I’m fascinated with tribal primate pecking orders. Sociologist Ronald M. Glassman, writing about the origins of democracy, says our ancestors accepted rule by the strongest to prevent constant destructive fighting. Weaker groups adjusted to lower status than stronger ones for similar reasons.

Most of us don’t look at our lives that way now, but our comfort and fascination with stratification remains strong. I see it in education issues all the time. I wonder if it might be adjusted in some cases to make schools work better than they do when the focus is on who’s at the top and who’s at the bottom.

Consider achievement gaps. Education researchers spend much time examining them. Big gaps between rich children and poor ones are considered bad, and small gaps are good. But there are instances when shrinking achievement gaps can be deceiving: It could mean children who were doing well have stopped doing so well.

Low-income students’ scores can drop, while high-income students’ scores drop even more. Low-income scores can remain steady, while high-income scores drop. The gap is narrowed in those cases, but to what end? The difference gets smaller, but somebody is still losing ground.

Why not focus on each student’s progress? Why these knee-jerk comparisons with other people who have different problems?

Three years ago, I found a study pointing out that the U.S. school district with the lowest racial achievement gap was Detroit. But Detroit’s overall achievement rate was among the worst in the country. So having a narrow achievement gap between students of different races isn’t especially encouraging if everyone is faring poorly.

The authors of that study wrote a letter to The Washington Post saying why it was wrong to ignore achievement gaps. “That’s like giving one runner a head start and saying the other runner’s complaint is unjustified,” they said. “Mr. Mathews would have us believe a race is fair as long as both runners are moving forward.”

That overlooks the fact that a school lesson is not a track meet. Each child is there to learn as much as possible, not beat the other students. I think many intelligent people, like the authors of that study, use sports metaphors in these cases instinctively because they connect so strongly to our tribal primate past. Should we tell students, as has been done in some schools, not to read any materials beyond what they are given for an assignment because that would be unfair?

Many people have told me they think “C” students should not be allowed to take Advanced Placement courses, even though the challenge often helps them and doesn’t slow down other students. Their argument: “Everyone who wants to play football doesn’t get to be on the football team.”

That’s tribal primate thinking. If you like a sport and want to get better at it, why shouldn’t you be allowed to join the team and practice with expert coaches? You might play just a few minutes in a game — if that — but those contests consume only a fraction of the time a team devotes to a sport.

My high school cross-country coach not only didn’t cut anyone, he wouldn’t let me leave when I told him all that running was uninteresting. Many coaches don’t cut players. John Gagliardi of St. John’s University in Collegeville, Minn., won a record 489 football games and four national championships without dismissing anybody.

I have suggested our most selective universities create more places for applicants by opening sister schools in other parts of the country. Some fine restaurant chains do that. Why not Yale? How about a Princeton campus in Pismo Beach, Calif.? That seems unlikely, but I see ways to reduce selectivity on a smaller scale.

I attended a college that admitted only a small fraction of applicants. Our student newspaper, following that tradition, rejected many undergraduates who wanted to participate. Making those cuts was the managing editor, whom I later married.

I remember a candidate she cut. After college, great newspapers hired him. He has written nine books so far and become one of the nation’s best-read chroniclers of American power and diplomacy. Eventually, my college paper decided to admit anyone who did a certain amount of work.

My wife doesn’t remember why she rejected the future star. His many accomplishments include being an example of how easing admission rules could be good for many of our tribes.