation in America, where egalitarianism is championed but very rarely defined.

Suppose I were a math teacher in a secondary school. Most people would enthusiastically agree that I should treat males and females equally. Knowledgeable people might point out that math teachers have at times behaved in ways that explicitly or implicitly discouraged females from pursuing mathematics. Other people might suggest that I be videotaped so that I and others can review my performance to ensure that I really am treating people equally.

Fewer people would be able to provide an operational definition of the word "equally." But if I am a teacher, this question is central. I need to know how I should act when I enter the classroom each day. How precisely should I behave to satisfy the requirements of equality?

Perhaps I should try to make sure that my responses to females are identical to my responses to males. It so happens that I am a reasonable actor; therefore, I can craft a standardized, preset response to a student (male or female) who commits a careless error while completing a problem on the blackboard. I would look it over, frown slightly, and ask the student to check his or her work, adopting a slightly chastising tone that suggests that he or she is really a better student than that and should be more careful. I believe that I can use the same words, the same facial expressions, and the same tone each time.

I suspect, however, that males and females might react in different ways to this treatment (on average--of course there will be exceptions). If a female student really has gathered the impression that math is for boys, perhaps she will find my criticism quite devastating; perhaps it will reinforce a stereotype that I would rather combat. Perhaps a male will not be so devastated--perhaps instead he will shake his head, grumble at what a nitpicky bastard I am, and fix the mistake. Conversely, if I use a much gentler and more comforting tone, the females might find it less devastating (again, on average), while the males might dismiss me as a softy.

If my students react in either of these ways, I have established equality of treatment, but not equality of outcomes. This problem stems from the basic truth that different people respond differently to the same stimulus. Incidentally, we need not posit gender differences in responses--if I were teaching a class comprised entirely of females, I would still expect a diversity of responses to a given approach.

I could try to create equality of outcomes, but it would seem to require inequality of treatment. I could, for example, tend to chastise the males while supporting the females. Better still, I could avoid treating students by gender and tailor my response to the individual student, chastising students who would benefit from chastisement and comforting students who would benefit from comfort.

Anyone who has ever dealt with children--a category that seems to exclude certain educational researchers--will know that kids will immediately pick up on differential treatment and demand to know the reasons for its existence. Individual students may take something of an extreme view and wonder why they have been singled out for abuse or coddling. Worst of all, even if I try to fit my responses to a particular student, instead of a particular gender, it might still be the case that I end up chastising more males than females, and comforting more females than males. Students will notice this too. If their parents hear about it, I will of course be in deep politically-correct doo-doo.

Demanding equality without defining it is like asking my math students to solve an equation with no terms on either side. It is a logical impossibility, and creates a problem with no hope of a solution.