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.