My entry into maths

This week, I've had a few reasons to recall a time in primary school at around age 8 or 9, when I discovered maths.  It was a discovery much like those medieval explorers who upon arriving in populated lands claimed (or had claimed on their behalf) discovery.

And so it should be.  I had travelled roads that were new to me using maps that warned me of dragons and other terrible monsters lurking in wait.  I continued going down those roads, finding dead ends, trying other routes and generally finding out new things about this maths at every turn.  I was an explorer and a discoverer!

So anyway how did I discover all of this maths that had already been discovered?

I was in year 4, which was called year 5 I think in those days and possibly even year 2 a few years before me.  I do not know how I came to be sitting in the library while the rest of my class was elsewhere but I was there.  I'm also not sure what I was doing but I imagine some generic form of work.  My class teacher, Miss Hutchins I think, was doing number investigations or surveys with children in my class.  So it was that I got to observe these tests for an afternoon.

I only remember one of the puzzles.  There were a number of light blue blocks and a number of orange blocks and we were asked if we could tell which colour had more blocks without counting.

I must have become interested in this process at some point and started paying attention to what was happening.  I guess Miss Hutchins noticed this and so started including me in the discussions.  No one was able to do the no counting puzzle.

I came up with a way to do this perhaps 4 or 5 children into the survey.  I had been included in a few children's attempts at it and had had a lot more time to think about it than any of the other children.  I remember solving that puzzle to this day though.  I don't remember much else about the other tasks or anything else I did in that year of school.  I do remember that research had shown that preschool children were more likely to be able to work that puzzle out.  I remember my teacher commented to my mum that since that day I seemed to like her more than I had previously.  I did not at the time have the impression that I was good at maths or smart.  At some point after that, I did but I don't know how much of an impact that test had in creating this impression for me. But it seems like a turning point to me now.

I have put together a story something like the following to make sense of this event.  I learnt something fundamental about numbers.  So fundamental that it was too easy to teach. But an idea that with out some degree of meditation on it, without the process of coming up with it yourself to solve a problem, you might not be able to discover as an important idea.  Because you have far more sophisticated tools to work with numbers, you could take the foundation upon which they are build for granted and lose much of the ability to create something new in mathematics.  I really am thankful to Miss Hutchins.  I can't imagine that I was aware of that at the time but must have shown it on some level.  Maybe just being aware that someone had taken an interest in me and I had been able to reward their faith in me.  I don't know but I remember her favourably to this day.

The idea has been with me ever since as well as the appreciation for understanding the fundamentals of whatever it is that I'm pursuing.  This is an aspect of maths education that I feel is not as well supported.  Fairly easy to understand why.  How would you get students to value for example, exploring why 2 + 2 equals 4?  It takes real insight to see the importance of this kind of investigation unless you have a problem you are interested in that requires that understanding.

Whilst preparing a programme on number sense and doing some consultancy with a young lady who is having trouble finding and activating her mathematical tools, I thought more about this and discussed it with a few people.  I have a sense of the power that I was given at that time though I'm sure that it was not a single event as in my story nor can it be used to solve everyone's problems in maths.  It holds some important lessons that I intend to delve into further.  I'd love to hear if anyone uses activities or has a programme that focusses on the real fundamentals of maths also.  Maybe even a discussion of what the fundamentals of maths are.