Seeing the forest for the trees in Maths

I have been accused of not seeing the forest for the trees. That I seem to have to know about each tree and how it fits into the forest before I know the forest. I will admit that I need to know 'why' before 'how'. I recently had an uncomfortable discussion with a colleague about teaching time to my early years class. It was uncomfortable because like many things I am passionate about, which is most things, I can get into what might be politely described as a rant. My poor colleague really didn't know what he had let himself in for.

I have found that many students become confused by decimals in relation to fractions and percentages. I personally can't see the point of expressing numbers as relationships. Fractions are numbers expressed as a division. Percentages are simply numbers expressed as a product of themselves and 100 (why?) I especially don't see the need to confuse small children with these relationships. Yet we do this early in their formal education.

For example when we teach time.

Time is expressed in hours, minutes and seconds. Today we frequently speak about time digitally. 'Seven, fifty five' is probably spoken as commonly as 'five to eight' for example, so why the necessity to teach year 2 students 'half past'?

I don't.

I teach my students the number of hours and the number of minutes. Once my students can understand counting by fives. That is the continuous addition of five plus five plus five etc. If they understand this concept we can hit the analogue clock. Yet there is an expectation that you teach 'o'clock' and then 'half past'. 'Half' what does that mean to a child of six or seven?

 Does it mean 1divided by 2?

 As they are only just experiencing the basic principles of sharing - I highly doubt it.

They think of 'half' as putting a line down the middle-ish of an object (generally a symmetrical representation of an object like a smiling clown face or a pizza) and you colour in one side - half. You write half like '1/2' but do they know why? Of course not.

So theses students experience of 'the forest' of learning the time with all these wonderful terms, with  a vague idea of their meaning, making up 'the trees'.

So perhaps a tree then forest approach might be a valid method at times.

When I am helping older students who are completely 'bamboozled' by fractions I ask them " Do you know what that little line is between the numbers?" They never do.

 "It isn't anything magical it just means 'divided by'."

School Holidays and ASD Kids

Sometimes the school holidays don't seem long enough. Two more days and we are back at the chalk face. It has been an interesting time being with my kids and a few hundred Scouts.

Of my own eight children, three are somewhere on the Spectrum. Each is unique. Diagnosis for all of us came late. My second eldest son was really the test dummy as far as managing the issues that arise when you are on the Spectrum. He is now twenty and not officially diagnosed but he was the start of this journey.

There is a tyranny caused by being different but not so obviously different that you are judged  to  have control of your more eccentric behaviours. My son's behaviours were blamed on my parenting and the trauma of going through a divorce. I could not convince the therapists that we saw, that my son has always had these behaviours and they were not typical.

He was a man/child ie  a man trapped in the body of a child. He didn't play and still prefers the company of older adults, particularly mechanically-minded, practical men. He is a very clever, respectful and the most hardworking person I know. His public persona is carefully managed. The stress this causes him makes his home persona more like Mr Hyde. Though after twenty years he has learned strategies to self regulate. Only after much provocation does he ever have a public melt-down. These are doozies and embarrass him to the point that he shuns public appearances for months.

My ten year old daughter is a different personality. When she gets overloaded from being in social situations the changes in the tone of her voice give her temperament away. A loud, witchy voice and she is reaching her tipping point. She also is the most sensitive to touch, and smells. Yet she scratches herself and used to rub her food on her lips before eating it. She has a fetish for  Huggies Baby Wipes and she relates better to animals than people, as long as she can stand their smell.

My eight year old son is very academic. He taught himself to read very young. He is great at maths and is a spelling whizz. He has a vivid imagination and gets scared by books and movies. Even those rated G. He has the more Hollywood version of ASD, a miniature Sheldon. He was the first to get officially diagnosed when he was five, as requested by his school teacher.

So in the course of these school holidays we have been shopping in a strange town, been squashed in a queue at the cinema, been in a competitive community event and spent far too long in the car. Oh and had visitors. These have all been challenges and though we have come through mostly unscathed it does remind me that my ASD kids have to work that little bit harder.