Congratulations on surviving your first term in teaching! Now that you’re into Term 2, and are getting used to proceedings, here are three suggestions that have always served me well in my teaching:

**Don’t plan lessons**

That was a little misleading, of course you need to plan lessons. But, as you may already be realising, topics don’t fit neatly into one-hour blocks. An hour on ‘simplifying expressions’ followed by an hour on ‘solving equations’ then an hour on ‘scatter graphs’ does not help your pupils to learn maths very well.

Think about learning more as a continuum, albeit a really messy, non-linear one. It may take one class ninety minutes to get the hang of the basics of solving linear equations where another class takes three hundred. In addition, once they’ve got the hang of it, they will forget it, so you’ll need to keep revisiting things if you want them to stick. Read up on ‘retrieval practice’ and ‘spacing’ to find out more about this.

So instead of planning to teach ‘solving linear equations where the unknown appears on one side’ in one or two lessons, think about it like this:

- What do you want all the pupils in your class to be able to do before you move on from this topic?
- Where are the places they will trip up? Each successive example below requires an extra level of understanding before we even encounter the unknown on both sides:
- Decide how you will plan to reduce misconceptions and address sticking points. How will pupils handle the negative coefficient of x in the last example? Do you want them always to manipulate to make the coefficient of the unknown positive or will they cope with dividing by a negative number? The answers to these questions depend on the pupils in front of you.
- How will you get your pupils from a place of no knowledge to a place where they can move on successfully? What types of practice will they do? What examples will you use? What questions will you ask?

A sequence of lessons approached in this way will be of variable length, depending on class, but considering these points is more valuable than spending time designing “fun” activities or changing fonts on a presentation. You don’t need every lesson to have a starter, main and plenary, and you don’t even need every lesson to be exclusively on one topic. Once you think in terms of sequences of learning, of going backwards and forwards concurrently, planning time is more productive.

**Think carefully about what your pupils attend to**

If you are teaching pupils to round you might give a couple of examples, such as 1.54 to 1s.f. and 3.485 to 2s.f., and then set them some practice questions. However, it is important that you consider what they are practising and how they are doing it.

Do practice questions reflect the examples you give or are pupils thrown in at the deep end with 0.00402 to 2s.f.? Do the questions allow pupils to practise with a range of numbers? Are they sequenced in a way that helps them to notice patterns, using ‘variation theory’?

Sometimes you might want pupils to have lots of straightforward practice, to help them commit a process to memory. Other times you might want to use a small handful of more involved questions that introduce cross-topic links or require more time to solve. Not all practice is equal and, as Dan Willingham says, “memory is the residue of thought” – what you think about you will learn.

The same principle applies to how you present the mathematics. In the early years of teaching it can be easy to waffle and muddle explanations or, conversely, to rush and not speak with clarity. Many beginning teachers fall into the trap of giving too few examples, leaving pupils to flounder when the questions get difficult. Discuss explanations and examples with colleagues, write them down or practise saying them so that when you are faced with thirty eager (or not-so-eager) faces you aren’t making it up on the hoof.

While you are doing this, keep asking yourself, “what will my pupils be attending to?” Is their attention directed at the mathematics or distracted by the context of an activity? Are they completing pages of repetitive questions when fewer would do, allowing time for different types of practice? Are they being rushed on before they have paid sufficient attention to learn the maths at hand? What you think about, you will learn. Make sure your pupils think about the mathematics at every opportunity.

**Use the right kinds of activities at the right times**

Consider how you spread out the elements of your lesson. If you present lots of examples in one go, before setting the pupils off to work independently, you may find that they get overloaded and struggle to get started. Breaking work down into smaller chunks can mitigate this, allowing pupils to grasp what they are learning in small steps. This is especially useful when a single topic can be built up progressively, such as ‘simplifying expressions by collecting like terms’. For many students, introducing negative coefficients too early is a step too far and for others, the concept that cannot be collected with causes great difficulty. Build it up gradually and you will see less confusion when it gets complicated.

Don’t be afraid of teacher-led, whole-class discussion. It’s okay to talk, but make sure you get the whole class involved so that no-one gets to be lazy. You might use mini-whiteboards to see everyone’s thoughts; you might get one answer and ask for hands up to show who agrees and disagrees before delving into their reasoning; you might get a handful of students to suggest their answers and justifications before doing a class vote, which is helpful to show you who holds what misconceptions. Provided you involve everyone, such activity is not something to shy away from.

Finally, a note on solving non-routine problems, such as the kind we often find in GCSE questions. The ability to solve a range of problems is an indicator of mastery of subject matter. Spending time in lessons solving problems can be a joy but it can cause chaos. Introduce non-routine problems too early, before the underlying mathematics is sufficiently understood, and you reduce your pupils’ chances of success (“I can’t do this, it’s too hard!”); do them rarely and you stop your pupils from seeing the creativity and struggle inherent in mathematics.

It is important to spend time solving problems but do it when the time is right and your pupils have a good chance of success. Success, by the way, is a good way to sum up any piece of advice I could give you in your career. Success breeds motivation – find ways to help your pupils feel successful in mathematics and their enthusiasm will follow.

*Why Don’t Students Like School?*, Daniel Willingham, Jossey-Bass, John Wiley & Sons, 2009.

Jemma Sherwood is Head of Mathematics at a Secondary school in Worcestershire, having taught maths for fourteen years. She has a master’s degree in Mathematics Education and spends some of her time training teachers of other subjects who want to convert to teaching mathematics as well as sitting on the governing board of a Primary school.

Jemma has written How to Enhance Your Mathematics Subject Knowledge: Number and Algebra for Secondary Teachers for the Oxford Teaching Guides series, which is a guidebook for new maths teachers, equipping them with the depth of knowledge they need to talk confidently about maths to students at all levels. Shop now via the Oxford Education website or on Amazon.