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'."