The tower of...

I had thought that if one could convey the very basic principles then so much of science can be explained so easily. For example, if fundamentals of electromagnetic spectrum can be laid-out then so many things can be readily understood (I don't mean to start from Maxwell's euqations, but that light in any form can be understood with a single concept of EM spectrum).

This, I found doesn't work in the class. Children simply fail to sense the magnitude of how fundamental the electromagnetics is. They are unable to see the path which appears to us as a grand short-cut from our learned point-of-view. To that extent a subject-expert may have a disadvantage in the class-room.

For most part, your goal in the class is not to unify information (that comes later) but to demonstrate the diversity of phenomena. In the present example, one will have to show students various things that happen to the light first-hand from radio waves to x-rays.

While its the business of science to unify diverse phenomena into smaller set of fundamental rules, the full sense and understanding of this comes only as a hind-sight. For most of the school life the focus is only on one brick at-a-time and view of the tower to be built. The tower of knowledge has to be constructed brick-by-brick, lots of bricks.

Small numbers...

In any class there is spread in abilities of children. They fall in three broad categories 1. Above average, 2. Average and 3. Bellow average.

In a smaller-sized class, the difference in their abilities stands out markedly. And there are small number of students in each of the three categories. This makes it harder for a teacher to adopt a single strategy which works for all. Any strategy will discount at least two of these three group of students.

In a large class, the number of students in the average category is large (middle of the Bell-curve) compared to those in the other two categories. A teacher can adopt a strategy which benefits maximum number of students; those in the middle of the distribution.

Thus I think the size of the class affects quality of learning (and teaching) and interestingly bigger class sizes may stand to benefit more. At least this effect is counter our perception of smaller the class is better. Obvious question is, What is the optimal size of a class for a teacher with given resource, time and ability, so that maximum students can benefit without compromising quality ?

PS : I don't imply that one should leave out above and below average students. We do need to challenge the above average students and give additional help to the bellow average students. But a single teacher can't have three strategies going on at the same time in a class.

Together we....

Its a very different experience to observe a class in choir practice. They are all singing together in-tune and in-rhythm, engrossed and taking cue from the conductor/teacher's hand. Their own collective voice makes them quiet and focused. If only one could get such behavior in the maths classes then so much more can be done.

However in many ways aims of choir and maths are in opposition. While in choir, we would like all to sing one note in sync, in maths we would like children to have varied response and approach. Further, there is no telling what thoughts would occur to different children. One would encourage a variety of explanations and methods of doing same problem. It would be full of kids questioning teacher and each other. So in many ways a maths class can never be like choir practice.

The great feeling that one gets from being together in choir has to come in maths class from collectively discovering inner workings of maths.