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.

How to solve a problem...

Usually, maths is taught with series of rules where - certain rules are taught to solve certain problems. As long as you learn these rules, you can solve those problems. However that doesn't mean you have understood how it works. So how to build understanding of how it works ?

I find this template from Rafe Esquith's book useful starting point for maths teaching. His steps are very practical. It's another matter as to how to get children to think like this.

• Step 1 - Put your pencil down, Collect data (what is given)
• Step 2 - Chose appropriate strategy -Act it Out, Chose an Operation, Draw a picture, Guess and check, Look for a pattern, Make a chart or table, Make a list, Reason with a partner, Work backwards
• Step 3 - Pick up your pencil, Give it a go
• Step 4 - Does the answer make sense ? No - don't worry, re-think. Yes - great you got it. Can you do it by any other method
  

This way one can build skills to look at same problem from different angles. Meta-rules can be built from which children can themselves derive rules.

But I can't draw

Drawing must be one of the first skills to erode as children grow. Up to age 9 children draw prolifically at a mere request. But ask an older child and he/she would make excuses. How much of this is due to self-awareness and how much is due to peer review ?

It is quite possible that passing remarks about your drawing starts to put you off . Or may be around this age, there is a burst in cognition of real world - as a result child realizes that his drawing can't really catch-up with the world in full detail. Thus grows the reluctance to put a pencil to paper.

Whatever may be the cause, there seems a barrier at around age 9-10 when children seem to grow out of purposeful drawing activity. Though they may continue to doodle well into their adulthood.

How old are you really !

In the last few decades, urban prosperity has made our children thrive. This investment in our childrens' health is visible in classrooms. Children are now taller, stronger and are exposed to a variety of things in the world early in their life.If you just go by their looks and talk they are like adults.

Emotionally however they are as much kids, as one would expect to be at their age. Material prosperity can't really speed-up emotional development of a child. Some times surprisingly small silly things excite them exposing their innocence.

This creates a, sort of, illusion between what you expect from their looks versus how they really behave emotionally. They are like smaller age kids trapped in the body of grown-ups, leading to a mismatch in our expectations from them.

To some extent, this may be unfairly contributing to our perception of todays generation being immature.

Point by Point ...

There are several ways to understand a concept. One of them is to "compare similar things point-by-point". Here is how you can do it,

• Collect a sample of similar things and make a list of their properties
• Which of the properties are similar ? Why ?
  
• Which of the properties are different ? Why ?
• Can you draw any generic conclusions from the comparison ?
  

If you collect roughly similar items then one can learn much by contrasting them with each other. If two things are completely dissimilar or completely similar then it dosen't tell much about their inner workings.

For example, in order to understand Earth's Atmosphere - you can compare Atmospheres of Mars, Earth and Venus - point by point. Look at their composition, structure, weather, ice, ocean cover, amount of Sunlight etc. This would generate a gut-level understanding of Earth's Atmosphere which is founded on a broader base.