Are computers a natural medium for mathematics?

One of the reasons I both love and hate twitter! I am casually flicking through some pages over breakfast and I happen on this blog post from Dan Meyer. In fairness the blog post seemed mostly to point out how helping mathematics education has not ever risen to the top of silicon valley's priority list. Whilst this is an interesting question, it was the question phrased in the title above that caught my attention. I love this because it is great when some one else's writing makes you stop and think - I hate it when the question pre-occupies your mind when you are trying to do other things. The result is that I am writing this long after I should be asleep, getting ready for tomorrow. Anyway, I think the below can stand alone, but can be put in to context by reading the blog post linked above. This was the response I left on the blog post.

As #57 says, who is still reading! I find though that putting these thoughts and reactions in writing is mostly only for my own benefit! In this case, it is because, whilst I understand and sympathise with the general view being expressed, I think I actually disagree with the statement about 'natural medium'! I read most of the responses and scanned the rest but the response from David Wees came closest to my reaction when he said '

'There are some tasks for which computers are perfectly suited in terms of mathematics'

and

'What you have suggested is that they are less than ideal for the quick communication of mathematics, and for deeper assessment of what mathematics students understand.'

Regarding the first point....

My relatively short teaching career (13 years) has spanned 'almost no access to computers' to 'working with a one to one program at my current school'. There is no doubt in my mind that computers have had a hugely significant effect on the way mathematics can be taught and, more importantly, discovered, because they provide a considerably more natural, able and versatile medium. A lengthy description of cases could follow, but I will limit myself to just a few...

Dynamic geometry, as has been mentioned by some already. This tool has done amazing things for helping teachers to create opportunities for students to make discoveries on their own and thus engage with mathematics. It can go beyond the teaching of geometry as well. Examples of activities  Indestructible Quadrilaterals   Circle Theorems ,  Trig Calculator all of these activities involve students creating mathematical objects in the medium of dynamic geometry.

Graphing software - largely by labour saving, but also through dynamic functionality - these tools as well have created new opportunities for exploring relationships. Examples of activities  Olympic Records ,  Straight Line Graphs 

Data Handing - This has come to life through computers with access to real, live data, the functionality to collect it and the ability to process it. All this means that the nature of data handling tasks can now vary in new ways. (I will not say 'more mathematical ways' although that it is what I think.) Examples of activities ,  Dynamic scatter graphs 

As suggested, I could go on and will in my head!

Regarding the second point....

Yes I agree that progress is slow on more able and intuitive user interfaces for communicating mathematics. I think that this has worked in our favour as teachers though. For example, taking the fractions, modern calculators now make it much easier to input and work with fractions than it used to be and this may have resulted in a poorer understanding of what fractions actually mean. The fact that computers don't find it easy to accept fractions means that users have to think about what the fraction actually means in order to input it. A fraction is easily written on a piece of paper with no understanding of its meaning.

Likewise, when programming with dynamic geometry (and I do consider constructions a type of programming), there is no 'rectangle tool', in order to construct one you have to know that a rectangle is made by two pairs of parallel sides intersecting at right angles. When you program it correctly it will always be a rectangle regardless of which points are moved. The process of drawing a rectangle on a piece of paper is not at all the same.

In summary, don't get me wrong, I estimate that computers are used for about 50% of our lesson time and I am a committed believer in variety of tasks that range from the pencil and paper, to the practical, to the virtual. That said, I am a passionate supporter of what computers have done for mathematics education. I am also a relatively new blogger and always have a sense of fear when 'submitting' such responses. I think most bloggers understand that expressing your views and reactions is the best way to develop them, so thanks Dan for making me think! Apologies if I have missed the point somewhere along the line, I feel better for writing this down either way.