Sunday, 7 May 2017

What is the place of facts in mathematics?


Friday Night Reflections

Last Friday evening I caught up with a few friends who I hadn't had a chance to spend any quality time with recently.

After we had solved the world's problems and analysed the youth of today, one of my friends came out with a very provocative statement:

"I think 'facts' are given too much importance in science," he said, or words to that effect. 

Now, let me say that the gathered assembly that totalled 4 people comprised science or maths educators (x4), well educated science graduates (x3), current or former president's of state professional associations (x2), and of course the mandatory partridge in a pear tree. You can use a Venn diagram to solve that one kids.

So this provocative statement about 'facts' soon generated some passionate discussion.

And three days later I am still thinking about it. 

And I think I agree - 'facts' ARE given too much importance:

  • not because I am pushing some sort of anti-intellectual glorification of ignorance agenda

  • not because of any Trump-esque view that 'facts' are subjective (although context and interpretation are always critical in understanding facts)

  • not because I am advocating a free-form content-less maths curriculum

BUT (and here is my big BUT)

  • because I believe that 'facts' - and this includes 'maths facts' - are just a starting point. 

What are these 'facts' of which you speak?

When I am talking about 'maths facts', these are a few of the things to which I am referring:
  • addition and subtraction facts
  • times tables facts
  • formulae
  • processes and operations
  • arithmetic
  • symbols and representations
  • notation
These things are often presented as "being the mathematics". When you Google for an image of "mathematics" you get chalk boards (do people still use them??) covered in squiggly notation and complex formulae. These are the things that are considered by many to "be" mathematics.

I don't think they are.

Just as an umlaut isn't the essence of German language, so too a square root sign isn't mathematics.

I think we have lost sight of the purpose of mathematics - to make life better/simpler/more beautiful. This purpose has been obscured by......'facts'.

So what then IS the place of facts in mathematics?

Let me back pedal a little to explain my position:
  • yes - it is useful to know the 'facts' - it is more efficient to know them rather than having to invent them each time I want to use them. 
  • yes - I still teach them to the kids in my class (where 'teach' means explore, play, investigate, pull apart and reconstruct - as well as memorise)
  • yes - a component of assessment needs to consider the mastery of 'facts' and 'skills'.

BUT (and here is my big BUT again)

1. These maths 'facts' are just the starting point. 

They are not the end in themselves. If my assessment is purely based on a student's ability to crunch numbers, recall formulae and perform calculations, then it is a pretty thin type of assessment.

2. 'Facts' need to be useful to make sense of a context. 

And the context is useful to make sense of the facts. 
Here is a fact - water boils at 100 degrees celsius.
Ah - except when...

3. There are bigger things than 'facts'

There are some 'big ideas' that are at the heart of education, things that we need to explore and consider on a daily basis. Things such as:
  • connection
  • equality
  • consistency
  • representation
  • form
  • function
  • cause and effect
  • (insert your favourite concepts here)
These are the things that I am hoping to get my 8 year olds to explore and dissect in the short time that they are with me. It is these things that I want them to know about. These are things that I want them to start analysing - using 'facts', but developing understanding.

Thanks to my PLN and the provocation last Friday night. Hopefully some of this makes sense - or at least provokes some thinking.

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