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Ready to study A Level Maths?

As well as the free resources provided below, I also provide 1:1 tuition online to help students prepare for A Level Maths, tailoring a course to each individual student's needs. With many years experience of teaching A Level Maths, I know what skills students need in order to be successful at A Level Maths. It is enough to understand and complete all of the free tutorials given below, but should you want extra help to give you that edge come September, please visit my 1:1 tuition page.

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Bridging the Gap from GCSE to A Level - A Level Maths Revision

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As well as the free resources provided below, I also provide 1:1 tuition online to help students prepare for A Level Maths, tailoring a course to each individual student's needs. With many years experience of teaching A Level Maths, I know what skills students need in order to be successful at A Level Maths.

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Maths retrieval starter. Choose 4 topics and generate a set of questions based on the chosen topics.

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Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.

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Diagnostic Questions

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Don't spend hours marking books

Diagnostic Questions is a world leading assessment tool that provides detailed insights into student understanding in a fraction of the time, simultaneously reducing your workload and improving student results and confidence.

Replace homework

In just three steps, assign a year's worth of assessments to your students created exclusively by AQA, OCR and Edexcel.

Learn more

25,000 Questions & Quizzes

Create your own or choose from the thousands created by teachers, awarding bodies and publishers.

Learn more

Actionable Insights

Use our powerful Data Analytics, Feedback and Planning tools to understand your students better than ever.

Learn more

Free forever

We're in the business of helping teachers. We know how tight departmental budgets are, we know the pain of change and we know how frustrating it is when a product you've come to depend upon starts charging. Well, we're giving you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free. It's a small gesture, but we hope it helps.

Supported Subjects

Expected in November 2016, the ultimate GCSE Computing companion, with Scheme of Work and 1000s of questions from OCR and teachers.

750 questions from the Royal Society of Chemistry plus 1000s of others from teachers across the UK covering, Biology, Chemistry and Physics.

We want to support the most popular subjects that you teach. Help us focus on subjects that will make a difference by voting for our next subject.

Resolving misconceptions improves performance

A continuous system of misconception identification provides teachers with the foresight they need to intervene effectively in students' learning.

"Good diagnostic questions encapsulate our best information about what students find difficult, and are an indispensable part of any teacher's repertoire."
Dr. Dylan Wiliam, Emeritus Professor of Educational Assessment @UCL

"...the single greatest step forward in AFL in the maths classroom for years. I think it would be hard to find any better AFL strategy out there."
William Emeny, greatmathsteachingideas.com

"...good questions help us know more about our students' learning and help us to address misconceptions. An outstanding new resource to help us do just that."
Colleen Young, colleenyoung.wordpress.com

"Discover key misconceptions before you teach, track progress, review students explanations and quickly give personalised feedback."
Mohammed Ladak, mathedup.co.uk

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Don't spend hours marking books Diagnostic Questions is a world leading assessment tool that provides detailed insights into student understanding in a fraction of the time, simultaneously reducing your workload and improving student results and confidence. In just three steps, assign a year's worth of assessments to your students created exclusively by AQA, OCR and Edexcel.

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SSDD

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What are SSDD Problems?

SSDD stands for Same Surface, Different Depth.

They are a special set of problems that may look the same at first glance, but which require different mathematical ideas to solve them.

SSDD Problems have become one of my key strategies to use with my students to help them become better problem solvers.

You can search for different topics using the tags on the right-hand side (or below if using a mobile device), and you can find out more about SSDD Problems on this page.

My online courses

I have created a series of seven online courses based around my model of a Learning Episode:

Each course consists of videos, links to research, resources, activities, podcasts, websites and more. They can be taken at a time and place of your choosing, and revisited as many times as you like.

The courses available are:

Focusing thinking

Atomisation

Making the most of worked examples

Intelligent Practice

The four ingredients of problem solving

The four ingredients of retrieval

Formative Assessment and Diagnostic Questions

In the Four ingredients of problem solving course I discuss the use of SSDD Problems in the classroom. In particular, I share loads of ideas from the schools I have been lucky enough to visit in the UK and overseas who have taken the basic idea of SSDD Problems and made it work for them, including their use as Starters, for exam preparation and for developing high-value skills.

My books

How I wish I'd taught maths, which discusses the use of SSDD Problems alongside purposeful practice, cognitive load theory, variation theory and much more is available directly from my publisher, John Catt Educational Ltd, from Amazon, and from most good (and evil) bookshops.

In my second book, Reflect, Expect, Check, Explain, I delve into what I have learned about SSDD Problems (amongst lots of other things) in the two years since my first book came out. Reflect, Expect, Check, Explain is available from Amazon, John Catt, and many other retailers.

Supporting this website

I do not make any money from this website, so if you did want to support its future development - and hopefully learn more about the pedagogy underpinning these ideas - then I would be so grateful if you would consider:

Taking one of my online courses

Buying Reflect, Expect, Check, Explain from Amazon, John Catt, and many other retailers (it's pretty thick, so if nothing else it should prove and effective door-stop)

Supporting my work at Patreon

Thanks so much for taking the time to read this - now go and enjoy the site!
Craig

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SSDD stands for Same Surface, Different Depth. They are a special set of problems that may look the same at first glance, but which require different mathematical ideas to solve them. SSDD Problems have become one of my key strategies to use with my students to help them become better problem solvers.

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Resourceaholic

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Resourceaholic - free resources and ideas for teaching secondary school maths

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Berwick Maths

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So my journey into finally making a website and a blog begins!

I have recently been having a lot of questions as to how I give examples in my lessons. I am honoured to be asked about this on a regular basis and am now excited to share all the types of examples I use for each topic with you.

It all started back in my training year (not that long ago) when I picked up the book "How I wish I'd taught maths" by the wonderful Craig Barton. I was fascinated by the simple, but incredibly effective method of example-problem pairs. These problem pairs became a regular occurrence in all of my lessons, however, this quickly got a little obsessive and I just thought that this was the answer to everything. I did not pay much attention to the rest of that chapter as I thought that my prayers had been answered! Turns out that there are more ways to present examples and it really does depend on the situation. I use example-problem pairs, supercharged worked-examples, examples by fading and supercharged examples with fading (my favourite).

Example-problem pairs are relatively easy to explain. They involve splitting the board into two with a fully worked example on the left of the board and a question on the right side of the board that students do to test whether they have grasped it or not. I often get students to be completely silent and refrain from answering any questions when I am going through the example. If I allow questions, then this interrupts the flow of me giving the example and can create misconceptions. Students copy the worked example into their books once I have fully explained it. I then get them to do a question from the right side of the board on their mini whiteboards. This is fantastic for AFL and discussing misconceptions that students have. I use example-problem pairs for when I am doing processes which are not particularly long. I sometimes do the process of giving an example followed by them doing a question twice. I like to cover all the situations. An example of an example-problem pair is given below.
Example-problem pair template
Supercharged worked examples involve almost the same thing as an example-problem pair, but we allow students to reflect on what they have done. I use this presentation method quite a lot with A-level groups. I even use this method for problem solving questions with my GCSE group. We write in the middle column about why we are doing each necessary step. This has had very positive results as the class progresses together in wider thinking of mathematical concepts. Here is a couple of examples of this below.
Supercharged template 1

Supercharged template 2

Examples by fading involve presenting a fully complete example on the board and then another example, but this time with one step removed. The number of blanks is increased with each following example until there is just the problem left for the students to solve. Simple but impactful! In Craig's book he references the work and evidence of Renkl and Atkinson towards this method. It is amazing to think that this research was actually written up in 2003, but not many teachers are taking note of this! I tend to use these with questions that involve a few distinct steps.

I have been presenting examples using these three ways for my training year and most of my NQT year, but I have always had the thought "Can they be better?". Turns out that I think they can. The combination of supercharged examples and examples by fading has proved to be a big hit with students. You are probably thinking "I want an example of how this can be achieved" so here is one below.
Supercharged with fading template
This method allows all students to understand how to solve linear equations with unknowns on both sides of the equals sign, whilst allowing deeper thinking. I start from the top left and work across. Rather than me just telling students how to do a question like this, I give them chance to reflect and think about why we have done something in the first place to develop their connections with maths. Once they have thought about it a little and we have discussed it as a class, I move on to an example by fading so that I can pick up any students who just need that extra boost of confidence. I then get them to do the question under the title of "Your turn" for an understanding check. I then do exactly the same with the bottom example. I use this presentation method with topics that have a lot of steps within questions. As you can imagine, this is used a lot in my algebra lessons.

My hope is that you will find this website useful. I will be building this website with more and more examples for each topic, as well as exercises that involve the use of variation theory. Please tell me what you think on twitter by tagging me @BerwickMaths. If you would like to contribute to this website, then please use the templates below the pictures and send it through twitter!

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So my journey into finally making a website and a blog begins! I have recently been having a lot of questions as to how I give examples in my lessons. I am honoured to be asked about this on a regular basis and am now excited to share all the types of examples I use...

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DrFrostMaths provides an online learning platform, teaching resources, videos and a bank of exam questions, all for free.

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Maths Conference

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At each conference, we ask delegates to bring along their favourite resources, ideas, hints and tips. Everyone has 90 seconds to tell a colleague about their idea, before swapping and hearing from them.

There is usually time for five or six 'dates', so be ready to spread the word about what is making your classroom buzz right now.

Feel free to bring handouts, weblinks, etc.

Happy dating!

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At each conference, we ask delegates to bring along their favourite resources, ideas, hints and tips. Everyone has 90 seconds to tell a colleague about their idea, before swapping and hearing from them. There is usually time for five or six 'dates', so be ready to spread the word about what is making your classroom buzz right now.

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Looking for reliable online Maths tutor in the UK? Our experienced tutors provide tailored, one-on-one support to help students of all levels achieve their academic goals.

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seneca virtual conference: maths tickets

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seneca virtual conference: maths london tickets

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Eventbrite - Seneca Learning presents Seneca Virtual Conference: Maths - Saturday, 4 July 2020 at United Kingdom. Find event and ticket information.

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Craig Barton CPD

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​Craig Barton has been involved in teaching maths for 15 years. He was the the TES Maths Adviser for 10 years and is now the Head of Education at Eedi. Craig is the author of the best-selling books "How I wish I'd taught maths" and

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http://mrbartonmaths.com/books/

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Books by Craig Barton

Here are the two maths books I have written, one I have edited, and a few novels from back in the days when I didn't know any better.

Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom

Some students think mathematically. They have the curiosity to notice relationships, the confidence to ask why, and the knowledge to understand the answer.
They are the lucky ones.

Many others just 'do' maths. They look at a question, think about how to answer it, answer it, and then move on.

In this book, Craig Barton, maths teacher and best-selling author of 'How I wish I'd taught maths', offers an approach to help all our students think mathematically. It requires the careful sequencing of questions and examples, the role of the teacher, and the mathematical behaviour of our students. It has transformed his teaching.

Drawing upon research into the Self-Explanation Effect, the Hypercorrection Effect and Variation Theory, together with two years of developing this approach with teachers and students around the world, Craig describes exactly what this looks like in the classroom.

But be warned: not everyone agrees. Indeed, it is this very approach that led to Craig being labelled as 'the most dangerous and clueless man in maths education'. If that is not a recommendation to keep reading, I don't know what is.

All activities, diagrams and resources mentioned in the book can be found here.

Contents
Foreword by Jo Morgan
Introduction
Chapter 1: Intelligent Practice
Chapter 2: Where does Intelligent Practice fit in?
Chapter 3: Different features of Intelligent Practice sequences
Chapter 4: Intelligent Practice FAQs
Chapter 5: Rule
Chapter 6: Different uses of Rule
Chapter 7: Pattern
Chapter 8: Demonstration
Chapter 9: Summary table
Chapter 10: Teachers writing their own sequences of questions and examples
Conclusion
A recipe for change?

Available from Amazon, John Catt Educational, and all good (and evil) bookstores.

How I Wish I'd Taught Maths: Lessons learned from research, conversations with experts, and 12 years of mistakes

'I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago...'

When you speak to the likes of Dylan Wiliam, Doug Lemov, Daisy Christodoulou, Kris Boulton and the Bjorks, you are bound to learn a thing or two. But when he started his Mr Barton Maths Podcast, Craig Barton wasn't expecting to have his whole outlook on teaching and learning turned upside down. How I Wish I'd Taught Maths is the story of an experienced and successful maths teacher's journey into the world of research, and what it looks like in the classroom.

Along the way we meet practical, easy-to-implement strategies including Supercharged Worked Examples, Silent Teacher, SSDD problems, low-stakes quizzes, diagnostic questions, Purposeful Practice, self-explanations, harnessing the power of the hypercorrection effect, how to (and how not to) teach problem-solving and much more. No matter your experience, teaching style or favourite number, every maths teacher will find something to think about in this book.

Chapters
1. How students think and learn
2. Motivation
3. Explicit Instruction
4. Focussing Thinking
5. Self-Explanations
6. Making the most of Worked Examples
7. Choice of Examples and Practice questions
8. Deliberate Practice
9. Problem Solving and Independence
10. Purposeful Practice
11. Formative Assessment and Diagnostic Questions
12. Long-term Memory and Desirable Difficulties

Available from Amazon, John Catt Educational, and all good (and evil) bookstores.

The researchED Guide to Education Myths: An evidence-informed guide for teachers

This accessible and punchy series, overseen by founder Tom Bennett, tackles the most important topics in education, with a range of experienced contributors exploring the latest evidence and research and how it can apply in a variety of classroom settings.

In this edition, Craig Barton busts the most damaging myths in education, editing contributions from writers including: Doug Lemov; Bob and Elizabeth Bjork; Mark Enser; and Claire Sealy.

researchED is an educator-led organisation with the goal of bridging the gap between research and practice.

Available from Amazon, John Catt Educational, and all good (and evil) bookstores.

Secrets and Mince Pies, tells the story of a modern-day family over the four days leading up to Christmas, all of whom have a secret to hide. The darkly comic, contemporary novel is played out over ninety-nine short chapters, each one written from the view point of one of the main characters, giving a humorous and interesting insight into modern-day family life.

John is struggling to cope with his role as the modern-day father in an ever changing world; Angela is struggling to cope with the lack of support and complete ignorance of her husband; nineteen year old Lewis is back from university and feels ever more distant from a family who have never understood him; sixteen year old Gemma has grown up and wishes her family would realise; and ten year old child genius Bradley cannot understand why everyone does not see the world as he does. When Angela's parents and Gemma's mysterious new boyfriend come to stay, and the stresses and strains of the festive period begin to take their hold, tensions rise, tempers flare, and those well hidden secrets begin to bubble to the surface.

Available from Amazon in print and Kindle formats

Tom and Jamie work at SuperSave supermarket. Variety is the spice of life, and for them variety consists of whether they will be on the pet foods aisle or in the freezer. With their lives seemingly going nowhere, and both needing money for very different reasons, Tom and Jamie decide to do what any normal pair of nineteen year olds would do - they decide to rob the supermarket.

Tell me a Story is a novel about what happens when two ordinary people try to do the extra ordinary, and the consequences it has for all involved. Along the way there are twists and turns, tears and laughter, and discounted dairy produce.

Available from Amazon in Kindle and print formats

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Books by Craig Barton Here are the two maths books I have written, one I have edited, and a few novels from back in the days when I didn't know any better. Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom Some students think mathematically.

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Cambridge Espresso

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Filtered research on mathematics education

Every two months we bring you an Espresso - a small but intense draught of filtered research on mathematics education, expressly designed with teachers in mind. Each Espresso considers one particular issue in mathematics education, and how the latest good-quality research can provide helpful guidance or further reading. Perfect with a biscuit; sip gently and combine with a drop of professional judgement for a benevolent stimulant effect.

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Each month we bring you an Espresso - a small but intense draught of filtered research on mathematics education, expressly designed with teachers in mind.

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More Same Less

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maths teacher resources for intelligent practice and challenge at more-same-less.co.uk

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Mannermatics CPD