Where did that elephant come from?

And I swear I did not discuss the Mathematical Elephant with my class....

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.

Mathematics is like an elephant

I'm coming to the conclusion that one of the biggest challenges in high school mathematics (and probably university mathematics too) is coming to grips with the fact that in so many different ways, mathematics is very much like an elephant.

Mathematics is like an elephant? Well yes - if you think about the story of the blind men and the elephant - depending on what part of the animal you feel, you get a very different idea of what an elephant is.  There are so many different aspects and representations in mathematics, that it's all too easy for both teachers and students to be so focused on the particulars of the trunk, the tusks, the ears or the tail - and fail to see the whole elephant.

 Based on Sophie Woods (1916), World Stories for Children

Another way in which mathematics is like an elephant is it can be a little terrifying to come to grips with. I remember going with my little 3 year old brother to zoo and he screamed blue murder when he saw the elephant. For some students, the experience of that elephant is like this amazing 1888 Japanese print of the blind men and the elephant story- which is just too special to even consider vandalising with cartoon bubbles onto....

http://commons.wikimedia.org/wiki/File:Blind_monks_examining_an_elephant.jpg

And maybe sometimes that's why as teachers we wrap those blindfolds on our students (and ourselves) and just hand the class a trunk or an ear to be examined. But the risk is, in the end, our students wonder why they are doing repeated exercises, year after year, on all these separate, unconnected body parts.

To work mathematically, you need to smell the whole elephant, hear its roar - and take pleasure in its beauty, strength and also its surprising grace and subtlety.  And if we don't want to scare the children? Well, who can resist a baby elephant?

Source: Matt Stanford (flickr)

In coming posts, I'll be considering other elephant aspects of mathematics, and what the elephant looks like when it's distributed in the Cloud....