19 August 2020

Maths Teacher FAQs

I joined Twitter back in 2014 because I was told it was full of maths teachers sharing resources. What I didn't expect - and the thing that really caught my attention - was that it was also like a mathematical curiosity shop. Soon after joining Twitter, I started bringing interesting facts and cool mathematical trivia into my lessons. With this came a huge boost in my enthusiasm in the classroom, which rubbed off on my students. 

Early on in my tweeting career (on 6th August 2014 to be precise), I spotted the classic 'Fibonacci - miles km conversion' thing, which I had never seen before. This delighted me. It turned out that lots of people on Twitter already knew about it and had discussed it a year earlier, long before I'd joined. Suddenly, I started wondering what else I'd missed. I had a serious case of FOMO.

I quickly realised that I didn't want all this cool maths stuff to be limited to an exclusive group of Twitter teachers. I wanted all maths teachers to have the chance to see it, even if they weren't on Twitter. This is why I started writing gems posts, to share all the best stuff I saw on Twitter more widely. 

But what my gems posts don't capture are the 'FAQs'. These are the questions that are asked all the time on Maths EduTwitter. They come up again and again. And each time these questions are asked, dozens of people reply, and the thread rumbles on for a few days. It often ends up being almost identical to the same thread from a few weeks, months or years earlier. 

I thought it would be helpful to pull some of these FAQs together. I came up with fifteen, but have narrowed it down to ten for this post. My thinking is, based on the frequency with which these questions are asked on Maths EduTwitter, there must be lots of non-Twitter teachers wondering the same things. In each case I provide a link to recent threads, plus recommended books, blog posts and podcasts.

1. What can I do about numeracy across the curriculum?
I'm not a big fan of the word numeracy in this sense to be honest. If we want students to be better at times tables, estimation, working with money, data literacy and all those things, can't we just call it maths? And can't we just address it through really good maths teaching?

I once visited a school where students were told to report when they'd spotted 'numeracy' in other subjects - they submitted bits of paper saying 'my English teacher wrote down the date' and things like that, and got rewarded for it. I'm really not sure it's a good use of time to reward students for spotting a date on the board, and I'm not convinced that this should labelled 'numeracy'.

Well-intentioned SLT (normally with Ofsted on their mind) often appoint a numeracy lead to introduce initiatives to ‘support numeracy across the curriculum’. When I was asked to do that by SLT in a previous school - and even given a budget to spend - I argued that it is often students’ confidence in working with numbers that has a cross-school impact. And I believe that this confidence largely stems from their fluency in times tables. So I used my numeracy budget to launch Times Tables Rockstars. My advice to anyone in the same position is: avoid distracting gimmicks, be honest with SLT about what might actually have an impact, and don’t burden teachers in other subjects with unnecessary workload. If you can, focus your effort on supporting maths teachers to ensure that maths teaching is consistently high quality.

Here are some links you might find helpful:

By the way – don’t confuse ‘numeracy across the curriculum’ with ‘maths in other subjects’. The former usually involves whole-school initiatives which are meant to increase students’ confidence in working with numbers, but often just highlight to students that 'numbers are everywhere' (which they probably already knew). The latter is where maths comes up in other subjects – this is where the maths department can and should support colleagues across the school. There’s mathematical content in many subjects including science, geography, DT, economics, business studies, PE and psychology. It's worth working with those departments to ensure consistency of approach and sensible scheme of work ordering. Check out the CPD for science and business studies written by Maths Lead Teresa Robinson to support the teaching of maths content in other subjects across her MAT. 

2. What method should I teach for factorising non-monic quadratics?
This must be one of the most frequently asked questions on Maths EduTwitter! I understand why it comes up so often. When I was an NQT I asked the same question. I was taught to factorise non-monics (i.e. quadratics with leading coefficient greater than 1) by inspection but my students demanded a more procedural approach. Until that point I had no idea alternatives even existed. 

Here are some links you might find helpful:
There are lots more Twitter threads on this - I can't list them all here, but they can be found using Twitter's search function.

3. How do I teach mixed attainment maths?
This is not a question I am able to answer. I haven't been trained to teach students in mixed attainment groups and I have very little experience of doing so. In this country (more so than others), the range in 'maths attainment' for secondary students is vast. In a typical comprehensive school we have Year 7s who are struggling with Key Stage 1 content, and others who are flying ahead with Key Stage 4 content. Whenever I've found myself temporarily teaching a mixed attainment Year 7 class, I've found it impossible to properly support the students who struggle the most with maths. Saying that, I'm sure there are plenty of teachers who are making mixed attainment teaching work well for all students. 

4. Is a cylinder a prism?
This (along with 'is a square root positive?', 'what's the difference between an equation and a formula?' and 'can the significand be negative in standard form?') ranks high in the subject knowledge questions that maths teachers frequently ask. This kind of thing normally comes up when a teacher is planning a lesson and thinking about the definitions they will use.

I asked the cylinder question myself back in 2015. It probably wasn't the first time a maths teacher asked this on Twitter, and it certainly wasn't the last. This is one of those questions where teachers are always 100% convinced that their answer is correct and get annoyed when anyone disagrees with them. 

It turns out some that definitions in mathematics are not as clear cut and universal as many of us thought. 

@DrPMaths recently tweeted this:

While I agree with Jonathan to some extent (perhaps definitions don't matter as much as we think they matter), I think it's great that Twitter has become a forum where maths teachers can develop their subject knowledge and seek clarification when they're not sure about something. And I think it's absolutely imperative that teachers can ask maths questions without fear of ridicule or judgement.

5. What should I buy with my maths department budget?
New Heads of Department often ask this question. Responses normally fall into seven categories:
  1. stationery
  2. textbooks
  3. subscriptions (e.g. MathsPad, Hegarty Maths and many others)
  4. competitions (e.g. UKMT maths challenge)
  5. CPD (including books)
  6. manipulatives
  7. visualisers
Here are some links you might find helpful:

6. Where can I find knowledge organisers?
It's worth knowing a bit of background here. First we had Joe Kirby's post from 2015 describing what knowledge organisers are and how to use them. Joe was teaching at Michaela at the time. In March 2018, at #mathsconf14, Dani Quinn and Hinal Bhudia presented a workshop on 'memorable learning' in which they explained what makes a good maths knowledge organiser. One of the key features should be the ability to 'cover up' the bit that students need to remember, so it can be used for self-quizzing (as shown in the extract below).

Around this time, a few schools started fully embedding the use of knowledge organisers across all subjects (for example, I spoke to a teacher who never had to set cover work because students always self-quizzed from their knowledge organisers if a teacher was absent). 

My colleague Andy visited Micheala to learn more about knowledge organisers and then implemented them with his classes as a trial. The knowledge organisers he made are here

Kris Boulton then wrote the post 'When shouldn’t I use knowledge organisers?' where he suggested that they aren't helpful in maths because in maths there aren't many facts to learn. After that, some people started using Kris's post to shut down anyone who tried to ask about knowledge organisers on Maths EduTwitter. So for a while it all went quiet on the knowledge organiser front. 

I don't fully agree with what Kris said. I have seen numerous GCSE students go into their exams not knowing some of the basic facts and formulae that they need to know. I published a set of self-quizzing books for maths and found that although we have considerably less 'knowledge' than other subjects, there was still plenty to include.

Anyway, fast forward a couple of years and there are still lots of schools trying to roll out knowledge organisers, but the idea has become a bit confused, as explained very clearly in this post

I have seen knowledge organisers used brilliantly in other subjects but I don't have personal experience of using them so I can't comment on their effectiveness in maths (if your school has embedded the use of knowledge organisers in maths and has evidence of their effectiveness, please write a blog post about it!).

There have been lots of beautiful resources created this year that have been labelled as knowledge organisers. Most of them would probably once have been labelled 'topic summary sheets' and used for revision. I feel like the line between knowledge organisers and topic summary sheets has become blurred, and I'm not sure I know what a knowledge organiser is anymore! Whatever these recent resources are, they are very useful - so thank you to the wonderful teachers who have been creating and sharing these.

7. Where can I get classroom displays?
Every summer there's a flurry of teachers asking for ideas for displays in their classroom and corridors. Because most of us won't be teaching in our own classrooms in September, very few teachers have asked that this year! But I'm sure the question will return next summer.

I have a page of display resources here. Although it doesn't include every single maths display available, there's plenty to choose from.

It's worth noting that since Craig Barton wrote about the dangers of displays in his book, there's been a fair bit of anti-display sentiment going around Twitter. These days when a teacher asks for display ideas you're almost guaranteed to get a response along the lines of 'well of course you shouldn't have any displays, it obviously distracts students'.

As far as I know, the idea that displays could be distracting was based on limited research in primary settings. It invoked a pretty extreme reaction, with some teachers immediately stripping their classroom walls bare. I'm not saying the conclusions of the research are wrong - I can totally see the logic in the argument. If you want students to focus on maths but the board is surrounded by clutter, then it probably is distracting. But there's something to be said for warm and colourful working environments over stark white walls, and there's also something to be said for teaching students to cope with distractions (after all, the world is full of them!) rather than removing them. 

I don't feel strongly about this (I've never enjoyed putting up displays!), but sometimes I would like to see a more balanced argument.

Here are some links you might find helpful:
And - before anyone says it - yes, we would all love whiteboard walls, but we are not all lucky enough to have the opportunity!

8. What will I be asked in my job interview?
When preparing for a job interview it's very sensible to make a list of possible questions and think about how you'd respond to each one. Every school has different recruitment process, but there are certainly common questions that come up in interviews for maths teaching jobs.

9. How can I incorporate literacy into my teaching?
In 2015 I made this list of 'golden rules' for literacy in maths lessons. 

I should clarify that on the last point I don't mean 'mark all work', I just mean that if you happen to spot a spelling mistake you shouldn't just ignore it.

Maths teachers are often asked what they are doing in their lessons with regard to literacy. I think there's a lot we can do on technical vocabulary (i.e. ensuring that our students understand mathematical terms and can use them confidently) - there are lots of tools and resources available to support this.

10. Who should I follow on Twitter?
When I joined Twitter I worked out who to follow by using the Twitter search function. Here's how:
  1. Search 'maths teacher' and click on the 'people' category. This shows everyone who has the word 'maths teacher' in their bio. Follow them.
  2. Search 'mathschat' and click on 'latest'. You'll see the people tweeting on this hashtag. Follow them.
  3. Read my gems posts to see which accounts I mention - these are tweeters who are blogging, sharing ideas or producing resources. Follow them.
  4. Find the Twitter accounts of the subject associations and other organisations supporting maths teachers (such as the MA, the ATM, MEI, the NCETM and so on). Follow them.
By this point you will be following the majority of Maths EduTwitter. Interact with them - ask them questions, respond to their tweets, tweet about what you've been doing in the classroom, share your ideas and resources using hashtags - and soon you will be part of a busy maths teaching community. You don't need to ask who to follow, and you don't need to seek out followers. All you have to do is get stuck in.

When teachers join Twitter and ask who to follow, people start listing their favourite accounts. I hate this! It feels crappy when you try really hard to be helpful on Twitter and you don't make it onto people's 'must follow' lists. 

I admit that I have made lists in the past (I wrote the posts 'Jo's #TwitteratiChallenge' and 'Five to Follow' in 2015), but since #listgate (when @tessmaths upset some people by leaving them off a list!) I've tried to avoid making follow lists.


A note on Twitter for maths teachers
Twitter transformed my teaching, no doubt about it. I went through the 'five stages' incredibly quickly!
WinterIsHere on Twitter: "5 stages of #twitter user #epic RT ...
I've spent the last six years devoted to making Maths EduTwitter a supportive and helpful place for maths teachers. I've worked really hard on it. For a while I felt like we were doing a good job, particularly back in the #mathsTLP glory days. When I first joined Twitter it was really fun - looking back at my tweets from 2014, I see lots of light-hearted friendly banter. Twitter teachers reflected on their lessons, shared resources and puzzles, and helped each other get ready for the introduction of a new GCSE. And if you saw a resource you didn't like, you just didn't use it. They were simpler times!

There are a lot more maths teachers on Twitter now (this is a good thing). Plus, the Twitter algorithms have changed notably, manipulating what we see in our timeline (this is a bad thing). 

These days, share an interesting misconception and someone will criticise your teaching; solve a puzzle and someone will boast that they have a better approach; joke about something funny that a student said and someone will tell you off; ask a question about a method and someone will question your values. I am regularly saddened by the way some tweeters are so judgmental, so belittling, so arrogant and so unkind. 

Don't get me wrong - it's not all bad, and the negativity and judgement can largely be ignored. For the most part, conversations are still encouraging, kind, friendly and supportive. But I feel that things used to be considerably more chilled. I'm not sure I'd call Twitter 'fun' anymore, but I still learn a lot from it, and I'd strongly recommend it to teachers. There are still countless ideas, resources and mathematical gems to discover. And if you have a question, please ask! All questions are welcome, even if they've been asked many times before, and as a community we will do our best to support all teachers who seek advice.

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