5 Maths Gems #147

Welcome to my 147^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers. 

1. Dr Austin's Resources 
Amanda Austin (@draustinmaths) has been updating her website draustinmaths.com over summer. She's added a number of new resources - see her Twitter feed for the highlights.

I've started to add Amanda's resources to my resource libraries, to save teachers time when planning lessons.

2. PolyPad
Mathigon's awesome interactive tool PolyPad has a load of new features including lots of cool stuff for both 3D geometry and statistics.

Big news: Polypad now supports 3D geometry! 🎉⚽️🎁 Use one of our built-in solids, or create your own net using polygon tiles. Then click “fold” and watch the magic happen… pic.twitter.com/lMeBZbvGSo

— Mathigon (@MathigonOrg) August 2, 2021

The clocks are new too:

The latest components added to Polypad are clocks! ⏰ If you want to learn more, sign up for our upcoming #BackToSchool workshops at https://t.co/L3QuGWHc3k pic.twitter.com/2Yc3JtZT9l

— Mathigon (@MathigonOrg) August 16, 2021

I love Mathigon and have blogged about it many times. Have you seen the Almanac of Interesting Numbers?

And this awesome Sieve of of Eratosthenes? This is brilliant for teaching students about prime numbers.

The new number grids on Polypad make it really easy to find prime numbers using the Sieve of Eratosthenes. You can colour or resize them quickly, and we’ve also added similar addition and multiplication tables! https://t.co/HDEd7BNKaK pic.twitter.com/NFqKjPZSLd

— Mathigon (@MathigonOrg) August 20, 2021

Great stuff from Mathigon.

3. Ofsted Maths Research Review
If you haven't had time to read the Ofsted Maths Research Review yet, or if you've read it and want to share the key messages with your department, then you might find this useful: George Stone (@DrStoneMaths) has shared a summary of the main points here.

George's PowerPoint includes reference to the criticisms of Ofsted's review. For more on this, it's worth reading the response of the Joint ATM and MA Primary Group here which explains some of the criticisms in detail.

4. MathsDIY
Thanks to Victoria Jennifer (@vics_jennifer) for tweeting about a website I'd not heard of. On mathsdiy.com, an experienced maths teacher shares GCSE Maths and A Level Maths past paper solutions, topic booklets and resources. Questions are drawn from WJEC papers. 

5. Guided Reading
Thanks to Jenny Hill-Parker (@JennyHillParker) for sharing a set of guided reading resources here.

Guided reading is a really interesting idea - check out my Gem Awards 2021 for more on this.

Update

Did you catch my last gems post? I published it in late July. In previous years I've done a lot of blogging over the summer holidays but this year I've just not had time, so two gems posts will have to do. I did manage to get away with my family for a couple of weeks though, which was lovely. The highlight for me was visiting Woolsthorpe Manor and sitting under Isaac Newton's apple tree. It's really delightful there - I highly recommend a visit.

I also had a lovely evening at Jamie Frost's maths teacher drinks. Jamie used to host these events three times a year but lockdown put a stop to it. It was so nice to see everyone again.

 

I'm looking forward to the return of conferences over the next few weeks. I find that going to a conference right at the start of a new academic year is a great way to get excited and inspired for the year ahead. First up is #mathsconfmini2 next Friday night. I'll be speaking about probability, and also more generally about reducing cognitive load.

Then on 4th September it's the national researchED conference which, incredibly, is an actual in-person event in London. I'm really looking forward to the pre-conference night out! I'm delivering a session at the conference called 'Skimming the surface of the maths curriculum'. Here's the blurb:

In this session we will look at the maths curriculum, considering both the content and the way it is delivered. We'll analyse research findings and discuss whether the practice of 'skimming the surface' of maths is widespread in schools. Are students accelerated onto new topics too quickly? Is adequate time provided to teach topics properly? Do teachers know how to teach topics in depth? And how can we do things differently?

If you're coming to the conference, do come along to my session - I have some interesting insights to share from the Key Stage 3 survey I did recently. Unlike all my other workshops over the last eighteen months, this one won't be recorded!

If you're preparing to return to school in a couple of weeks, here are two pages you might find helpful:

• Year 7 Maths Activities
• Displays

And finally, just a reminder to those of you who subscribe to my blog posts by email: the emails will now look a bit different so please don't be alarmed! I had to swap the subscriptions over to a new provider (because Google stopped its email subscription service), and I managed to lose a lot of subscribers along the way. If you want to receive my blog posts by email, you can sign up here.

I'll leave you with this nice little problem from @BerrySlime3 which would be suitable for Higher GCSE students. Hat tip to @blatherwick_sam for sharing it.

5 Maths Gems #90

Welcome to my 90^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Probability Task
Thanks to John Rowe (@MrJohnRowe) for sharing this challenging probability puzzle. If you like this then you'll find similar tasks for a wide range of topics on the fantastic website openmiddle.com which I've blogged about before.

2. Exam Wrapper
Thanks to Alice Leung (@aliceleung) for sharing an exam wrapper for students to complete after an assessment. I like it that students are asked to reflect on whether they did sufficient preparation for the exam.

 3. Number Properties Puzzle

Here's a great number puzzle from @OCR_Maths.

4. A Level

If your Year 12s have internal exams coming up, you might find my revision quizzes for pure and statistics helpful. I've told my students to print off a load of these and test themselves at home until they get everything right. The statistics quiz has a huge number of definitions! 

There was a helpful discussion about A level taster lessons on Twitter this week, initiated by Adam Creen (@adamcreen). You can read the full thread here. I have found in the past that Pascal and Binomial works well. I've also used Susan Wall's lovely 'Find the coordinates' task successfully as a starter activity in A level taster lessons.

5. Euclid

Thanks to @MrsMathematica for sharing this video about Euclid - I enjoyed watching this.

Also check out The History of Non-Euclidian Geometry - Squaring the Circle and The History of Non-Euclidian Geometry - The Great Quest.

Update

In case you missed it, I recently wrote a subject knowledge post about algebraic highest common factor and lowest common multiple. Writing this made me rethink my approach to teaching this topic. 

I also published three sets of breakfast warm up resources for both Higher and Foundation GCSE. It's been lovely to see so many schools using these to calm nerves and warm up brains on the morning of exams.

I also published a set of Year 3 topics in depth packs created by Nikki Martin - please share these with primary colleagues.

There have been a number of good maths education blog posts lately that are worth reading, including:

• 'Test-Homework-Test' by Mark Horley (@mhorley) 
• 'A Mastery Curriculum in Scotland - A Review of Year 2' by Chris McGrane‏ (@ChrisMcGrane84)
• 'Simultaneous equations: an insight from playing with technology' by Tom Button (@mathstechnology)

I'm looking forward to presenting at #mathsconf15 in Manchester in two weeks - my workshop is not just an opportunity to share loads of cool indices stuff, but also to explain the principle of planning and teaching topics in depth. In a world of quick fixes, I'm going in the opposite direction... I wrote a post about this last year.

If you're coming to the conference, print a copy of my #mathsconf15 bingo in advance and play along on the day.

Finally, did you see these awesome biscuits made by Ella Dickson (@elladickson) for her Year 13 students? Amazing!

How I Wish I'd Taught Maths

Craig Barton's new book 'How I Wish I'd Taught Maths' is a game changer... in a game that very much needs changing. It's absolutely superb. I genuinely think it might have a huge impact on the way maths is taught. Or at least, I hope it does.

Craig's teaching has transformed significantly in recent years. Through a charming and witty narrative, Craig explains how he used to teach - back when he was a highly successful 'Ofsted outstanding' advanced skills teacher - and why he teaches totally differently now that he has properly engaged with education research. He jokes about how ineffective his previous approaches were, and this may make uncomfortable (but worthwhile) reading for maths teachers who still teach in this way.

Teachers are trained pretty quickly in this country, particularly those on school based schemes. New teachers are often thrown into classrooms with no knowledge of cognitive science whatsoever. As Craig writes, "a teacher not considering how their students think and learn is kind of like a doctor not being overly concerned about the workings of the body, or a baker taking only a casual interest in the best conditions for bread to rise". Thankfully Craig's book gives both new and experienced teachers the opportunity to remedy this.

Craig's anecdote about 'The Swiss Roll Incident' (in which his students remembered swiss rolls instead of maths after a messy jam-filled lesson) perfectly illustrates the notion that "students remember what they think about". Throughout the book Craig's anecdotes and reflections beautifully exemplify some of the common mistakes that teachers make. Each anecdote comes with a description of Craig's key takeaways from the relevant research and an explanation of what he now does differently. This provides a clear way forward for maths teachers looking to improve the effectiveness of their practice.

In his chapter on deliberate practice, Craig writes about identifying sub-processes and isolating skills. He shares examples of short activities which allow him to pick up on specific misconceptions and address them before they get wrapped up in more complex processes. The example below is part of a series of short activities for teaching students how to add fractions.

I'm not sure that this kind of activity is currently common practice, but like many approaches featured in Craig's book, I think it may become recognised as a highly effective approach over the coming years. It's great that Craig has shared so many specific examples of activities, resources and explanations. These are incredibly helpful to teachers. 

In summary, I love this book! Not only has Craig put all the relevant education research in one place, which is perfect for overworked and exhausted teachers like me, he has also interpreted broad education research specifically in the context of maths teaching. Most of the research isn't new, but Craig adds so much value by describing how it relates his own practice that even teachers who keep up to date with the latest research will benefit from reading Craig's interpretations. His advice is easy to understand and instantly transferable to the classroom.

Craig's book is a real pleasure to read and had me giggling throughout ("keep this quiet, but I flipping hate 3D trigonometry!"). It has the potential to have a huge impact on the way maths is taught. It's delightfully controversial at times and I'm certain that it will spark lots of interesting discussions in maths departments all over the country. Once you've read it, do let me know what you think.