When developing our analysis and problem solving skills the intention is to see the big picture. Often when we teach we are hoping that the children will come to our desired conclusion, however in reality they will perceive things differently and often we'll wonder at how they think.
We need to accept their thinking processes and discuss their conclusions, however invalid or inconvenient they may seem. This will allow them to express themselves. We should also encourage them to see how others think as well - this gives them a better insight into how they operate. Once they understand how they think they can start to realise we are all different and they can concentrate in understanding where their perception begins and ends.
This frees them from generic thought processes and encourages independence. If they get to the stage that they are confident in their own views then they may start to develop interests, hopefully in mathematics, that leads to active learning.
As teachers and parents I feel we should be there to guide and provide, allowing them the freedom to develop.
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