I’m not sure why (someone probably asked me at school) but yesterday I started thinking about what I think leads to a good ethos in an A Level class and what I strive to achieve with my classes.

My guiding principle with A Level groups is equality – I don’t want to be seen as a teacher who is above them. Real mathematics is a collaborative attack on problems where you are looking for an elegant, neat solution; this is hard to achieve amongst a group of people who don’t feel equal. I don’t want them to see me as a teacher above them who they can only ask questions of – I want them to suggest approaches and paths to the solution of problems too. I think one of the easiest ways to encourage this is to let them call me by my first name. I know some teachers wouldn’t like this, and it is of course important to keep a professional distance from your students, but, I really think little things like this encourage them to be comfortable to give me their thoughts and suggest ways to tackle a question that they are doing as a class.

Another thing that I think is important for an A Level group to understand is the necessity to be stuck. In a Further Maths group especially some of the students have probably never struggled with maths before and it can be a shock when they begin to. For this reason I try to emphasise in the first few weeks that this is ok and a normal part of doing mathematics. Problems which either can’t be solved, or can be solved in multiple approaches, one of which takes significantly longer than another approach are valuable to reinforce that being stuck is ok! I also use exercises that I haven’t looked at until I get into the room as examples for this reason – I believe it’s good for them to see that I don’t always do the correct thing first time when solving a problem.

Collaborative working is something that I try to foster with certain activities – certainly for me, maths at A Level was a very solitary activity. This isn’t really reflective of the world of mathematics and whilst it is important for students to have plenty of practice at solving questions on their own, talking about and discussing mathematics is incredibly valuable.

This post is a work in progress and I’m going to add to it as I think of other things…..

*Related*

Hello,

The feeling of being ‘stuck’ is all too common amongst my FE students. It can be challenging t and students often feel frustrated because they just don’t know where to start. Reassuring students that this is okay I think builds confidence and resilience in maths.

Talking through the thought process of how we might attack a problem is incredibly useful. It’s a skill to be able to explain your thinking and reasoning which we should encourage in our students.

I think it’s important that students do not put us on a pedestal as the ‘giver of the answers’. I often hear myself say that I am more interested in how they students got to an answer than the actual answer.

It’ll be interesting to hear what other folks think!

Great post

Thanks for the kind words! Building resilience and confidence is half the battle to getting good grades I think. Once we have that the rest is a lot easier ;?

Hi Tom, I agree I always felt that it is totally different teaching A level – in the past I’ve worked through any questions we’re going to use myself and the students used to ask to see my “exercise books” to check their answers. Very quickly they could see that I too made mistakes and also the expectation of how to lay their work out was very clear.

Look forward to seeing this post develop

That’s a really nice idea. I may try that actually because my work is normally set out much better (my handwriting is also significantly better) on paper than it is on the board!

Really interesting reading. I’ve just finished my first year of teaching A Level and I’ve taught it in isolation with no one on hand immediately to ask for advice. It’s of great comfort to see many of my ideas are common.

I always like to work through exercises and work at the same time as the students for the same reason. A Level Maths is supposed to be difficult and it has aspects that will cause anyone to struggle. The also see parts that I am inherently comfortable with. My manipulation of algebra; the knowledge of my trig graphs; strategies for approaching questions I’m not sure what the end result will be.

These are the things they can all work to get better at.

This sentence struck a chord with me: “some of the students have probably never struggled with maths before and it can be a shock when they begin to” – I vividly remember having a huge meltdown during Core 4 as I was in that position personally, and it’s a story I share with my students every year, particularly as it has the happy ending that “I got there in the end”.

As I’ve increased in confidence with my A Level teaching (now in my fourth year of doing it), I’m also taking a similar approach using unseen problems. I think it takes a while as a teacher to get that confidence though – a bit of struggle and working through is fine, but it’s a bit embarrassing if you do that and then can’t solve it, particularly if you’re new to teaching A Level!

I’ve had a group of three pupils in my Year 13 class this year (the other group is much bigger; it’s a timetabling thing) and it’s been one of the most enjoyable years I’ve had teaching A2. We’ve done a lot of collaborative work on the board and working through exam papers together – if they are working independently, I also sit and work through the exercises and comment about my thought processes to prompt them if they are stuck.

Some great points made, Dr Bennison 😉 My first job was in a sixth form college so I was fully used to students calling me by my first name. My last job was in an 11-18 school though and I was still supposed to be Mr Price, even with sixth formers. They gave me the name ‘SXP’ as per the school’s initialling which I quite liked and which has since stuck in my Twitter name! I’m back to being Stu(art) again in my current job and happy about that.

I think a couple of things stand out in my classroom: one is the students always having mini whiteboards on hand. Sometimes they use them to sketch out ideas and explore a problem; other times we use them actively for some whole class work. If a student has got in a mess with a long question (eg a Mechanics 2 situation or maybe a long C3/4 question), they’re used to me saying “why don’t you come up here so we can try it on the board together”. I actually don’t contribute much except to perhaps nudge them with the usual prompts about drawing a diagram or how to present things more clearly. The change of scene from staring at their page is often all that’s needed. We also use the main class boards for some team work. (I asked for a total of 3 big w/bs when I took on the classroom last autumn.)

Another thing my students know me for is being very careful with mathematical language. Early in the year I banned the word ‘it’ and made a poster to that effect. Too many vague comments such as ‘it equals zero?…. [tries to read my facial expression]…’. If a student is saying ‘it’ then they probably don’t have a complete understanding of what’s going on. I’ve also adopted what I think is an Americanism, referring to f'(x) and dy/dx as the ‘gradient function’. Call it what it does!

I did consider printing out a large number of the “classic mistakes” posters but as it turns out, I’ve settled for three of the “Every time you do this, a [cute animal] dies.” We have a puppy, a kitten and a hamster. You will hear my students saying “Oh wait, I think I just killed a puppy.”

My current work in progress is to use the language of functions much more carefully, right from the beginning of C1 if I can. I’m hoping this would help students better understand the process they are going through when they solve trig, exponential and logarithmic equations and stop things like “sin x = 0.5, therefore x = 0.5/sin”…