The post Lucy Crehan: Cleverlands appeared first on Mr Barton Maths Blog.
]]>Lucy is a former Science and Psychology teacher, turned international education consultant and explorer. She is also the author of one of my favourite books of the last few years, Cleverlands. In order to write the book, Lucy helped out in schools and lived with teachers in Finland, Canada, Singapore, Japan, New Zealand and Shanghai, spending a month in each place. As soon as I started reading Cleverlands, I knew I had to get Lucy on the show to dig deeper into some of her findings, and dispel some of the myths you often hear about education in these higher performing regions.
So, in a wide-ranging conversation we discussed the following things, and much, much more besides:
You know what I am going to say here, because I say it all the time, but only because I really, really mean it – I loved every minute of this conversation. Lucy has a unique perspective on education across the globe having immersed herself in it, speaking and living with teachers, parents and students. The episode is a nice complement to my second interview with Ed Southall where we focussed on the way maths is taught in Japan, and I discuss two of my own takeaways after the interview.
If you buy one book as a result of the podcast, then obviously make it Cleverlands. However, if you buy two then maybe consider snapping up “How I wish I’d taught maths”. And if you have bought it, firstly thank you, and secondly if you have time to give the book a quick review – ideally a positive one – on Amazon, then I would be eternally grateful.
On Twitter Lucy is: @lucy_crehan
Lucy’s website is: lucycrehan.com
Cleverlands is available to buy from Amazon here
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
My book: How I wish I’d taught maths
The post Lucy Crehan: Cleverlands appeared first on Mr Barton Maths Blog.
]]>The post Increasingly difficult questions: Mean average – TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
I have long been a fan of David Taylor’s Increasingly Difficult Questions (IDQ) website, so I was absolutely delighted to see he had uploaded his wonderful resources to TES to share them with a wider audience. So, to celebrate, the least I could do was to choose one of them for Resource of the Week! The concept behind IDQs is so simple and yet so powerful. Students are presented with a series of questions on a given topic, but they get progressively more difficult. More than that though, as we can see in this example on the mean, they incorporate a wide range of other topics, allowing students to benefit from the positive effects of interleaving, whilst also starting to see maths as they connected subject that it is.
How can it be used?
Increasingly Difficult Questions are ideal to use at the end of a topic unit. So, you have taught the basics of finding the mean from a list of data, and now you present your students with the selection of questions in this resource. As they work their way through the sheet, students are confronted with the challenge of applying their skills at calculating the mean when negatives, decimals and finally algebraic expressions are involved. The selection and progression through the questions is excellent, and the answers are even included too! Brilliant stuff!
Thanks so much for sharing
Craig Barton
Download: Increasingly Difficult Questions – Mean Average
View the author’s other resources
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]]>The post SSDD Problems Question Pack appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
At MathsConf14 in Kettering I presented an idea for a set of problems that I have been using with my Year 11 class. For 12 years of my career I had been batching similar problems together. So, for example, following a sequence of lessons on Pythagoras’ theorem, I would present my students with a range of questions, set in a variety of contexts (ladders leaning against walls, ships sailing between buoys, etc) all of which had Pythagoras at their core. The problem was, those kind of questions do not allow students to identify a Pythagoras question when it is presented in isolation. So, I started creating sets of 4 problems where the surface structures are the same, but the deep structures are different- thus forcing students to think carefully about what the question is actually asking. Hence, SSDD was born, and this is a wonderful example of these type of questions.
How can it be used?
We use SSDD problems at lead twice a week with our Year 11s in the build up to exams. Presenting students with 4 problems which, on the surface, look very similar has provided an incredible challenge as they battle through trying to discern exactly what the question is about. Indeed, a set of questions like the ones in this wonderful resource could take a class all lesson and lead to some fascinating and useful discussions. You also get the added advantage of revising four topics for the price of one. SSDD problems could also be used for homeworks or end of topic tests, this benefiting from the positive effects of spacing. The SSDD problems revolution starts here!
My website, SSDD Problems, can be found here: ssddproblems.com
Thanks so much for sharing
Craig Barton
Download: SSDD Question Set 1
View the author’s other resources
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]]>The post Conference Takeaways: BCME – Day 4 appeared first on Mr Barton Maths Blog.
]]>This podcast comes live from the end of Day 4 at the BCME Maths Conference 2018. It is recorded with my co-host Jo Morgan (@mathsjem on Twitter and the creator of the online bible of maths resources, resourceaholic.com) . This episode we discuss…
1. Hanna Fry update
2. The answers aren’t important – Ed Southall
3. Revealing mathematics – Dave Bedford and Ben Sparks
4. Lessons learned from GCSE Maths – Neil Ogden
5. Investigating mathematics attainment and progress – Colin Foster and Jeremy Hodgen
Some photos from Dave and Ben’s session:
And some from Colin and Jeremy’s:
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
My book: How I wish I’d taught maths
The post Conference Takeaways: BCME – Day 4 appeared first on Mr Barton Maths Blog.
]]>The post Conference Takeaways: BCME – Day 3 appeared first on Mr Barton Maths Blog.
]]>This podcast comes live from the end of Day 3 at the BCME Maths Conference 2018. It is recorded with my co-host Jo Morgan (@mathsjem on Twitter and the creator of the online bible of maths resources, resourceaholic.com) . This episode we discuss…
1. Prioritising students’ engagement through and in mathematical reasoning at A Level – Nicola Bretscher
2. Blocking in primary maths – Ruth Merttens
3. Problem solving for the new A Level – Nikki Gupta
4. Different problems same answer – John Burke
5. Hannah Fry plan of action
Nikki Gupta’s website is: markit.education
John Burke’s resources can be accessed at: mrbartonmaths.com/teachers/rich-tasks/something-in-common
Here are some photos from Nicola Bretsher’s session:
The GCSE points from AQA’s Andrew Taylor:
And some from John Burke’s session:
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
My book: How I wish I’d taught maths
The post Conference Takeaways: BCME – Day 3 appeared first on Mr Barton Maths Blog.
]]>The post Conference Takeaways: BCME – Day 2 appeared first on Mr Barton Maths Blog.
]]>This podcast comes live from the end of Day 2 at the BCME Maths Conference 2018. It is recorded with my co-host Jo Morgan (@mathsjem on Twitter and the creator of the online bible of maths resources, resourceaholic.com) . This episode we discuss…
1. Challenging topics in GCSE maths – Carol Knights
2. A brief history of problem solving (1982 – 2017) – Paul Metcalf
3. Changes to mathematics education in Englad – Charlie Stripp
4. Using manipulatives in secondary maths – Michael Anderson
5. Pop-up maths – David Sharpe
6. Developing excellent in mathematics – Simon Singh
7. Fact and fiction in the history of mathematics – David Acheson
8. Why exams do not tell you what your students know – Andrew Taylor and me
9. The big one… our quiz team
Links to Simon Singh’s materials: goodthinkingsociety.org and parallel.org.uk
A few photos from the history of problem solving session:
The link to the wonderful Dominoes resource on the STEM Centre is here: https://www.stem.org.uk/elibrary/resource/35317
And a few photos from that session:
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
My book: How I wish I’d taught maths
The post Conference Takeaways: BCME – Day 2 appeared first on Mr Barton Maths Blog.
]]>The post Conference Takeaways: BCME – Day 1 appeared first on Mr Barton Maths Blog.
]]>This podcast comes live from the end of Day 1 at the BCME Maths Conference 2018. It is recorded with my co-host Jo Morgan (@mathsjem on Twitter and the creator of the online bible of maths resources, resourceaholic.com) . This episode we discuss:
1. How the flipping heck do you pronounce BCME?
2. David Spiegelhalter’s keynote address about probability
3. Anne Watson’s session on Variation
4. Jo’s very own session that she will be presenting on Thursday
5. What we are looking forward to tomorrow
Below are some photos from the exercises in Anne’s session that we discuss on the podcast, and the hand-outs from the session can be found here: pmtheta.com/publications.html
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
My book: How I wish I’d taught maths
The post Conference Takeaways: BCME – Day 1 appeared first on Mr Barton Maths Blog.
]]>The post Conference Takeaways: researchEd Blackpool 2018 appeared first on Mr Barton Maths Blog.
]]>This is another of my conference Takeaways, where I sit down at the end of a conference with a fellow delegate to share our main takeaways for the benefit of people who are unable to attend. This time the event was researchEd Blackpool, which was held in the Las Vegas of Lancashire on March 24th 2018.
Now, this was my first ever researchEd event, but it will certainly not be my last. As you will hear, the line-up of speakers is ridiculously good, and I know of no other way to tap into such a diverse wealth of experience and insight. I had a great time.
In this episode you will hear takeaways from the sessions delivered by:
Baroness Estelle Morris
Tom Bennett – @tombennett71
Carl Henrdick – @C_Hendrick - and Robin Macpherson – @robin_macp
Mark Healy – @cijane02
Tom Sherrington – @teacherhead
Harry Fletcher-Wood – @HFletcherWood
And some annoying Maths bloke from Preston
Huge thanks to researchEd Blackpool organiser Simon Cox for organising such a wonderful event, and squeezing out a few final drOps of energy to talk to me for this podcast after such a long day. And to the living legend that is Tom Bennett, for creating a movement which truly does have the power to change students’ and teachers’ lives for the better all around the world.
On Twitter, my co-host for this episode, Simon is @MathsMrCox
The website of Blackpool Research School, where you can access the research articles Simon discusses can be found here
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
My book: How I wish I’d taught maths
The post Conference Takeaways: researchEd Blackpool 2018 appeared first on Mr Barton Maths Blog.
]]>The post Graph matching: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
For me, there are two distinct skills involving in conquering graphs at GCSE, whether they be straight lines, quadratics, cubics or reciprocals. The first is the ability to plot points and draw graphs from a table of values. This requires students to be competent in algebraic substitution, and is something that most students are able to grasp. However, in my opinion, by far the more difficult skill is to be able to sketch a graph from its equation. In other words, to be able to understand the significance of each component of that equation and what it means for the shape, direction and axes crossing points of the resulting graph. Such a skill is crucial both at GCSE and A Level, and this resource is absolutely perfect for helping students develop it. Given a selection of graphs, students must match their question to the sketch. And as an extra twist, there is one equation that does not match-up, and a blank set of axes just crying out to be filled in with the relevant sketch.
How can it be used?
This resource covers straight line graphs, quadratics that are in completed the square and factorised format, and the new range of non-linear graphs students need to know for GCSE. So, it is perfectly possible to pick out the relevant activity to use with each class after a topic has been covered – straight line graphs with Year 8s, quadratics with 10s, for example. However, for me the power of this activity is when it is used in its entirety, for that is when connections between straight line graphs and quadratics are made, and a more thorough, wide-ranging understanding of graphs and their equations can develop. As such, this is the ideal revision activity to use with a group of Higher tier Year 11 GCSE students in the build up to their exams, and with A Level students in the first week of their course. Set them off on the challenge, and fire up Desmos when going through the answers.
Thanks so much for sharing
Craig Barton
Download: Graphs matching
View the author’s other resources
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]]>The post Oliver Lovell: Planning, running a maths department and Cognitive Load Theory appeared first on Mr Barton Maths Blog.
]]>Ollie is the head of Senior Maths and a Learning Specialist at Sunshine College in the west of Melbourne. Sunshine College is a diverse multicultural school which is attended by students of over 50 nationalities.
This is a special episode. I have wanted to have Ollie on the show for ages. Like me, he is more than a little obsessed with educational research and crucially how to apply it in a practical, effective way in the classroom. As the host of the Education Research Reading Room Podcast, and via his blog and weekly newsletter – something we discuss in the interview – Ollie is amazing at sharing ideas, asking questions, chaelling assumptions, and provoking deep thinking.
So, in a wide ranging conversation, we covered the following things, and much, much more besides:
I am going to say it straight away – this is my longest ever interview, and one of my all-time favourites. In total we spoke for 4 hours, and I could have gone on all day. It is rammed full of practical takeaways and food for thought. I will reflect on many of these in my Takeaway at the end of the show – including one idea that I literally raced into the maths office to tell me Head of Department about as soon as the interview was finished. It is a game changer.
On Twitter, Ollie is @ollie_lovell
Ollie’s website is ollielovell.com where you can also sign up for his weekly Twitter takeaways
You can check-out Ollie podcast, The Education Research Reading Room here
Links to things discussed (hopefully this is everything!!!!)
Pygmalion Effect:
Andrew Martin podcast here
James Mannion podcast here
Clark and Stephens paper, ‘assessment tail wagging curriculum dog’ here
Anki blog post here
The messenger app Ollie uses for Show-Call when presenting his students’ work is Riot.im
The blog post where Ollie discusses planning the Year 12 programme of instruction is here
The three questions Ollie asked members of his department were:
Principles Ollie is trying to work by this year:
Ollie’s excellent interview with John Sweller can be found here
Sue Gerrard’s article about biologically primary and secondary knowledge is here
Ollie kindly sent a photo of one of his student’s Reflection Sheets, which I discuss in the Takeaway:
Oliver Lovell’s Big 3
1. Twitter, in particular Harry Fletcher-Wood
2. Why don’t students like school by Daniel Willingham
3. How to win friends and influence people by Dale Carnegie
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
My book: How I wish I’d taught maths
The post Oliver Lovell: Planning, running a maths department and Cognitive Load Theory appeared first on Mr Barton Maths Blog.
]]>The post Problem of the day: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
This year on Resource of the Week I have been making a conscious effort to dip into the wonderful world of primary maths resources – and I am so glad I have, because I have uncovered some classics that have gone down a storm with my Key Stage 3 and even Key Stage 4 students. Take this incredible resource, for example. It is the complete collection of the daily problems White Rose Maths shared with teachers in the build up to the 2017 Key Stage 2 SATs. The problems come complete with teacher notes and answers, they are beautifully presented, they cover a wide range of topics, and the quality of them is superb. What is not to like?
How can it be used?
Regular exposure to unvoential problems (problems in context, questions asked in a weird way, problems that combine more than one topic, etc) is crucial to develop students’ confidence and ability to tackle them. Hence, this lovely selection could be used regularly with Year 7 and 8 classes. There are enough questions here to use a couple of times a week and last the full year. They could be used a starters, or included on homeworks or low-stakes quizzes. Students could first tackle them on their own, and then share their strategies and ideas with their classmates. They could also form part of a whole-schools Problem of the Week, and be stuck on a noticeboard in the maths corridor to encourage discussion of mathematics outside of lessons. However you choose to use these problems, I strongly encourage you to use them, as they are brilliant.
Thanks so much for sharing
Craig Barton
Download: Problem of the day
View the author’s other resources
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]]>The post Conference Takeaways: MathsConf14 appeared first on Mr Barton Maths Blog.
]]>Now, this is an episode with a difference, and one which I hope will be the first in a series of similar episodes. I know many people are unable to make it to maths conferences and CPD events for a variety of reasons, and whilst it is incredible how Twitter can make you feel like you are there, and those who blog about their experiences share some incredible insights, I wondered if there was room for something else. Hence, the idea of a Conference Takeaway series of podcasts.
So, after the Maths Conference run by Mark McCourt and the La Salle team, which took place in Kettering on 10th March 2018 – the 14th such Maths Conference – myself and Jo Morgan (@mathsjem on Twitter and the creator of the online bible of maths resources, resourceaholic.com) sat down to chat about our takeaways from the wokshops we saw. The conversation lasted just over half an hour – which was quite the revelation for me as I assumed podcasts are legally obliged to last for at least two hours.
Here you will hear our thoughts on the following sessions:
I really hope you find this discussion useful, whether you attended the conference or not. Thanks so much for Jo for taking the time to talk to me, to all the amazing workshop presenters who give up their time to share their ideas, and to Mark McCourt for creating something very special with MathsConf. Hopefully Jo and I will be back for some BCME Takeaways!
The two new websites I launched at MathsConf14 are:
MathsVenns
SSDD Problems
Image from Naveen’s session on fractions:
My sequence of intelligently varied questions on sharing in a ratio:
And here is me and Jo just before the recording:
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
My book: How I wish I’d taught maths
The post Conference Takeaways: MathsConf14 appeared first on Mr Barton Maths Blog.
]]>The post Trigonometry Pile-up: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
I am a big fan of “pile-up” activities. I don’t know of any other type of resource that crams so many questions and challenges into such a confined space. Images are piled on top of each other, and students must work their way from the bottom to the top, filling out crucial information as and when they calculate it. There are a number of lovely pile-ups on TES, including this one on Angles and this on Pythaogras. This resource uses the pile-up format to take trigonometry to the limit, for to succeed here students will need to identify and carry out calculations involving Pythagoras, SOHCAHTOA, and the Sine and Cosine Rules.
How can it be used?
This trigonometry pile-up is ideal to be used at the end of a teaching unit on Further Trigonometry, or as a revision exercise to assess students knowledge of Pythagoras, SOHCAHTOA, and the Sine and Cosine Rules. Crucially, not only does it assess how well students can use the rules, but also how well they can select which rule is needed in a given situation, which is a key skill that many students in my experience fall down on. Students can be challenged to work through it on their own, or with a partner, and I am pleased to say that the answers are available. Once complete, we always have the classic option of asking students to create their own version. This is likely to be a significant challenge, but ultimately a worthwhile one.
Thanks so much for sharing
Craig Barton
Download: Trig Pile-up
View the author’s other resources
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]]>The post Anne Watson and John Mason: Variation, questioning, visualising and developing mathematical thinkers appeared first on Mr Barton Maths Blog.
]]>Now, I started the Mr Barton Maths Podcast over two years ago purely so I could talk to and learn from my heroes. And I have been ridiculously lucky with the guests who have been kind enough to give up their time to talk to me – Dylan Wiliam, the Bjorks, Doug Lemov, Kris Boulton, Bruno Reddy, the list goes on. But Anne and John have been at the top of my “Wanted List” for some time now. I finally plucked up the courage to ask when I saw John at an event in London, and I am so glad that I did. Their influence on mathematics education is unrivaled, and their knowledge and experience is phenomenal. Indeed, in the time since they agreed to talk to me to the interview itself, I have been revising like it was my finals at uni – the only difference being I was slightly more sober this time.
In their incredibly distinguished careers, John and Anne have found time to be the authors of one of my all time favourite books: Questions and Prompts for Mathematical Thinking, and the co-authors, along with Chris Bills and Liz Bills of another: Thinkers: activities to promote mathematical thinking. Both of these are linked to in the show notes, along with everything else we discuss in the interview.
And when I announced on Twitter that Anne and John were coming on the show, the reaction was incredible. In fact, it was summed up nicely by the following Tweet from Anushka Rao who said: Give them my love all the way from India ! In this land of gods, they’re still my main ones
So, in an incredibly wide-ranging conversation we discussed the following things, and much, much more besides:
Sometimes when you meet your heroes it does not live up to expectations. Fortunately, the experience of talking to Anne and John for over two hours was better than I could have hoped. I loved the first half of the conversation, hearing about their careers, experiences and beliefs, and then I loved the second half, where I try to drill down into the practical takeaways so we can all learn from their experiences. As ever, I will reflect on some of the many things I have taken away from this interview in my Takeaway at the end of the show.
Speaking of my Takeway, having listened it, Anne and John disagree – can you believe it?!? – with my belief concerning what I consider to be the winning combination of direction instruction versus what I call Intelligent Practice. I have included their comments in the show notes, followed by a brief reply by me, so you can read them and see who you agree with after you have listened to the interview and the Takeaway. I think the safe money is with Anne and John
The usual plug for my book: “How I wish I’d taught maths”, which contains an entire chapter on my person take on the importance of the choice of examples and practice questions we give our students, which has been heavily influenced by the work of Anne and John and the principles of Variation Theory that we discuss throughout this interview.
Anne and John’s response to my takeaway:
Now about your post-interview comments – lots of interesting stuff here but one thing worries us which is about the ‘direct instruction’ you talk about. If students know what a unit fraction is then finding something like two-fifths depends only on being able to find one fifth and then knowing how to get two of something, and we would not agree that you HAVE to directly instruct them to find any fraction of any amount – you can instead be sure they understand how to find unit fractions of any amount and what to do with them. The point is surely that if you have one fifth of something (i.e. unit fractions as operators) then working out two-fifths is a problem to be solved rather than a method to be applied, and then if you next ask me about three fifths I can try and apply the same method I have just invented, and hey presto if I am aware of that I can construct for myself a way to do it in future based on meaning
My reply:
I also agree that – in this instance – you would not “have” to direct instruct students how to find, for example, 2/5 like you may have to to enable them to find 1/5. However, it is my preferred way of doing so in this case. Let me try to explain why. I want my students to have a method to find any fraction of any amount. This method would be something we had discussed, and then it would be introduced via the Silent Teacher and Example-Problem pair approach I describe in detail in my book. I firmly believe this is the best way to give all students the greatest chance of being able to use the method successfully. The purpose of (what I call) the Intelligent Practice that follows is not so they can discover how to find 2/5, but to look at how the answer – using the method I have taught them – to 2/5 is related to 1/5, and likewise how that answer is related to the answers to the connected questions that follow. It is in these relations where real understanding develops. So, my sequence of intelligent practice questions may look like this:
I guess it comes down to a choice of order. I prefer my students to do it this way around so they always have a method to fall back on – on which they can carry out successfully – and it is this method that allows students to notice the relationships between the questions and answers, and hence start to appreciate the deep underlying structure. I hope that makes some kind of sense!
On Twitter, John is @JohnMOxford
Anne and John’s website is: pmtheta.com
Their book Thinkers: activities to promote mathematical thinking is available from the ATM here
Another influential book of theirs Questions and Prompts for Mathematical Thinking is available from the ATM here
The Structured Variation Grids (SVG) that John describes can be found here
The paper Seeing an exercise as a single mathematical object can be downloaded as a pdf here
Maths teacher Danny Brown has written a lovely blog post about questioning based on this interview
To see the complete selection of books recommended by all my podcast guests, click here.
Anne Watson and John Mason’s Big 3 (or Big 5!)
1. Underground maths
2. What We Owe Children: The Subordination of Teaching to Learning by Caleb Gattegno
3. Polya’s video “Let us teach guessing”
4. How children fail by John Holt (available for free as a pdf here)
5. How To Teach Mathematics for Mastery by Helen Drury
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
My book: How I wish I’d taught maths
The post Anne Watson and John Mason: Variation, questioning, visualising and developing mathematical thinkers appeared first on Mr Barton Maths Blog.
]]>The post Trigonometry GCSE Revision: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
We are approaching that time of year again when thoughts turn towards the summer’s GCSE. As a teacher of Year 11s I am always on the lookout for resources to help my students prepare for these exams as effectively and efficiently as possible. That is why I absolutely adore this Trigonometry resource, and the entire bundle of resources that it comes from. It consists of a single A4 worksheet containing 12 SOHCAHTOA questions. These vary both in terms of the trigonometric ratio required, and the complexity of steps needed to arrive at the solution. What could be better than 12 really well constructed, beautifully presented questions, I hear you ask?… well how about if I told you the worked solutions are also included
How can it be used?
I can think of three ways I will use this resource:
1. For focussed practice. This is perfect to use following the end of a teaching unit on trigonometry, right before we start to look at application questions
2. In a revision lesson. If, like me, you have a class of Year 11s who would benefit from some additional trigonometry practice, then give them this resource. Perhaps 20 minutes to try as many questions as they can, and then project up the answers. If students are having problems with any question, it will become immediately obvious and you can intervene accordingly.
3. For independent revision. The fact that the answers are included means that this resource – along with the rest in this excellent series – can be utilised by students for practice outside of the classroom. Print it out, make it into a booklet, or simply email it to students, and they have an ideal means of gaining valuable additional practice, which is helped no-end by the fact that the answers are included.
Thanks so much for sharing
Craig Barton
Download: Trigonometry GCSE Revision
View the author’s other resources
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]]>The post Helen Hindle: Mixed attainment teaching and growth mindset appeared first on Mr Barton Maths Blog.
]]>Helen is the Director of Studies for Mathematics at a secondary school in East London
Now, regular listeners to the show will know that one of the many areas of maths education I am pretty clueless about is mixed ability, or mixed attainment teaching. I have always taught in sets in the two schools I’ve spent my career, and only experienced mixed ability teaching during my AST outreach work. So, when I spoke to Lucy Rycroft-Smith on this podcast, I made a pledge to find out more about it, and as such I was desperate to get Helen on the show. As well as being an experienced teacher, Helen is also the organiser of the Mixed Attainment Maths Conference, which brings together leading practitioners in the field to share challenges and effective strategies. And when I announced on Twitter that Helen was coming on the show, I was inundated with questions concerning mixed attainment teaching, thus suggesting it is an area of interest to many of you.
So, in what I thought was a fascinating conversation, we covered the following things, and much, much more besides:
Now, let me say this at the outset – Helen keeps me on my toes. It is clear that we have quite different ways of thinking about lessons, and the best ways to help our students understand key concepts. This made it a challenging, but incredibly fun conversation, and I think there is little doubt that Helen came out on top. Indeed, following our conversation I went on another of my long walks to process Helen’s arguments, and reflect on my own teaching, and I will be sharing my conclusions in the Takeaway at the end of the interview. And whether you teach mixed attainment or setting, I know you will get something out of this interview.
Just before we crack on, I just wanted to say a huge thank you to all podcast listeners who have been kind enough to buy my book, “How I wish I’d taught maths”. If you enjoyed it, and have a moment to share a review on Amazon, I would be eternally grateful. If you didn’t enjoy it, then maybe keep it to yourself.
On Twitter, Helen is @HelenHindle1
The Mixed Attainment Maths website is: mixedattainmentmaths.com
Examples of the Learning Jounreys that Helen talks about are here
Helen has written a great blog post about her experiences of mixed attainment teaching here
The blog post by Kris Boulton I discuss in the Takeaway is here
Dylan Wiliam’s slide about the difficulty getting students in the correct set is:
Helen Hindle’s Big 3
1. Mixed attainment maths
2. Inquiry Maths
3. Open Middle
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
My book: How I wish I’d taught maths
The post Helen Hindle: Mixed attainment teaching and growth mindset appeared first on Mr Barton Maths Blog.
]]>The post Multiple Choice Starter Questions: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
I have made no secret whatsoever about my love of a good diagnostic multiple choice question. So, you can imagine my reaction when I came across this simply amazing resource which promises a multiple choice question for every single GCSE Maths objective. Once I picked myself up off the floor, I downloaded the resource and dove right inside. It is brilliant, both in the way it is organised, and in the quality of the questions. There are 194 slides, divided up into in the main topic areas, and you can navigate to each subtopic and back again via really nicely designed section slides.
How can it be used?
Such diagnostic multiple choice questions are designed for quick-fire, accurate assessment in the classroom and to identify any misconceptions students may have – in this sense they allow for exactly the model of responsive teaching that formative assessment should be. As they cover the entire GCSE course, it is our Year 11s who are likely to benefit the most (although there is nothing stopping you picking out relevant questions for other year groups). There are a number of ways of using such questions. I have used them as part of homeworks and low-stakes quizzes, but they perhaps lend themselves best to starters. Getting into a routine of using, say, 3 of these questions every day with Year 11s, chosen from different topic areas. If students get the question correct, then delete the slide. If they don’t then have a discussion about it, keep the slide in the presentation, and it will come back around in a few weeks. This resource is an ideal way to help them prepare for the summer’s exams.
Thanks so much for sharing
Craig Barton
Download: Multiple Choice Starter Questions
View the author’s other resources
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]]>The post Whole-One Search: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
I’ll be honest – I am no longer a big fan of using word-searches in lessons. In the past I have used them to try to get students to consolidate their knowledge of key mathematical terms, such as parts of a circle or different types of statistical diagrams. And the abundance of free word-search generators on the internet makes the production of such an activity dead easy. However, is trying to find such vocab amongst a muddled up grid an efficient way of helping students remember such terms and their meanings? I don’t think so. So, just as I was about to face up to the fact that I may have used my last ever word-search in mathematics, I stumbled upon this little beauty. It is a wordsearch with a difference. For a start, there are no words to find. Instead, students must look for combinations of fractions, decimals and percentages that sum to 1. And it comes with answers!
How can it be used?
This activity is ideal to use at the end of a teaching unit on fraction, decimal and percentage conversions, or as a nice way of revising the topic. Students need to be systematic in their searching, and the different presentation of the activity means they may well get through more mathematics than if this was presented as a worksheet with 20 calculations to check. In addition, once students have finished, their is the opportunity to challenge them to create their own such activities, which can then be used to test their friends. Addition of fractions, negative numbers and collecting like terms all lend themselves very well to a structure such as this. This is a lovely resource.
Thanks so much for sharing
Craig Barton
Download: Whole-One Search
View the author’s other resources
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]]>The post Convince Me – Arc Length: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
A blast from the past year. For many years I was obsessed with Tarsia Jigsaws. In fact, rarely would a week, or even a day, pass without me reaching for the scissors and glue. However, after a while I became concerned that students were not learning as much as they could. Too much time was taken up cutting and sticking – time that could have been spent learning. So, I tweaked my use of Tarsia by introducing “Tarsia Convince Me”, and I’m delighted to see a wonderful example here on arc length and converting units of measurement. Here, students are presented with a completed jigsaw but are challenged to find the 5 incorrect answers and explain why, and also solve 3 problems that do not have an answer. This cuts out all the faffing about with scissors and glue, and instead gets to the heart of the matter. Students have to think hard, and it is that hard thinking that is the most likely to lead to learning.
How can it be used?
The first thing to say is that students need to be familiar with how Tarsia Jigsaws work in order to understand how to complete this activity. A quick demo should suffice to get them up and running. And then they are away! This activity lends itself pretty well to paired work as it provokes some great discussion, especially (as is the case here) if the wrong answers have been carefully chosen to address some common misconceptions. Once students have completed this, there is always the option to have them hop onto a computer and use the free Tarsia software to create their own Convince Me activity. This is great to do for revision in the build up to an exam. Students can take a topic each, and before you know it you have a set of top-quality revision resources that the whole class can benefit from.
Thanks so much for sharing
Craig Barton
Download: Convince Me – Arc Length
View the author’s other resources
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]]>The post Amir Arezoo: Lean maths departments, deep work, schemes of work appeared first on Mr Barton Maths Blog.
]]>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. I have wanted to get Amir on the show for a while. Listeners have requested more interviews with experienced and successful teachers, so they can learn from their habits, processes and past mistakes. I am a keen follower of Amir’s blogs – The Lean Department and At The Edge of Chaos – and like me he is interested in taking research findings and looking for practical ways to apply them to his work as both a teacher and a leader.
So, in a wide-ranging interview, we covered the following and more:
I loved talking to Amir. He is someone who regularly evaluates what he does, and asks whether it has worked or not, and what he can change to make it more effective. He is a lifelong learner, and I certainly learned lots from talking to him I particularly enjoyed discussing the challenges and practicalities of running a department, and also the section about Deep Work. I reflect on both of these, and a bit more, in my Takeaway at the end of the interview, so try to stick around for that if possible.
Just a quick announcement – and by announcement, I most certainly mean “plug” – to say that my book “How I wish I’d taught maths” is available to buy. I have tried to distill all the lessons I have learned from guests like Amir, Dylan Wiliam, Kris Boulton, Greg Ashman, the Bjorks, Dani Quinn, and many more – over 100 hours of interviews, in fact – into an accessible, practical guide. If you have snapped it up – and I am so grateful that so many of you have – and you enjoy it, then please leave a quick review on Amazon. I am particularly interested in which areas of the book you found most interesting and useful. Thank you.
On Twitter, Amir is @WorkEdgeChaos
His blogs are: theleandepartment.wordpress.com and mrarezoo.wordpress.com
Links to the books Amir recommends teachers read can be found here, along with the recommendations of all my other guests.
Amir Arezoo’s Big 3
1. MEP CIMT
2. Teaching for Mastery – Mark McCourt blog series – Part 1
3. What does this look like in the classroom?
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Book: How I wish I’d taught maths
Mr Barton Maths Podcast
The post Amir Arezoo: Lean maths departments, deep work, schemes of work appeared first on Mr Barton Maths Blog.
]]>The post What went wrong?: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
Once again I am dipping into the pool of outstanding primary maths resources available on TES for another gem. “What went wrong?” consists of a series of scenarios (presented on small cards for ease of printing) where a classic mistake has been made. For example: Year 6 are doing some quick calculations. Adel has to work out 112 – 99. He knows he can do this mentally by changing 99 to 100 then adjusting. He gets the answer 11. What went wrong? It is the student’s job to spot, explain and correct the mistake. Topics covered include ordering numbers, use of inequality signs, rounding, negative numbers and basic arithmetic.
How can it be used?
I have found these scenarios work well as starters – simply project one on the board, give students a few minutes to ponder it in silence, and then discuss it with their partner. Some of the resulting discussions are superb. Likewise, a few could be placed together as the main part of a lesson, or in preparation for a test. Once students have experience of seeing and explaining errors presented in this form, a brilliant thing to do is to challenge them to create their own. Can they come up with a scenario where a fictional student has made an error, write it down on one piece of paper, and then explain the error on another. Not only does this provide a challenging, worthwhile activity for students, but it also has the potential to create a whole other set of “what went wrong” cards to use with this or other classes. This really is the resource that keeps on giving.
Thanks so much for sharing
Craig Barton
Download: What went wrong?
View the author’s other resources
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]]>The post Angles in Parallel Lines – comparing methods: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
The beauty of many of the more complex questions involving angles on parallel lines is that they can be solved several different ways. It is important that students experience seeing different methods so they can build up a more comprehensive understanding of the topic, as well as being armed with several different ways into a problem should their preferred method let them down on a particular question. This resource from Jo Morgan is fantastic for enabling students to develop more flexible approaches and get them talking to each other. It is really well presented and structured.
How can it be used?
I run this activity exactly as Jo advises. I give students sufficient time to try the problems on their own, and then ask them to discuss answers and compare methods. I found doing the first question and then discussing was more successful than allowing students to try all the questions first as it means students can use what they learn from that first discussion in the subsequent problems. It is also useful to try to tease out of students which method or approach was most suitable for which problems, and why this might be the case. All of these things serve to widen their understanding, as well as helping them, develop a more flexible, robust problem-solving toolkit for similar angle problems. We also have the option to challenge students to create their own problems that can be solved in multiple ways, possibly going as far as creating a mark scheme for each approach.
Thanks so much for sharing
Craig Barton
Download: Angles in Parallel Lines: Comparing Methods
View the author’s other resources
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]]>The post Exploding Surds: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
I love surds. I love the way they represent irrational numbers so efficiently, how many of the ways of manipulating them are directly related to the rules of algebra, and above all that feeling when a complex 7-mark epic of a problem pops out with an answer of root-2. Unfortunately, not many students share my love, and surds are definitely a topic that many struggle with. So, I am always on the lookout for ways to practice the key skills of surds – simplifying, multiplying and rationalising – in a format that is appealing to students. And this wonderful, explosive resource does exactly that. Key skills are covered across 8 worksheets with questions that that have been presented in a really clever way.
How can it be used?
The really beauty of these worksheets are the varying amounts of information that is given each time. Sometimes students are given the question and the first step. This provides a nice way in for students to get their confidence up. But, on the very same sheet, these first two steps may be omitted, and students will need to work backwards from the third or fourth step to see if they can determine how the problem began. This provides both a challenge and an excellent opportunity for class discussion. How did students do it? How many possible answers are there? If students can successfully fill in this selection of explosive worksheets, their understanding of surds will be secure. This is a truly wonderful resource.
Thanks so much for sharing
Craig Barton
Download: Exploding Surds
View the author’s other resources
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]]>The post Jane Jones: Ofsted, observations, marking, reasoning appeared first on Mr Barton Maths Blog.
]]>Jane is a former teacher and head of maths who is now the HMI National Lead for Mathematics.
As regular listeners to this podcast will know, over the last two years I have significantly changed my approach to teaching. And frequently, when I present these new ideas to teachers, I hear things like “that’s all well and good, but Ofsted wouldn’t like it”. Well, here was my perfect opportunity to find out if that really is the case.
So, in an epic 3 hour interview, we covered the following things, and much, much more besides:
I flipping loved this conversation. Jane was a superb guest. She is down to earth, and really understands the pressures of both teaching maths and being a head of department, because she has been there. So, whether you are preparing for an inspection, just had one, or are genuinely interested in Ofsted’s views on teaching and learning in mathematics, then this is the episode for you. I personally felt refreshed and reassured.
Just before we crack on – you know what is coming here – I just wanted to mention my book “How I wish I’d taught maths”, which is being published by John Catt Educational. I have been incredibly fortunate to receive positive reviews from the likes of Dylan Wiliam, Doug Lemov, Jo Morgan, Dani Quinn, Will Emeny, Bruno Reddy and Peps McCrea, as well as a foreword by Kris Boulton. The book comes in at a whopping 150,000 words – 135,000 of which are Kris’ foreword… only messing. It is everything I have learned in the last two years, I am really proud of it, and I hope those of you who choose to snap it up will really enjoy it.
On Twitter, Jane is @JaneJonesHMI
Ofsted’s website is: www.gov.uk/government/organisations/ofsted
Jane Jones’ Big 3
1. NCETM
2. Made to Measure / Understanding the Score
3. Subject Associations: MA, ATM, NAMA, AMET and NANAMIC
Two really useful summaries of the interview:
@mathsmrgordon takeaways from the whole interview: teachinnovatereflectblog.wordpress.com
@mistersetchell about differentiation: https://sites.google.com/view/mistersetchell/home
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Book: How I wish I’d taught maths
Mr Barton Maths Podcast
The post Jane Jones: Ofsted, observations, marking, reasoning appeared first on Mr Barton Maths Blog.
]]>The post Practical Maths Ideas: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
Increasingly these days I find myself dipping into the wonderful world of primary maths resources on TES. A lack of knowledge of exactly what maths is taught and how maths is covered in Key Stage 1 and 2 has been a real failing of my career to date, and I am determined to rectify that. And this resource is perfect for exactly this purpose and more besides. It gives an overview of the kind of skills students need to develop in Key Stage 1, early Key Stage 2 and upper Key Stage 2. This is useful in itself, but the resource also provides suggestions and links to superb resources and activities that could be used to help consolidate and develop students’ understanding without using a worksheet.
How can it be used?
As I say, from the perspective of providing an overview of the breadth and level of maths students study at primary school, this resource is essential for me as a secondary school maths teacher. I now always have it to hand when planning a lesson for my Year 7s. But it is also incredibly useful for giving me ideas. For example, the links to NRICH activities for basic number operations, together with practical suggestions for developing conceptual understanding of fractions are top-draw. I will certainly be making use of this wonderful resource when planning Year 7 lessons, but also when planning for all my classes and I am looking for an alternative to a worksheet, or something to help support the development of conceptual understanding.
Thanks so much for sharing
Craig Barton
Download: Practical maths ideas
View the author’s other resources
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]]>The post How to use an average: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
Averages are a staple of a student’s’ mathematics education. They encounter them for the first time around Year 4, and yet they are still plugging away at them in Year 11 and beyond. Averages are also a strange topic in the sense that whilst students have covered most of the basics early on, they are not really mastered by many students until much later, if ever. Finally, averages represent a substantial challenge to us teachers for the very reason that we need to teach them each and every year. This often means we have to come up with novel ways to present material to students to keep them interested and keep their understanding developing. To cut a long story short – those are three reasons why I love this resource. It tackles what can be one of the most complicated and often abstract concepts in the entire topic – the appropriateness of averages.
How can it be used?
This is a PowerPoint presentation that is intended to be used as a lesson, and the structure of the lesson is superb. There is a starter activity which sets up the ambiguities presented by using averages perfectly. Then comes my favourite part – lots of scenarios that present great discussion opportunities. The house price example is particularly powerful and well illustrated. Then we have a very clear way of tackling the pros and cons of each average for a number of situations, before finally looking at some real-life misuses of average. In short, this is just about the best lesson on the concept of appropriateness of averages that I have ever seen on TES. However, as with all resources, it should first be checked out, edited and adapted to suit the needs of your students.
Thanks so much for sharing
Craig Barton
Download: How to use an average
View the author’s other resources
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]]>The post Carl Hendrick and Robin Macpherson: What does this look like in the classroom? appeared first on Mr Barton Maths Blog.
]]>Robin is a history teacher and currently an Assistant Rector at Dollar Academy in Scotland. Carl is an English teacher completing PhD at King’s College in English education, and is also head of Learning and Research at Wellington College. They have both worked on the Telegraph Festival of Education, and speak regularly at education conferences like researchED.
Now, the reason I wanted to get both Carl and Robin on the show is that firstly we have an inclusive policy here on the Mr Barton Maths podcasts – both mathematicians and non-mathematicians are welcome – and secondly, because they are the co-authors of what is probably my favourite book of 2017 – What does this look like in the classroom? It is one of the most successful attempt to bridge the gap between research and practice, and the lineup of contributors is, quite frankly, ridiculous. Are you ready for this? We have fellow podcast guests Dylan Wiliam, Daisy Christodoulou, Doug Lemov, Tom Bennett and Nick Rose, together with Lucy Crehan, Martin Robinson, David Didau, and more. It is like the Ocean’s 11 of education books, only there’s 18 of them.
I love the way the book is written, with the contributors responding to pertinent questions posed by teachers, such as “I want to improve my questioning style, what three bits of advice would you give me?”, and “what is the best way to deal with low-level disruption?”
Throughout the interview I tried to dig into the key takeaways from the book, and much more besides:
This episode is definitely one to share with your non-maths colleagues, with Carl and Robin sharing the kind of strategies that any teacher can benefit from. I hope the episode also provides a good overview of what I genuinely think is a superb and very important book.
A podcast about a book would not be complete without a plug about a book, so here it comes, as subtle as ever. My own book, How I wish I’d taught maths: lessons learned from research, conversations with experts, and 12 years of mistakes, published by John Catt Education, is released in January 2018. It is a collection of all the things I have learned over the last two years, looking back on the mistakes I have made, and what I now do differently in the classroom. In her review of the book, Jo Morgan says: Craig summarises the key points of the relevant research succinctly and his advice to teachers is perfectly pitched and instantly transferable to any maths classroom. For the sake of our current and future students, I certainly hope that this book becomes essential reading for maths teachers – and she wasn’t even under that much duress from me when she wrote it. Anyway, I hope you find the book useful.
On Twitter, Carl is @C_Hendrick
His website is chronotopeblog.com
On Twitter, Robin is @robin_macp
His website is robin-macpherson.com
What does this look like in the classroom? is available from Amazon here
Links to the books Carl and Robin recommend teachers read can be found here, along with the recommendations of all my other guests.
Carl Hendrick’s Big 3
1. Ben Newmark’s blog
2. Michael Fordham’s blog
3. Doug Lemov field notes
Bonus: Becky Allen for Data Lab
Robin Macpherson’s Big 3
1. Learning scientists blog
2. Tom Sherrington’s blog
3. Mark Healy’s blog
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Book: How I wish I’d taught maths
Mr Barton Maths Podcast
The post Carl Hendrick and Robin Macpherson: What does this look like in the classroom? appeared first on Mr Barton Maths Blog.
]]>The post GCSE Revision Masters: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
This is a phenomenal collection of homeworks. They have been designed for the 9 to 1 GCSE Maths specification and cover Foundation, Foundation/Higher and Higher. They are really nicely laid out, making them very easy to mark, and the choice of questions is superb. They also share two features that always go down a storm with me and my colleagues. Firstly, the answers are provided (woo hoo!). Secondly, they are in Word format, meaning they can be easily edited, giving you the option to remove questions you deem not suitable for your students, or make copies of the homework, change a few numbers, and voila you have another one good to go.
How can it be used?
There are two main ways I will be using these wonderful resources. The first is for homeworks. These days I am a great believer that wherever possible homeworks should not be topic based. Instead they should encompass a wide range of topics so students can benefit from spacing and interleaving, and these homeworks certainly tick that box. The second is for low-stakes quizzes. One of the most significant changes to my teaching that I have made this year is the inclusion of a low-stakes quiz every single lesson, and I am always on the lookout for good content for these quizzes. This resource is superb, in both the challenge and variety of the questions, and fact students can mark it easily due to the lovely way it is laid out. It’s a cracker!
Thanks so much for sharing
Craig Barton
Download: GCSE Maths 9-1 Revision Masters
View the author’s other resources
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]]>The post Fractions Connect 4: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
Students first encounter operations with fractions in primary school, and yet I have taught many Year 11s who still require practice some seven years later. In such situations, it is important to keep the practice as varied as possible, so that students who have had bad experiences with fractions in the past do not immediately assume that they also will not be able to do it this time around. That is why I love this resource. Students have the opportunity to practice all four operations – first with proper fractions, then with mixed number fractions – in the context of a gem of Connect 4. There is an answer grid provided, but students are not told which answer goes with which question, hence the opponent has every incentive to carefully check their rival’s work.
How can it be used?
An activity like this would work really well at the end of a unit on fraction operations, or as a revision activity for a class who have studied this in the past. The danger with games is that students think more about the game than the maths involved, but this should not be the case here. Reminding students that they need to check each other’s work is a good way to ensure both parties pay full attention for all of the game, instead of each merely being interested in their own move. I also like to give each student a Calculator Token, which can be exchanged one to check an opponent’s answer. This has the added advantage of encouraging students to carefully consider when best to use this support, which helps them evaluate the complexity of each question.
Thanks so much for sharing
Craig Barton
Download: Fractions Connect 4
View the author’s other resources
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]]>The post Colin Foster: Mathematical Etudes, Confidence and Questioning appeared first on Mr Barton Maths Blog.
]]>Colin 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. He is an author, has written numerous research papers, and is the creator of three outstanding websites: foster77, mathematical etudes and mathematical beginnings.
Colin shares a keen interest in three areas that I am more than a little obsessed about – purposeful practice (or what Colin refers to as a mathematical etude), measuring students’ confidence in their answers, and effective questioning. If any of those area peak your interest too, then I can promise you are in for an absolute treat.
In a wide-ranging interview we covered the following, and more:
This is one of my favourite interviews I have ever done. Colin is incredibly passionate and knowledgeable, and it was just such a pleasure to discuss and debate with him over subjects that fascinate me. I learned so much. I really hope you find it as useful and enjoyable as I did.
A quick mention that depending on when you listen to this podcast my book – How I wish I taught maths – may be either about to be released, available for pre-order, ready to buy, or sent to the pulping factory due to lack of sales, Alan Partridge style. It is a collection of all the things I have learned from two years of talking to the world’s leading experts, and reading all the research I could get my hands on. Some would say it is the ideal Christmas present, but I could not possibly comment.
On Twitter, Colin is @colinfoster77
The EEF report “Improving Mathematics at Key Stage 2 and 3″ is available to download here
Links to the books Colin recommends teachers read can be found here, along with the recommendations of all my other guests.
Colin’s main website is foster77.co.uk
His Mathematical Etudes website is mathematicaletudes.com
His Mathematical Beginnings website is foster77.co.uk/mathematicalbeginnings
Colin Foster’s Big 3
1. mathshell
2. Cambridge maths espressos
3. Daniel Willingham Articles
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Book: How I wish I’d taught maths
Mr Barton Maths Podcast
The post Colin Foster: Mathematical Etudes, Confidence and Questioning appeared first on Mr Barton Maths Blog.
]]>The post Measurement – Metric and Imperial: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
This is a beautifully designed and presented history of metric and imperial measurements. Students are shown the history of inches, feet and yards, including some royal interference that I was not aware of. Later on in the PowerPoint we are introduced to metric and imperial conversions, which provides opportunities to recap work on ratio, decimals and general arithmetic. My favourite part is the final slide, which explains:
8 furlongs made a mile,
40 poles made a furlong,
100 links made a chain,
10 chains made a furlong.
6 feet made a fathom,
100 fathoms made a cable
Thank God we went metric!
How can it be used?
Whilst the formal requirement for students to know the full set of metric and imperial conversion rates no longer exists at GCSE, that does not make such a wonderful resource redundant. I am a great believer in showing kids the history of our wonderful subject, and its applications and relevance to the world they live in. Here is a rare example of where we do not have to show-hour in some faux real-life context. We can show students how things used to be, and throughout this journey they can do a fair amount of maths along the way.
Thanks so much for sharing
Craig Barton
Download: Measurement – Metric and Imperial
View the author’s other resources
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]]>The post Dog Transformations: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
If you and your students have transformed more quadrilaterals than you care to remember, then this is the resource for you. For, what better thing in the world is there to transform but everyone’s favourite canine friend? Translate the wandering dog, reflect the ice skating dog, rotate the Aussie dog, and enlarge the greedy dog, all whilst practising the fundamental transformation skills students will need for GCSE maths. There are more vertices than on standard shapes that students usually transform, so the challenge all the better. Full answers are provided, along with the original Excel file that allows you to easily adapt each of the transformations to produce an infinite number of varieties.
How can it be used?
It will come as no surprise that I am going to suggest using the worksheets to help students practice the basics of transformations. The fact that the object being transformed is different to usual may inject a bit of much needed variety into the world of transformations. But with the accompanying Excel file, you can take things even further. Being able to project the dog onto the interactive whiteboard allows you to ask questions such as: if I add one the the number at the bottom of the vector, what will happen to the dog? What would I need to change the translation to so the dog’s nose is at (4, -3)? Or, what if I change the angle of rotation to 180°? Students can then consider the answer, discuss it with their partner, and then you can reveal it stantly, without the need to print out extra sheets. This resource really is the top dog.
Thanks so much for sharing
Craig Barton
Download: Dog Transformations
View the author’s other resources
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]]>The post Doug Lemov: Teach like a Champion and Top Tips for delivering training appeared first on Mr Barton Maths Blog.
]]>Let’s be honest, Doug is a legend. He is probably best known as the author of Teach like a Champion – a book which has had a huge influence on the last few years of my teaching and thinking, and which I believe is a must for all teachers to read, jam-packed as it is with loads of practical, easy to implement strategies that can be truly transformative. Doug is also the coauthor, along with his Teach like a Champion colleagues, of Practice Perfect and Reading Reconsidered: A Practical Guide to Rigorous Literacy Instruction. He is a former teacher, the former Managing Director of Uncommon Schools (something we talk about in the interview), and his CPD sessions are regarded as some of the very best in the world.
In a wide-ranging interview we covered the following, and more:
I’ll be honest, I was incredibly nervous in the build up to the interview. I even had to knock back two cups of Mellow Birds coffee to take the edge off. I guess I should be used to talking to my heroes on this show by now, but Doug was someone I had wanted to have on for so long. But I need not have worried – Doug was humble, knowledgeable, engaging, and just a superb guest. This is another of those interviews to share with your non-maths colleagues, as the ideas and insights Doug shares are incredibly useful no matter what subject you teach. Oh, and if you haven’t snapped up Teach Like a Champion 2.0, then I promise you will not be disappointed.
Speaking of books – notice the seamless transition there – let me quickly take this opportunity to mention – and when I say mention, I of course mean shamelessly plug – my book. In tribute to Doug, perhaps I should have called it Teach like a maths teacher who has been getting it completely wrong for 86% of his career, but in the end I went for How I wish I’d taught maths. It is based on my thoughts from two years of interviewing the world’s leading educational experts on this podcast – including Dylan Wiliam, Robert and Elizabeth Bjork, Daisy Christodoulou, Greg Ashman, Kris Boulton, Doug, and many more – reading over 200 research papers and books, and most importantly of all, trying, failing and modifying the strategies based on the experiences of my students. It is published by John Catt Education, and it should be out in time for Christmas 2017 – just in case you are short of gift ideas for your mum, son, Granny, dog, etc.
On Twitter, Doug is @Doug_Lemov
His website is teachlikeachmpion.com
Teach like a Champion 2.0 is available from Amazon here
Links to the books Doug recommends teachers read can be found here, along with the recommendations of all my other guests.
Doug Lemov’s Big 3
1. Harry Fletcher Wood’s blog
2. Jo Facer’s blog
3. Carl Hendrick’s blog
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
Just the Job Podcast
The post Doug Lemov: Teach like a Champion and Top Tips for delivering training appeared first on Mr Barton Maths Blog.
]]>The post Algebra Exit Tickets: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
Exit tickets are a very popular form of formative assessment. They usually consist of a single question given out in the final few minutes of the lesson for the students to complete, which is then handed back to the teacher as students leave the room. The idea is that the answers given by the students help inform the planning of the next maths lesson. For exit tickets to be successful they need to be super-quick to mark, and also kind on the photocopying budget. Fortunately, this wonderful collection of algebra exit tickets is exactly that. The questions are really well chosen, beautifully presented, and organise so four tickets fit on each side of A4.
How can it be used?
Exit tickets can certainly be used in the traditional sense, but I have a little twist I like the throw into the mix – the Delayed Exit Ticket. Given the widely cited distinction between learning and performance and the benefits of spaced learning, we can potentially make exit tickets an even more powerful tool by delaying their release. Say I have just taught a sequence of lessons on straight line graphs to my class, and last term we studied solving equations. In the final few minutes of the lesson I might presented them with two exit tickets. The straight line graphs one would give me an indication of how students are performing in the current topic and allow me to identify any misconceptions, whereas the solving equations exit ticket would give me a indication of how much students have retained from that previous topic, whilst also tapping into the benefits of spaced retrieval.
Thanks so much for sharing
Craig Barton
Download: Algebra Exit Tickets
View the author’s other resources
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]]>The post Peps Mccrea: Planning, Memorable Teaching and Teacher Expertise appeared first on Mr Barton Maths Blog.
]]>Peps 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. Peps has three Masters degrees (in Engineering Design, Educational Leadership, and Educational Research) and holds Fellowship Awards from the University of Brighton and the Young Academy. He now leads on the Institute for Teaching’s Masters in Expert Teaching course.
In short – I was once again well out of my depth.
I absolutely love Peps’ books on lesson planning and memorable teaching and I am fascinated by the challenges of developing expertise in teaching. Hence, I had been wanted to get Peps on the show for ages, and he did not disappoint.
In a wide-ranging interview we covered the following, and more:
I don’t want to build this up too much, but I am going to have to. This is one of those special episodes. I reckon I need to listen to it about 48 times to take in all the nuggets. It is also one to share with your non-maths colleagues as the vast majority of Peps’ points about planning, memory and the development of expertise are applicable to all teachers and all subjects. So please spread the word. And if you enjoy this episode, or any of the other 30-odd, then a quick review on iTunes would be hugely appreciated.
I’d also like to take this opportunity to officially announce that I have written a book. It is called “How I wish I’d taught maths”, with the subtitle “reflections on research, interviews with experts, and 12 years of mistakes”, and is being published by John Catt Education, the home of such wonderful books as What every teacher needs to know about psychology and the recent What does it look like in the classroom?. My book is essentially a collection of all the lessons I have learned from speaking to my wonderful podcast guests, reading the books and research they pointed me to, and trying out ideas in the classroom. It is very much a tale of regret when I think back to all the things I used to do, but hopefully it will be of interests to you, my dear listeners. It is currently being read by Kris Boutlon, and assuming I survive that experience, I hope it will be available before Christmas.
On Twitter, Peps is @pepsmccrea
His website is pepsmccrea.com
His first book is Lean Lesson Planning
His second book is Memorable Teaching
Links to the books Peps recommends teachers read can be found here, along with the recommendations of all my other guests.
Peps Mccrea’s Big 3
1. John Sweller TES piece
2. David Wees stuff around Instructional Activities
3. Keep an eye on the IFT website > going to be publishing some stuff
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
Just the Job Podcast
The post Peps Mccrea: Planning, Memorable Teaching and Teacher Expertise appeared first on Mr Barton Maths Blog.
]]>The post Mean from a Frequency Table Generator: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
You know sometimes you are looking for something very specific, to suit a certain need, and then you find it, and life is good? Well, that happened with this resource, and so I could not resist making it my Resource of the Week. I was planning a lesson on calculating an estimation of the mean from a frequency table for my Year 9 class, and I simply wanted some examples that they could do – lots of them. And this resource does just that. It is an Excel mean from a frequency table generator. Every time you hit “new question” you get a brand new table to complete, and best of all you can reveal the necessary steps to the solution step-by-step.
How can it be used?
I used this resource four ways:
1. I used it when going through a worked example. I took a screenshot of the incomplete table, pasted it onto a PowerPoint, and used this to talk students through the necessary steps. I was then free to flick back to the Excel version to check my calculations.
2. I next used it to generate examples for the students to practice. Again, the facility to check solutions at the click of a button was brilliant. And as a top-tip, I would recommend saving 4 versions of the resource, and then you can project 4 questions on the board at any one time. I show you what I mean in the video.
3. I used this resource to create practice questions and answers for my students’ homework
4. Finally, I have this resource saved on my desktop so I can quickly project a question at any stage to ensure students have never gone more than a month without practising this key skill
Thanks so much for sharing
Craig Barton
Download: Mean from a Frequency Table Generator
View the author’s other resources
The post Mean from a Frequency Table Generator: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>The post Lucy Rycroft-Smith: Cambridge Mathematics, Setting, Times Tables and Anxiety appeared first on Mr Barton Maths Blog.
]]>Lucy is a former maths teacher and head of maths, who is now the Research and Communications Officer at Cambridge Mathematics.
The reason I wanted to have Lucy on the show is that I am a little bit addicted to her espressos. Now, anyone who knows me will know my chosen brand of coffee is a very milky and pathetically weak cup of Mellow Birds, but these are mathematical espressos – bite-sized chunks of mathematical research into key areas. I originally planned to ask Lucy about five of these areas, and have everything wrapped up in under an hour – just in time for my evening Mellow Birds, in fact. But once we started talking, we could not stop, as Lucy dropped nugget after nugget.
So, in a wide-ranging interview we covered the following, and more:
I promise you, this episode is gold – and it is absolutely nothing to do with me. Lucy is incredibly well-read, but has the impressive ability to relate all of the research to experiences she has had during her many years in the classroom. This leads to a series of fascinating and practical takeaways that you can build directly into your teaching.
Lucy mentions lots of papers, and there are links to everything on the podcast page, along with a link to my own research page in case this has left you wanting more. Also, Lucy forgot to mention Black Mathematicians Month, which is happening in October. Again, there are links to this on the podcast page.
And just before we crack on, my podcast hit a significant milestone just before I recorded this episode – 100,000 downloads. Thank you so much to all my guests who have helped transform the way I teach and continually make me strive to be better. And thank you to all of you who listen and who have helped spread the word about this podcast. I cannot tell you how much it means to me to know people find these interviews as useful as I do. Long may they continue.
On Twitter, Lucy is @honeypisquared
Cambridge Maths can be found at cambridgemaths.org
On Twitter, they are: @CambridgeMaths
The books Lucy recommends, along with recommendations from all previous guests, can be found here
Other links from the episode:
Expectancy effects
TRU framework
Black Mathematician month here and here
Lucy Rycroft-Smith’s Big 3
1. Cambridge Mathematics salad and espressos
2. Chalk Dust Magazine
3. Aperiodical
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
Just the Job Podcast
The post Lucy Rycroft-Smith: Cambridge Mathematics, Setting, Times Tables and Anxiety appeared first on Mr Barton Maths Blog.
]]>The post Finding Turning Points: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
Often really good resources for teaching A Level maths are hard to find, largely because not as many teachers deliver the course. Hence, while you can find no end of top-quality lessons, activities and resources across TES for Key Stages 1 to 4, as soon as we hit that post-16 area, things get a little more barren. But there are gems out there, such as this delightful lesson on the nature of stationary points. It is a beautifully designed, detailed PowerPoint that gives a crystal clear explanation how to determine the nature of stationary points, together with several well-chosen worked examples. I particularly like the way common misconceptions or covered via a series of handy hints. For example, the fact that the graph can contain y-values lower than the minimum point, and a minimum followed by a maximum does not automatically guarantee that the graph is a cubic. These can often be overlooked and may lead to problems later on.
How can it be used?
As with all PowerPoint lessons on TES, I always advise adapting it to suit the needs of your students The slides are very detailed, and stripping them back may add clarity. There is also always a danger when having pre-written solutions to worked examples that you may wish to change things based on something a student says, and yet your hands are tied if all the steps of the example have been typed out and animated. But the detail in these slides could be used to your advantage by turning them into printed notes that could be given to students for revision, or to any student who may have missed the lesson. This is a wonderful resource to aid the planning of any lesson on the nature of stationary points.
Thanks so much for sharing
Craig Barton
Download: Finding turning points with calculus
View the author’s other resources
The post Finding Turning Points: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>The post Tick-Trash-Improve – Standard Form: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
Who doesn’t love a bit of Tick or Trash? For years it has been my go-to way of getting students to reflect on common errors in a bid to ensure they themselves do not make them. In my Pedagogy Place series, I discussed the research surrounding this approach to teaching (LINK TO SPOT THE MISTAKE). Here we have an upgrade to a classic. As well as being asked to either tick or trash an answer to a standard form question, there is now a third option – improve. This is for answers that are not entirely incorrect, but which could certainly be made better. This adds an extra degree of complexity to the activity, and could help ensure students’ understanding of the topic is even more secure.
How can it be used?
As I discussed in my Pedagogy Place article, activities like this are great for promoting a deeper understanding of a skill or concept, but should probably be left until students’ understanding of the basics is reasonably secure as there is a risk that they will not be in a position to distinguish between correct and incorrect approaches, and hence my in fact develop some misconceptions. As such, I like to use them at the end of a topic unit, maybe as part of a homework. Standard form lends itself particularly well to the tick, trash, improve approach as you can write answers that are mathematically equivalent, and yet not in standard form. However, the topic is by no means unique. Calculations involving fractions that have not been fully simplified, formulae that have not been fully rearranged, missing units, and indeed any question that has not been quite finished off would work just as well. Let’s hope this is just the beginning of tick, trash, improve!
Thanks so much for sharing
Craig Barton
Download: Standard Form: Tick, Trash, Improve
View the author’s other resources
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]]>The post Kris Boulton – Part 2: Minimal guided instruction, Understanding, How before Why appeared first on Mr Barton Maths Blog.
]]>Since I last spoke to Kris, it is all change in his professional life as he has a brand new job. He is now the Director of Education at UpLearn – a project with the tagline: learning with certainty, powered by AI and neuroscience. Indeed, Kris is currently looking for teachers and tutors to work with him on this exciting venture, and you can find more details in his blog post.
Kris’ first appearance on the show caused a bit of a Twitter sensation, as he spoke at great length about how he planned a sequence of lessons on simultaneous equations. Indeed, “how do you plan a lesson?” was pretty much the only question I ask. Kris followed this up with a wonderful series of blog posts that I highly recommend checking out..
The danger with having a guest on twice is that the sequel never quite lives up to original. However, I am delighted to report that this is very much a case of Terminator 2 than Titanic 2.
So, in a wide-ranging discussion, we covered the following things, and more:
Scattered throughout this are Kris’ philosophical tangents about values, purpose, outcomes, expertise, scientific thinking, and much more besides. It is an absolute treat. I was cognitively knackered afterwards, and had to join my wife in watching an episode of Geordie Shore just to recover. And Kris has promised to return to the show to discuss such matters as schemes of work, variation theory, questioning, problem solving and teacher training. Some of Dan Carlin’s Hardcore History podcasts are 5 hours long – I reckon Kris and I can trop that, with some Hardcore Maths.
Speaking of podcasts, a quick shout-out to three new education ones that I have enjoyed listening to recently:
Learning Scientists – one of my favourite blogs for practical applications of education research now have their own show, and it is excellent.
Michaela Community School – hosted by Thomas Kendall, and featuring interviews with Michaela staff, including Joe Kirby on knowledge organisers. My advice to Tom would be to keep that trouble-maker Dani Quinn off the airwaves – we all know what happened after she appeared on this show.
TES - whose new Podagogy series not only features a good pun for a title, but also an impressive line-up of guests, including Daisy Christodoulou and Dylan Wiliam. I feel a bit like Daisy and Dylan have cheated on me by appearing on another podcast, but I will let them off.
Whilst these podcasts are great for my ears and brain, they are doing my iTunes ranking no favours whatsoever, so any help you can offer in terms of a review or spreading the words to your colleagues is highly appreciated.
On Twitter Kris is @Kris_Boulton
His excellent blog can be found at: tothereal.wordpress.com
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
Just the Job Podcast
The post Kris Boulton – Part 2: Minimal guided instruction, Understanding, How before Why appeared first on Mr Barton Maths Blog.
]]>The post 50 Maths Questions Ideas: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
This resource has been designed for primary maths lessons, but do not be fooled – this is something that could (and should!) be used in all maths classrooms across the land! This book includes ideas for questions that could be used in a maths lesson (or at any point in the school day) to inspire some mathematical thinking in your students. Each idea is followed by a more detailed explanation, and then examples to show how it could be used across several maths topics. There are classics in there, such as “True/False” and “Odd One Out”, but also some that I was not as familiar with. I am a now a particular fan of “Correct, Almost, No Chance”, and “What’s the same and what’s different?”, both of which are incredibly versatile, with the potential to promote deep thinking across multiple topics.
How can it be used?
Questions like these are ideal when reviewing topics, or for providing some extension material to students.Take “What’s the same and what’s different?”, for example. This could be used at the end of a unit on quadrilaterals, challenging the students to think about and discuss what is the same and what is different about a square, a rhombus and a rectangle. Similarly, following a unit on decimals, students could be presented with 3.45, 3 and 2.9 and asked the same question. I would also be tempted to print out these ideas and either stick them up around the room or have them close at hand when I need inspiration for a question during a lesson. Likewise, these are ideal to use when planning lessons to ensure your questions really get students thinking.
Thanks so much for sharing
Craig Barton
Download: 50 Maths Questions
View the author’s other resources
The post 50 Maths Questions Ideas: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>The post Clumsy Clive On Averages and Range: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
Over the course of 2017, I have become more than a little obsessed with Clumsy Clive. It is such a wonderful idea for a series. In short, one of my all-time favourite TES authors, under the guise of a student called Clive, answers a series of questions, in this case on averages and range. The problem is, Clive is prone to making the odd mistake. It is the job of the students to cast their eyes over Clive’s work to see if they can spot, explain and correct the mistakes. The beauty is, the mistakes Clive makes have been carefully chosen to reflect common misconceptions in the topic, and hence completing this experience is a fantastic way to assess and help resolve any lingering misconceptions students may have.
How can it be used?
There is now a whole series of these covering a wide range of topics (click on the author’s name to visit his shop), and so you can bring Clive into many lessons if you choose. There is always the worry that presenting students with misconceptions may actually cause them to develop misconceptions that were not there in the first place. The evidence for that is limited at best, but it is probably fair to say that to fully benefit from this approach students must first know the correct procedure. So, my advice would be to either use these resources at the end of a topic unit as an effective way of assessing understanding, or use it as an introduction to a topic unit that you know students have studied in previous years as a means of assessing baseline knowledge. I love Clumsy Clive!
Thanks so much for sharing
Craig Barton
Download: Clumsy Clive On Averages and Range
View the author’s other resources
The post Clumsy Clive On Averages and Range: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>The post Teach for Understanding Bigger Picture: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
I dread to think how many department meetings I have say through over the course of the last 13 years, and likewise what proportion of that time has been spent doing painful admin – filling out forms, checking dates, writing predictions, etc. Bringing meaningful, effective CPD into such meetings can be a tricky business, but this lovely resource offers one possibility. It is called “Teaching for Understanding”, and its stated aim is to encourage discussion amongst maths teachers about how to teach for understanding instead of tricks. A variety of topics are presented, including fractions, indices and negative numbers, and teachers are challenged to write down:
1. The method – the basic approach
2. The understanding – why does the method work?
3. The bigger picture – how and where does this topic fit in the real world application?
How can it be used?
I am a great believer in the power of habit. Too many times I have seen a good teaching idea, hammered it to death for a couple of weeks, and then never returned to it. Students only really see the benefit once something become habitual. I believe the same is also true for something like this resource. Use it once in a departmental meeting, and you are unlikely to see much long-term benefit.; However, make this a regular part of meetings – it should only take around 10 minutes to fill-in and discuss once colleagues are used to how it works – and the benefits could be significant. It is an opportunity for colleagues of all experiences and backgrounds to share their knowledge, expertise and opinions in a positive, structured way,. And it is fascinating to see the different approaches.I highly recommend giving it a try.
Thanks so much for sharing
Craig Barton
Download: Teach for Understanding Bigger Picture (Maths CPD)
View the author’s other resources
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]]>The post Andrew Blair – prequel: Inquiries and being a Head of Department appeared first on Mr Barton Maths Blog.
]]>Last episode I interviewed Andrew about running inquiries. There has been a fantastic reaction to the interview, and I am pleased to see that it has given other people plenty to think about, and not just myself. Indeed, I am not sure my head has quite finished spinning. If all goes to plan, next episode I will be recording Part 2 of my interview with Kris Boutlon, and I want to discuss directly the points Andrew made about outcomes, fluency and purpose.
So, in preparation for that, I thought it would be a good idea to release my first interview with Andrew Blair, that I recorded back in 2014 when I used to host the TES Maths Podcast. Here Andrew describes in detail a far more open-ended, less structured inquiry than the one he talked about last episode. It is fascinating to listen to how you plan and deliver a lesson that – quite literally – could go in any direction, and that direction is determined 100% by the students themselves. As a bonus, Andrew also shares his invaluable experiences and advice on being a head of department.
I hope you agree with me that this is a superb listen. No takeaway this time, so I won’t see you on the other side, but I will see you soon, and I hope you enjoy the journey back to 2014 – a time when I could sleep at night, unconsumed as I was with concerns about working memory, cognitive load and desirable difficulties. It was also a time when I used to record in a professional studio, had different intro music, an alluring female voice to introduce me, and considered interviews over an hour rather excessive. How times have changed. Enjoy.
On Twitter, Andrew is: @inquirymaths
Andrew’s Inquiry Maths website can be found at: inquirymaths.org
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
Just the Job Podcast
The post Andrew Blair – prequel: Inquiries and being a Head of Department appeared first on Mr Barton Maths Blog.
]]>The post Times Tables Mastery: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog here
What is it?
There is little doubt that the ability to fluently recall times table facts is a huge advantage across many areas of the mathematics students need to learn at school, from fractions to ratio, equations to angle facts. However, once students are able to recall times tables, the next step is to enable them to flexibly use these relationships in a variety of contexts. That is where this wonderful collection of resources comes into play. For exam times table there are three sets of 10 questions. These questions do not simply ask things such as “what is 4 x 8?” Instead they probe students deeper with a variety of word problems, challenges to convince why something works, and links to decimals. If students can do these, then mastery of times tables is in sight.
How can it be used?
With three sets of questions for each times table there are plenty of questions to keep students occupied. Using a couple of these sheets each week with a key stage 3 class, especially at the start of the year, might be a good idea. However, I have two quick points to make. The first is that these sheets are only really effective if students are fluent in the basics of times tables. If students are having to use up valuable working memory capacity trying to calculate, for example, what 4 x 7 is, then the challenge of applying this to solve a word problem or a related question involving a decimal is likely to be too much. Secondly, once students have been through one cycle of these sheets, there is a fantastic opportunity to interleave. Simply copying a question from each of the times tables and creating a super sheet is a great way to push students on to the next level, calling upon all their times table knowledge at once.
Thanks so much for sharing
Craig Barton
Download: Times Table Mastery.
View the author’s other resources
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]]>The post Andrew Blair: Inquiry Maths appeared first on Mr Barton Maths Blog.
]]>Andrew is the Head of Maths at Haverstock School, in Camden Inner-London, and the creator of inquirymaths.org.
Now, in recent episodes this podcast has featured guests who favour an explicit instruction approach to teaching – most notably my interviews with Greg Ashman and Kris Boulton. Speaking to these guests, together with the reading of educational research I have been doing over the last 12 months, has led to me moving rather rapidly along this path myself, favouring teacher-led instruction ahead of the rich tasks and investigations I so passionately believed in for most of my career.
This was why I was so keen to have Andrew on the show. I have known Andrew for many years, he is someone I admire and respect greatly. Indeed I interviewed him about inquiries and being a head of maths back in 2013 when I used to do my TES Maths podcast – a time where I considered a 1 hour interview a little on the excessive side. I will release this old interview as a special podcast in the next few weeks, as listening back to it in preparation for this show may me realise it is still very much worth a listen. Andrew’s Inquiry Maths website is a gold mine of ideas, complete with teacher guidance, examples of students work, and supporting resources for those wishing to try out inquiries. But there is no doubt that this approach to teaching and learning is the polar opposite to that favoured by many of the traditionalists. As the homepage of the Inquiry Maths website explains:
Inquiry Maths is a model of teaching that encourages students to regulate their own activity while exploring a mathematical statement (called a prompt). Inquiries can involve a class on diverse paths of exploration or in listening to a teacher’s explanation. In Inquiry Maths, students take responsibility for directing the lesson with the teacher acting as the arbiter of legitimate mathematical activity.
So, in a wide-ranging interview, we covered the following and more:
I know I say this every time, but honestly, this is an absolute cracker. If – like me – you have been convinced by the arguments of Greg Ashman and Kris Boulton in recent episodes, I promise you this interview will give you food for thought. I had to go on a long walk after it – followed by a long lie down, followed by a pint of Guinness – to try and organise the thoughts whizzing around in my head. I will share what I have come up with so far in my Takeaway at the end of the interview.
The usual desperate plea to give me a rating and a quick review on iTunes if you have a spare minute, and thank you so much for those of you who have, and the incredibly kind words you have written.
On Twitter, Andrew is: @inquirymaths
Andrew’s Inquiry Maths website can be found at: inquirymaths.org
Andrew’s post on discovery learning
Andrew’s post on fluency
Andrew Blair’s Big 3 (with one extra!)
1. Bruce Ferrington – Authentic Inquiry Maths
2. Graham Henshaw – Enquiry-Based Maths
3. Simon Gregg – Following Learning
4. Amanda Klahn – Doing Maths
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
Just the Job Podcast
The post Andrew Blair: Inquiry Maths appeared first on Mr Barton Maths Blog.
]]>The post Distance, Speed & Time – Find Someone Who: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>What is it?
A classic start of year activity might be to play a game of “Find Someone Who…”. Challenging your students to find someone who has an older brother, or a birthday in August is a good way to encourage them to talk to their fellow classmates, forming the bonds that may prove vital for the challenges ahead. That is all well and good, but how about something even better – a mathematical version of Find Someone Who? Yes, instead of attempting to unearth generic information, students instead are asked to track someone down who can write 30 minutes as a decimal or (my personal favourite) can calculate the distance travelled (to 3 s.f.) when travelling for 8 hours 10 minutes at a speed of 55 km/h. That is the kind of person I would want to know better.
How can it be used?
This wonderful resource is ideal for the start of the year, especially if students have been moved into different classes. However, it could be used all year round as a way of revising key concepts in a productive, cooperative manner. Better still, why limit ourselves to the study of speed, distance and time? A similar format could be used with any topic, and with any age of student. All you need are a nice selection of questions. Of course, careful consideration will need to be given to behaviour management to ensure things do not get out of hand, but there is a great deal of potential here.
Thanks so much for sharing
Craig Barton
Download: Distance, Speed & Time – Find Someone Who…
View the author’s other resources
The post Distance, Speed & Time – Find Someone Who: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.
]]>The post TES Maths Back to School appeared first on Mr Barton Maths Blog.
]]>Happy new school year! September is back and so are your students, all of whom seem to have forgotten every ounce of mathematical knowledge they once had.
So, get the new term off to a flying start with this selection engaging, mathematically sound and, dare I say, even fun exercises, designed to make the return to school as painless as possible. And for even more inspiration, why not visit the GCSE maths hub, jam-packed with resources that have been hand-selected by the Tes Maths panel?
As always, a big thank you must go to the generous and incredibly talented members of the Tes Maths community, whose resources make time fly and provide invaluable support for teachers all year around. It’ll be Christmas before you know it!
Craig Barton, Tes Maths Adviser
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]]>The post Primary School Teacher Rachel Webster: How your Year 7s have been taught maths appeared first on Mr Barton Maths Blog.
]]>Rachel is a former primary school teacher who is taking on the role of a Primary Maths Specialist with the White Rose Maths Hub from September.
The reason I wanted to interview Rachel is that for many years I do not feel I have been teaching each new crop of Year 7s as well as I could have done. Dylan Wiliam has said one of the most important things for a teacher to know is where their learners are at, and I have made the mistake of pretty much assuming these Year 7s know very little about maths. I have introduced concepts such as fractions, factors, ratio and algebra as if they have never seen them before. Perhaps just as importantly, I wasn’t sure exactly what these Year 7s would be expecting maths lessons to be like based on their prior experiences. Just in case any other teachers out there want to know a bit more about the mathematical background of their Year 7s, I thought it would be worthwhile having an experienced primary teacher such as Rachel on the show, and thank goodness I did, as it proved to be a cracker!
In a wide-ranging interview, we covered the following and more:
If you have Year 7s at all this year, or if you have any influence over your school’s transition policy, then hopefully this will prove an invaluable listen. I know it will change how I approach my teaching, and I will reflect on that during my takeaway at the end of the interview.
The books Rachel recommends, along with the book recommendations of all my previous guests, can be found at mrbartonmaths.com/teachers/books
My research page, summarising my takeaways to over 100 papers can be found at mrbartonmaths.com/teachers/research
Rachel Webster’s Big 3
1. NRICH
2. TES for the White Rose Maths Hub Schemes of Work
3. YouCubed
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
Just the Job Podcast
The post Primary School Teacher Rachel Webster: How your Year 7s have been taught maths appeared first on Mr Barton Maths Blog.
]]>The post Chief Examiner Trevor Senior: How GCSE Maths exams are written appeared first on Mr Barton Maths Blog.
]]>Trevor is AQA’s Chief Examiner for the Maths GCSE.
As those of you teaching maths in the UK in the last couple of years will have experienced, there has been a tremendous amount of uncertainty, anxiety and expectation surrounding the new maths GCSE. It’s kind of been like awaiting the new series of Game of Thrones, only with slightly fewer dragons but possibly slightly more violent twists. Now, two years on, we have finally had the first set of students through and – at the time of recording – are awaiting the inaugural set of results. So, I thought it would be interesting to talk to one of the people behind the creation of the exams, and so it proved it be.
In a wide-ranging interview, we covered the following and more:
If you teach GCSE maths now, or are planning to in the future, or if you have any interest whatsoever about how questions and exams are written, then I think you will like this one. Trevor is a knowledgeable, experienced, and an all-round superb guest. The episode is a nice companion piece to my interview with Daisy Christodoulou where we focussed in depth on assessment, and indeed I will discuss more about that in my Takeaway at the end of the interview.
The usual desperate plea that if you enjoy these interviews, and you have a spare minute, then please give the podcast a rating and a quick review on iTunes if. It really does make a difference and mean a lot, and thank you so much to those of you who already have. A new podcast seems to have entered the education chart this week – the Sexplanationas Podcast. I am not sure my three hour discussions of lesson planning, misconceptions and the subtleties of assessment objectives, will appeal to their audience, so I will need to rely on my own. Thanks you so much continuing to listen.
Trevor Senior’s Big 3
1. Graphpapermaker.com
2. All about maths
3. How grades are awarded
Thanks so much for listening, and I really hope you enjoy the show!
Craig Barton
I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:
mrbartonnmaths.com
Mr Barton Maths Blog
Twitter: @mrbartonmaths
Diagnostic Questions
Mr Barton Maths Podcast
Just the Job Podcast
The post Chief Examiner Trevor Senior: How GCSE Maths exams are written appeared first on Mr Barton Maths Blog.
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