The Mathematical Elephant - really?

Some email responses from friends, colleagues and people wiser and more experienced than myself have suggested I've perhaps overplayed the importance of working with the "whole mathematical elephant" - that there are even more critical aspects of maths education we need to come to grips with. 

Mary Barnes suggested that more important than showing the whole elephant is "the need to evoke curiosity, surprise, amazement (or amusement)".  How many of our maths lessons involve these elements? It is by creating an environment for students to experience these things that they may then want to see more of the elephant.

How's this for curiosity, surprise and amazement?
Mind you - I prefer my elephants in the wild - I think they are even more surprising there.
http://commons.wikimedia.org/

Mary also suggests another key element is working out how to encourage ongoing, continuous effort: "But learning/doing maths also requires effort, and to make effort worthwhile there needs to be a payoff. For most kids (and adults) the satisfaction of solving a problem or understanding a new idea is not sufficient payoff for the effort they have to put in to get there." For some time now, I've been a strong advocate of real-life based mathematics, especially in a science context (can't help myself) - but another part of me says we also shouldn't totally give up on trying to share the conceptual, abstract joys of mathematics with students.  With respect to effort, my "mathematics is an elephant" metaphor makes me think of 22-month gestation period of an elephant - although I don't think that's going to help my student very much.

  

Ultrasound of 3 month elephant foetus (Whipsnade Zoo, UK)
http://www.zsl.org/zsl-whipsnade-zoo/news/jumbo-ultrasound-at-zsl-whipsnade-zoo,765,NS.html

I would argue though that by not showing the wider, connected view of mathematics, and its connectedness the rest of the world , we make the task seem so much more arduous, arbitrary and without direction.

Several people also highlighted the perennial student question about the relevance of mathematics: "What's the point of this? What is the value? And can't computers do all this anyway?". The other day as I was typing a simple mathematical equation in Microsoft Word 2010, I was stunned to see the program proceed to auto-correct by inserting the answer! There's going to be repercussions in the classroom when students realise just how much even their text editor can do! I can't think of a mathematical elephant response to this challenge ... yet - except that elephants can be very sneaky.

And last but not least, is the challenge of needing to build up skills, layer upon layer, year after year. Unlike other subjects, we can't just do a topic and move on - if a student misses a part of the mental construction, their building will be shaky indeed.

So putting it all together - I'll concede my mathematical elephant metaphor isn't the most useful pedagogically - but just perhaps it might help us think a little about how we approach our subject - and the many complex, fascinating and interconnected aspects of maths, education and students. Next time you go to grasp a trunk or an ear, don't forget there is a whole elephant that might be worth revealing in the context of the problem.