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Teaching, Some Good New Ideas and Teacher Tips On How To Teach Maths

Updated on September 12, 2015

Successful Teaching - The Basics

How To Teach (Especially Maths)

A Beginner’s Guide

To begin with I, should begin by introducing myself.

I am the Head of Maths at an inner city secondary school, on the outskirts of Birmingham, and I have been teaching Maths for 15 years.

The school I work at is one which is described as being in ‘challenging circumstances’ and has previously been in special measures, back in 2004.

Now, however, it has become quite successful and in terms of Maths, we have progressed from a GCSE pass rate at grade C or better of 14% the year before I took over our Maths teaching to 40% last year, and rising.

At our present rate of progress, and using our KS3 results as a barometer, we should be achieving 55%+ in 2 years time. We have been described, overall, as one of the most rapidly improving schools in England.

During my time as a teacher and an HOD, I have trained a good many new teachers through the Teach First, SCITT, PGCE, GTP and SAS teaching and education programmes, so I hope that, by now, I have enough experience to help you to become a success in your classroom.

So . .. that’s enough about me!

Let’s turn our attention to the challenges facing you as a teacher and try to help you answer your questions about 'What Is Teaching?'

It may be that you are about to embark on a teacher training programme, starting in September.

You may have just completed your training year, through one of the ITT programmes and are now a NQT

Or, it could be that you are a recently qualified teacher, who is about to embark on your 3rd or 4th year.

On the other hand, you might just be a more experienced teacher who has been involved in education for a number of years and is reading this purely out of interest!

People (especially governments, government advisors, journalists and a host of ‘experts’) tell us that teaching needs the best possible graduates if we are to raise the standard of Maths education, teaching and learning.

Hmmmmm . . . . not sure I actually agree with that and let me tell you why:

The worst teachers that I have encountered and ones who, during their training year, have been failed and removed from the programme they were on, have been some of the best qualified graduates I have met!

In fact, most of the poor Maths teachers I have met, in general, have been amongst the best qualified teachers that I have met : 1st class degrees and a bucket full of A’ levels at grades A and A*

And yet, some of the truly great Maths teachers I have met have had lesser qualifications.

Seems to be a bit of a contradiction there, doesn’t there?

That doesn’t mean to say that if you are a graduate with an excellent degree you are destined to become a poor teacher! Far from it. BUT, you need to keep your own level of Maths ability and achievement in context and you need to remember that, although you find Maths to be incredibly easy, interesting and useful, you will be working with a lot of young people who view Maths differently. So, a crucial skill you need to develop is to, mathematically, get yourself down to the level of the year 7 or year 8 pupils you will be working with. You need to be aware of the risk that you could work at a level that is way above the pupils you are teaching.

My experience is that it is often the things we find to be really easy that we struggle to teach the most!

Let us start off by remembering that we are, in the main, teaching to GCSE level. Think about it for a moment. Do you really need to be a first class honours graduate to be able to teach an 11 year old how to calculate basic probabilities (such as rolling a die and getting an even number)?

Do you really need to be a first class honours graduate to be able to teach a 16 year old how to factorize 12a + 8? Or to be able to work out if a triangle with sides 6cm, 9cm and 11cm could be right angled?

You are surely smart enough to work the answer out for yourself.

You will, however, need to get right down to the basic level and try to understand why a 15 year old struggles to work out the total cost of buying 27 pencils at 39p each, or if 318 pupils go on a school trip and a coach will carry 45 pupils, how many coaches will we need often produces answers like 273, 363 or 14310, instead of 8.

Sure, if you are going to be teaching A’ level then a good Maths degree becomes important, but if you consider that you will be teaching pupils who range from level 3 (you will also have a handful below that) to level 6, as your typical client base, then you can see why so many of us, who actually KNOW what we are talking about, scoff at some of the theories that are spouted by such notable experts as Carol Vorderman!

In that case, what DO you need, if it isn’t a brilliant degree from an Oxbridge university?

Rule 1



I am sure you realise that the reason I put that little lot into bold italics is because it is important!

Well, I cannot stress how important that rule is.

Over the years, I have seen the occasional teacher who has maintained a stable environment, where pupils work hard and do what they are told, through fear. But, in truth, I cannot think of more than a few teachers, at most, who fit into that category.

I have, however, seen a great many teachers who have classrooms where the atmosphere is superb, pupils are attentive, work is done to a really good standard and a voice hardly ever raised, and yet, those teachers have not been disciplinarians (as such). Not in the sense of being ‘The Bitch From Hell’ or ‘The Bastard Who Must Be A Close relative Of Satan’

What they DO have, however, is the ability to build good relationships with their pupils.

Let me be clear at this point, about what I mean by ‘good relationships’.

Some people, misguidedly, think it means being the pupil’s best friend and that is NOT the case.

Building good relationships does not mean you are soft, let pupils get away with murder or allow yourself to be walked over in a classroom where there are no standards whatsoever (which is what some people seem to think it implies).

Good relationships are all about the way that you treat pupils and the way you communicate with them and the standards you expect from them.

Here is a bit of a checklist

1. Speak to them in a decent way and remember that if we want good manners from them, we should display good manners ourselves. It is awful to see a teacher losing control and yelling “SHUT UP” in the face of a pupil and then going absolutely incandescent when the pupil answers back with ‘Why don’t YOU shut up?’ We have to model the type of behaviour we expect to see from our pupils. Another example; If you don’t want pupils to get their mobile ‘phones out in lessons, then don’t start using yours either! You would be amazed at the number of teachers who use their ‘phone during a lesson and then wonder why pupils think it is ok for them to use theirs also!

2. Explain things to pupils. If you are asking a pupil or a group of pupils to do something, tell them WHY it is important. They are far more likely to engage in an activity with commitment if they know there is a reason that goes beyond “ BECAUSE I SAID SO, THAT’S WHY!” One example of this is when I start a lesson with a 10 question mental test. At the start of each new academic year, I tell my classes that we will do one of these every 4-6 lessons and I explain why it is important for them to be able to develop good mental Maths skills.

I then explain the rules: “The test is done in the back of your book, number each question. I will read each question twice and if you don’t hear it or don’t understand it, sit quietly and wait for the next question – I will explain the questions when we go through the answers. We will do the test in complete silence and we will work through the answers in the same way. Hands up if you can tell me why it is important for us to do this particular activity in silence?”

A few pupils usually contribute things like ‘it is important to listen carefully so we will understand the question’ or ‘We can concentrate better if there is no noise or distractions’

Job done. There is a rule. I have explained it. The pupils have agreed that they can see a reason for this rule. They cooperate fully with it. No problems.

3. Talk to them! As they enter the room, say ‘Hello’ and ask them what their last lesson was, did they enjoy it? What did they do in that lesson? Did they have a good weekend? Just COMMUNICATE with them. Be human and create an environment where they behave in a human way too!

4. If you are unhappy with a pupil (or a group of pupils) then explain to them WHY you are unhappy with them. Explain what they have done wrong and why that is a problem. For example, after 45 minutes of a 60 minute lesson, when you discover that 2 pupils have done virtually no work, don’t go berserk at them and issue lots of unenforceable threats. Instead, ask them “How impressed do you think I am with the amount of work you have done?” or “When we move on to the next level of work, tomorrow, how are you going to cope when you haven’t even attempted today’s work?” or “If I photocopy the work you have done today and send it to your parents, how impressed do you think they will be with what you have done today?”

Of course, you can just shout at them and threaten them etc. BUT, in my experience, a degree of embarrassment works a lot better than a lot of shouting and threatening.

I learned an excellent lesson from my very first head of department.I never heard him shout at a pupil. Ever.

Instead, when he was not pleased with someone, he would glare at them for a few seconds and then ask the key question:

“Why do you think I am not happy with you right now?”

He would then just wait, silently, until the pupil gave him the right answer. It worked absolute wonders because by doing it this way, the pupils actually LEARN for themselves what is wrong and what they need to do about it and if you repeat this pattern enough times, it becomes embedded in the way pupils respond to you. It also removes the need for protracted arguments with pupils, which far too many teachers allow themselves to be drawn into.

5. When a pupil or a group of pupils has done well, TELL THEM! There is a management phrase that I lived by in my career, before I became a teacher, and it applies equally as well to teaching as it does to business and management: “Always try to catch them doing it right!”Just think about this for a minute. It works for you, doesn’t it? I mean, if your head of department or head teacher says to you “Well done. You did a great job” don’t you go home that evening with those words trickling through your thoughts? Of course you do! And what’s more, that praise makes you try just a tad harder the next day, too. Well, the same thing works with children. If they think that you are pleased with them, that they have done something well, they will generally try to earn more praise next time, by ‘doing it right’ again.

6. Try a little humour, from time to time. When I talk to young people about which teachers they particularly like and why, the same themes crop up time and time again. Their favourite teacher(s) make them laugh, or they are ‘really nice’ or ‘they talk to us, like people and don’t always yell at us’ and, ‘they explain things clearly so we can understand and do our work’.

So, apart from good relationships, what else can you do to give yourself the best chance of success, in the classroom?

Well, here’s another checklist!

1. Get them in, sitting down and busy, quickly. Have an activity ready for when they enter the room and tell them to make a start on the activity as soon as they are in. Remember, busy pupils cause a lot less problems

2. Make your instructions clear. Use precise, specific, descriptive language. If you are doing a worked example from the IWB and you want them to copy what you are doing, TELL THEM CLEARLY! When I do that type of activity, at the beginning of the main lesson, I tell the class “In this next part of the lesson we are going to work through an example from the board, together. I want you to copy what I write as we are working though this. There won’t be time to copy at the end because once I have finished, I will be taking the example down and replacing it with your first task”

That way, everyone in the room is clear and to reinforce this, I check that they are following this instruction as I work. If anyone is not doing this, I will ask the class “Can anyone put their hand up to tell me what George should be doing, instead of sitting there staring blankly into space?”

Believe me, there will be a whole host of volunteers ready to show that THEY understand what to do and are doing it! Using pupil power to your advantage works wonders, at times!

3. In your early days, until you get to know your groups well, don’t make the work too difficult. Better to work slightly below what you THINK is their level, so they are all engaged with the tasks you set. If the work is slightly too easy you can always use extension tasks to stretch them and get them up to the level they should be working at. By doing things this way, they should all (or mostly) be on task whereas, if the work is too hard, they will mostly be off task and disruptive and then you will have to work twice as hard in future lessons to ‘get them back’

4. If you make a threat, follow it through. So, think carefully before threatening a sanction. You are on to a BIG loser if you threaten a detention and then, don’t follow it up. Also, make sure you really understand your school’s rewards and sanctions system (and use plenty of the rewards, not just the sanctions. The ideal ratio is 5:1 (rewards : sanctions). To make sure you have a good understanding, ask other teachers how they apply the school systems. Maybe even ask one if you can watch a lesson of theirs to see how it works.

5. Stay calm. Always. I know that a lot of the time you may not feel calm, but try your damndest not to show it. Try to appear relaxed and whatever they try on you, don’t rise to the bait. Keep your voice at a reasonable level. No excessive shouting. Sure, we all need to raise our voice above the general classroom noise at times, but don’t become a teacher who shouts your way through every lesson. In my first year, I learned a very valuable lesson. I had a year 9, set 2 group and in that group were 3 troublesome girls, who played up every lesson. They were a nightmare. Rude, offensive, defiant, off task all lesson and causing disruption among other pupils. I used to go mental, every single lesson! Finally, after about a term and a half, I spoke to my HOD and asked him to help. He interviewed the girls and moved them. Afterwards, he gave me some words of advice. When he had asked them why they were doing this in my lessons, they said “because it is just so funny to see him go mad. We know exactly what to do to get him going, so we do it just for fun!” So, remember, if some of your pupils do something and you react, then it is only human nature for them to do it every lesson, for pure amusement. We all do it as adults, don’t we? I know I do! If I know that something winds someone up, I really enjoy doing that thing, just for the pure hell of it and to get a reaction that makes everyone laugh!!

So, there you go. Just a few little words of advice and a few pointers that may (or may not) help. I will add to this in due course but in the meantime, if you have any questions, ask!

Remember the importance of planning too. But don’t go inventing a new wheel. When it comes to a new topic, ask your colleagues if they have any ideas. They will have loads and they will happily pass their ideas and lesson materials on to you, if you just ask. And remember, when you have some good lesson content or activities, pass them back. It’s a two way street.

If you have found any of this article to be of any use at all, then keep coming back to it. I will endeavour to add more content as the weeks and months go by.

In the meantime, I hope you enjoy good teaching and if any of you have any good stories to tell, please, pass them on to all of us through the comments section below. Perhaps you might like to vote the article up, if you have found it useful or interesting. At the same time, why not share the article with friends using the toobar at the end of the article.

If you need helpful resources, I have created an Online Teaching Book Store which has a lot of very good and useful books and resources for you. Just click the Online Book Store Link to see what is on offer. Throughout my career I have gained valuable benefits from books such as the ones I have put in there, just for you. Also, This Link will take you to another article I have written which has 10 ready made lesson starter activities for you!

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    • Eiddwen profile image

      Eiddwen 5 years ago from Wales

      Very interesting indeed and I vote up here.

      Looking forward to many more to share.

      Take care


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