I’m sure we’ve all had those experiences where we’ve explained something to our students, done some examples together and then got the response, “*I don’t get it!*” or, “*I don’t know what to do!*” It can be frustrating for us as teachers under pressure to teach all the required topics and to help our students to pass exams. We inevitably consider how we can make this easier or more accessible for them.

I don’t know about you but, speaking for myself, when a student starts to explain what they’ve done and talks me through their steps of working, I often find myself getting lost – I can’t follow what they’re telling me, particularly when there are several steps and sub-calculations. As a maths teacher, I think I should be able to follow, but I can hide behind my own wider knowledge, the experience and confidence of alternative methods, and an answer scheme.

Now, thinking from the student’s point of view: if I can’t follow their explanation, why should I have the expectation that they can follow mine? Especially when they are learning a new topic. We might reason that we started the topic by recapping a ‘previously learned’ topic and building upon that. I think that’s an important approach, but it does carry the assumption that the ‘previously learned’ topic was actually learnt, stored in long-term memory and made sense. Maybe it didn’t!

If I don’t follow a student’s explanation, I tell them, “*Sorry, I can’t follow that*”, and ask for some time to work through it myself. Then when I’m not under the pressure of following at the student’s pace, I can usually follow what they have done quite quickly, but sometimes I need to work out the answer my own way and then compare the two methods. I think it must come as a relief when students hear their teacher admit something like this because it reduces their own expectation of being able to follow a new topic so easily, and gives them a little more space to understand it in their own way. Sometimes I’ve even pretended I didn’t follow, just to give a student this message.

The advice I often give my students, especially when working on more difficult or unfamiliar topics, is, “*you don’t have to do it the way I taught you – there may be a perfectly good alternative method that seems more logical to you – it’s probably right.*” I remember when I was sitting a test at school, thinking I could remember the method the teacher taught me, and yet there seemed to be a simpler method in my mind. I chose to try using the teacher’s method and got it wrong, as I didn’t have the confidence to try my own way.

With the current restrictions on interaction with our students and intermittent remote teaching, we have found many sources of short video lessons. Not all video lessons teach techniques in the same way. Why not let students watch and re-watch recorded lessons as well as giving them our own lessons?

If your school or college is registered with the AMSP, you will have free access to many A level Mathematics and Further Mathematics videos. Please get in touch with your local Area Coordinator if you’re having trouble finding these. If your school or college isn’t yet registered, you can do so now on the AMSP website.

I try to find ways of letting my students work out and check their own answers without the embarrassment of making their errors known. Working on whiteboards or scrap paper and then copying a correct solution into their books feels much safer than a solution with several crossed-out attempts that they don’t want you to see, and also makes for good revision material as they can try the same question again later, having a good model answer to refer back to if needed.

Here are a few ‘fear-free’ ideas for teaching a new topic using Desmos or GeoGebra (students can easily use these programmes for free, without the need for accounts and passwords etc.):

## Gradients of linear graphs

Draw the graph of **y = 3x + 4**.

Experiment:

- How can you make the line steeper?
- How can you make it flatter?
- How can you make it slope the other way?
- Can you draw a horizontal line?

Make it like a quiz or competition – adding the fun factor.

## Rearranging equations to make the subject

Draw the graph of **y = 3x – 2**.

Rearrange to make **x** the subject (that means it must start with ** x =**).

Draw the graph of your rearranged equation. If it matches the original equation, you know that you’ve rearranged it correctly.

## Transformations of graphs

Draw a graph such as **y = sin(x)**.

What would it look like if you translated it by **[0-3]**?

Now try drawing it. What would the equation look like?

Extend it: how can you shade the area between the two graphs?

Extend it further: start with **y = sin(x)**. How can you reproduce this pattern? You’ll need to use inequalities for the shaded parts:

Make some designs of your own. Make it fun – you could collect all of the designs to make a wall display.

Here’s some inspiration: