Author: Luke Pearce

This is a follow up to last week’s introduction to teaching live lessons online.

The big takeaway for me this week is that I have realised that being forced to teach online will change my classroom practice. Sometimes it takes a shock to bring about innovation. Here are three approaches that I want to continue when I return to teaching in person:

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1. Ask students to write down their thoughts / strategy in the middle of an example.

I started doing this on Zoom as a way to check that the whole class are concentrating, but it has proved so much more useful than this.

• I can see what everyone is thinking, give individual feedback and ask the students who have the most useful responses to share them with the class.
• Similarly, I can see who doesn’t understand. This gives me a hint as to who might need extra help when others start.
• It gives an opportunity for all students to express their ideas and show off their understanding, reducing the frustration sometimes encountered when working through a problem with a mixed-ability class.
• Forcing students to write a sentence tests whether they can use topic-specific vocabulary to explain their ideas- something that is crucial if they’re going to be able to help each other.

It’s so easy to do this online, it’s a shame that it’s going to be harder in person. I think it will work OK with mini-whiteboards.

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2. Decide on the core questions that all students must complete before we move on.

I am used to setting questions to incorporate a wide range of abilities, starting easy and getting gradually more difficult. The first set of questions I set to students on Dr Frost Maths was like this. Then I realised that some students were just never going to complete it.

This felt unsatisfactory – I didn’t want students have incomplete tasks on their ‘to do’ list, so I have really pared back the questions that I set to all students to just include a few key questions. This has really made me think about what I want everyone to do.

Additionally, it has helped to control when I move on from a topic to the next. Usually I move on when I feel from the work I am seeing that all pupils have a good understanding of the topic (a word I try to avoid because it is so overused: ‘mastery’). Having the data in front of me on the screen has made me realise that some pupils take much longer than I realised to answer the questions that I considered ‘standard’ when planning the lesson. They definitely haven’t mastered the topic.

DFM has been great for this as I can see exactly who has done the questions, and it also allows for plenty of extensions, including lots of revision and interleaving, for students who complete the set work quickly. I may continue to use it in the classroom.

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3. Test prior knowledge with an online quiz or individual questions.

During the past couple of years, I’ve been really focussing on testing prior knowledge before teaching something new. I have done this mostly on mini-whiteboards. This works ok and allows me to provide immediate feedback, but students generally recall knowledge at varied rates and so it is tough for me to help those who need it, whilst challenging others.

Instead, I should do this with individual tasks. Why on earth have I not been doing this?! It allows me more time to work with the students who need it, and gives others opportunity for extension.

Whilst online, I’ve been using Quizizz for this, mostly to provide a change from DFM. I would consider sticking with this in the future – it provides a clear bar chart showing who is doing well and who probably needs extra help.

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Other points, related to my first, were made by Beth Plaw and Heather Scott on twitter: Students have been asking lots of sensible questions and often phrasing them more carefully and specifically than usual.

Next week I’ll be back, with more tips on Zoom, including how to get students working in groups and monitor this, as well as how point 2 above has encouraged better differentiation and useful collaboration with my Head of Learning support. And hopefully more…

I made this video to share my ideas after a week of teaching online lessons. Thank you to my colleagues Harriet, Jodie and Sandra for acting as my students!

My school has decided to keep to the standard timetable, so I teach lessons at the same time I normally would. The students generally seem to like this as it gives structure and normality to the day. I met with the parents of my tutor group after school on Friday and their feedback was overwhelmingly positive too – they were really impressed by how occupied their children were, and hence how they could get their own work / chores done! One change we have made is to reduce each of our lessons by 5 minutes, to give everyone a bit more time away from the screen in between lessons.

Feedback from the students is that they much prefer live lessons to pre-planned and assigned work / videos as it gives them more of the interaction that they would normally get. I perhaps only used this a little in the video, but ‘narrate the positive’ has been more useful than ever, as I can provide commentary on the progress I see online which helps to motivate students who may otherwise feel rather lonely.

I think it’s better to spend less time than you usually would on whole-class teaching and provide links to videos, along with more individual or small group help. What’s nice about the Zoom setup is that the whole class can listen to (and watch, if they wish) any small-group tuition you are providing.

At first, I found it hard to manage a large group and would have most of the class muted most of the time, but over the course of the week, I can work with larger and larger groups of students unmuted, as we all grow accustomed to the process. Nevertheless, some lessons have been slightly stressful, as I struggle to help all pupils that need it and keep track of what a whole class are doing. But then this can happen with normal lessons too! I have read lots of concerns from leaders about workload. This definitely could be a problem for teachers who are having to look after their own children, but for me, work has been easier than usual (hence, I have time to write this blog!)

My back-up plan of extension work was initially Dr Frost Maths, but this was struggling under the strain of unprecedented demand. Instead I set some non internet-based problems, but it was difficult to assess how well individuals worked on them. I think I will return to DFM now the servers have been upgraded as it gives such a great overview of the work pupils have done and has a huge bank of challenging problems. I have also invested a lot of time to program my schemes of work into it (it’s very flexible in this regard – which is why I chose it over the competitors) and hope that this is now going to pay off!

One point that I couldn’t remember in the middle of making this video was the option to “view side by side” which moves the videos of students from the top, to the side. You can then slide the bar across to reduce the area given to your shared screen (as you don’t need to see it) and increase the number of students you can see. I have added this to the written guide which you can find here:

Next steps: Try out the ‘Breakout Rooms’ feature of Zoom in order to set groups of pupils working together on problems. Think of some tasks which get students away from the screen for some time – I may leave this one to subjects other than maths, but if you have any ideas, let me know.

Links Mentioned in the video:

• www.zoom.us
• www.quizizz.com
• www.drfrostmaths.com
• www.classroom.google.com

And some other useful links:

• www.goformative.com
• www.eedi.com

A first for me in my new school is the concept of a taster visit – a pupil comes along to school for the day to help decide if they want to join the school. It’s interesting to see how children from other schools approach problems and a recent visit made me realise how important a particular feature of my Scheme of Work is… Forming Equations.

The taster-day student was tackling the problem above. He was doing the whole thing on his calculator; I could see that he had some good ideas, but there were just too many steps. I encouraged him to use pen and paper but he just started writing down the steps that he was typing into his calculator.

The problem: He couldn’t write down the sine or cosine rule, substitute and solve the resulting equation. This skill is crucial when you get to a level (which everyone does eventually) where you can’t solve problems in your head.

I wanted to shout at him… Form a Flippin’ Equation! Why do students struggle to do so? I feel that it’s because they haven’t been trained to.

My solution, as so often: Follow the Highgate way. Teach forming equations as an independent topic, at least once per year, and insist that students employ the strategy within other topics at every possible opportunity.

To find out more about the first part of this approach, see my resources on forming equations.

The second part is to reinforce this when teaching other topics. I think the first place I’d usually do this is when teaching students about circles, although this could also be applied to simpler shapes too. Perhaps another argument for teaching more number and algebra before shape?

For example, I would insist that pupils solve the following circle problem like this:

I do sometimes encounter some resistance to this level of detail – inevitably some students just want to do 12 divided by pi and write down the answer. In order to head this off, I ask students to solve the following problem before I teach this:

This is a difficult problem, which students at this level can’t normally solve, and this helps to provide the motivation to practise this strategy.

Moving forward, students can apply the same approach when applying Pythagoras’ Theorem:

If you continue to insist that pupils write their solutions like this whenever the opportunity arises, you’ll give them a powerful tool which will enable them to solve difficult problems.

Maybe I’m wrong. Maybe all schools teach this already. But based on pupils who move into my classes, I am doubtful.

I will leave you with the work of Cora, in the first term of year 10. I’ve taught her for 2 years and so she has been through the Highgate-style forming-and-solving training. I was so impressed with how she made such light work of this problem, which normally stumps even very capable students.

One of the neatest ways of describing approaches to teaching that I’ve heard recently came from Jo Morgan on one of Craig’s podcasts: Maths teachers usually operate in on of three modes: I do, we do, you do.

It’s an oversimplification, but I like the way you can categorise approaches with this terminology. You might say that discovery is ‘you do, we do’, whereas ‘I do, you do’ is the lecture model and the Socratic method, that I was trained to use in my first school, is perhaps ‘we do, you do’.

Jo had been working with an inexperienced teacher who was struggling with a ‘we do, you do’ approach. Her suggestion was that the teacher should first show the pupils – employ the ‘I do’ mode, before moving on to involving pupils in a problem. Unsurprisingly, I disagree.

I’ve tried out ‘Silent Teacher’, traditional lecture and had a fairly substantial craze on discovery after my GTP, but I always come back to the Socratic method. Why do I like ‘we do’ so much?

Firstly, it ensures that you build up the mathematics in small steps that the pupils understand. In other words, it helps you to avoid the curse of knowledge. In the ‘I do’ mode, you may be making logical leaps that are too large but you won’t find out until it is too late.

Secondly, it emphasises to the pupils that maths is an interrelated web of ideas which can be developed from each other, and encourages the teacher to carefully consider how they will introduce a topic in a way which the pupils can make the steps.

Finally, it forces you to check that all pupils are listening to and understanding what you are saying. If pupils know that they may be called upon at any moment, then they have to be listening. Of course, it’s not perfect: they may not be listening, but at least you’ll find out and correct that.

That said, I empathise with new teachers’ struggle. It takes time and experience to deploy this approach effectively and at Highgate we spent a lot of time training people to do so. Some key strategies:

• Hands-down questioning with no opt-out: My mentor used to say “You have to have an idea. It can be a terrible idea, but you have to have one.” This way you find out what the pupils are thinking, and any misconceptions they may have.
• Back a step: If a pupil gives an incorrect answer, ask them an easier question to help build up to the original question. This requires good understanding of the prerequisite knowledge on the part of the teacher, and is easier if you have a clear Scheme of Work.
• Bounce-back: Another option is to pass the question, or a simpler one, on to another pupil, then come back to the original intended target.
• Differentiation: I’m not a huge fan of this, but I do sometimes differentiate my questioning; I’m looking for a balance between not asking too much patience of the high-attainers, whilst making sure the lower-attainers understand.

You can see (or at least hear) me employing ‘we do’ as the initial approach to instruction in this video:

Overall, I feel that ‘we do’ strikes a good balance between discovery and direct instruction: The teacher uses their expertise to guide the learning, but still gives the pupils a stake in making decisions and the experience of creating new mathematics.

Indeed, when I was speaking to my old HoD about this last week, he told me about the most consistent positive feedback his pupils give in surveys: Compared to their previous schools, they enjoy taking part of the development of new techniques, rather than just being shown how to apply them. (ps. they also get probably the best A-level results in the UK)

What do you think? I would love any feedback on the specific lesson or the idea in general.

No, not these gems: http://www.resourceaholic.com/p/maths-gem.html

These ones: https://www.gemsworldacademy-switzerland.com/

One of the great advantages of Twitter is that it allows me to communicate with a lot of UK maths teachers, despite the fact that I work 1000km away in Switzerland. So I was particularly excited when I found out that one of the teachers I am in touch with happens to work just 30 minutes along the lake (the Suisse-Romande version of “down the road”) from me. Last week, I paid a visit to Dan Pearcy and his department at GEMS, so I thought I’d write about what I learned there.

The first thing that really stood out was how different the International Baccalaureate Middle Years Program (MYP) is from GCSEs. The pupils frequently produce pieces of work (I guess we would call them controlled assessments), which count towards their final grade and are assessed against different objectives. The first one – knowing and understanding – seems familiar to GCSE teachers. The other three – investigating patterns, communicating and applying mathematics in real-life contexts – are all clearly important parts of mathematics education, but it seems that they are taken much more seriously in the MYP.

Teachers are expected to understand a wide range of types of pupil inquiry and, for example, teach pupils to create their own problems and write clear conclusions. If you’re a teacher who particularly values these parts of mathematics (perhaps you’re sad about the demise of GCSE coursework), then I suspect that you would really enjoy teaching the MYP. The catch? You still have to teach the same curriculum content as GCSE, so it’s tough to fit everything in. I have seen nowhere near enough to conclude definitively but it seemed to me that, at times, understanding of mathematical ideas was sacrificed in order to allow sufficient time to learn how to apply them. I know several teachers who think that this is a good thing: one ex-colleague used to advocate heavily for this approach.

Moving on to some positive points that I picked up from the lessons I observed. Some simple, but when you’re the only maths teacher in a school, it’s really useful to have a reminder:

• In two lessons I observed, I was reminded of the general principle of ‘pictorial before abstract’. The lessons were on gradients and lengths of line segments, to year 7 and 9 respectively. In both, the initial questions had lines clearly drawn on grids, which enabled pupils to apply the key ideas, without the cognitive load of dealing with coordinates.
• Every lesson I saw ended with a ‘plenary’: even if brief, the summary of what pupils had learned tied things together nicely.
• Common sense checking of answers was encouraged. “Does it look about right?”
• All of the teachers gave regular time warnings before a change of activity – a classic strategy, but good to see it being used well.
• With a small class, giving pupils the opportunity to have a go at an example themselves just before / simultaneous to a teacher demonstration – gives the higher-achieving pupils chance to try their ideas, whilst supporting pupils who can’t see what to do.

Finally, it was really interesting and useful to talk to Dan about leading a department and growing a school from scratch. We discussed homework marking policies and how parents can be unhappy about inconsistency between teachers. One thing that particularly struck me was that it seemed, based on a short visit, that keeping the teachers in his department happy was Dan’s first priority. This may be common, but was not the case with my first two HoD’s, who prioritised consistent pedagogical approach and exam results respectively, so it was good to see it.

John Von Neumann’s quote often rings true, but I’m not sure that’s not a good thing.

I saw this quote on twitter a few months ago. I can’t remember where I read it first, but it may well have been courtesy of Dylan Wiliam.

It immediately resounded with me. I feel that I learned a lot of maths this way. And I got a first from Cambridge, surely it must be fine?

On the contrary, whilst I was lucky enough to muddle through regardless, I think that this approach is not effective for the majority of learners.

Greg Ashman makes a good case for not focussing too much only on axioms, but I don’t think (m)any teachers are doing this. In my experience of teaching and observing, the opposite is much more common and I think this is mostly caused by the ‘curse of knowledge’.

I’m new to teaching mixed-ability classes and I’m experiencing this a lot personally, particularly in the lower years. I recently taught an introduction to algebra to year 7. Even after several similar examples, some of the pupils were struggling to simplify d+d+d+d as 4d. They were either not sure what it should be at all, or would write it as d^4.

In my previous selective schools, this was assumed knowledge from primary school so I never even thought about it. In retrospect, I suspect that some pupils didn’t understand it but just got used to it.

When I encountered this misunderstanding, I was at first tempted to say something like “d+d+d+d… it’s just 4 d’s” Unfortunately, this falls down when you get to d×d×d×d, but I also think it falls into the Neumann trap of just asking learners to get used to things. Instead, I should have checked that my pupils understood that 7+7+7+7=4×7. This understanding is important to avoid other future problems: pupils incorrectly substituting into expressions such as 2d, or not knowing what to do when faced with equations such as 2d=7, both because they’re not aware that 2d means 2×d.

I’ve updated my lesson plan to including a check of that knowledge at the start of the topic. I hope that in future this will help pupils to understand how to simplify d+d+d+d, rather than just get used to the answer.