Worked Examples

Michael Pershan's book 'Teaching Math With Examples' was one of many books I'd purchased and not got around to reading. My better half hates me for it, but at least I'm not buying golf clubs any more! A long car journey to Legoland gave me an opportunity in the summer, but my 4 year old had other plans. One chapter on, and put on hold for a few months.
Since then she's started swimming lessons and I've managed to read a bit while she swims, and whilst watching a film on Christmas Day I managed to get through the rest!

I found it to be thought-provoking and enjoyable. Michael's writing style is accessible, even to someone who finds it difficult to pick a book up and stick with it, and ultimately, I've been convinced to bring worked examples into my lessons as part of my repertoire.
I think that pupils need a broad and balanced diet in their education, and if it would be appropriate for me to introduce an idea with a worked example, rather than through the standard method of me telling them stuff or an inquiry approach, then great!

My main take away from the book is that pupils won't learn unless they're thinking. This is a common theme through CPD I've taken in lately and arcs back to Willingham's "Memory is the residue of thought" quote.
For me, it means that automaticity needs to be broken to encourage thought, taking pupils out of autopilot and their normal routine by doing something different, or asking a different question where it might not be expected, and making changes to how ideas are shared is a simple way in which to do this. 

I'm thinking mostly about using them to introduce an idea - during the early acquisition phase. Maybe to introduce a new formula, so pupils see a formula and its use simultaneously, or to introduce a simple procedure so that I don't oversimplify things in my own explanations and pupils engage with, and think about, this new idea fully.
Having introduced a formula through worked examples, problem solving tasks can then build upon the new knowledge. This way pupils have had the opportunity to learn something new in a different way to how we'll discuss problem solving - rather than me always verbally telling them something, then them working on it, and repeat.
But what about multiple methods to do the same thing? Well, we can present these as worked examples side-by-side, referred to as 'case comparisons'. This will give pupils the opportunity to idea what's the same and what's different between the methods to develop a deeper understanding. 

An interesting piece in the book was about attributing an example to a person - fictitious or an actual person in the room - and how this can discourage pupils from using this method ("This is what Molly does, not me..."), and so I'm likely to not use names with worked examples, but to present them as either correct or incorrect. Method 1 and method 2 would work just as well as 'Dave's method' and 'Mel's method'. 

A different option I'm exploring is to use a worked example to begin problem solving, in what we call 'Red Zone conditions' - independently of others, and the hardest thing they'll do that lesson. Self-explanations will be key here, to give pupils a real opportunity to engage with the problems deeply and to develop deeper understanding. In the early stages, that's likely to require prompts to allow pupils to develop the behaviour of self explaining, which might be something like:

What was the first step?

Would it have been OK to write _____? Why/why not?

Why was _____ and _____combined?

I'm also looking at their use with incorrect worked examples to elicit understanding and reasoning. A huge part here is that they must be clearly labelled as incorrect, potentially with a giant red cross, so that pupils don't interpret them as a correct worked solution. Now, does this mean that when presenting a correct worked example, this should be labelled as so, maybe using a big green tick? 

Michael's book has also put me on the track of backwards faded examples, where an example is presented in full, with successive examples fading out the latter parts allowing pupils to build up the methods from the end backwards. This follows with the hierarchical nature of mathematics, with preceding steps being an extension of earlier developed ideas.

You can buy Michael's book from John Catt or from a more devious bookseller. 

I hope you enjoy it too.