Children and Numbers - My Belief

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Children and Numbers – My belief
It is my long-held belief that all children start out as capable mathematicians.  They see the patterns and problems around them.  They love sorting, grouping and noticing.  They love the pattern-based nature of numbers and absolutely love counting out loud.  If you listen to pre-school children playing, a lot of their discussions would be classified as ‘mathematical’ in nature.  They have no pre-conceived idea that mathematics is hard; it is the way we approach the teaching of it that gives them that idea.  To children, mathematical thinking comes naturally and it is that innate ability that our mathematics programmes need to harness.  Our teaching should not stem from what they do not know, but from the known.  We need to use the playful way children have always used to explore ‘mathematical’ concepts and build on these, introducing and guiding new concepts through play.  This approach leads to confident mathematical thinkers, who believe they can ‘do’ maths.  The ‘level’ of the children I teach never limits me.  If our discussion and activity for the day leads into concepts that may appear beyond the age of the children in the class or stage that they are at, I don’t let this stop me.  Talking about concepts that may appear hard for them at the time leads children to build up a certain pre-knowledge, so they later think that these are things they do know, and they are not hard.  An example here is place value.  Within my level, place value learning consists of learning about 10, making and using a ten.  However, if through our explorations we come across larger numbers, we will explore the place value of these, and how they fit together. I believe children need to be given the big picture in mathematics to see where their learning ‘fits.’
My teaching in maths also sits well alongside the teaching of a growth mindset.  Too often children are put off maths because it seems hard, they don’t believe they can do it and they give up.  They can’t see the pattern, the reason for it, and have not been given the ins and outs of how everything fits together.  We often fail to relate mathematical concepts to their own language of play and this creates a disconnect between what children have learned through exploring their world and the abstract world of numbers we are introducing them to.  Through everyday teaching and learning, we need to foster the concept of a growth mindset; children need to see that the struggle is part of the learning; that mistakes are more than ok, and that the brain is like a muscle.  My favourite word is ‘yet.’  “I may not be able to do this yet, but I will get there if I persist.”  Reflection is huge; reflecting on mistakes, what we can do differently, reflecting through discussion, actually allowing children to deliberately talk about where they went wrong and what they could do next time.  Too often children start to think that they have to ‘fix’ their answer, or that the answer they have written needs to be correct 100% of the time. If we can rejoice in our mistakes and build reflection into our programme, we will create learners who will strive to get it right, but if they don’t they will accept this easily and will not be embarrassed about it.  They will not be the ones peering over the shoulders of their peers for the answer, or madly scribbling out what they have written because they are embarrassed that it is “not right.”  It is important that children learn to enjoy the struggle. It is the struggle that creates the learner and creates a superb learning disposition that will see them succeed. 
I believe we are so intent on filling gaps in maths that we have lost sight of the fact that through mathematical exploration children fill in their own gaps.  When given authentic situations in which to explore concepts, children will begin to see how everything fits together.  How often have you struggled with something, not understood how it all works, then been given an authentic situation where everything falls into place when you actually ‘need’ that piece of knowledge? I know it happens to me all the time. 

I am not saying that the teaching of knowledge has no place. Don’t get me wrong; there are essential pieces of knowledge along the way that all children need to have if they are to operate as confident mathematicians.  But don’t hold them back if they don’t have certain knowledge.  Don’t put them in the ‘bottom’ group and leave them there, repeating the same learning over and over.  Put mathematical problems in front of them, allow them to struggle and watch those knowledge concepts suddenly make sense to them…watch the light bulb moments when for example a child who is learning to read numbers to ten suddenly realizes that this abstract scribble actually relates to the number of cows he needs to have in the farmer’s paddock.  Have faith that by putting authentic learning situations in front of them, the knowledge that is required to successfully work out the problem will eventually make sense. 

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