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.

Knock-Knock !

Typically, some children seem to be decoupled from the whatever is happening in the class. Albeit they are small in number, but still worrisome. Its not like they are trouble maker. I wish they were, for then I could engage them one way or other. They seem disinterested in whatever goes on in the class. I have a feeling that this is not wholly due to quality of teaching or bad schooling - but something larger happening in childrens' lives .

May be we are over simulating them with all the audio, video, brightly colored life. They have seen the best, the costliest, the fanciest and coolest things. Real life must appears too dull to them. Consider then how History or Maths text book would appear to them.

It is harder now for a Teacher to turn around these children. In a job which is already extremely demanding it has become near impossible to turn around decoupled children.

Whatever this trend is, it is less present in the younger children and the apathy seem to be gradually growing upon them. So may be there is a clue in this some where.

It's getting real !

I have seen that these days children (age 8 yrs and above) prefer realistic stories like adventures or exploration (like Bribal-Badashah or Famous Five etc) as compared to make-believe stories (like when animals talk or wild things happen).

A librarian confirmed my hunch when she said - over the years the pattern of books borrowed by children has changed towards realistic books.

If this is true then its sad, as children probably aren't exercising ability to imagine or believe in things - as a thought experiment. They want it 'as-it-is'. May be they will lose out on model building or imagining scenarios.

[ I think Cinderella and Harry Potter exceptions are created by media. They are selling more, not as books, but as advertised products . ]

Marking with a difference

Why are we giving marks to the answers and assignments ? Only a minority of students take a clue from their poor marks and work hard to improve on specific skills (if ever we tell them what those skills are).

We know very well that absolute performance has a wide spread in any class, so it hardly helps if one child gets 2 out-of 10 and another 9 out-of 10. The good grades of one child don't percolate to another child like osmosis !

Percentile is even worse way to evaluate a child (compared to absolute marks) as it enhances the competency differences and has less to do with progress of each child. These marking schemes are like a fuzzy snap-shot of progress in time.

It's the progress per child that we want to track and not the absolute performance.

So shouldn't we be giving marks for how much a child has improved on the Simple Evaluation Metric (SEM) between the last assignment (the slope of the gradient) and the current one ? Larger the improvement greater the n, e, s score.

The marks should say - you have improved n, on neatness; e, on English; and s, on Subject understanding - between the last assignment and the current assignment !.

• So a good teacher is one whose class has high average <n>, <e> and <s>, averaged over all the students over one academic year
• A good school is where average <n>, <e> and <s> is high for all students, all classes.

Its a place where all students do far better, as compared to themselves, year after year.