It is a common practise in schools to directly teach children how to, say add, subtract or find the HCF or LCM and only after that a set of word problems which deal with the same sum is given to them to solve – which is so unchallenging!
These are not the stories that I am talking about. Because they pose no challenge and are just an appendage to the main topic that they learn.
In fact children find their own creative and intelligent ways to address these unchallenging ‘word problems’. If the numbers are similar and large, then they subject them to addition or subtraction, if they are similar but smaller then they multiply them up and if one is way too large than the other then they just divide the larger with the smaller.
Take for instance this story, telling them that at a party there were 25 chairs. Every 3rd chair had a chocolate hidden under it and every 5th chair had a balloon under it. Which chair would have both the chocolate and the balloon under it. Again children would find many ways of doing this. Some would actually draw tally marks for chairs and mark them out, while others would skip count in their minds, whatever, it is a problem solving process and the child must be encouraged to solve it on his own even if it takes time. Thinking cannot be fast or slow. It is a mental process and the child may be making many mental trial and errors before she hits upon the solution. At this point I must mention that drawing a sum has huge advantages. There are children who will understand a story sum when they visualise the statements and draw them.
The above was an example of LCM sum, but if you ask the 10 year old to carry out the LCM, he will be flummoxed. Words like multiples, common, least, etc are new to his or her vocabulary and have not been experienced by them in their daily life. But if you say which chair had both the balloon and the chocolate, it is very easy for them to understand. They may employ multiplication to find the common multiples, or they may not – but they would understand the concept and see patterns emerge. This is called inductive thinking and requires some time as this is process of discovery of patterns. After all math is about patterns.