How many levels should there be?

“I don’t want to stay in Honors Geometry. It’s too difficult!”

“I’m bored in regular Geometry. It’s too easy!”

We hear remarks like these from a sprinkling of students — sometimes both of them  from the same student — usually someone who has moved down a level to escape from an honors course and now finds the new course unchallenging. What’s the right thing to do? I’ll continue to use geometry as an example here, but my arguments apply to almost all math courses.

Many schools offer a variety of levels of the same math course — perhaps two levels of geometry, or three, or even seven. Other schools offer classes that are completely heterogenous, with all students mixed together. So what’s the optimal number of levels? One? Two? Five? The fictitious (but all too real) student quoted above is unhappy with having to choose from only two levels and wants a third level, in between regular (college-prep) and honors. Such students, and their parents, often ask for a third level.

I’ve been in schools that offer three levels of geometry: level 1 (honors), level 2 (college-prep), and level 3 (basic). There are just as many students who complain that level is too hard and level n+1 is too easy.

I’ve been in schools that offer four levels of geometry: level 1 (honors), level 2 (accelerated), level 3 (college-prep), and level 4 (basic). There are just as many students who complain that level is too hard and level n+1 is too easy.

You get the idea. My first reply to those who complain that they fall through the cracks between two levels is that we can’t win. No matter how many levels we have, someone is going to play Goldilocks and say that this is too hard and that is too easy and the one level we don’t happen to have would be just right. But, as the Rolling Stones observed, you can’t always get what you want, even in Lake Wobegon…or should I say Weston?

Then I go on to explain three other reasons why we have concluded that two levels of each math course is the right number. We shouldn’t have a third because…

  1. As I say, I’ve been in schools with three levels. In fact, that’s what Weston had when I arrived there in 1997. The effect is that the lowest level is a disaster: students in that class see no role models of successful students, since anyone who is sufficiently motivated will insist in moving up to level 2.
  2. Scheduling becomes a disaster, at least in a small high school. By increasing the number of courses, we would automatically decrease the number of sections in each course. It’s already hard enough to juggle kids’s schedules to give them the courses they want/need.
  3. Finally, a related but subtler point concerns teamwork. A good part of the success of the Math Department at schools like Weston is the teamwork among teachers of the same course. We exchange ideas, plan together, give some common assessments, look at student work together, help each other’s students, and share the task of writing and revising worksheets. All of these give a significant boost to the quality of our instruction and the quality of student learning. If we had 50% more levels, a lot of courses would have only one or two sections, which would be taught by only one teacher. The tremendous advantages of teamwork would go out the window.

So, we have four reasons why we shouldn’t have a third level: the fact that “you can’t win” anyway, the need to provide role models in every class, the task of making schedules that work, and the benefits of teamwork.

All of this might suggest that we should abolish levels altogether and have completely heterogenous classes. I’ll save the argument against that proposal for another post.


Categories: Teaching & Learning, Weston