Children Have Their Own Strategies For Learning
Vibhor, aged 7, was once asked if he knew what 'seven lots of eight' are. He said he didn't. He was then asked, "Can you work it out?" There was a long pause. Then Vibhor said, "56". "How did you get that?" "Well", answered Vibhor, "ten eights is 80. Then take away 8, that is 72, again take away 8, 64, take away 8, 56."
Shanta, a Class 3 child, was asked to solve 189 - 67. She said it was 3 + 30 + 89, that is, 122. This strategy of hers, was considered 'wrong' by her teacher, because his method to get the answer was '189 take away 7, take away 60'.
Discouraging children from evolving their own strategies results in blocking their ability to think, to build connections and look for patterns in mathematics.
Instead, they learn mathematics as a series of disconnected and meaningless facts and rules to be blindly memorised and applied (for example, the multiplication tables).
If you allow children to solve mathematical problems by their own methods, you would find an amazing variety of thought processes. Consider what this friend of mine has to say.
"While teaching children mathematics, I have often been surprised by the manner in which children arrive at answers to questions. Between the problem and the answer there is a string of arguments and logic which is often a creation of the child. I once taught children multiplication of a two-digit number by a two-digit number. I worked out a few examples and explained the algorithm to them a number of times. Then I gave them the problem, 12×13 The first child to report having done the problem gave the answer 156. On looking at her notebook I found the answer written just below the problem. I asked the child for the rough work She produced the following figures 100 20 30 6. On repeated questioning the girl said, "I multiplied 10 by 10 first, and then 2 by 10, and so on."
On another occasion I was doing problems in simple interest that involved finding out the rate of interest. Giving them a problem, I was just beginning to relax when a hand shot up. I was amazed at the speed, and asked for the answer.
He gave the correct reply, 5%. I mentally patted myself for a successful presentation of the complex algorithms. Then I suddenly thought, "Let me look at the notebook and find out how he has solved the question." There was a lingering doubt in my mind that he was perhaps coached at home. The child came with a blank notebook I asked him where he had solved the problem. "Oh! I solved it using what you had said yesterday", he said. "You had said that banks give 5% interest on money deposited." "
What do you deduce from these two examples? Would you agree that they add to the evidence that children develop their own strategies to solve problems?
They may either be correct or wrong, from the adult's point of view. But, for the child they are always correct. A child continues modifying old strategies and developing new ones to match and understand her mathematical experiences.
Given the right environment, this process goes on, and enables the child to become capable of doing and thinking mathematics naturally. But forcing children to follow one single strategy, without deviation or creativity, gradually dampens their urge and ability to create their own strategies and conceptual thinking.