18 April 2021

Gem Awards 2021

Next week it's resourceaholic.com's seventh birthday! It's become a tradition for me to mark the anniversary of my blog by publishing an annual 'Gem Awards' post. Here I look back at all the ideas I've shared in my gems posts and choose some of my favourites. 

1. Subject Knowledge Award
I love nothing more than finding opportunities to develop my subject knowledge. This doesn't mean being 'better at maths'. It means having a greater depth of knowledge about the content I'm teaching, from a pedagogical perspective.

The last time I handed out a Subject Knowledge Award was in 2017 - it went to Ed Southall for his book 'Yes, But Why?'. Although there have always been books about maths education, Ed's excellent book was the first one I knew of which focused on pedagogical subject knowledge. Since then a few more subject knowledge books have been published, including my own book about methods. Ed's book remains an essential read for maths teachers, and it's great to see that there's a forthcoming second edition.

This year the Subject Knowledge Award goes to Sudeep Gokarakonda of Boss Maths for the brilliant vocabulary resource I featured in Gems 121. The idea of learning more about the technical language we use in the classroom was relatively new to me when I first started blogging back in 2014. It's now something that I regularly incorporate into my lessons. Sudeep's vocabulary resource is ideal for extending my subject knowledge. Every single page is fascinating! It's perfect for use both in lessons and in maths department meetings.

Highly commended in this category is Nathan Day for his classroom displays featuring famous mathematicians of the world and mathematical quotations. The content of these lovely displays is valuable for both teachers and students seeking to expand their knowledge of the field.

Also highly commended in this category is James Tanton for his fabulous video 'The Story of the Vinculum'.

2. Bright Idea Award
This award goes to Miss H for her induction booklet idea that I shared in Gems 129. Last year our incoming Year 6 students were unable to join us for their usual induction days so she came up with the idea of an induction booklet. The version she shared included loads of activities for her new joiners to do over summer, plus an introduction to the maths teachers in her department. Inspired by this, I created my own version - I used loads of Miss H's ideas, so she saved me a lot of time, and I know countless other teachers did the same. This is why sharing ideas on Twitter is so valuable. 
Highly commended in this category are the teachers who collaborated to produce the fantastic set of Guided Reading Activities I featured in Gems 137. I love the idea of maths comprehension exercises - it's not something I'd considered before. The design and content of the resources in this collection are perfect. Using a template shared by @MrHand__, these exercises have been created by Katie Pollard, Andrew Baxter, Nicola WhistonVandana Sethuraman and Nix. Katie and Andrew's guided reading sheets can now be downloaded from TES.

3. CPD Award
This award goes to the team at La Salle Education for the incredible conferences they have run since the start of the pandemic. They quickly adapted when the world moved online, developing a highly impressive conference platform with an outstanding user interface. This has resulted in a consistently high quality experience for both delegates and speakers. 

In addition to their regular conferences, La Salle's CPD offering is extensive. It includes their Teacher CPD College which offers over 120 courses for a cost of £7 per month.

Highly commended in this category are:
  • Loughborough University Mathematics Education Network (LUMEN) for their provision of incredibly high quality professional development videos which are freely available to maths teachers.
  • Teacher Tom Manners who during lockdown shared numerous free maths CPD videos for secondary and primary teachers on his website. This includes his #ResourceFULL series in which he interviews guests about maths resources. 
  • Rhiannon Rainbow and Dave Tushingham for #GLTBookClub. The format of this CPD is highly engaging and effective. In the expertly run book club meetings, teachers have the opportunity to participate in incredibly rich discussions. They reflect on the ideas presented in the books they've read, and discuss the application of those ideas in the classroom. 
  • Craig Barton for the many things he does to support maths teachers including his fabulous podcast and his excellent online CPD courses. I already gave him a Gem Award in 2017 for his podcast so I can't give him another one, but it's still by far the best education podcast there is.

4. Pedagogy Award
This award is for the big thinkers. It's for the teachers whose insights and ideas encourage us all to reflect on our practice in the classroom. 

This year the award goes to Chris McGrane for his ongoing work on curriculum and task design. In addition to the publication of his brilliant book Mathematical Tasks, he regularly shares his thoughts on Twitter and through his website startingpointsmaths.com. On his website he publishes tasks that he has written himself, such as this FDP task which is designed is to help students reinforce connections between division and multiplicative representations in decimals, percentages and fractions. 

Chris also publishes numerous tasks contributed by other authors, such as this excellent powers task from Kyle Gilles:

Highly commended in this category are:

5. A Level Award
This award goes to Devina Jethwa. I featured her new A level website jethwamaths.com in Gems 133. This website features lots of useful new content for A level teachers - resources include worksheets, practice papers, topic tests and calculator tutorials.
Highly commended in this category is Seb Bicen. On his excellent YouTube channel he has videos and accompanying resources for Edexcel A level Maths and Further Maths. What makes the videos unique is that they are recorded live with his classes, so they have an authentic classroom dynamic. His explanations are very clear, so these videos aren't just useful for sharing directly with students, they could also be useful CPD for inexperienced A level teachers who are preparing to teach their own lessons.

Also highly commended in this category is Jack Brown. He has been running his excellent website TLMaths.com for eight years now. He has shared over 4200 videos and had over 16 million views, and continues to make new content to support students and teachers with their A level studies. Jack is also active on Twitter, supporting and advising A level teachers. 

6. Task Design Award
This award goes to Miss Konstantine for the incredible collection of tasks she has published over the last few years. She is constantly producing wonderfully creative tasks and sharing them for free on her blog mathshko.com. Her tasks are always a delight. She thoughtfully listens to feedback from teachers as well as reflecting on her own experiences of using her tasks in the classroom.

In the bar model task shown below, she has clearly reflected on the underlying skills that students need in order to work fluently with bar modelling techniques. I haven't seen many other tasks that specifically address these skills.

Here's another example of her tasks: this one aims to get students thinking about negative numbers. In the blog post that accompanies it, she explains her rationale for creating the task. I'm sure many of us have encountered students who find it difficult to see that 7 – 2x is the same as – 2x + 7.

I could share dozens of Miss Konstantine's tasks, but here's just one more example to give an idea of the variation in her style and approach. Here's a lovely pattern colouring activity for number properties.

Highly commended in this category is Ashton Coward who creates really cleverly designed tasks and shares them through his website. One example is his gap fill task for significant figure rounding.

7. Interactive Tool Award
I don't like to give an award to the same people three times, but this award is going to have to go to MathsPad yet again! Well done to James and Nicola for creating the brilliant Place Value interactive tool that I featured in Gems 143. Freely available to all, this tool gives teachers the opportunity to fully explore place value with students to really deepen their understanding. It's very cleverly designed. Do check it out, along with all their other outstanding interactive tools.

Highly commended in this category is the author of sineofthetimes.org Daniel Scher for his Zoomable number line activity. I loved this so much when I did it with my Year 7s this year, I immediately wrote a blog post about how brilliant it is.

Also highly commended in this category is Mathigon's Multiplication by Heart tool. These virtual flash cards use spaced repetition to teach multiplication facts. The tool is free to use, and is just as high quality and beautiful as all the other wonderful treasures on Mathigon.

8. TES Author Award
This award goes to Andy Lutwyche who continually publishes excellent resources on TES. It feels like he's been doing it forever! His generosity is incredible, with over 2000 resources uploaded to TES including popular collections such as 'Erica's Errors', 'Spiders', and codebreakers with terrible punchlines. An example of one of his many resources is his Non-Examples Reasoning Tasks in which students are asked to identify examples and non-examples and explain their thinking. I featured this resource in Gems 118.

Another example is this excellent resource for the quadratic formula which I featured in Gems 130.

Highly commended in this category is TES author cparkinson3 who I wrote about in Gems 110Gems 116 and Gems 117. His collection of free resources features bundles of high quality slides and activities for numerous topics. Pictured below is a vectors task from his shape transformations collection.

9. Teacher's Website Award
This award is designed to celebrate classroom teachers who dedicate their spare time to producing or collating resources for others. By doing so they save many teachers a significant amount of time in planning lessons. I try to showcase some of the less well-known websites in this category. 

This award went to Dr Frost back in the Gem Awards 2016 when his website was relatively unknown (compared to now!). 

This year the award goes to GoTeachMaths.co.uk which has over 4000 free resources for Key Stages 2, 3 and 4. I first featured this website in Gems 109. A number of teachers have since contacted me to recommend it, telling me that the vast collection of well-organised resources saves them lots of time. Shown below is a short extract from their measuring angles PowerPoint.
This the is the sort of website that seems to have an activity for practising every skill you can think of! For example, here's an extract from a worksheet on ratio and angles.

Highly commended in this category are the following:
  • Mrs Jagger for her website jaggersmaths.co.uk which features lessons, teaching resources, enrichment activities, tutor time tasks, revision materials and much more. She has generously shared her full five year scheme of work too.

  • Amanda Austin for her website draustinmaths.com which features a collection of KS3 and KS4 IGCSE and GCSE Maths resources, as well as resources for AQA Level 2 Further Mathematics.
  • mathsteacherhub.com which features an extensive bank of differentiated resources. There are starters, exercises and homeworks at multiple levels of difficulty for Key Stage 3 and 4.

Apologies if I've missed anyone's favourite website here! There are many more I could have included. 

There are a number of new websites that have been launched over the past year - keep an eye on my gems posts for updates on these sites as they develop.

10. Lifetime Achievement Award
The 2021 Lifetime Achievement Award goes to The Mathematical Association. This year they celebrate 150 years since they were first established in 1871 to challenge the way geometry was taught.

150 years is a really long time in education. For a subject association established in Victorian times to still be actively supporting maths teachers today is quite remarkable. I love their origin story, and I love what they do, which includes (among many other things):

  • running a brilliant Twitter account which keeps maths teachers updated on all the important stuff happening in maths education
  • running the Primary Maths Challenge and First Mathematics Challenge, getting children excited about maths from a young age
  • representing members in important consultations regarding developments in maths education
  • running brilliant conferences and CPD events, including those run through its many branches around the country
  • publishing numerous excellent teaching journals and books
  • owning (and making available to view) a library comprising nearly 11000 books and 700 runs of periodicals from many different countries, plus over 1100 older or rarer items going back to the sixteenth century. The MA's library is a unique primary source for the history of the mathematics curriculum in the UK. It's incredible!

The members of the MA's Council and committees are volunteers. Many have spent their entire working lives (and beyond!) working hard to ensure that the MA continues to support maths teachers. They are very worthy winners of one of my Lifetime Achievement Awards.

Congratulations to all the winners of the Gem Awards 2021!

And thank you to every single member of the maths teaching community who shares ideas, collaborates, produces resources, gives advice and supports other maths teachers. There are many people who I've not mentioned here who have helped to fill my gems posts with resources and ideas. I've been on Twitter for seven years now and continue to feel privileged to be part of such a supportive and generous community. Good work, Team Maths.

If I'm still blogging in 2024 (the ten year anniversary of my blog!) then I hope I will be able to host an in-person glitzy awards ceremony. We can all get dressed up and drink champagne and I can hand out proper awards to say thank you.

If you're new to my blog and you enjoyed this post then visit my Gems Archive you'll find an index of 143 gems posts - they are all full of great ideas and resources. You might also want to check out the Gem Awards 2019Gem Awards 2018, Gem Awards 2017, Gem Awards 2016 and Gem Awards 2015 to see who has won awards previously. 

Happy 7th birthday resourceaholic.com. Thank you to my readers for all the support!

3 April 2021

5 Maths Gems #143

Welcome to my 143rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers. 

1. Place Value Tool
When making the CPD course Marvellous Maths 2 I struggled to find a virtual manipulatives tool that really effectively conveyed the relative sizes of tenths, hundredths, thousandths and so on. Luckily James and Nicola from MathsPad watched the course and this prompted them to go off and make one!

What they have produced is incredible. Freely available to all, this tool gives you the opportunity to fully explore place value with students to really deepen their understanding. 

Do have a play with it. It's awesome.

James and Nicola have also started publishing their Curriculum Booklets which are packed full of brilliant activities. Read their latest update for more information about their excellent booklets. 

2.  Powers
I really like the ideas explained in this Twitter thread from Sam Blatherwick (@blatherwick_sam). When teaching fractional powers, he gives his students a power chart like this:

Students can use these charts to answer questions like this:

Read Sam's thread for the full description of how he uses this chart to develop understanding. 

I really like this. It reminded me of my favourite indices resources - Mental Mathemagician from yummymath.com, and 3 Power Line and 5 Power Line from Don Steward.

3. New App
I don't often feature resources that aren't free but this one caught my eye. The Arc Maths app (@ArcMathsApphas been developed by a maths teacher and looks rather good. 

It's aimed at students aged 11 - 16 and gives users a highly personalised experience. Schools with access to iPads can subscribe and make use of this app in the maths classroom, in tutor time or in intervention. 

I don't know many state schools with class sets of iPads, but it's worth knowing that parents can subscribe to this app for their child at a cost of £3.49 a month. This may be something that schools can advise parents to invest in if they ask for ideas of how to help boost their child's maths grade.

4. CPD
The collection of free CPD videos from the Loughborough University Mathematics Education Network is brilliant. Maths teachers looking for CPD for either themselves or their department would benefit from exploring the videos on offer. The latest addition is Improving Language Use in Maths by Dani Quinn.

5. Simple Linear Graphs
As I mentioned in Gems 141, Dan Draper (@MrDraperMaths) has published loads of great blog posts lately. His post 'x=a, y=b: When?' looks at curriculum and concept development through a series of well-designed tasks.


I enjoyed the first day of the MA conference. Delegates who attended my session can download my slides here. And you can listen to the post-conference podcast with me and Craig Barton here.

Did you see my recent blog post? I wrote about the The Power of Modelling and Exemplars.

If you enjoy my blog posts then you can subscribe here. You will only be emailed when I publish a new post, which is normally once every three or four weeks.

I'm very glad to be on my Easter break after a crazy Spring term. As well as attending the three-day MA Conference, my holidays will mainly consist of hanging out with my lovely daughters, and completing endless Only Connect style puzzle grids from the website puzzgrid.com (which I am a bit addicted to). I'm trying to keep work to a minimum this Easter because I desperately need a rest, but I do have a few things coming up over the next two weeks:

  • I'll be reading Michael Pershan's book 'Teaching Maths with Examples' which looks excellent.
  • I'll be recording a podcast with Ben Orlin, chatting about bygone maths symbols
  • I'll be attending #GLTBookClub on 13th April. We'll be talking about Chapter 18 (angles in polygons) from my book A Compendium of Mathematical Methods.

I'll leave you with the news that Tarquin are now taking orders for empty protractors. I spoke about this idea in my Angles in Depth CPD. A lot of the mistakes made in measuring angles come from students relying on reading scales on protractors (which they often misread) rather than using reasoning. Protractors without numbers help students think logically about the measure of turn. 


20 March 2021

The Power of Modelling and Exemplars

Last week I observed an art lesson which featured expert use of modelling. The teacher wanted students to use a particular technique to create a piece of artwork. Before the lesson she'd used a visualiser to record herself performing the task. The video was shot from above, recording only her hands. She played the recording to the class while she narrated what she was doing and pointed out the difficulties she had encountered along the way, advising students of how they could overcome those difficulties when it was their turn to have go. She then left recording running on a loop on the screen while the students performed the task, meaning they could look up and refer to it throughout. What an excellent technique! 

I occasionally do something similar in maths - when teaching constructions I leave gifs playing on a loop on the board so students can refer back to them whilst practising:

I think this is really powerful in topics like constructions. 

It is very easy to leave animated written examples running on a PowerPoint while students practise (like in the example below). But here it's probably more helpful to instead leave all the steps and solutions static on the board, rather than an animated version. It's the same idea though. We model how to do the process and we show students what the final outcome looks like. And then we leave that with them to refer to, rather than hide it away and expect them to remember it.

In generic whole school CPD, I'm often surprised to hear people talking about the importance of modelling examples as if it's a new or unusual idea. But perhaps it is, in other subjects. For maths teachers it's just so ingrained in everything we do. We are always modelling. Students are constantly getting to see us do 'live' maths. From our modelling, students can see what the final outcome should look like. 

Students don't get the same benefits from PowerPoints which are clicked through to show animated step-by-step solutions as they do from live modelling. They need to see 'pen and paper' modelling, done during the lesson by their teacher, whether on a whiteboard or a blank PowerPoint slide, or under a visualiser. Because otherwise, how can they possibly know what their work should look like?

A few years ago there was a trend for using 'WAGOLL' techniques in many subjects ('what a good one looks like'). This is a logical thing to do - if you want students to produce something of a certain standard, how can they achieve that if they are not shown what that standard looks like? It's like when we follow a recipe to bake a cake or cook a meal - we start by looking at a picture of the final outcome, so we know what we are aiming for. 

There are a number of commonly used techniques for showing students 'what a good one looks like' in many subjects, including the live modelling I've described. Another technique is using a visualiser or photo to share examples of excellent work by other students. For example if a student's book is laid out immaculately and you want other books to look the same, simply show the class what that good book looks like. Just moaning at a student that their workings are a mess won't help them improve. Find a good example and show them.

In maths, the exemplar response materials provided on Edexcel's Emporium are perhaps one of our most useful tools for showing 'what a good one looks like' in terms of the maths itself. 

Take this Edexcel exam question for example. What would a good answer look like?

Edexcel has provided us with an excellent solution given by a student in their GCSE exam. Note that reasons are given throughout, that workings are clear and presented vertically down the page in a logical order, and they have even used a 'therefore' symbol (not essential, but nice to see!). This student knows what they're doing.

When teaching circle theorems, it is so useful to show examples of answers gaining full marks. This helps students know what they need to do to get marks in questions like this, particularly in terms of the wording of their reasoning. 

Edexcel also provides examples of student answers to the same question that did not gain full marks. As a class you can discuss where students went wrong and where their misconceptions lie. Looking at real student answers and seeing how marks can be gained and lost is powerful stuff. 

Analysing exemplar responses is also incredibly useful for maths teachers. Edexcel very helpfully provides accompanying comments which explain the misconceptions and tell us where students lost and gained marks.

I could show you endless examples here, but I will just share one more. This is an angles questions from an Edexcel Foundation paper. The first solution gains full marks. The second got one out of three.

Can you guess what the second student did to come up with the angles of 120 and 150? 

The comments from Edexcel tell us that this student appears to have measured the angles with the protractor. We are urged to remind our students that diagrams are not drawn accurately and they should not be measuring anything (unless specifically asked to do so!). This is not something I would have anticipated students doing in this question.

I'm sure you'll agree that exemplar answers are an incredibly useful teaching tool, not only for showing students 'what a good one looks like', but also for our own CPD purposes. You can find Edexcel's brilliant exemplar resources on the Emporium:

We are very fortunate in maths to have access to such useful resources to support our teaching.

13 March 2021

5 Maths Gems #142

Welcome to my 142nd gems post. This is where I share some of the latest news, ideas and resources for maths teachers. 

1. Times Table Packs
Thank you to Sarah Farrell (@SarahFarrellKS2) for sharing a set of times table packs. Each one has a 25 different activities aimed at targeting conceptual knowledge and quick recall in each multiplication table. These will be very useful to primary teachers, and I can imagine that they'll also be a helpful resource in secondary interventions.

2. Website
Thank you to Matt Woodfine (@PiXLMattTheApp) for sharing his website
mathswhiteboard.com. This website features examples pairs, mini whiteboard activities, retrieval practice, a worksheet generator, starter activities, class interactive keypads and more. It's all free and easy to use, and Matt has done a lot of work on it recently.

3. Tasks
There have been loads of great tasks shared on Twitter recently. I have probably missed many of them, but here's a selection:


4. Virtual Escape Rooms
Thank you to Grant Whitaker for sharing three online maths escape rooms that he has made: one for Key Stage 1, one for Key Stage 2 and one for Key Stage 3.
Some of my readers have asked about maths escape rooms before. Grant asked me to share a link to an online course where teachers can learn how to make an online escape room. 

5. Foundation Booklets
Thank you to Mr Kingsley (@KingsleyMaths) for sharing a set of Foundation GCSE booklets. Each task contains ten 1/2 mark questions, which can be used as lesson starters. They build up in difficulty in both calculator and non-calculator topics.

I have a page of GCSE revision resources here.

I am having a tough time at the moment to be honest. I was so excited to get back in the classroom and I spent a long time preparing to teach some awesome topics, but ridiculous lateral flow test policies have sent many of my students home already. This has upset me. On top of that, being the member of SLT in charge of cover in a year with high staff absence has finally broken me. But Easter is round the corner (a much-needed break after my Covid-filled Christmas) and I'm sure things will improve in the summer term.

Before my teaching of Pythagoras to Year 8 was interrupted, I'd delivered a lovely lesson revising squares and square roots (with and without a calculator) - this is a really important pre-requisite skill in this topic, so I feel that it was time well spent.

In case you missed them, my most recent blog posts were:

If you haven't already booked, don't forget to get a ticket for the MA's April conference which is coming up soon. If you're not sure, just check out the workshops on offer! They are fantastic, and it's amazing that you can access them on demand for only £10.

Thank you to La Salle for running #mathsconf25 today, and to all the speakers. This was the seventh year in a row that I have attended a maths conference on Pi Day weekend!  Thank you to everyone who came to my session on GCSE Topics: What and How?. I focused mainly on simultaneous equations. The video will be released by La Salle soon. 

Thank you also to people who have bought a copy of my book A Compendium of Mathematical Methods over the last fourteen months. It took a lot of time and effort to write a book, and it's hard to be a female author in a male-dominated field, so I really appreciate the support. I probably don't tell people about my book as often as I should, because promoting your own book seems to bring disapproval from many. I need to stop shying away from it though - the tiny amount of extra income is helping me slowly save for a small loft conversion so my daughter can have her own bedroom, so it is important to me. If you want to 'try before you buy' then there's a sample chapter here, and a free Seneca course here which covers two chapters.

I'll leave you with this fun iceberg drawing tool from @JoshData. I love this!