Following a brief exchange on Twitter this morning, I decided it would be worthwhile putting together a post that explains how I go about teaching Maths. There is no significant focus on any particular topic, but simply my general approach and why I do things that way.

## Context

Firstly, it’s essential to talk context. What works for one class in one room with one teacher is unlikely to be successfully transplanted anywhere else without due regard for context.

I must admit that from a teaching point of view, I’m pretty fortunate: I only teach A level (Maths and Further Maths) and I have small classes, typically fewer than ten students per class. The worst behaviour I generally have to deal with is a sly bit of mobile phone usage. My students usually (though certainly not always) complete prep on time and to a good standard. Ability-wise more than half of the students are relatively strong: A/A* standard from GCSE, although a significant proportion join us from overseas (Russia, China, Thailand, Spain, Germany,…) and it can be hard to benchmark their entry standard.

We teach Edexcel’s syllabus, currently offering AS Maths (C1, C2, S1) and AS Further Maths (FP1, M1, M2) to lower sixth students and the corresponding A2 subjects to the upper sixth. Our AS Maths classes can contain a mixture of Maths and Further Maths students – the proportions depend on how the timetabling works out. Each class has a 70 minute lesson every day, although one lesson per week is given over to testing – our school’s policy is to test and formally grade (A1 etc) students in every subject, every week. A further maths student will have two 70 minute classes: one for maths, one for further maths.

## My Ideal Lesson – Parts 0 and 1

At risk of infinite recursion, my ideal lesson begins the lesson before. (I should emphasise that I am not some kind of super-teacher. I have good days and bad days; well-planned lessons and, ahem, not so well-planned lessons; favourite topics and dreaded topics…) Where possible, I like to finish a lesson with some kind of puzzle, problem or challenge (what’s the difference? I have no idea) that whets the students’ appetite for the next lesson. I don’t offer hints or help, let alone the solution. I listen to their ideas. Usually, I (deliberately) don’t even leave enough time for them to reach a full conclusion.

The following lesson, that puzzle will still be on the board or I will inconspicuously write it up again. Where possible, I like to begin lessons with a warm-up/starter/do now activity. This comprises questions that draw out prior knowledge and allow students to check they are secure with prerequisite concepts that will be built upon in the coming lesson. Recently, for example, I tweeted the starter questions which were the prelude to discussing the locus of

(Naturally, I had asked them to have a go at sketching this, and other, loci in the previous class.)

## My Ideal Lesson – Part 2

My students know (because I tell them often enough) that they are in my room to *do maths*. However, this does not mean I run a problem-based learning/inquiry based learning ship. Chalk and talk happens. I explain things as clearly as I can. I involve the students in the explanation. They challenge the explanation and embellish it. We take particular care with mathematical language. When we’re all happy, they write their notes. (Some students cope with this better than others: a few are too eager to copy down anything as soon as I write it on the board. But they learn – the hard way – after seeing me change my mind, seeing diagrams erased and improved, and seeing numbers changed and errors corrected in my hastily constructed examples.)

## My Ideal Lesson – Part 3

Finally it’s time for the part the students have all been waiting for: the opportunity to work on problems at their own pace. I have no qualms about using textbook exercises (though typically pick a shortlist of recommended questions) and I point out how the explanations and examples in the textbook may mirror or differ from our own. I will also choose questions from Edexcel papers or just about any other board (I have a vast Dropbox folder full of boards’ papers from the past 10 years). I will also photocopy exercises from other books when I feel they are helpful.

Knowing your students well is essential at this (and, well, every other) stage. Some of mine like ‘drill and kill’ – they want routine practice. Others want to go straight to problem-solving. I try to ensure that there is enough variation in the questions I select to keep them all relatively happy.

For the complex loci lesson to which I’ve already alluded, I chose four questions from recent CCEA FP1 papers. These tackle simpler loci but push the students’ geometric thinking.

## My Ideal Lesson – Part 4 (where 4 = 0)

Confession time: I never really got the hang of successful plenaries. Whatever I tried just felt a little too forced and artificial. Or simply fell flat on its face. But then I reasoned thus: the purpose of a plenary is for me to establish how the students’ understanding has developed as a result of the lesson. I can gauge that while circulating, helping and discussing the problems with individuals – one of the perks of small class sizes, perhaps.

So how do my lessons end? By giving the kids a puzzle to solve that will bridge to the next lesson.

## Think, Pair, Share

- Do add your thoughts and comments below – I’ve tried to be as clear as possible, but then I already know how my lessons run…
- Do you have a different approach that works well for you? Have you written a blog post about it?
- What sources of questions do you use with your groups? How do you differentiate for mixed ability sets? I’m always interested to hear more ideas. Do you run successful plenaries? Please tell me the secret!

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Stuart,

Thanks for writing this up. I finally got to reading it after our further exchange this morning.

I would say my philosophy is fairly similar to yours. I really like your idea of not having students copy notes until after you’ve worked through the problem. I wonder how that affects the flow of the lesson though?

How much time do you spend on the chalk and talk/notes section vs. the problem solving section?

Finally, when you say plenaries, are you referring to getting closure for the lesson?

All my best,

Steve (@sgnagni)

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