Explicit Instruction

Three months into my foray into the world of blogging / twitter, I realised that my choice of twitter handle (@discoverymaths – now changed!) is more controversial than I thought! Whilst I champion guided discovery, explicit instruction still takes up more of my lesson time than discovery.

One time when the Head of my previous school observed my class, he saw a pretty standard lesson involving only explicit instruction. He said that he was impressed by my questioning and pushed me to think about how to pass on ideas to the new teachers I was mentoring. Here are my thoughts:

Everything is a question
Only add something to the class board notes once a student has said it, so all the ideas have to come from the class. Constant questioning means that you’re less likely to overestimate understanding and that pupils have to remain alert as they may be asked at any time. And on that matter…

What did Sarah just say?
This is one of my favourite questions, deployed in almost every lesson with larger classes. If you ever sense that someone isn’t listening to their peers, ask them to repeat what was just said. They’re usually pretty embarrassed if they can’t. Even if they can, it helps to reinforce important points and encourage listening skills.

Personalised
Target questions according to understanding to challenge all students appropriately. Break down the problem into many more steps than an experienced mathematician would.  This enables you to ask lower-attaining students to make small logical steps and higher attaining to come up with bigger ideas.

No opt-out
One of my mentors used to say “You have to have an idea. It doesn’t have to be a good idea, but you have to have an idea”. If you reach a total block, ask a simpler question which will help, either to the that or another student, before returning to the first student with the original question.

Bounce back
Hopefully your students will be inspired by all the questions you’re asking to ask their own. How to respond… Can you use your expertise to ask them an easier question which will help them come to the answer themselves? If not, pass it on to another student to keep all involved.

Pause / Think-Pair-Share
Pausing to get all students to individually think about or have a rough go at a question you have posed (and then discussing in pairs if you wish) during a period of explicit instruction is a good way to break up the time and give pupils a chance to refocus.

Subject Knowledge for Teaching and Learning
What really helps you ask good questions is knowing the misunderstandings that students often have and how to break your questions down into smaller steps or re-frame them in a different context to overcome these. As Jamie Frost emphasised on Mr Barton’s Podcast, this is not just about knowing the subject, it needs to be learned.

Aspirin for a Headache?

I really like Dan Meyer’s metaphor of presenting maths as the solution (aspirin) to a problem (headache), simply because it reminds me that I should start a lesson by making clear in some way what the problem is, before diving in to introducing new ideas.

I like it so much I was talking to some (mostly non-teaching) friends about it the other day. It went a little like this:

Luke: …isn’t that a great metaphor?

Alice: It sounds a bit negative.

Becky: It sounds as if you’re saying that maths is a headache.

Luke: no, no, no…

Alex: Yes, but I don’t want to have to take Aspirin.

Alice: I never take Aspirin anyway, even if I do have a headache. I think that’s more of an American thing?

Luke: Have you got a better version?

Alex: You want to undertake a journey but there is a river in the way. Maths is the bridge you need to cross the river.

All: *wretch*

So, I’m sticking with Headaches and Aspirin for now… anyone have a better suggestion?!