# data[].attributes.attachment_link.title
Recommended Educational Research Papers for Teachers to Read on Mr Barton Maths

# data[].attributes.attachment_link.description
Resourceaholic - free resources and ideas for teaching secondary school maths

# data[].attributes.attachment_link.description
The cookie settings on this website are set to "allow cookies" to give you the best browsing experience possible. If you continue to use this website without changing your cookie settings or you click "Accept" below then you are consenting to this.

# data[].attributes.attachment_link.readable_text
Unfortunately, my father Don Steward passed away from Covid-19 on 3rd May 2020.

Throughout his working life he was passionate about improving the teaching of mathematics and has requested that all of his work remains freely available.

As per his wishes, I have uploaded all of his work to this Blog in the pages section which contains links to google drive where slides and presentations can be downloaded for free.

Don has also requested that those who use his work make a discretionary donation to charities supporting education in Africa.

We have set up a Justgiving fundraising page to support this wish below:
https://www.justgiving.com/fundraising/jessesteward

Many thanks for all of the kind messages we have received which are of great comfort to myself and the family.

Kind regards,

Jess

# data[].attributes.attachment_link.description
ideas and resources for mathematics teachers of 10 to 16 year olds

# data[].attributes.attachment_link.description
Almost 10 years after it started, the aim of this website remains the same: to get everybody enjoying their maths a bit more. Whether you are a teacher looking to plan a great series of lessons, or a student looking for some extra help with a topic, hopefully mrbartonmaths.com will have something fo…

# data[].attributes.attachment_link.readable_text
This website is my attempt to assemble a collection of high-quality, sequences of questions and examples using key principles from Variation Theory. By holding key features between questions and examples constant, together with the mathematical behaviour that I call Reflect, Expect, Check, Explain and the supporting role of the teacher, I believe we can help students better understand key mathematical ideas.

You can find out more about the site and the different types of sequences available by visiting the Introduction.

You can access all the sequences of questions and examples from the Topics menu above.

My 2020 book, Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom, goes into detail about making the most of these activities in the classroom. You can order the book from Amazon, John Catt, or wherever you get your books.

My 2023 book, Tips for Teachers: 400+ ideas to improve your teaching, details my most recent thoughts on using these sequences effectively. You can order the book from Amazon, John Catt, or wherever you get your books.

I have an online course store which offers low-cost, high-quality CPD on-demand. Each course contains short videos, resources, research, activities and questions to reflect upon. The courses most suited to the sequencers on the Variation Theory website are:

# data[].attributes.attachment_link.description
Sequences and behaviour to enable mathematical thinking in the classroom - by Craig Barton @mrbartonmaths

# data[].attributes.attachment_link.readable_text
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.

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

# data[].attributes.attachment_link.description
Better results, more confidence, less time

# data[].attributes.attachment_link.description
Welcome to Corbettmaths! Home to 1000's of maths resources: Videos, Worksheets, 5-a-day, Revision Cards and much more.

# data[].attributes.attachment_link.readable_text
Every Summer, there's this energy on Twitter where math and maths teachers are energized and ready to discuss math problems and puzzles, do Twitter chats on a week night(!), and grow professionally through spirited debate on how to best teach students.
What I've assembled together are magnificent people to follow now and to put in a Twitter Summer reading list, so that once the school year is over you can double-dose on some amazing tweets and threads.
If you are looking for conversations that are longer than 288 character responses, you can certainly try out the UNLIMITED CHARACTER mathematics conversations on this website Cake.co. Here are recent conversations on Cake about mathematics, problem solving and general education.

https://www.cake.co/topics/ZYpZ23P/mathematics
https://www.cake.co/topics/532WTLG/problem-solving https://www.cake.co/topics/QxBX00P/education Top 50 Math Educators to follow on Twitter this Summer
(1a). Craig Barton ‪@mrbartonmaths ‬

Author of "How I Wish I'd Taught Maths: Lessons learned from research, conversations with experts, and 12 years of mistakes". Host of The Mr. Barton Maths Podcast. Creator of maths resources website for teachers and students.

(1b). Drew Foster ‪@drewfoster0 ‬

For those not involved in the maths education universe on Twitter, Drew is an amazing mathematician, educator and recreational maths puzzle expert. He's been involved in multiple online learning platforms including learningclip.co, which he co-created, and Maths-Whizz. Drew's recreational maths puzzles on Twitter are regularly enjoyed by maths educators and their students. He is a frequent presenter at maths conferences throughout the UK.

(2). Joel Bezaire ‪@joelbezaire‬

Reading novels in math class.
https://www.kqed.org/mindshift/50640/how-reading-novels-in-math-class-can-strengthen-student-engagement
(3). Mazed70 @mazed70

Math Puzzles

(4). Dan Finkel @mathforlove

New York Times published columnist, TED Talk Speaker, presenter at math conferences, panelist in "How do you make Maths Fun?"

(5). Mr. Ball III ‪@MathBaller1080 ‬

Student connections

(6). Bonnie Basu ‪@GotMathHelp ‬

(7). Sunil Singh ‪@Mathgarden ‬

Mathematical Jester. Author, Pi of Life: The Hidden Happiness of Mathematics. New York Times writer. Math Learning Specialist.

(8). Math Prof ‪@mathematicsprof ‬

Higher level maths enjoyment

(9). David Wees ‪@davidwees ‬

Master Teacher

(10). P A Hunt ‪@TeachFMaths‬

Creator of #MathOlympiad18

(11). Mr Bayew ‪@MrBayew

The Art of Pedagogy

(12). apm @autismplusmath

Summer mathematician. Puzzles most Fridays at noon when school is out for the Summer and maths teachers will play.

(13). Dan Summerrell @ponderingDan

#edtech

(14). Melynee Naegele

‪ #ElemMathChat‬ moderator

(15). Tiffany Ott @TechieTeachOtt ‬

‪ #masterychat‬ founder

(16). Christina @CLeeMath

Student Connections

(17). Amanda Williams @amwilliamsedu ‬

Problem Solving

(18). 1to9puzzle @1to9puzzle

The amount of time they put into creating these (almost) daily maths puzzles is incredible. All winners are recognized and cheered.

(19). Henry Picciotto @hpicciotto

I've been a big fan of this master teacher for several years. Great resources on his blog and website and he's always willing to share ideas and to problem solve with new teachers (NQTs). Frequent presenter at math conferences.

(20). Mr. Mattock FCCT @MrMattock

(21).

**********
Help me to complete this list before Summer by sharing your recommendations here or on Twitter.

# data[].attributes.attachment_link.title
50 Top Math Educators to follow on Twitter this Summer

# data[].attributes.attachment_link.description
Every Summer, there's this energy on Twitter where math and maths teachers are energized and ready to discuss math problems and puzzles, do Twitter chats on a week night(!), and grow professionally through spirited debate on how to best teach students.

# data[].attributes.attachment_link.readable_text
To complement FREE online resources ATM provides elsewhere on this website, to help with home and class schooling, this page provides free material to expand teachers' professional knowledge and development. Content will be regularly updated.

CPD Videos - Teacher Development Resources

Welcome to this new collection of short 10 minute video's designed to support teachers at all stages of their career.

Thanks to the group of members who have contributed to this project, including Jenni Ingram, John Mason, Anne Watson, Tom Fancome and Mike Ollerton

Noticing and attention in maths classrooms

Methods of moving from arithmetic to algebra

The Symbols and the Symbolised, Cambridge Branch Presentation 11/06/20

Hosting Workshops Online - An Example

Holding meetings and workshops online - for example, so as to abide by social distancing rules in the wake of the Covid-19 pandemic - presents its own special challenges for audience feedback and engagement. A meeting of the joint ATM and Mathematical Association (ATM/MA) Cambridge branch may provide some helpful suggestions.

On June 11th (2020) Pete Griffin - Assistant Director in the Secondary Team at the NCETM (National Centre for Excellence in the Teaching of Mathematics) - gave a virtual workshop presentation entitled 'The Symbols and the Symbolised', via the Zoom app. The session on exploring the use and understanding of mathematical symbols attracted 46 online attendees. The Zoom session was recorded and the video is below:

Host Pete designed stimulating exercises, involving virtual actions on mental imagery. Teachers joined in the Zoom breakout sessions and enjoyed the workshop, making lots of connections to other things they had read and experienced in school.

More suggested background on lesson design can be found in ATM Publication On teaching and learning mathematics with awareness or ebook

Full classroom resources accompanying the video - including templates, and supplementary papers and materials - are available to ATM members in the Member Only Resources area of this website.

ATM branch meetings are open to all (including non-ATM members), and are great for teachers to network and learn from colleagues.

Join today and receive 12 months' membership, which includes:

# data[].attributes.attachment_link.keywords[]
training 
teachers 
atm
association of teachers of mathematics
cpd

# data[].attributes.attachment_link.description
To complement FREE online resources ATM provides elsewhere on this website, to help with home and class schooling, this page provides free material to expand teachers' professional knowledge and development. Content will be regularly updated. Welcome to this new collection of short 10 minute video's designed to support teachers at all stages of their career.

# data[].attributes.attachment_link.title
Direct instruction: planning & delivering

# data[].attributes.attachment_link.description
Talks I have given about curriculum and lesson planning using principles of direct instruction, also known under the names of 'explicit instruction' or 'teac...

# data[].attributes.attachment_link.title
Being Mathematical With And In Front of Learners_John Mason_2015 ATM Conference Opening Plenary

# data[].attributes.attachment_link.description
Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math.

# data[].attributes.attachment_link.title
GeoGebra - the world's favorite, free math tools used by over 100 million students and teachers

# data[].attributes.attachment_link.description
Free digital tools for class activities, graphing, geometry, collaborative whiteboard and more

# data[].attributes.attachment_link.readable_text
The Random Topic Generator allows you to choose from a variety of topics and assign the options you want for those topics. You can then decide how many questions you want before creating a random set of questions from those topics. You can either display these questions on the board, or turn them into a printable worksheet. You can refresh any question you don't want, and show and hide the answers to all questions, or individual questions.

The Specified Topic Generator allows you to choose how many questions you want, and to then choose which topic you want for each question. You can then choose the options for each individual question. These can then be displayed on the board, or turned into a printable worksheet. Each question can be individually refreshed within the given question options, and you can show and hide the answers to all questions, or each individually. You can also save a particular setting to create new questions of the same types at a future time.

# data[].attributes.attachment_link.description
The Random Topic Generator allows you to choose from a variety of topics and assign the options you want for those topics. You can then decide how many questions you want before creating a random set of questions from those topics. You can either display these questions on the board, or turn them into a printable worksheet.

# data[].attributes.attachment_link.readable_text
Mr Barton Maths Podcast

Contents

The Mr Barton Maths Podcast: " changing useless time into CPD time" - @MrsG on Twitter

On the Mr Barton Maths Podcast I interview guests from the world of education who interest and inspire me. They may be fellow teachers, bloggers, thinkers, or people of influence. As well as discussing my guest's particular areas of interest, I always like to dig deep into their lesson planning process, and ask them to describe lessons that did not go so well and what they learned from the experience. Be warned, these interviews are intended to be long and in-depth, and are probably best digested across a few journeys to work or a few laps of the park with your dog.

It makes me so happy that many teachers are using these podcasts as CPD, either listening in the car, on long walks and bike rides, or doing the dishes. That was never the original intention, but it makes sense - I learn so much from each of my guests, so I shouldn't be surprised that others do too :-) I really hope you find my guests as interesting and inspiring as I do, thanks so much for listening, and please help spread the word!

The Mr Barton Maths podcast is available on every major podcast platform. Just search for it, and it should come up. There you can follow/subscribe for free so you never miss an episode. Here are some links to a few of those platforms.
Apple Podcasts
Google Podcasts
Spotify
RSS feed

Alternatively you can stream an episode directly from the episode show notes page, all of which are linked to below.

Often my guests recommend books and research papers for teachers to read. You can find details of all of these here:
Recommended Books for Teachers to Read
Recommended Educational Research Papers for Teachers to Read

Do you have a product, service or event that you would like to promote?

Have you found that advertising at conferences, sending emails, buying adverts in publications, or producing flyers are either expensive or have relatively little impact?

Would you like to reach thousands of engaged, influential teachers to help spread your message in a relatively low-cost, innovative way?

If so, then you may wish to consider sponsoring an episode of the Mr Barton Maths Podcast. There are single and multi-episode options available.

You can listen to examples of sponsor slots at the start of the following episodes:

Please drop me an email at [email protected] to discuss further.
If you are new to the podcast and are looking for 4 episodes to get you started then, try these three beauties, all of which had a profound influence on how I think and teach.
Dylan Wiliam - Author, Researcher, Trainer and Assessment for Learning Expert
Dylan Wiliam is my hero. I know this is a big claim, but I think this interview is an absolute must-listen for teachers of all subjects, possibly all humans full-stop. We spoke about feedback, planning, questioning, research, lesson observations, what Dylan wishes he had known when he started teaching, and so much more. I genuinely have listened back to this interview more than 5 times, and I pick up something new on each listen. Thank you Dylan!

Peps Mccrea: Planning, Memorable Teaching and Teacher Expertise
Peps has done it all. He is a former Fasttrack maths teacher and Senior Lecturer in mathematics education. He has been a National Curriculum Advisor for the DfE, External Examiner at the OU, and is the author of Lean Lesson Planning and Memorable Teaching. He now leads on the Institute for Teaching's Masters in Expert Teaching course. We had a great time digging into three areas that really interest me: lean, effective lesson planning; making our teaching memorable; and helping teachers determine and develop expertise in their profession. Get your pen and paper ready for this one, there are nuggets left, right and centre.

Slice of Advice: What did you learn this year?
In an experimental episode, I asked 50+ of my favourite people one question: "what did you learn this year?". You will hear from the likes of Dylan William, Andrew Smith, Katharine Birbalsingh, Claire Sealy, Andrew Percival, Dan Meyer, and many others talking all things from feedback, work-life balance, signalling, metacognition, working abroad, and everything in between. A must listen for teachers of all subjects and age groups.
When I am lucky enough to attend a conference, I like to sit down with a fellow delegate at the end of the day and discuss the sessions we attended and our key takeaways. Hopefully these episodes are useful to those who could not make it on the day.

Conference Takeaways: MA Conference 2021
Join Jo Morgan and I for 3 days at the "virtual" MA maths conference, for discussions about race, problem solving, ratio, parental influence, misconceptions and much, much more.
Day 1
Day 2
Day 3

Conference Takeaways: MathsConf24 - Online - October 2020
Join me and Jo Morgan for a Conference Takeaways podcast from the second ever online MathsConf. We discuss a controversy about moving the decimal point, the importance of tasks, ratio tables, Increasingly difficult questions, technology, maths tricks, Times tables and much, much more.

Conference Takeaways: MathsConf23 - Online - June 2020
Join me and Jo Morgan for a Conference Takeaways podcast from the first ever online MathsConf. We discuss online CPD, Don Steward, magical maths, exact trig values, misconceptions with angles, teaching the what before the why, and much, much more.

Conference Takeaways: MathsConf22 - Manchester - March 2020
Join me and Dani Quinn for a Conference Takeaways podcast from MathsConf in Manchester, where we discuss percentages, algebraic thinking, surds, circle theorems, and I try to find out exactly how Dani and her team got those incredible GCSE results.

Conference Takeaways: MEI 2019
Join me and Jo Morgan for a controversial Conference Takeaways podcast from the wonderful MEI 2019 Maths Conference, where we discuss everything from calclator use, schemes of work, and a potential issue with manipulatives.

Conference Takeaways: ATM MA Conference 2019
Join Jo Morgan and I for 2 days at the ATM MA joint maths conference, for discussions about the evolution of maths vocabulary, problem solving, lesson observations, listening to learners, visual representations and much much more!
Day 1
Day 2

Conference Takeaways: Educating Northants 2019
Join Jo Morgan and I for a jam-packed discussion following the excellent Educating Northants Conference about mastery at primary, a knowledge curriculum, multiple mathematical methods, dual coding, variation starters... and a breathing exercise.

Conference Takeaways: researchEd Blackpool 2019
Simon Cox and I sat down to discuss our key takeaways from the excellent sessions we saw at researchEd Blackpool 2019. Hear reflections on workshops by the likes of Mark McCourt, Mark Lehain, Anne Watson, Oliver Caviglioli, Colin Foster, Simon Cox and Ben Gordon. It's a good one!

Conference Takeaways: Festival of Education 2018
I had the pleasure of attending and speaking at the Festival of Education. And if that wasn't enough, I also got to reflect on each day's session with Kris Boulton (@Kris_Boulton) from a sun-soaked Master's garden. So sit back, relax and listen to us discuss everything from curriculum, knowledge, reading, measuring progress, Ofsted, and even Love Island
Festival of Education Day 1
Festival of Education Day 2

Conference Takeaways: Comparative Judgement
In this special Conference Takeaways episode, myself and English teacher Jon Sellick reflect on what we learned from attending a workshop entitled R efining assessment and reducing workload, delivered by Daisy Christodoulou, which was all about the fascinating concept of Comparative Judgement. And just as you are getting sick of our voices, I am delighted to say that Daisy herself joins us to answer a few key questions, marking her return to the podcast following her very well-received 2017 appearance.

Conference Takeaways: BCME 2018
Jo Morgan (@mathsjem) and I spent four days at the BCME conference in April of 2018, and decided to record a podcast each night - it sounded a good idea at the time. Hear our thoughts on all things from variation, manipulatives, A Level teaching, tough GCSE questions, pub quizzes and Hannah Fry...
BCME Day 1
BCME Day 2
BCME Day 3
BCME Day 4
The podcast started out being just for maths teachers. But as the show developed, and my research widened, I realised I had so much to learn from teachers and researchers in other subjects. These episodes are hopefully of interest to everybody, no matter what subject or age of children you teach.

Doug Lemov: Tips for the return to classrooms
Doug Lemov returns to the podcast to share tips to support teachers and students for the return to classrooms. Sharing takeaways from 3 books - Teach like a Champion 3.0, Teaching in online classrooms and the Coach's guide to teaching - Doug provides strategies, theories and resources to help make the return to classrooms as effective as possible. This episode was incredibly timely in March 2021, but is relevant whenever you may choose to listen.

Ollie Lovell: Cognitive Load Theory in Action
Ollie Lovell returns to the show to discuss one of our favourite subject - Cognitive Load Theory. But instead of going over the usual stuff, Ollie talks about the things surprised him whilst doing research for his new book, what Cigntive Load Theory has to say about remote teaching and online lessons, and finally Ollie helps me get my head around some aspects of the theory that I have long found confusing!

Peps McCrea: Motivated teaching
Peps McCrea returns to the podcast to talk about the secret ingredient in learning - motivation. Peps argues that it is motivation that dictates what students pay attention to, and it is what they pay attention to that determines what they are likely to remember. Peps describes the 5 core drivers of motivation, and provides practical suggestions for how teachers can tap into these in their classrooms. A must listen!

Mark Healy - Part 2: Sleep, growth mindset and teaching amid Covid-19
Mark is a psychology teacher and Deputy Head from Scotland who joins me for the second time to discuss the challenges of teaching amidst the Cobid-19 outbreak, the importance of sleep for both students and teachers, and he thoughts about Dwek's growth mindset. Hopefully this episode will keep you awake... in a good way.

Jemma Sherwood - Part 2: Preparing for September 2020 & being a Head of Department
Jemma returns to the show for a surprisingly maths-less episode as she discusses her and her department's plans for what will prove to be a challenging return to school in September 2020, as well as sharing advice for Heads of Department that is timeless.

Adele Bates: Behaviour and relationships
Adele has transitioned from an opera singer to a teachers, specialising working with students who have behavioral challenges both in mainstream schools and alternative provision centres. In this episode Adele shares her experiences, anecdotes and advice that will be useful to all teachers no matter how experienced you may be.

Mark Healy: Cognitive science versus cognitive psychology
Psychology teacher and Deputy Head, Mark Healy, joins me to discuss the distinction between cognitive science and cognitive psychology, their potential misuse in schools, and how schools can build a culture whereby staff willingly engage in meaningful CPD. Mark will also return soon to discuss sleep!

Paul Kirschner and Carl Hendrick: How learning happens
Paul Kirschner and Carl Hendrick join me to discuss their excellent book: How Learning Happens. But over the course of 2 hours we delve into so mich more, including the writing of and reaction to Paul seminal paper, Why Minimal Guidance During Instruction Does Not Work and what advice Paul and Carl would have for teachers trying to help their students learn amidst school closures.

Special episode: Online learning during the Covid-19 outbreak
In the wake of the Covid-19 outbreak, I sat down with 3 teachers from France who are a week ahead of the UK in terms of providing online learning to their students following school closures. Listen as we discuss what works and what doesn't. Stay safe everyone.

Kris Boulton - Part 3: Is cognitive science almost useless for designing effective teaching?
Kris Boulton returns to the show to complete the trilogy - although Parts, 4, 5... and 23 may not be far away as I have so much to talk to him about. Here we delve deep into Kris' belief that cognitive science has severe limitations when it comes to actually helping teachers improve, and what his alternative is. It is a cracker!

Multiple Choice Questions on trial with AQA's Zeek Sweiry
In a special episode of the show, I speak to AQA's resident multiple choice question guru, Zeek Sweiry to discuss the merits of diagnostic multiple choice questions both as a teaching tool and a tool of assessment.

Slice of Advice 2019: What did you learn this year?
The band are back together again to reflect on what they learned in 2018/19. Expect contributions from the likes of Dylan Wiliam, Mary Myatt, Harry Fletcher-Wood, Tom Bennett, Oli Caviglioli, and many, many, many more. Roll on the summer!

David Didau: Making kids cleverer
David Didau is a former English teacher turned educational consultant, blogger and author. He has written two of my favourite educational books of all time: What If Everything You Knew About Education Was Wrong? and What Every Teacher Needs to Know About Psychology, which he co-wrote with former podcast guest Nick Rose. David now has a new book out - Making Kids Cleverer: A manifesto for closing the advantage gap - and it is a little on the controversial side! In this thought-provoking conversation we cover everything from intelligence, IQ, heritability, cognitive load theory, desirable difficulties, and parenting!

Slice of Advice: What does the first lesson with your class look like?
Slice of Advice returns, and in this episode over 30 world-class educators give their answer to the question: What does the first lesson with your class look like? You will hear about specific activities, setting expectation, establishing routines, and much more from the likes of Bruno Reddy, Mark McCourt, Jemma Sherwood, Jo Facer, and many more besides. I love this episode!

Slice of Advice: What did you learn this year?
In an experimental episode, I asked 50+ of my favourite people one question: "what did you learn this year?". You will hear from the likes of Dylan William, Andrew Smith, Katharine Birbalsingh, Claire Sealy, Andrew Percival, Dan Meyer, and many others talking all things from feedback, work-life balance, signalling, metacognition, working abroad, and everything in between. A must listen for teachers of all subjects and age groups.

Doug Lemov: Teach like a Champion and Top Tips for delivering training
Doug Lemov is a legend. As the author of Teach Like a Champion, he has had a major impact on my teaching and thinking over the last two years. I this interview we discuss several key strategies from the book, looking at the practical ways we can implement them in the maths classroom. We then turn our attention to teacher training, and Doug shares some wonderful advice for anyone delivering a training session to their colleagues. This is a cracker.

Peps Mccrea: Planning, Memorable Teaching and Teacher Expertise
Peps has done it all. He is a former Fasttrack maths teacher and Senior Lecturer in mathematics education. He has been a National Curriculum Advisor for the DfE, External Examiner at the OU, and is the author of Lean Lesson Planning and Memorable Teaching. He now leads on the Institute for Teaching's Masters in Expert Teaching course. We had a great time digging into three areas that really interest me: lean, effective lesson planning; making our teaching memorable; and helping teachers determine and develop expertise in their profession. Get your pen and paper ready for this one, there are nuggets left, right and centre.

Robert and Elizabeth Bjork - Memory, Forgetting, Testing, Desirable Difficulties
Robert and Elizabeth Bjork are my heroes. The Godfather and Godmother of memory (my name for them, not theirs!), and they have transformed my teaching. It was an honour to talk to them. We spoke about how memory works, why forgetting is so important, why tests are far more than tools of assessment, when and why to make learning difficult, optimal spacing schedules, how to interleave successfully, and a whole lot more.

Greg Ashman - Cognitive Load Theory and Direct Instruction v Inquiry Based Learning
Greg is a head of maths in Australia and a prolific and influential blogger at Filling the Pail. We spoke about the implications of Cognitive Load Theory for planning and teaching mathematics (although the lessons are applicable to all subjects), and why Greg prefers direct instruction as opposed to inquiry based approaches to learning.

Tom Bennett - Behaviour, Teacher Workload and ResearchEd
Tom is the UK's leading figure on behaviour in schools, and the founder of ResearchEd. We spoke about in depth about managing behaviour in the classroom, including addressing some common myths. We also spoke about how best to tackle teacher workload, and what Tom considers to be the most important pieces of educational research.

Dylan Wiliam - Author, Researcher, Trainer and Assessment for Learning Expert
Dylan Wiliam is my hero. I know this is a big claim, but I think this interview is an absolute must-listen for teachers of all subjects, possibly all humans full-stop. We spoke about feedback, planning, questioning, research, lesson observations, what Dylan wishes he had known when he started teaching, and so much more. I genuinely have listened back to this interview more than 5 times, and I pick up something new on each listen. Thank you Dylan!
I am not going to lie - these episodes contain plenty of maths chat. There may be ideas that transfer across to other domains, but I make no promises!

Christian Bokhove: Coherence, textbooks and research best bets
Christian is an Associate Professor of Maths Education at the University of Southampton. In this conversation we discuss the importance of coherence in a curriculum, why a god textbook is so important, and what are his best bets for education research?

Anne Watson and Kris Boulton in conversation
Previous guests on the show, Anne Watson and Kris Boulton, come together to discuss 10 big questions in maths education, including "what does it mean to understand something in mathematics?" and "what, if anything, are the most important things from cognitive science for teachers to be aware of?". What follows is 3+ hours of enlightened discussion and debate, with me doing my best to keep up!

Michael Pershan - Worked Examples - Part 2
In a follow-up to Part 1 (see below), US teacher, blogger and author Michael Pershan joins me to compare and contrast our two approaches to delivering worked examples. And then we discuss two fresh and fascinating areas: the role of mistakes in worked examples, and then the issue of using names in worked examples (either real or fictions). I loved this conversation.

Michael Pershan - Worked Examples - Part 1
In a podcast cross-over episode, Ollie Lovell from the wonderful Education Reading Room podcast interviews US teacher, blogger and author Michael Pershan about worked examples. How does Michael plan his worked examples, what do they look like in the classroom, what does the research say, and why is self-explanation so important?

Jo Morgan: tips and resources for teaching online
Jo Morgan returns to the show to discuss how she is approaching online teaching 6 months on from when she first experienced it. It turns out lots has changed. Jo has some great advice and resources for making remote teaching effective and manageable.

Jo Morgan: Teaching Key Stage 3 maths
Jo Morgan returns to the show to discuss how she is finding it this year with no GCSE or A Level classes. It turns out she is loving it, and we discuss in depth the beauty of teaching Key Stage 3 maths, the mistakes she sees other schools make with this phase, and the simple strategies for improvement that any school or teacher could implement.

Jonathan Hall: MathsBot, teaching visually and behaving mathematically
Jonathan Hall, the creator of the incredible MathsBot website joins be to discuss why he has moved to teaching in a more visual way, what this looks like in the classroom in terms of physical manipulatives versus virtual manipulatives, and what he means by behaving mathematically.

Robert Kaplinky: Depth of Knowledge, Open Middle Problems and effective CPD
Robert is a US maths educationalist and all round legend. He is the brains behind the Open Middle website, and the depth of knowledge framework. In this episode we delve deep into problem solving using those two key ideas as a stimulus, and also discuss effective CPD. It is a good one!

Tom Francome - Part 1: Supporting novice teachers, planning lessons and... Excel!
Tom is a former maths teacher and head of maths, and now lecturer, researcher and teacher trainer. In this epic conversation I manage to ask about 3 of my planned questions because the answers Tom gives are so insightful. We cover planning lessons, working with novice teachers, where lessons can go wrong, and much, much more.

Topics in Depth: Indices with Jo Morgan (supported by TES)
Jo Morgan and I go deep into the topic of indices, looking at resources, sequencing, misconceptions, historical background, and other key issues. This is available in audio form and also as a video. On the podcast page you will also find a link to download the PowerPoint used that contains all the resources.

Alex Bellos: Puzzles, Perception and Pool Tables
Alex is a journalist, the man who runs the Guardian's fortnightly Monday puzzle, and the author of some of the best-loved Maths books of recent times, including Alex's Adventures in Numberland. As I found out, he is also just a brilliant person to have a chat to. We talk about puzzles, writing about maths, the perception of our subject, and plenty more!

Julia Smith: Teaching GCSE resit and the 5Rs approach
Julia is a former teacher, who is now a teacher trainer, author, and pioneer of the 5Rs approach. This simple way of breaking down lessons into manageable chunks, each of which serves a key purpose, has been revolutionary in terms of the impact it has had on GCSE resit students. But, as we examine in this conversation, its application could go much wider.

Rob Eastaway: Estimation, perception of maths and the importance of haha
Rob is a mathematician, author, presenter and puzzle writer. In this episode we delve deep into the importance of estimation, even in the an age of technology. We also cover the public perception of maths, humour in lessons, the writing and answering of maths puzzles, the relationship between cricket and maths, and even a bit of parenting advice. It is a good one!

Jonny Griffiths: Rich tasks, mental health and problem solving
Jonny is a legend of maths education, being the brains behind the wonderful RISP activities. And of course in this conversation we dig into those. But we also delve into lots of other territories, ranging from problem solving, textbook writing, and an important discussion about mental health issues in teaching.

Chris McGrane: Task design and changing your mind
Chris is a former head of mathematics in Scotland who now works for La Salle education. Like me, he has undergone something of a mid-career crises when he started to engage in educational research. However, we have reached slightly different conclusions in a number of key areas. In this conversation we delve deep into those areas, as well as discussing how to create or choose a good mathematical task.

Michael Pershan: Example-Problem Pairs, problem solving and moving schools
Michael is a maths teacher and blogger from the US. I have been a fan of Michael's writing for a long time, and it was fascinating to get the opportunity to talk in depth about areas of pedagogy that are close to our hearts. We talked about the difficulty of moving schools, our views on problem solving and then the big one... Example-Problem Pairs (spoiler alert: we don't agree upon the best way to use them!)

Naveen Rizvi - Part 1: Scripted lessons, examples and social media
Naveen Rizvi is Maths Curriculum Advisor for United Learning, and has previously taught at Michaela and Great Yarmouth schools, both of which have been in the public eye over the last few years. In what will no doubt prove a controversial episode (always good for the listening figures!) Naveen takes us through how she plans a sequence of lessons on rearranging formulae, completed with a scripted resource booklet which you can download from the podcast page. It is fascinating listening.

Chris Smith: Injecting fun into lessons, Resources, Pi Day, Revision Days
Chris Smith is a maths teacher, Pi Day lover, TED Talker, popular newsletter writer, and the 2018 Scottish teacher of the Year. In this conversation we cover everything from lesson planning, time-management, running successful revision days, and the role of fun in maths lessons. Enjoy!

Jo Morgan: 100th Maths Gems Special
In this special podcast to celebrate Jo's 100th Maths Gem blog post, we end up talking about so much more than resources - although there is plenty of chat about that, so don't you worry. We also cover the role of fun in lessons, practical use of cognitive science in teaching, SSDD problems, what Jo has learned this year, and plenty more besides. Oh, and there is even a quiz!

Helen Williams: Early Years teaching and manipulatives
Dr Helen Williams has been teaching, and learning about mathematics teaching, for over 30 years. Her particular expertise is in learning maths with children from 3 to 8 years of age, which is most certainly not my area of expertise! In this wide-ranging conversation, we discuss exactly what an early years maths lesson might look like, why manipulatives are so important for children of all ages, and why Helen is not exactly sold on Cognitive Load Theory!

Bernie Westacott: Teaching maths with visuals and manipulatives
Bernie Westacott is a master of teaching key mathematical concepts in a visual way, using manipulatives and other representations. In this episode he takes me through 3 demonstrations: introducing number, operations with negative numbers, and simultaneous equations. In a world first for the Mr Barton Maths Podcast, this episode is available in both audio and also video so you can see Bernie in action, and watch me struggle!

Hannah Fry: Algorithms, love and being a mathematician
Dr Hannah Fry is a mathematician, and a legend. In this interview we discussed her career, books, and TV work, covering topics such as the role maths can play in relationships, parenting, solving crime and driverless cars. The includes a discussion of Hannah's book Hello World, which is outstanding.

Jeremy Hodgen: Teaching low-attaining students, relevance and fingers!
Jeremy is a Professor of mathematics education researcher at UCL Institute of Education, the co-author, along with Dylan Wiliam, of Mathematics Inside the Black Box, and the co-creator of the ICCAMS project. We had a fascinating and wide-ranging discussion that covered is findings on a project into the best way to teach low-achieving students, the importance of mathematical stories, how to deal with relevance in mathematics, and the key role fingers have to play in learning!

Simon Singh: Fermat's Last Theorem and stretching high-attainers
In this episode, I got to interview one of my all-time heroes, Simon Singh. Simon is the author of some of my favourite books, including Fermat's Last Theorem and the Codebook. But not content with retelling some of the most wonderful stories about our subject, Simon also wants to help develop mathematics excellence through his work with the Parallel Project. This is an episode not to be missed.

GCSE Maths Special: Graham Cumming and Karen Wilkinson
With the summer 2018 Maths GCSEs finally behind us, I thought it would be nice to reflect on the experiences of teachers and students over the first two years of sitting of the new GCSE Maths specification. And who better to join me on this voyage of discovery than my very own Head of Department, Karen Wilkinson, and the Head of Maths at Edexcel, Graham Cumming. Settle yourselves down for an enlightening discussion on good and bad questions, tiering decisions, and much, much more.

Alison Kiddle and Charlie Gilderdale: NRICH
Alison and Charlie work for NRICH, a website of rich maths activities and problems that I am sure most of my maths teaching audience have heard of and visited. But how can we get the very best out of NRICH? Are the activities only suitable for our highest attainers? And how on earth will my students develop fluency in key skills whilst doing them? It is these questions and more that I wanted the answers to, and Alison and Charlie certainly delivered!

Oliver Lovell: Planning, running a maths department and Cognitive Load Theory
Ollie Lovell is a high school maths teacher from Australia. He is also an incredible thinker. Like me, he is a little obsessed with educational research and how he can apply it to the greatest effect in his classroom. In an epic 3+ hour interview we dig into how Ollie has planned out a new approach to teaching Year 12, how he runs a maths department, and his views (and questions!) about Cognitive Load Theory. I loved this interview!

Anne Watson and John Mason: Variation, questioning, visualising and developing mathematical thinkers
Anne Watson and John Mason are two of the most influential people in the history of mathematics education. Their books, papers and workshops have influenced generations of maths teachers and this directly improved the experience of teaching and learning maths for hundreds of thousands of students. In this interview we look back over their careers, and then dive deep into the principles of Variation Theory, how to ask good questions and the importance of visualisation.

Helen Hindle: Mixed attainment teaching and growth mindset
Helen is an experienced maths teacher and head of department. She is also the organiser of the Mixed Attainment Maths Conference. Mixed attainment (or as I often mistakenly call it, mixed ability) teaching is an area I am woefully inexperienced in and clueless about, so it was incredible to speak to Helen to get to the bottom of why she believes in it so much, and how to make it as effective as possible. Along the way we also tackle the concept of a growth mindset, and how Helen tries to instill that in her students.

Amir Arezoo: Lean maths departments, deep work, schemes of work
Amir is an experienced maths teacher, someone who has been head of maths in several schools, and who is now Vice Principal for Raising Achievement at Horizon Community College in Barnsley. Listeners have requested more interviews with experienced and successful teachers, so they can learn from their habits, processes and past mistakes, and Amir certianly delivers. We talk about running successful departments, planning lessons, creating opportunities for deep work, what makes a good scheme of work, and a lot more!

Jane Jones: Ofsted, observations, marking, reasoning
Jane is a former teacher and head of maths who is now the HMI National Lead for Mathematics - to me and you that means she is the most senior maths specialist in Ofsted. In this revealing interview Jane discusses everything from observation and marking, setting and reasoning, and a lot more besides. Whether you are due an Ofted inspection, just had one, or simply curious about what Ofsted are looking for, this is the interview for you.

Colin Foster: Mathematical Etudes, Confidence and Questioning
Colin Foster is a former maths teacher who is now an Assistant Professor at the Centre for Research in Mathematics Education in the School of Education at the University of Nottingham. We talked about Mathematical Etudes, or what I term Purposeful Practice. I believe this is one of the most important types of practice we can give our students, allowing them to become fluent in key skills, whilst also developing problem solving capabilities. We also discuss the role of confidence in learning, and what makes a good question. I loved this interview.

Lucy Rycroft-Smith: Cambridge Mathematics, Setting, Times Tables, Anxiety
Lucy is the Research and Communications Officer at Cambridge Mathematics. I base my interview around five key questions from Lucy's espresso research series: What are the effects of attainment grouping on mathematics learning? What are the issues in learning and assessing times tables? How does maths anxiety affect mathematics learning? How does assessing confidence affect learning and testing in mathematics? How can mathematics teaching be measured? But we cover a lot more besides!

Kris Boulton - Part 2: Minimal guided instruction, Understanding, How before Why
Kris returns to the podcast for another epic. This time we cover Kris' concerns with minimal guided approaches to teaching, such a discovery and inquiry based learning. We also delve into what it actually means to understand something in maths, and whether we as teachers can ever truly assess that understanding. Finally, how do you decide if you should teach the How before the Why?

Andrew Blair interview from 2014: Inquiry Maths and being Head of Department
My first interview with Andrew caused something of a stir (in a good way!), so I thought it would be useful to release an interview I did with Andrew back in 2014 for my TES Maths Podcast. Here Andrew describes a completely open-ended inquiry lesson, as well as sharing some excellent advice on being a Head of Department.

Andrew Blair: Inquiry Maths
Andrew is a head of maths at the creator of inquirymaths.org. We spoke about planning and delivering inquires in mathematics, explicit instruction, developing fluency, problem solving, and evaluated evidence related to memory, motivation and purpose.

Rachel Webster: How your Year 7s have been taught maths
Rachel is an experienced primary maths teacher. We spoke about what primary maths lessons look like, what topics they have covered, their problem solving skills, their use of manipulatives, what students might be expecting maths lessons to look like at secondary school, and much more.

Chief Examiner Trevor Senior: How GCSE Maths exams are written
Trevor is AQA's Chief Examiner for the Maths GCSE. We spoke about when the GCSE maths writing process starts, who is involved, what makes a good question and what makes a bad question, what are the difficulties, how exams are marked, and much more. This is a great listen now we have finally made it through the first new specification GCSE cohort, and essential listening as we prepare for the next!

Dani Quinn - Part 2: Michaela School, Behaviour, Drills, Culture
Dani Quinn, the Head of Maths at Michaela Community School, returns! In the follow-up to the controversial first interview we spoke about the behaviour policy at Michaela, the practice of drilling, teaching for understanding and the staff culture.I wonder if I will get told to "go to hell" as a result of this one.

Dani Quinn - Part 1: Michaela, Lesson Planning and Low Stakes Tests
Dani is the head of mathematics at the controversial Michaela Community School. We spoke at length about what maths lessons at Michaela Community School looks like, the importance of their weekly test, and how competition between students is used.

Paul Rowlandson - Bar Modelling, Questioning, Shanghai, Tokyo & Training Teachers
Paul is a maths teacher and a leading expert on bar modelling. We spoke about planning for understanding, bar modeling, advice on questioning, what Paul learned from his trips to Shanghai and Toyko, advice for teacher training and much more.

John Corbett - Flipped Learning, Making Videos and Corbett Maths
John is an experienced maths teacher and the legend behind the ridiculously good Corbett Maths. We spoke about planning and delivering lessons using a flipped learning approach, the process that goes into creating maths videos, writing good maths questions, and advice for new teachers.

Beth Lilley - A year as an NQT
At the time of recording, Beth had just finished her first year as a maths teacher. We spoke about the pressures of being an NQT, maintaining a work-life balance, and Beth shares her top tips for surviving and thriving during a grueling year.

Jamie Frost - Dr Frost Maths and Teaching High Achievers
Jamie is an experienced maths teacher at the high achieving Tiffin School. He is also the creator of the outrageously good Dr Frost Maths website. We spoke about planning sequences of lessons, the importance of internalising concepts, and teaching high achievers.

Mark McCourt - Ofsted, emaths, La Salle Education and NCETM
Mark is a legend in the world of maths education. He is a former head of maths, Ofsted Insepctor, Headteacher, creator of emaths, creator of Complete Maths, and the organiser of the amazing La Salle Maths Conferences. We spoke about Ofsted lesson observations, teacher training, being Head of Department and why Mark has never marked a book in his life!

Stefanie Sullivan - Maths PGCE Tutor from Nottingham University
Stef is in charge of the PGCSE programme at Nottingham University, and was my tutor when I trained there many years ago. We spoke in-depth about the lesson planning process, habits of successful trainees, and the most common reasons for teachers leaving the profession.

Will Emeny - Great Maths Teaching Ideas and Numeracy Ninjas
Will is a genius. He is a head of maths, blogger, and the creator of Numeracy Ninjas. He also has a keen interested in cognitive science, and memory in particular. We spoke about being a successful Head of Department, prior learning dependency flow and the fascinating subject of memory

Dan Meyer - dy/dan, 3 Act Math and Desmos
Dan is possibly the most famous maths teacher in the world. His TED talk and subsequent work on 3 Act Math had a huge influence on my career. We spoke about good and bad uses of technology in teaching and learning, the future of Desmos and the excellent Aspirin and Headache series.

Charlie Stripp - NCETM and MEI
Charlie is a very important man in the world of maths education. He is the head of both the MEI and the NCETM, as well as still finding time to teach maths. We spoke about the importance of times tables, Mastery teaching and the best and worst features of the new maths GCSE.

Bruno Reddy - Times Table Rockstars and MrReddy.com
Bruno is incredible. He is the former head of maths at the pioneering King Solomon Academy, and the creator of the global dominating Times Tables Rockstars. We spoke about creating the right culture in lessons and in school, homework and written feedback, mixed attainment classes, Mastery, Shanghai, and much, much more!

Mel Muldowney - JustMaths
Mel is part of the award winning JustMaths team, a prolific blogger, and experienced maths teacher. We spoke about running a maths department, moving to a new school, and her now award-winning way of preparing students for the demands of the Maths GCSE.

Jo Morgan - Resourceaholic
Jo is a maths teacher, head of maths, and award winning blogger. Her Resourceaholic blog is a must visit for all maths teachers, and her Maths Gems posts are always overflowing with gold. We spoke about organising resources, blogging, Twitter and advice for NQTs.

Oxbridge Interview Special
On this episode I interviewed four Year 13 students about their experience in their recent Oxford and Cambridge interviews, which should be useful for anyone thinking of applying or helping a student prepare.

Neil Ogden - Maths Specialist at OCR
As part of my trilogy of interviews with the awarding bodies about the new Maths GCSE, and what it is like to do their job, I spoke to Neil Ogden from OCR

Graham Cumming - Head of Maths at Edexcel
As part of my trilogy of interviews with the awarding bodies about the new Maths GCSE, and what it is like to do their job, I spoke to Neil Ogden from OCR

Andrew Taylor - Head of Maths at AQA
As part of my trilogy of interviews with the awarding bodies about the new Maths GCSE, and what it is like to do their job, I spoke to Neil Ogden from OCR
Here you will find a series of episodes featuring fellows at the Mathematics Education Centre at Loughborough University. The aim of this series is to take a look at some of the most innovative research going on in the field of mathematics education, and consider what the implications are for the classroom. Episodes will be available throughout November and December 2020. Season 1 of this show (episodes 1 to 10) is kindly sponsored by The byOxford Revise GCSE Maths and Season 2 (episodes 11 to 19) is kindly sponsored byArc Maths.
1. Language and dyscalculia with Julia Bahnmuller 2. Parental engagement with Tim Jay
3. Estimation, equals sign and working memory with Iro Xenidou-Dervou
4. Maths anxiety with Kelly Trezise 5. Fingers and game-based apps with Korbinian Moeller 6. Cognitive Load Theory with Ouhao Chen 7. Designing and interpreting educational research with Matthew Inglis 8. Numbers and space with Krzysztof Cipora 9. PhDs and maths textbooks with Beth Woollacott 10. When to tell and teaching algebra with Dave Hewitt
11. University transition and oral assessments with Paola Iannone 12. Inquiry as a way of being with Barbara Jaworski 13. The self-explanation effect and how experts read maths differently with Lara Alcock 14. Counting in the animal kingdom with Krzysztof Cipora 15. Children's early understanding of number with Francesco Sella 16. Writing a maths curriculum with Colin Foster 17. Executive function with Camilla Gilmore 18. Comparative judgement with Ian Jones 19. Teaching mixed-attainment with Tom Francome I have teamed up with Jo Morgan (@mathsjem) and TES to delve deep into key matheamtical topics, looking at progression, misconceptions, resources, etymology and much, much more. Each of these episodes was filimed, and the videos are embedded into the show notes page. You will also find the PowerPoint Jo uses so you can access all the resources.
Topics in Depth: Indices Topics in Depth: Angles and Parallel Lines This is a series of episodes dedicated to supporting teachers who are working from home amidst the Covid-19 outbreak of 2020. There will be technology focussed episodes - just how does remote teaching work? But also episodes focussed on the practicalities of coping with setting students appropriate work whilst also having to look after your own children at home. Then there are issues of safeguarding, differentiation, mindset and more that I hope will come up as we progress. There will be maths teachers, teachers of other subjects, and primary school teachers. There will be teachers from the UK and overseas. Hopefully something for everyone.
Ben Rooney - structure, social interactions and experimenting with technology
Michael Pershan - Zoom, Assessment for Learning and a careful choice of questions Jo Morgan - Hegarty Maths, family life, and why she will not be doing "live" lessons Dan Pearcy - Google Meets, Poll Everywhere and 5 principles for remote teaching Adam Boxer - retrieval, conducting interviews, and staying safe and sane Jon Hutchinson - making videos for primary school students Helen Williams - supporting Early Years students Jules Daulby - supporting students with Special Educational Needs Ollie Lovell and Bryn Humberstone - Checking for understanding, Desmos and lessons learned Matt Hood - Oak National Academy and ResearchED Home Jamie Frost - Dr Frost Maths and virtual whiteboards
The podcast is free, and always will be. However, if you wish to support the show, there are 3 ways you can do so:

1. Write a review (ideally a nice one) wherever you access the podcast from

2. Tell a colleague about the podcast - maybe starting with recommending an episode for them to check out

3. If you wish to make a donation to support the production and hosting cots - or, more accurately, to buy me a Mellow Birds coffee, then you can do so via my Patreon page here: patreon.com/mrbartonmaths

How I wish I'd taught maths
Speaking to the wonderful guests on my podcast also inspired me to write my own book: How I wish I'd taught maths: Lessons learned from research, conversations with experts and 12 years of mistakes. The book is my attempt to distill all I have learned, and the practical changes I have made to my planning, lessons and thinking. It is published by John Catt Education Ltd, and can be bought via Amazon or directly from John Catt. For details on the associated series of workshops, please click here. I really hope you enjoy it.

Reflect, Expect, Check, Explain
This book is my attempt to take some core principles from Variation Theory and utilise them to help students get more from practice questions, better remember and understand rules, and harness technology such as Desmos and GeoGebra to its full potential. The book also contains an epic 45,000 word chapter that looks at how schools around the world have taken the core ideas from my first book, How I wish I'd taught maths, including Diagnostic Questions, SSDD Problems, Silent Teacher and more, and adapted them in the two years since the book's release. Reflect, Expect, Check, Explain is published by John Catt Education Ltd, and can be bought via Amazon or directly from John Catt. For details on the associated series of workshops, please click here. I really hope you enjoy it.

# data[].attributes.attachment_link.description
Mr Barton Maths Podcast Contents The Mr Barton Maths Podcast: " changing useless time into CPD time" - @MrsG on Twitter On the Mr Barton Maths Podcast I interview guests from the world of education who interest and inspire me. They may be fellow teachers, bloggers, thinkers, or people of influence.

# data[].attributes.attachment_link.readable_text
"That podcast you do," says Dave, my PE-teacher friend who I have known for 30 years - since we both started school in 1988, in fact. "I like it. Do it more."

Dave is the last person I would have expected to listen to an education podcast, let alone one that interviews academics about their research on education-related topics. Yet, he is an avid subscriber to Tes Podagogy and listens every week on his way to work.

Since Tes launched the podcast in September 2017, we have found many an unexpected listener to the series (and many who we expected might listen have tuned in, too). People listen in their cars, on their rail commute, sat with a glass of wine, even in the bath. The success of the series has been a huge but pleasant surprise.

We have had some extraordinary people come in to chat, on a really diverse set of topics. What remains constant is that we try to ensure we end up with a practical, applicable and useful collection of tips for teachers by the time the podcast ends.

Each episode has its merits, but to mark the end of series 4, we thought we would run down the top 10 most listened-to episodes. Watch out for series 5, starting 9 January, but in the meantime, here is the list in no particular order (you can find all episodes on the Tes Podagogy Hub).

1. Cognitive-load theory and classroom research

Guest: Dylan Wiliam, emeritus professor of educational assessment at the University College London Institute of Education

Date published: 13 September 2017

What he says: Wiliam talks us through how research can play a role in your classroom - and why it should; how "what is interesting is not what works in education, but under what circumstances does it work"; and why we should all be brought up to speed on cognitive-load theory.
To listen, click here
2. What teachers need to know about the teenage brain

Guest: Sarah Jayne Blakemore, professor of cognitive neuroscience at the UCL Institute of Cognitive Neuroscience, and author of books including the multi-award-winning Inventing Ourselves: the secret life of the teenage brain

Date published: 28 November 2018

What she says: "One of the messages of my research, the papers we write and the books I have written, is that we should be more understanding of teenagers, of this really critical period of development," says Blakemore. She explains how this developmental period affects decision-making, behaviour and more.
To listen, click here
3. What should assessment look like in schools?

Guest: Daisy Christodoulou, former head of assessment at Ark Schools and author of books including Seven Myths about Education

Date published: 6 September 2017

What she says: Christodoulou explains why effective assessment is so important; what she feels are the key problems with assessment in schools; and why she has taken a leap of faith on the method of comparative judgement.
To listen, click here
4. What every teacher needs to know about memory

Guest: Professors Robert and Elizabeth Bjork, Bjork Learning and Forgetting Lab at the University of California

Date published: 22 January 2018

What they say: "Beyond an early point in your life, all new learning is a matter of linking it up and relating it to what you already know," says Robert Bjork. "If you are a teacher, all the kids are going to come in with very different backgrounds of what they already know and don't know - that can be an important guide as to how to individualise learning...One thing that characterises a lot of gifted teachers is that they can understand what things the students are interested in and what the students' background is - they can take new material and relate it to that."

Elizabeth adds: "What is it that the kids are caring about now in culture; how can I relate this better to the other things they are doing outside the classroom? This is a challenge - how do we find a way to reach all of our students?"
To listen, click here
5. Why teachers need to create routines for learning

Guest: Doug Lemov, teacher trainer and author of Teach Like a Champion and Reading Reconsidered

Date published: 29 November 2017

What he says: ""Sometimes our most rigorous intentions in the classroom are undone by a lack of attention to mundane details of how things should go right," says Lemov. He details some of the routines that he advocates in the podcast, including "cold calling" and "tracking". These stem from his observations of expert teachers.
To listen, click here
6. Why growth mindset is not a silver bullet

Guest: Carol Dweck, Lewis and Virginia Eaton professor of psychology at Stanford University

Date published: 18 October 2017

What she says: In a robust defence of her work after much criticism, Dweck sets out what growth mindset actually is and states: "We don't think it works every time; we want to know where it does not work so we can find out why. We are not putting out something we are saying is the gospel, we are saying this is our current understanding, we are putting it out there and we are getting feedback, and if someone finds something different, we are saying great, let's learn from it."
To listen, click here
7. What every teacher needs to know about dyslexia

Guest: Professor Maggie Snowling, president of St John's College, Oxford, and one of the world's leading dyslexia researchers

Date published: 22 November 2017

What she says: "People used to think dyslexia was a clear-cut syndrome with signs and syndromes like a medical disease, but it is actually much more like blood pressure - it can range from very low to very high," says Snowling, who goes on to detail the best ways schools can identify and then support children with dyslexia. She also addresses common misconceptions.
To listen, click here
8. Three golden rules for supporting autistic students

Guest: Dr Luke Beardon, senior lecturer working within the Autism Centre at Sheffield Hallam University

Date published: 7 November 2018

What he says: "Being a teacher and having that level of expectation to engage with the autistic community without really good, solid levels of support is massively unfair on the teacher, the child and the family," explains Beardon. "But there is no doubt we are failing these kids." He offers his tips for turning this around.
To listen, click here
9. How much of your lesson should be teacher talk?

Guest: Neil Mercer, emeritus professor of education at the University of Cambridge and director of Oracy Cambridge

Date published: 25 April 2018

What he says: "I always say to primary teachers, 'You are the only second chance for some children to have a rich language experience. If these children are not getting it in school, they are not getting it," explains Mercer. He talks at length about the research on teacher and student talk, and about strategies that teachers need to implement to improve both their own spoken language skills and those of their students.
To listen, click here
10. What every teacher needs to know about trauma

Guest: Essi Viding, professor of Developmental Psychopathology at UCL and Eamon McCrory, professor of developmental neuroscience and psychopathology at UCL

Date published: 31 October 2018

What they say: "It is important not to overinterpret this, to see it as brain damage," says McCrory on the effects of childhood trauma. "What we are seeing is that these changes are adaptive...and there is no reason these systems cannot recalibrate. A new set of environmental experiences can lead to new calibrations. Plasticity continues into early adulthood."
To listen, click here Every week, Tes brings you the latest research to help your day-to-day job as a teacher. To subscribe, visit the Tes shop

# data[].attributes.attachment_link.description
"That podcast you do," says Dave, my PE-teacher friend who I have known for 30 years - since we both started school in 1988, in fact. "I like it. Do it more." Dave is the last person I would have expected to listen to an education podcast, let alone one that interviews academics about their research on education-related topics.

# data[].attributes.attachment_link.readable_text
If you would like David to speak at a conference, lead some staff training, or discuss how to implement any of the ideas discussed on his blog, please contact Katie via email or call on 01522 708897.

Please be aware that if you do book David for an event there will be no fidget spinners, no emojis, no sugar paper and no group work. If that's the sort of thing you're after we can recommend plenty of folk who'll be happy to provide it.

# data[].attributes.attachment_link.description
The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

# data[].attributes.attachment_link.description
Brilliant - Build quantitative skills in math, science, and computer science with hands-on, interactive lessons.

# data[].attributes.attachment_link.readable_text
1. Set and monitor work, either with fixed questions of your choice, an exam past paper, or flexibly adapts to each individual student.

2. Advanced data analytics allow you to identify class misconceptions, see task performance by topic, see student working and provide formative feedback to students.

3. Create worksheets to export to Word.

4. A virtual whiteboard for classroom use allows you to connect with students and import questions.

5. Thousands of downloadable teaching resources, used in tens of millions of lessons worldwide.

Register

# data[].attributes.attachment_link.description
DrFrostMaths provides an online learning platform, teaching resources, videos and a bank of exam questions, all for free.

# data[].attributes.attachment_link.title
Conception of the good - Insights into our current education system

# data[].attributes.attachment_link.description
Insights into our current education system

# data[].attributes.attachment_link.description
Zest for Learning... into the rainforest of teaching

# data[].attributes.attachment_link.title
MathsChatLive Episode 5 - Atul Rana, Mark McCourt, Anne Watson, Emma McCrea and Daniel Pearcy

# data[].attributes.attachment_link.readable_text
At Up Learn, we provide a customised learning experience to each student that guarantees results. We do this by creating courses that focus on delivering the material in the most effective way.

Our methodology is built on a foundation of research from the field of cognitive science. We use the latest scientific research when creating our lessons to ensure that students are absorbing and retaining content efficiently. Our team only select the most academically robust studies to develop the best learning experience.

We then combine this research with a artificial intelligence that determines a student's strengths and weaknesses and is able to track how they are performing in real-time.

Our students learn how to grasp new concepts quickly because we focus on explaining topics concisely. With the use of science and technology, we've built a system that enables students to learn as fast as possible and retain knowledge for as long as possible.

And 97% of our students go on to achieve A and A* grades in their exams, so we're confident that we're on to something.

Scroll down to take a detailed look at a subset of the scientific concepts that go in to our methodology!

Our Core Concepts

The Science We Use

Now you've explored some of the methodology behind our courses, why not try one out? Sign up and join the thousands of other students benefiting from Up Learn.

# data[].attributes.attachment_link.title
Science Behind Up Learn | Up Learn - A*-A Exam Success Guaranteed

# data[].attributes.attachment_link.description
At Up Learn, we provide a customised learning experience to each student that guarantees results. We do this by creating courses that focus on delivering the material in the most effective way. Our methodology is built on a foundation of research from the field of cognitive science.

# data[].attributes.attachment_link.title
Webinar Preparing for September - 24th August @ 11am

# data[].attributes.attachment_link.readable_text
The short answer is: not all educational approaches have had the backing of research. For example, for decades, the notion of "learning styles" has been prevalent. This is the idea that when instruction is tailored to an individual's learning style, they learn better. But no Introduction
For years, centuries really, educators have experimented with different learning tools, techniques, and curricula. Some efforts have been more successful than others, of course. But how many of them are based on science with a robust body of research behind them?
​
rigorous ​ evidence supports this view.

For the nation's education system, though, the bigger question is: How do we best educate our children so that they learn better, and learn how to learn, in addition to learning what to learn? Additionally, and arguably just as challenging, is: How do we translate this body of research into classroom practice effectively?

Enter the "Science of Learning: Research Meets Practice." The goal of the project is to get the science of learning into the hands of teaching professionals as well as to parents, school leaders, and students.
What Is The Science Of Learning?
​Experimental research into how people learn over a century ago. In the decades following World War II, cognitive psychologists became more and more interested in first began how people remember incoming information, the differences between novices and experts, the course of expertise development, and the development of reasoning in children.

As researchers consolidated this knowledge in the 1980s and 90s, there was a growing interest in applying this knowledge to classroom settings. Especially since the mid-2000s, collaborations between teachers and researchers have validated many of the central ideas first explored in the 1970s and early 80s. These collaborations have also often led to fruitful teaching innovations.

We still have a long way to go, however. For example, many still use misguided study practices like blocked approaches to studying, where one concept is studied repeatedly before a new concept is explored. Instead, people should use interleaving - or mixed practice - which is far more effective.

The Goal Of The Project
The goal was to bring the science of learning into the classroom and kickstart the development of easy-to-use professional development materials. We also wanted to collaborate with teachers, and learn from them what was effective, or not, when implementing science-based practices. In other words, we were interested in listening to teachers about implementing the research, rather than telling them what they "should do."

What would happen, for instance, if learning scientists met with experienced classroom teachers, and had a conversation about how concepts in cognitive science could possibly translate into the classroom?

As learning scientist Megan Sumeracki explains,

It's really important to have bi-directional communication...where the researchers are talking with the teachers and saying, 'here's what we know based on the science,' and the teachers are saying, 'here's what we know based on what's going on in the classroom."

We selected schools with a wide range of student and teacher profiles, racial, ethnic, and socioeconomic backgrounds. Project partners included Leading Educators, Teaching Lab, and Wellington Road Productions.

Seven schools were chosen for the project, from urban Memphis, Tennessee and East Baton Rouge, Louisiana, to suburban Kenner, Louisiana, Leominster, Massachusetts, and rural Medomack, Maine. With project partner Leading Educators, who helped with the selection of teachers in the Memphis and East Baton Rouge/Kenner Louisiana areas, 16 different teachers were invited to participate.

The conversation with teachers included an initial interview to learn about their teaching experiences, what they felt they knew about the science of learning concepts that they'd be working with, as well as a meeting with their learning scientist. The teachers and researchers would then check in a few times during the duration of the project. The interaction culminated in a final filming of teachers in the classroom, and a debriefing among the teachers and learning scientists about what worked and what didn't when trying out specific teaching strategies.

Additionally, teachers were asked to tape themselves in at least one self-reflection piece and send it to our videographer. All of these elements were included in the final product: a video on the specific science of learning strategy that could be disseminated to decision-makers, classroom teachers, parents and students alike.

The Strategies
We focused on six distinct strategies; although they can be used in relation to one another, and often lend themselves to specific subjects and concepts, they can all be adapted to a wide variety of classroom settings, grades, and subject areas.

"Retrieval practice boosts learning by pulling information out of students' heads, rather than cramming information into students' heads," according to cognitive scientist and author, Dr. Pooja Agarwa.

"For example, simply asking students, 'What did we do in class yesterday?' rather than telling them 'Here's what we did in class yesterday' significantly boosts long-term learning."

Frequent low-stakes quizzing is the signature example of retrieval practice.

"Dual coding is about combining images or visual representations with words. When used well, combining those can provide two ways of remembering information," states learning scientist Dr. Megan Sumeracki.

But, not all graphic representations are created equal, and likewise, just creating a picture is not enough. According to researchers, visuals must be directly linked to the text without many distractions. ​

Spacing is "coming back to information that was learned previously in order to refresh it," states learning scientist, Dr. Yana Weinstein-Jones.

In short, spaced practice is the opposite of cramming, and experts like Weinstein-Jones recommend that learning is stretched out over time, optimally over the course of a number of sessions.

Teachers should intentionally bring up skills and concepts, strategically spaced, to improve how well students grasp the material.

Interleaving is studying different problem sets, "or mixing up different types of problems or...different concepts that you're trying to learn," according to learning scientist Dr. Megan Sumeracki. This can help students to see links and similarities between different ideas and concepts and can improve long-term learning. Sumeracki adds that when a teacher introduces interleaving into the classroom, "there might be some struggle early on, but over time the students will probably get more used to it, and then those successes will be really exciting."

Metacognition is most often defined broadly as, "thinking about thinking." However, what we know, via the cognitive sciences, includes a much more specific notion of metacognition. The Center for Teaching at Vanderbilt University describes the value of planning, monitoring and assessing one's own learning.

According to learning scientist Dr. Regan Gurung, "The more we can make the thinking process visible, the better we can understand how to make it more effective. That's what metacognition is all about."

In everyday contexts, we often use "elaborate" to mean "describe in more detail." But psychologists mean something a little different by the word "elaboration." In this context, elaboration is fundamentally about "making meaningful associations to a particular concept...it's the opposite of just rote memorization," states. Dr. Stephen Chew, learning scientist.

Chew adds, "what elaboration does is it increases the number of ways of accessing information." For example, when teaching students about the topic of variation in statistics, asking the students to come up with an example from their lives of high variation and low variation would be a good way to encourage elaboration.

Acknowledgments: We're grateful to the Overdeck Foundation for funding this project. We also thank Megan Sumeracki and Yana Weinstein-Jones who reviewed the document and provided feedback.

# data[].attributes.attachment_link.title
The Science of Learning: ​Research ​Meets Practice

# data[].attributes.attachment_link.description
The short answer is: not all educational approaches have had the backing of research. For example, for decades, the notion of "learning styles" has been prevalent. This is the idea that when instruction is tailored to an individual's learning style, they learn better.

# data[].attributes.attachment_link.description
maths teacher resources for intelligent practice and challenge at more-same-less.co.uk

# data[].attributes.attachment_link.description
Lasting Learning is a community of the world's foremost learning scientists with a focus on providing information about the best ways to enhance long-term re...

# data[].attributes.attachment_link.readable_text
Suggested study hours 30

Format pdf for 10 booklets

What's included

There are three components to the materials.

PM751 One booklet containing notes on the central importance of generalisation in secondary mathematics, and a large collection of situations which call upon expressing generality.

PM752 Five booklets each on a different mathematical theme: decimals, infinity, notation, picturing functions and doing and undoing, full of tasks with some commentary.

PM752A: Actions into words

PM752B: Doing and undoing

PM752C: Approaching infinity

PM752D: Picturing functions

PM752E: Dealing with decimals

PM753 Four booklets providing a structured approach to preparing to teach any topic, exemplified in equations, probability, ratio and angle.

PM753A: Preparing to teach angle

PM753B: Preparing to teach ratio

PM753C: Preparing to teach equations

PM753D: Preparing to teach probability

The structured approach is described more fully in Mason & Johnston-Wilder (2008) and other academic publications.

Who is the course for?

PM751 and PM753 could be used by secondary students looking for further stimulation beyond the regular curriculum. They could be used by people studying to become teachers or by teachers who want to extend their appreciation of mathematical themes and topics.

# data[].attributes.attachment_link.keywords[]
project mathematics update: view as single page

# data[].attributes.attachment_link.description
Suggested study hours 30 Format pdf for 10 booklets What's included There are three components to the materials. PM751 One booklet containing notes on the central importance of generalisation in secondary mathematics, and a large collection of situations which call upon expressing generality.

# data[].attributes.attachment_link.readable_text
Maths Venns is my collection of Venn Diagram activities covering many mathematical ideas. Students must think hard to find examples that meet different combinations of criteria in order to complete the diagram. Are some regions impossible to fill, or have students simply not found an example yet?

You can search for different topics using the Topics menus above, and you can find out more about Maths Venns on this page.

My 2020 book, Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom, goes into detail about making the most of these activities in the classroom. You can order the book from Amazon, John Catt, or wherever you get your books.

My 2023 book, Tips for Teachers: 400+ ideas to improve your teaching, details my most recent thoughts on using these sequences effectively. You can order the book from Amazon, John Catt, or wherever you get your books.

I have an online course store which offers low-cost, high-quality CPD on-demand. Each course contains short videos, resources, research, activities and questions to reflect upon. The courses most suited to the activities on the Maths Venns website are:

# data[].attributes.attachment_link.description
Rich Venn Diagram maths activities from Craig Barton @mrbartonmaths

# data[].attributes.attachment_link.description
Share your videos with friends, family, and the world

# data[].attributes.attachment_link.description
Share your videos with friends, family, and the world

# data[].attributes.attachment_link.title
The limits of my language mean the limits of my (mathematical) world