I’ve read many books on education. Some have been very good, some ok, some distinctly average and a small number were so bad I stopped before I got to the end. Craig Barton’s “How I wish I’d taught maths” doesn’t fall into any of these categories because I think it is quite possibly the BEST education book I’ve ever read. Yes its pure focus is on teaching mathematics in a secondary situation which just so happens to be what I do for a living as well, but it is so much more than that and I am convinced that many of the ideas contained within this book would work equally well in primary schools and across other subjects at secondary level.

Craig distils what he’s learned from his teaching career (and the mistakes he’s made) in a book which is an organised elaboration of his fantastic website. He draws on extensive reading around the research on these ideas – very much the “I’ve read these daunting educational tomes so you don’t have to” and puts it into the context of what it would (or should!) look like in a mathematics classroom.

I’ve been an avid listener of his podcast’s and learned so much from them but this book takes many of the ideas mentioned in the podcasts and, using the solid foundations of educational research, gives them flesh and bones and brings them to life in the classroom. What gives Craig and his book credibility ahead of other books of this nature is that he is still a classroom practitioner and he practices what he preaches.

They often say that you can’t teach an old dog new tricks – well I’ve been teaching mathematics for 23 years and done it relatively successfully (I think – though you ought to check with my pupils from the past 23 years) and I’m here to tell you this book has taught this old dog a number of new tricks. Tricks is possibly an ill judged metaphor because this book is not about the ‘tricks’ which are the enemy of depth of understanding and focused purely on short term exam performance. This book and the ideas contained within are definitely NOT tricks but about teaching in a way where long term understanding prioritised and championed.

Craig Barton’s book has re-invigorated the teaching and learning aspect of my teaching career and for that I will be eternally grateful to him. I’ve gained so much from this book and have already put some of these ideas into practice in my own teaching (purposeful practice, example-problem pairs, extensive use of diagnostic questions, spacing effect to name just four have become more regularly – but most importantly – more deeply thought out aspects of my teaching armoury). I have plans in place to incorporate many more of the ideas (tailored for my classroom of course) as well as embedding the ones I’ve already worked on into my teaching in the new school year.

In my opinion **this book should be required reading for any PGCE or trainee mathematics teacher** – it is that good and that important. As a department we intend providing copies of this book for our trainee teachers and NQTs in the future (budgets allowing of course – but a number of us in the department have copies of our own already). More importantly however this book should definitely NOT be bracketed as a book for trainee or ‘newbie’ teachers – ALL mathematics teachers should read this book and enact some of the great ideas explained in it. Buy it – read it – do it!

Of course usual disclaimers hold – I’ve probably missed some obvious ones and some are here that maybe I missed on the papers. Of course there will be many other topics in the papers that have been examined in June and November 2017 and of course this is only for the EDEXCEL papers not AQA or OCR.

However, with these proviso’s and the fact I take absolutely no responsibility for any of these topics turning up or not, in the spirit of collaboration here is my list…

FOUNDATION

Knowing which two numbers a square root is between (non-calc)

Working with mixed numbers – possibly some division of fractions (could be a cross over with higher) – haven’t spotted a division of fractions on any paper.

Multiplying and dividing whole numbers (possibly decimals connected with percentages) using non-calc methods

LCM and HCF

Giving answers in terms of pi (so circles on the non-calc paper?)

Ordering standard form numbers

Finding the mid-point of 2 coordinates and the gradient between them

Plotting a quadratic graph (maybe completing a table and plotting)

Interpreting gradient and intercept on a real life graph

Linear Inequalities – maybe also displaying on a number line

Solving simultaneous equations graphically

Finding one number as a percentage of another

Simple interest

Compass constructions

Angles in a quadrilateral

Interior/Exterior angles

Congruence

Drawing/Explaining enlargements

Conversion between metric and imperial units

Area of composite shapes

Exact values for sin cos tan

Maybe a harder crossover question involving pythagoras/trig where you have to find an intermediate answer

Vector additions and multiplications

Relative frequency

Tree diagrams

Mean from ungrouped table (grouped was on in November P1)

HIGHER TIER

Finding HCF or LCM using prime factorisation

Answers in terms of pi

Surds (maybe in the context of pythagoras – there was an awkward rationalisation one in P1 in November)

Rounding to significant figures

Interpreting the gradient and intercept of a real life graph

Completing the square when a > 1

Interpreting the roots and completing the square in terms of a graph

Composite functions

Quadratic formula

Factorising a quadratic when a > 1

Maybe a disguised quadratic

Given graph of y = ab^x find a and b

Trig graphs

Transformation of graphs

Solving simultaneous equations graphically

Term to term rules

Proportion (Direct on P1 in Nov and indirect P1 in June)

Loci and compass constructions

Congruence

Circle Theorems – finding an angle and justifying with geometrical reasons (ensure they know the proofs to them all – the one for angle in a semi-circle was on P3 in Nov)

Conversions between imperial and metric units

Pythagoras/Trig where you have to find an intermediate answer

3D Trig

Vector multiplication and addition

Invarience

Drawing a cumulative frequency diagram

]]>I’ve been busy with other non-OfSTED activities though. As you will know I’ve created daily revision calendars for Y11 students to use from September through to the end of April for this school year. They’ve been well received at school and here via twitter. (You can download them all from here.)

I’ve done one last calendar which kicks in when the final one on my site ends – 1st May.

This is designed to give some final revision over the last month or so before the exams.

There are three calendars – a higher tier one focused on those who are looking at getting level 6 and above, a foundation plus one focused on those who are aiming for a 4 or 5 but entered for foundation and a foundation one which is more tailored to those who are aiming at 4 or below.

From 1st May to 23rd May the questions are designed to be done without a calculator to help prepare for paper 1 on 24th May (the Edexcel one that we do is non-calculator for paper 1) and from 25th May onwards these are calculator questions.

I’ve tried to cover a variety of topics and I’ve produced fully worked (and I hope correct?) solutions for each one also.

As always – feel free to use if you feel they are useful! You can download them below (Ideally they should be printed out on A3 if your photocopying budget allows)

Best wishes to you all in preparing your students for their GCSE mathematics exam!

HIGHER TIER

A bit of maths each day LETS GET READY MAY 2018 HIGHER TIER (Editable Word Version of calendar)

A bit of maths each day LETS GET READY MAY 2018 HIGHER TIER (PDF version of calendar)

LETS GET READY HIGHER SOLUTIONS (Solutions)

FOUNDATION PLUS (Aimed at those going for level 5 on foundation)

A bit of maths each day LETS GET READY MAY 2018 FOUNDATION PLUS TIER (Editable Word Version of calendar)

A bit of maths each day LETS GET READY MAY 2018 FOUNDATION PLUS TIER (PDF version of calendar)

LETS GET READY FOUNDATION PLUS SOLUTIONS (Solutions)

FOUNDATION (Aimed at those going for 4 or below)

A bit of maths each day LETS GET READY MAY 2018 FOUNDATION TIER (Editable Word Version of calendar)

A bit of maths each day LETS GET READY MAY 2018 FOUNDATION TIER (PDF version of calendar)

LETS GET READY FOUNDATION SOLUTIONS (Solutions)

]]>HIGHER TIER

FOUNDATION PLUS

FOUNDATION

If you want to download the editable word file you can below

]]>HIGHER TIER

FOUNDATION PLUS

FOUNDATION

Solutions….

Higher Tier

Foundation Plus

Foundation

If you want to download the questions as an editable word file you can below…

Revision Questions 3 12_4_18 C

And with solutions…

]]>HIGHER TIER

FOUNDATION PLUS (For those doing foundation but aiming for a 5)

FOUNDATION (for those doing foundation aiming for a 4 or below)

SOLUTIONS

HIGHER

FOUNDATION PLUS

FOUNDATION

If you want to download the editable Word file with these on, you can download them below

Revision Questions 2 11_4_18 C

And with solutions…

]]>Todays is a non-calculator offering..

HIGHER TIER

FOUNDATION PLUS

FOUNDATION

The solutions…

If you want the word file with all three questions on…

Revision Questions 1 10_4_18 NC

And with solutions…

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I will put mark schemes up eventually – when I’ve worked through them.

Feel free to use as you wish – as always everything I post is free for anyone to use – all I ask is that if you find them useful, mention it on twitter.

**Paper 1 – Non-Calculator**

Solutions

Higher Tier Practice Paper 1 SOLUTIONS

**Paper 2 – Calculator**

Solutions

Higher Tier Practice Paper 2 SOLUTIONS

**Paper 3 – Calculator**

Solutions

]]>- Don’t leave your preparation too late – it may be 100 days till your first exam but those 100 days will pass quickly and you have other exams to prepare for as well. The earlier you start, the better prepared you will be
- Don’t just read a revision guide or read your exercise book and think that is enough – the only way to learn mathematics is to do mathematics
- Don’t just concentrate on things you can do – it is nice to do things you can do – its easy and self affirming. However if you find it easy, you already know it.
- Don’t ignore the advice of your teachers – the best way to learn from mistakes is to learn from other peoples mistakes and believe me your teachers will have made loads in their life!

- Know your enemy! Know the gaps in your mathematical knowledge and understanding. Given a list of topics you probably know your gaps but use assessments and mocks from school to help identify them. I’ve produced a revision list which (I think) covers all the topics that could be examined in your GCSE. You can download them below:

Foundation Tier: GCSE Revision List FOUNDATION TIER

Higher Tier: GCSE Revision List HIGHER TIER

- Start your preparation NOW. Plan a revision schedule – don’t be too brutal though and make sure you fit in some time off and some rewards (like some time watching TV or going out with friends). Too much revision and you will burn out and this is a big reason to start early!
- Get prepared – make sure you have the right equipment – pens, pencils, ruler,
**scientific calculator**, protractor, pair of compasses - Make sure you have resources ready to use – your school exercise books should be your best revision guide. Invest in a decent revision guide/workbook (my school use the CGP revision guides). Ensure you know where to get access to past papers – your school may provide these for you but many are available (with mark schemes) online free of charge from the exam board websites.
- Remember that whilst you may be doing the Edexcel GCSE (for example) all the exam boards follow the same set of topics. Whilst they may structure how their papers differently, don’t neglect other exam board past papers – they will give you useful practice.
- Focus on what you CAN’T do! It sounds simple but it is crucial! Use my topic list to decide what you need to focus on and concentrate your efforts on these topics.
- Revisit the topics you have already revised. I don’t mean do things you can do, but if you’ve covered a topic (lets say factorising quadratic equations) which you’d identified as a gap, and you think you’ve cracked it, leave it a week and revisit it. The more times you re-learn something, the better it sticks!
- Do little bits regularly! There are so many free resources out there for you to use and a little bit, often, is the best way to revise any subject. I recommend the following… ALL of which are free! In each case click on the picture to link you to the recommended webpage.

My own revision calendars offer you the opportunity to do a little bit of daily revision with a wide variety of topics

Maths Genie is a great site where you can download past papers from all the exam boards as well as loads of other revision resources

Just Maths – a great site where you can download topic specific questions from the sample papers from each exam board that were prepared before last years exams (the link below takes you to the Higher Tier questions but there is a link on this page to take you to foundation questions)

Corbett Maths is a fantastic website which has online tutorials for each topic and sub-topic covered at GCSE as well as practice questions. The five-a-day page also allows you to get regular, daily practice from a range of topics.

Hegarty maths, just like Corbett maths, has some great online tutorials for the range of topics you need to know before you sit your GCSE. This is the free site which Mr Hegarty developed before his more advance (and very good) paid for site. You have to register with an email but the site is free.

The most important thing to remember about revising for mathematics is….

**THE ONLY WAY TO LEARN MATHEMATICS IS TO DO MATHEMATICS**

I set my class a single homework each week. The homework is essentially split into three parts (they aren’t in any particular order as I describe them nor on the sheets). The first is testing their understanding of what we are covering at the moment. The second is, based on their previous homework sheet, what they struggled on. Of course I will have done some follow up on this after marking the sheet and before setting the next one which hopefully will show evidence of success when I mark the next one. The final part is picking a topic we have covered in the past to ensure that my students are going back on past work and re-learning it with the hope that by revisiting (more than once over a year – maybe twice or three times) the understanding sticks that little bit better. It may be that this topic is an underlying skill needed for the next topic I want to cover, but not always.

Where possible I also add links to Corbett Maths videos to enable students to use these to help them to try and develop a little more self reliance and resilience. They get a copy of the sheet but I upload one to Show My Homework (the homework package we currently use) as a PDF which they can download and simply click the link.

The most recent sheet contains questions on Pythagoras’ theorem which we are currently covering, some questions on compound measures which caused problems on last weeks sheet (a topic we covered last week) and then I’ve decided to re-visit solving simultaneous linear equations – something we covered before Christmas.

Anyway – as I say – nothing earth shattering but it has been received well by my students and it does seem to be having an impact on their confidence in assessments. I’m just putting it out there if anyone finds them useful. If you do, please let me know. I’ve uploaded all bar the first one below (I can’t seem to find the first one!!!) as word files.

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