23 June 2014

Shortcuts vs Concept Development

I highly recommend this book Nix the Tricks - ‘a guide to avoiding shortcuts that cut out math concept development’. I felt uncomfortable reading it at times - my own teaching is full of these tricks and shortcuts because I’m strongly influenced by the time pressures and exam focus that the author references in her introduction. The book covers a great many teaching tricks and in each case makes excellent points about why these tricks should be avoided. Helpfully, alternative approaches are suggested. I’m not going to stop using crocodile references when introducing inequality symbols (I like the crocodiles!) and I'm not (yet) going to stop teaching gradient as 'rise over run', but I will certainly think twice about many of my methods now I’ve read this book.

My blog focuses on sharing teaching ideas and some of my posts include exactly the kind of shortcuts that this book is so opposed to - like sohcahtoa triangles, or this trick for remembering exact values of trigonometric ratios (which doesn’t replace the triangle method - but it's a nice trick and worth sharing).

It was my excitement at discovering this method for multiplying matrices that inspired me to write this blog. I was astounded that I’d never seen this method before and immediately showed it to my FP1 students, who were equally impressed. I mentioned this method to a colleague, prompting a conversation about other 'alternative methods' we knew of. She told me about this method for finding Highest Common Factors. Again, I was astonished that I’d been happily teaching the Venn method - which I’d learnt from my mentor during a PGCE placement - when a quicker and easier method existed. I felt like I'd unnecessarily overcomplicated things for my students.

We all know that quicker methods aren’t always better methods. ‘Maths hacks’ such as these and shortcuts (such as those discussed in Tina Cardone's book) do nothing to help students’ underlying understanding of mathematics. But I still believe there's value in teachers sharing tips and alternative methods because sometimes we discover hidden gems - like the wonderful matrices method - that change the way we teach a topic for the better.

By the way, if you enjoy the book then there's more (including new sections in draft) on nixthetricks.com.