This is something I'm really proud of, and something I'm really happy with and enjoying with my classes - and they really like it too.

I've created a web site at http://taylorda01.weebly.com and have started to upload a number of resources that I've referred to as 'Increasingly Difficult Exercises', using increasingly difficult question sets.

The idea came from training from the White Rose Maths Hub in school at the beginning of last year and came to fruition following Maths Conf 7 at the Royal Armouries in Leeds after asking 'Why don't these things exist?' and realising I could do them and make them available.

The intention of this blog is to share how I use the resources in my own classroom.

I've been annoyed over the last few years by students not taking care in their work and their books becoming messy. My colleagues get around this by having students work on whiteboards, but I don't like students not having something to refer to in their books, so I've decided to meet them halfway.

I don't have standard whiteboards in my room. I use plastic wallets with printouts inside, that can be rearranged for different purposes. I was given these ages ago, and I believe that they were called 'Leeds MathsPaks' at one point, but this might not be true. I've created another sheet to put in their packs that looks like this:

The students work through the shorter question sets on their whiteboards in the space on the left, writing down their answers in the space provided on the right and erasing their workings before going for the next question. After 10-15 minutes, I stop them and go through the answers, explaining where students need more explanation as to why this is the answer.

## Tuesday, 8 November 2016

## Wednesday, 31 August 2016

### Teaching isn't that hard... Just teach them stuff!

I went to school on Thursday for results day and had a great time. We'd been under much scrutiny this year and delivered on the requested improvements, and our top end was more successful than ever. I was extremely proud and pleased with my own class's results - 9 A*s, 9 As, 9 Bs and 2 Cs, 93.1% 3LOP+, 65.5% 4LOP+, average residual of 4.7.

Having let the dust settled, I took to SISRA to look at the departmental results. 93.1% 3LOP+, 76.9%, 70.4%, 52.4%, 71.4%, 33.3%, 0%, 0% with an overall figure of 57.6%. I'm struggling to gain much positivity from these figures, and as a result, I've been thinking about what changes we could make as a department to improve over the coming year.

The coming year scares me because so much of it is unknown. We're playing a game where we're not sure of the rules, not sure how to score, and not sure how to win. Our departmental figures are set to take a huge dive, and I've been thinking of ways that we might limit this damage.

Teaching isn't that hard. Basically, the job is

**know what the kids can't do, and teach them how to do it**. I know that there are more aspects to it than this - meeting student needs, behaviour management, office politics and so on - but I think this is something that is largely skimmed over by a lot of staff.
Targets, exams, 'that C grade'. These things take up teachers' thoughts and set their objectives.

'But their targets are Bs and they're getting Es' is a scenario where teacher response is 'Well I'd best teach them the

*grade B stuff*!'.
'But this, this, this and that are on the exam' is normally followed by 'So I'd best show them how to do that'.

'But they need to get

*that C grade*'is normally followed by 'So I should teach them key topics, right?'.
I think this is the key -

**know what the kids can't do, and teach them how to do it**.
Why teach students

*the grade B stuff*if they don't understand the topics that prove scaffolding for these objectives?
Why show them things that are on the exam if they don't understand the topics that lead to these questions? I'm thinking about multiplying pairs of brackets when students can't expand simple brackets.

Why teach them key topics when their understanding of other topics that support those objectives isn't secure?

Two years ago we started a new scheme of work at KS3 where students work towards a number of objectives in Number, Algebra, Area and Perimeter, Angles and Statistics, and until they score 80% on their assessments they don't move on to the next aspect of each part. It's not a perfect way to go, but it has been working for us. Unfortunately, we don't work like this in Key Stage 4, and I think we maybe should do.

For every assessment my students complete, I fill in a spreadsheet for what kids could and couldn't do (number of marks achieved on each questions). It creates a print out sheet for them to take away, and it gives me a lot of information on what my students achieved their marks on.

They get this as a printout. It tells them where they dropped marks, what they need to revise and gives them the appropriate Mathswatchvle.com clip number to take away and work on that.

I get this:

This is what my Year 11s did in their final two 'proper' lessons with me - one final mock, to get a decent idea of what grade they should be getting and give them some confidence/a kick up the back side. It also told me, in no uncertain terms (as they were done in exam conditions), what my students were and weren't able to do in an exam - and whilst this isn't the be all and end all of our jobs and their education, it's how they're judged, and as a result, what I'm aiming for.

We don't send kids on study leave, but rearrange their timetable to provide 'revision lessons' or something. From this, I was able to say that my students needed, as a matter of urgency, to revisit:

For every assessment my students complete, I fill in a spreadsheet for what kids could and couldn't do (number of marks achieved on each questions). It creates a print out sheet for them to take away, and it gives me a lot of information on what my students achieved their marks on.

They get this as a printout. It tells them where they dropped marks, what they need to revise and gives them the appropriate Mathswatchvle.com clip number to take away and work on that.

I get this:

This is what my Year 11s did in their final two 'proper' lessons with me - one final mock, to get a decent idea of what grade they should be getting and give them some confidence/a kick up the back side. It also told me, in no uncertain terms (as they were done in exam conditions), what my students were and weren't able to do in an exam - and whilst this isn't the be all and end all of our jobs and their education, it's how they're judged, and as a result, what I'm aiming for.

We don't send kids on study leave, but rearrange their timetable to provide 'revision lessons' or something. From this, I was able to say that my students needed, as a matter of urgency, to revisit:

- Identifying the 'identity' sign and making use of it.
- The area of a parallelogram.
- Writing the negative root of a simple quadratic equation, rather than just the positive one.
- Algebraic fractions.
- Writing the equation of a linear graph.
- Understanding speed, distance and time.
- Probability - specifically, use of a sample space diagram when rolling two dice.
- Bearings.
- Basic angle facts.
- Drawing and interpreting a cumulative frequency diagram instead of a frequency diagram.

Some took five minutes, some took fifty, but I had a good idea of what my students couldn't do - specifically on that paper, but it's a good place to start. Except it wasn't a start, as I'd been doing the same thing since March, and as a result, the topics were changing and I was identifying different things that they couldn't do -

**and teaching them it**. I didn't go for the back end of the paper, and I didn't think 'Oh, but what if this topic's on the paper? I should cover that...'. I covered the things**that they couldn't do**.
I do this for all year groups all of the time, now, and their progress is fantastic. I mean, it makes total sense.

My main aim for this post is to identify some issues that will face some teachers this year. You, me, your mate, that bloke down the corridor who rocks in at 8:45 and leaves at 3:15, are going to take over classes this year where kids are working 'below their target grades'. I am, definitely, and I would have at every school I've ever worked at, because I've always been picking up the pieces left by others it seems. My advice is...

You are only able to affect the students in the time you teach them. If you get kids who are on track, great - if the kids you get are a bit behind, then teach them what they don't know. If you don't have the data, give them a baseline assessment and work from there. Progress happens when students are taught something they didn't know and then they do - if you teach them it and they still don't know it, don't get angry and teach it again in a different way (I've been there, done this, shouted and shouted and shouted... But it achieved nothing. I've regularly said 'I'm not angry at you. I just know that you don't know this when you should, and that's frustrating. We're going to do it again, and if you still can't do it, we'll do it again, and again, and again...'). Students must make progress whilst in your care - this is your job and this is your role. If they make progress and don't meet targets, this is not the end of the world. If they don't make progress, you've got to change something, because

Enjoy 2016-2017! I intend to!

You are only able to affect the students in the time you teach them. If you get kids who are on track, great - if the kids you get are a bit behind, then teach them what they don't know. If you don't have the data, give them a baseline assessment and work from there. Progress happens when students are taught something they didn't know and then they do - if you teach them it and they still don't know it, don't get angry and teach it again in a different way (I've been there, done this, shouted and shouted and shouted... But it achieved nothing. I've regularly said 'I'm not angry at you. I just know that you don't know this when you should, and that's frustrating. We're going to do it again, and if you still can't do it, we'll do it again, and again, and again...'). Students must make progress whilst in your care - this is your job and this is your role. If they make progress and don't meet targets, this is not the end of the world. If they don't make progress, you've got to change something, because

**teaching them something they don't know, so that they do**is the basis of your job.Enjoy 2016-2017! I intend to!

## Monday, 8 August 2016

### After... A Year of The One Hundred Minute Lesson

At the end of last year my school made the decision to move from 60-minute lessons to 50 and 100-minute lessons. I taught one 50-minute lesson every fortnight, and as a result, I've focused on the use of activities within 100 minutes rather than 50 - to be fair, the 50 is very close to 60 and wouldn't be too much different to 'traditional' lessons.

That said, I feel the same about 100-minute lessons now. I found that after a difficult first term, with teachers and students getting used to a necessity to work for longer before their next break (between lessons, or break or lunch), pupils were more amenable to the longer working periods and were becoming quite used to longer periods of concentration.

Over time, I found it easier to plan the longer lessons, and it became easier and quicker to plan my 13 100-minute lessons a week than 22 60-minute lessons.

Our school is continuing to move forward with 50 and 100-minute long lessons and I'll continue to work through them in the following way...

... leaving 5 minutes to set homework, clear up, be ready to go!

I have at least another term of 100-minute lessons. I like them. This is the plan.

I have written some other blogs on 100-minute lessons, which you can access by clicking those links.

That said, I feel the same about 100-minute lessons now. I found that after a difficult first term, with teachers and students getting used to a necessity to work for longer before their next break (between lessons, or break or lunch), pupils were more amenable to the longer working periods and were becoming quite used to longer periods of concentration.

Over time, I found it easier to plan the longer lessons, and it became easier and quicker to plan my 13 100-minute lessons a week than 22 60-minute lessons.

Our school is continuing to move forward with 50 and 100-minute long lessons and I'll continue to work through them in the following way...

**0 - 10/15m**is a settler activity. This is typically a recap of work covered in the medium/long-term, but can be handed over to feedback from a recent assessment or homework.**10/15 - 20/25m**is time for sharing learning objectives (and success criteria), as well as having students note down the appropriate MathsWatch clip number to facilitate independent study. They'll then take a short amount of time to recap things that they need to know/be able to do for the forthcoming lesson.**20/25 - 35/40m**is my bit. I talk, they listen. I ask questions, they answer. I ask them for ideas and they share, continuing on from each others' ideas. I link to things they've done before and extend to things they'll do in future.**35/40 - 50/55m**is a short amount of time set aside for students to do some 'messy' work on whiteboards. I'll use some of the Increasingly Difficult Questions sets (and create more accordingly) where students will be able to find their own level of difficulty for a longer amount of time.**50/55 - 70/75m**will give students an opportunity to work on a task suited to their level in their books, based on the diagnostic task they'll have just done, working at four different levels.**70/75m - 95m**will offer an opportunity to recap what we've done, apply this to a problem or to exam questions and to make links between different topics.... leaving 5 minutes to set homework, clear up, be ready to go!

I have at least another term of 100-minute lessons. I like them. This is the plan.

I have written some other blogs on 100-minute lessons, which you can access by clicking those links.

## Sunday, 7 August 2016

### Robotics at School

A little time ago, I noticed a tweet from @MissBLilley about a STEM club and activities to run within it. A reply to this tweet (which I favourited to go back and take a spy at) directed me to the Tomorrow's Engineers EEP Robotics Challenge. I put an application in and whilst I was away on residential with next year's Young Leaders I received an e-mail offering us a place on next year's event. Huzzah!

The challenge is open to 11-14 year olds who will work in teams to work through 'space missions' involving teamwork, robots, designing, discovery and lots of Lego and fun! (Or so the web site says...)

My plan is to offer the event/challenge to our students in year 8 and year 9 from Week 2 in September and start to deliver 6 90-minute sessions to those interested. I have a few ideas to run alongside this, which are...

1. I attended a Leeds Festival of Science event called 'The Great Leeds Build Off' at The University of Leeds. As a part of this, students were in teams of 4 and assigned roles. One student could view a model and sketch it, a second could view the model to check their sketch, a third was to 'buy' the materials required to re-build the model themselves and the fourth was to build the model from their partners' specifications and materials. It was a fun hour-long activity that the kids bought into, but I wouldn't necessarily say it was worth travelling to the University for, and it would've been better as a roadshow event.

I intend to do something similar to have kids get to know one another across different year groups, with Lego that I used to have as a child.

2. I've bought a couple of robots! A Sphero 2.0 and a Sphero Ollie (A Darkside version, naturally) so that kids can have a bit of a play around with robots before working with them. Both can be controlled using a Bluetooth-enabled device, such as a phone or tablet, and my intention is to use them to race against each other (around a loop, timed, or around a course outside, racing), potentially battle against one another and bowling (I've already had 10 pins cut for this). The ICT department also have two Spheros, so we can have four teams racing/battling.

3. We have some BigTraks in the department. They work in the same way as the old computer programme 'Logo', and students will have a course to programme a route around, given an amount of time to plot their route and fire their rockets (we have rocket launcher attachments) at three targets. This should give students the chance to programme some robots before they get into the kit offered by Tomorrow's Engineers.

I'm thinking of having ten members in our team, but offering this to all and being selective once we've been through the opening bits. An ICT teacher at school has a plan to run a robotics club, and as a result the remainder can continue with him.

I have five of this year's outgoing Year 11 students coming back after college to gain work experience/help out and I'll assign these students as mentors to our team to help them work through the challenge. Two for each one will work out well!

As well as this, @MissBLilley and I have spoken about organising some 'fixtures' to compete against each other before we go to local competitions for a bit of a dry run! Very much looking forward to this!

The challenge is open to 11-14 year olds who will work in teams to work through 'space missions' involving teamwork, robots, designing, discovery and lots of Lego and fun! (Or so the web site says...)

My plan is to offer the event/challenge to our students in year 8 and year 9 from Week 2 in September and start to deliver 6 90-minute sessions to those interested. I have a few ideas to run alongside this, which are...

1. I attended a Leeds Festival of Science event called 'The Great Leeds Build Off' at The University of Leeds. As a part of this, students were in teams of 4 and assigned roles. One student could view a model and sketch it, a second could view the model to check their sketch, a third was to 'buy' the materials required to re-build the model themselves and the fourth was to build the model from their partners' specifications and materials. It was a fun hour-long activity that the kids bought into, but I wouldn't necessarily say it was worth travelling to the University for, and it would've been better as a roadshow event.

I intend to do something similar to have kids get to know one another across different year groups, with Lego that I used to have as a child.

2. I've bought a couple of robots! A Sphero 2.0 and a Sphero Ollie (A Darkside version, naturally) so that kids can have a bit of a play around with robots before working with them. Both can be controlled using a Bluetooth-enabled device, such as a phone or tablet, and my intention is to use them to race against each other (around a loop, timed, or around a course outside, racing), potentially battle against one another and bowling (I've already had 10 pins cut for this). The ICT department also have two Spheros, so we can have four teams racing/battling.

3. We have some BigTraks in the department. They work in the same way as the old computer programme 'Logo', and students will have a course to programme a route around, given an amount of time to plot their route and fire their rockets (we have rocket launcher attachments) at three targets. This should give students the chance to programme some robots before they get into the kit offered by Tomorrow's Engineers.

I'm thinking of having ten members in our team, but offering this to all and being selective once we've been through the opening bits. An ICT teacher at school has a plan to run a robotics club, and as a result the remainder can continue with him.

I have five of this year's outgoing Year 11 students coming back after college to gain work experience/help out and I'll assign these students as mentors to our team to help them work through the challenge. Two for each one will work out well!

As well as this, @MissBLilley and I have spoken about organising some 'fixtures' to compete against each other before we go to local competitions for a bit of a dry run! Very much looking forward to this!

## Sunday, 3 July 2016

### Increasingly Difficult Questions

Last week at MathsConf7 at the Royal Armouries in Leeds, I went to my final session about teaching for depth with the West Yorkshire Maths Hub.

I'd had the training before and as a result, at that time, I tried to start a notice board in our staff workroom called 'If this is question 1, what is question...?'. The intention was that staff would add question 2 with a logical increase in difficulty, and another member of the staff would add question 3, and so on... It didn't exactly take off, which was frustrating, so I ditched it.

I then had a conversation on the day with a lady at my table in the session which went similar to:

Me: "So, if we're all aware of these exercises, why has no-one released a text book with a load in?"

Her: "Collins are on the way to doing some, and have some primary ones, but the secondary ones are due soon."

Me: "I'm not even talking about a textbook, to be fair. Just, like CorbettMaths.com, why has no-one done some exercises and put them online?"

It was then that I realised that I was being a little selfish. Why aren't they out there? Why can't I use them? I want them, and they're not there... Maybe I could make them, maybe I could share them, and maybe I could add a bit to other's classrooms, just like others offer a lot to mine.

Me: "I'm very aware, now, that I could've done it, and I'm aware that I haven't. Just, how come someone hasn't?"

So, here goes...

Introducing 'Increasingly Difficult Questions' @ taylorda01.weebly.com.

Over the next 5 hours, a tweet will go from my account every 20 minutes highlighting a different exercise that I've added to the page. Most are 'Number'-based, but a small handful of others are available. In the future, I will tweet whenever new content is added.

In the future, I'm hoping to open this up to submissions, but I'm a bit of a stickler for fonts, layouts and sizing, and as a result, I'm not sure how to go about this. Any feedback on the resources, or ideas about how this can go forward, are gratefully received.

Dave

I'd had the training before and as a result, at that time, I tried to start a notice board in our staff workroom called 'If this is question 1, what is question...?'. The intention was that staff would add question 2 with a logical increase in difficulty, and another member of the staff would add question 3, and so on... It didn't exactly take off, which was frustrating, so I ditched it.

I then had a conversation on the day with a lady at my table in the session which went similar to:

Me: "So, if we're all aware of these exercises, why has no-one released a text book with a load in?"

Her: "Collins are on the way to doing some, and have some primary ones, but the secondary ones are due soon."

Me: "I'm not even talking about a textbook, to be fair. Just, like CorbettMaths.com, why has no-one done some exercises and put them online?"

It was then that I realised that I was being a little selfish. Why aren't they out there? Why can't I use them? I want them, and they're not there... Maybe I could make them, maybe I could share them, and maybe I could add a bit to other's classrooms, just like others offer a lot to mine.

Me: "I'm very aware, now, that I could've done it, and I'm aware that I haven't. Just, how come someone hasn't?"

So, here goes...

Introducing 'Increasingly Difficult Questions' @ taylorda01.weebly.com.

Over the next 5 hours, a tweet will go from my account every 20 minutes highlighting a different exercise that I've added to the page. Most are 'Number'-based, but a small handful of others are available. In the future, I will tweet whenever new content is added.

In the future, I'm hoping to open this up to submissions, but I'm a bit of a stickler for fonts, layouts and sizing, and as a result, I'm not sure how to go about this. Any feedback on the resources, or ideas about how this can go forward, are gratefully received.

Dave

## Sunday, 26 June 2016

### #MathsConf7

I spent yesterday at the Royal Armouries in Leeds, a beautiful building next to where I lived during my first year of Uni, across the river from where I lived during my first and second years of teaching and from where I teach now. It may surprise you that I've never step foot in the Royal Armouries until today, but it's the truth.

I arrived early, mooched around the exhibition area picking up a few things and went to take a seat in the main hall. I sat for a while, did some admin and was joined by @MissBLilley, whom I'd never before met, but I follow on Twitter. We said we'd share notes via blogs, so here's my half of that agreement...

After the normal MathsConf stuff from Mark McCourt and Andrew Taylor (this was my second, so I assume it's normal), they welcomed Mike Askew to the stage (@mikeaskew26). I enjoyed listening to him. particularly to research-based recommendations. The first of which was to '

The next was to '

3 and 4 could be different problems, with 5 being a solution to a harder question, and so on and so forth. I'll look to try this, but potentially as a part of my cover work for when I'm on residential over next week.

The third suggestion was to '

The final suggestion was to '

The whole presentation made me think of the advice from the Maths Hub that our department were given in September last year - 'plan for what you want students to think, not what you want them to do', and to plan for students to develop proficiencies rather than plan for exercises and doing.

The next piece of advice was something I've written down as a 'meeting idea', as I'd like to make more use of departmental meetings for teaching, and have teachers bring the activities that their students have worked through over the past week or two, and ask 'are they good enough?', 'what is their purpose?', 'do they develop proficiency?'. The research suggested that whilst many tasks are developed to promote proficiency and deeper thinking, two thirds of the activities declined into routine within the first five minutes when students encountered difficulty and teacher responses declined to 'Just use the formula' and spoon-feeding. Take away: press for reasoning, and don't let it go. Don't give students an easy way out because they want it.

The next part of his presentation centred around the ABC of problems. Authentic (problems and solutions), Believable or Curious Challenges. Problems should be something that students might encounter or that they might never encounter, but is interesting (If Bolt's latest race was ran against his world record time, how far behind his record setting self would he finish?). Problems should also never have an image that contradicts a narrative, or a narrative that doesn't add to the picture, and we looked at an open problem using a box wrapped up with string (1m of string, a 300mm bow, dimensions of the cuboid?) - a low threshold/high ceiling activity - differentiated through the use of prompts and supporting materials and stretch materials, with an opportunity at the end for consolidation (How much string would I need for a 20cm by 15cm by 100mm box with a 300mm bow?).

Teaching for problem solving is something I do, but don't do well and don't really have a real plan for. Here's my new one:

Choose the task (with a particularly skill in mind).

Set it up (tell a story, show a picture).

Orchestrate the discussion of solutions (the bit I struggle with). I need to give 'private talk time' and 'public talk time', a chance for students to talk in pairs, and then with others, before asking them to share their solutions publicly. Students need to repeat, revoice, rephrase, build on and agree/disagree with each other's statements, and I'm thinking that I should invest in a visualiser to aid my lessons here. I'll choose the solutions that move the discussion on and show great understanding and a variety of methods.

Above all, my largest take away here was '

I signed up for this session with our department in mind, and it dawned on me prior to Mark starting his presentation that I'd basically signed up for an advert for Complete Mathematics. That said, I have a few takeways.

The

A fully resourced, collaboratively produced, scheme of work should be in place for all teachers from September.

Teachers should consider the use of externally produced and quality assured textbooks and teachers guides. This one has always bothered me. I know teachers who look down on other teachers for handing our textbooks, and advocate the use of worksheets. Well, I hate to break to this to those people, but textbooks are just worksheets glued together. If you have a selection of worksheets collated for use, and an exercise is appropriate for your learners, go ahead and use it!

Staff should engage in collaborative planning instead of spending a great deal of time planning individual lessons. We've done that this year, and the results are mixed. We started this to support our Year 7 and 8 teachers, of which I am not one, but became a part of the joint planning. I spent a good hour putting together a worksheet on perimeter that increased in difficulty between questions 1, 2 and 3 and within questions 1, 2 and 3, suiting the lesson I had planned perfectly. Unfortunately, another (number of) colleague(s) had thrown something together and added a CorbettMaths workbook as the worksheet. The objective was the area of triangles (if I recall correctly) and if you've seen the area of triangles workbook from CorbettMaths, it's not just area of triangles for Year 7! Joint planning is wonderful in theory, but when two people are asked to plan a lesson together, and they each plan half and throw it together it isn't collaboratively planned, and when teachers teach 20 hours a week and can't find the time to plan collaboratively, they go back to the same routine that they find themselves in day-to-day, and their collaborative planning matches the issues that we're trying to avoid.

The DfE has said that 'if your current approach is unmanageable, stop. If you're spending hours every night marking books, you need to ask yourself what the marking needs to achieve for the pupils and strip that back'.

The bit that made me laugh was how Mark has been in to schools and seen schemes of work where Year 7s always study position-to-term rules for sequences first. He knows that that SOW isn't fit for the students in that school because he wrote it, years ago, for the year 7 cohort he had that year. Your schemes of learning need to suit the students in front of you, and quoted a school that has 40 schemes of work in place. Of course, all that means is that they have 40 classes and each class works on different things at a different pace, probably because they have different abilities and starting points.

This session made my head swim, a bit. It was very dense, but useful and may well transform how I approach some things in lessons.

The session was about the difference between facts, processes and concepts, and how many facts require a good grounding in many concepts. Learning that '2 is the smallest prime number' requires you to understand the concept of the number 2, the concept of something being the smallest, and the concept of a prime number. Knowing that 'the Earth is a sphere' requires conceptual understanding of the Earth, and what a sphere is.

These concepts need to be taught well in order for students to understand facts and develop fluency. We've all had that student who has seen an irregular 5-sided shape and responded with 'What shape is this?!' 'Well, count the sides' 'That's a pentagon?!' They know what a few pentagons look like, but don't really understand what a pentagon is. As an aside, the L-shape, that compound shapes typically look like, is a hexagon. Tell this to your classes and observe their responses - confusion and realisation that they've been lied to, probably.

'Everybody can learn what we need them to learn, if we find the find the right way to teach it to them'. This reminded me of a film released in the early 2000s (I think) called Road Trip. They travel to see one of the character's girlfriends, or something, and find that she's traveled to see him (I think!). They find out that one of them has been lied to about a final assessment at college and he becomes concerned that he doesn't know anything about the subject as they make their way back. One of the characters claims that he can teach Japanese to a monkey in 46 hours, and that the key is just finding a way to relate the material to that monkey. In this case, he compares ancient philosophy to the WWF (wrestling, not World Wildlife Fund) and he goes on to pass.

Concepts were put into five categories. For

The basis is, begin with a 'non-example', then show a minimally different non-example, an example, a maximally different example, a different non-example and a different example. Give students a chance to show their understanding, and orchestrate a discussion allowing students to articulate their learning. Just because a student can't articulate their understanding, doesn't mean they don't understand, and lower ability students in particular may not understand worded descriptions, but will develop understanding based on the non-examples and examples, even though they can't get the words out.

The final category was

I left with a lot to think about and enough to share with others. But having typed that up, I think I have more questions than answers.

I've never considered going into leadership roles before this year. I have a TLR, but it's more classroom based, and I didn't like the idea of being too involved and knowing too much. This year has changed that, though, and I'm hoping for greater responsibilities within the department sooner rather than later. I attended this session in the hope of getting some ideas about what I may need to do over the summer should the opportunity arise. The following are just sub-headings and some thoughts...

Again, my head is swimming and I think I'll have to park this until I have a role to work in!

I've had much of this training before, in school, when the Maths Hub visited us to do a bit of training to support out department, so my notes may be a little lacking.

The session centred around the increase in challenge and expectation of students as we move towards the new GCSE and how this filters down to younger year groups and the requirement around their learning.

The first key point was how our classrooms are centred around memorising and not around fluency and reasoning. A UK text book might have 16 questions focused on the same skill, with the same level of challenge throughout, and the idea is that we need to move away from this to a model seen in Shanghai in recent exchanges, whereby their exercises increase in challenge with almost every question. 16 questions with the same skill, or 10 questions challenging students? Their example was adding fractions with the same denominator, and where the UK text book stuck to solutions with proper fractions, the improved activity started simple, then moved on to having answers as 1, then using this fact in subtracting, and then using this to add fractions with different denominators (in pairs, so that their sum is 1). This is followed by a quick consolidation task of the same ilk, with 5 seconds on each question, with a negative fraction as an answer. At this time, a 'check list' was mentioned on our table, to make sure that exercises can be extended by introducing decimals, fractions, negatives and algebra to most tasks and concepts to extend students understanding.

The next part of the session was about how we can support all learners in the classroom with open-ended questioning. Consider three pandas eating bamboo, 51 pieces altogether, they all eat an odd number of pieces. How many do they eat each? Get as many answers as you can. As an extension, how can you be sure that you have all the answers? To support others - give them a strategy, pick an odd number and half the rest. Is that one answer? Can you find another? Try another question - using the digits 0 - 9, write a sum showing a 3-digit number and a 3-digit number resulting in a 4-digit number. To extend, is this the only answer? To support, make it 2-digit and 2-digit to make 3-digit, or provide digit cards so that they have something to hold on to. For those frustrated learners, who try to give up, give the answers (1089, 1098), and fill in the rest.

We finished by discussing the need to teach for depth and understanding, and how our teaching needs to allow students to apply their learning to problems, and how being able to memorise is great (knowing your times tables, for instance), but can't apply this (like my Year 10 student).

A good day, energising, and great to be a part of that energy despite my unwillingness to move from my seat and become involved in a greater way. I hope my notes are of use to others.

I arrived early, mooched around the exhibition area picking up a few things and went to take a seat in the main hall. I sat for a while, did some admin and was joined by @MissBLilley, whom I'd never before met, but I follow on Twitter. We said we'd share notes via blogs, so here's my half of that agreement...

**00 - La Salle/AQA/Mike Askew**After the normal MathsConf stuff from Mark McCourt and Andrew Taylor (this was my second, so I assume it's normal), they welcomed Mike Askew to the stage (@mikeaskew26). I enjoyed listening to him. particularly to research-based recommendations. The first of which was to '

**space learning over time**'. This resonated with me as I recently 'liked' a tweet that suggested that starters/settlers should be binned as they waste learning time. I didn't argue at the time, but my thoughts around this are that students require regular repetition of subjects in order to consolidate their understanding - as a result, each and every lesson starts with a 3 - 5 question long settler activity on things they've studied in the past. I'd previously raised this as a concern with SLT prior to our move to 100 minute lessons, reducing the number of opportunities for repetition, and I'm still unsure of this 35 weeks into the school year.The next was to '

**interleave worked examples with problems to solve**' whilst students are working independently. Question 1 might look like 'Solve 5 + 3x = 20', with question 2 being 'Here's a solution for ..... Study each step. Can you improve your previous solution?'3 and 4 could be different problems, with 5 being a solution to a harder question, and so on and so forth. I'll look to try this, but potentially as a part of my cover work for when I'm on residential over next week.

The third suggestion was to '

**connect abstract and concrete learning**', taking from Guy Claxton's 'Intelligence in the Flesh' and Lackoff and Johnson's 'Metaphors we live by' (apparently) and is something I'm probably quite good at - my takeaway was that the way I would go about teaching area and volume scale factors (bringing students back to a 1 x 1 square and enlarging by a scale factor, and highlighting the increase in area by that scale factor squared and volume, cubed) is a thoroughly effective way.**Quizzes**(to introduce a topic, or to re-expose students to a key concept at a later date) reared their heads, and I'm aware that this is a part of the White Rose Maths Hubs suggestions in schools and something that I'll look to work on with the new GCSE and years 10 and 11 over the next academic year.The final suggestion was to '

**ask deep explanatory questions**'. Always ask 'why?' and 'how?', use problem solving and reasoning, and Askew stated that 'mathematical reasoning is more important than knowledge of arithmetic'. I agree, and see this so clearly in a year 10 boy whose arithmetic is outstanding, but he struggles to apply it to basic concepts like volume, and as a result one of my takeaways that we could probably use a problem for all topics as a part of our schemes of work to help develop reasoning skills.The whole presentation made me think of the advice from the Maths Hub that our department were given in September last year - 'plan for what you want students to think, not what you want them to do', and to plan for students to develop proficiencies rather than plan for exercises and doing.

The next piece of advice was something I've written down as a 'meeting idea', as I'd like to make more use of departmental meetings for teaching, and have teachers bring the activities that their students have worked through over the past week or two, and ask 'are they good enough?', 'what is their purpose?', 'do they develop proficiency?'. The research suggested that whilst many tasks are developed to promote proficiency and deeper thinking, two thirds of the activities declined into routine within the first five minutes when students encountered difficulty and teacher responses declined to 'Just use the formula' and spoon-feeding. Take away: press for reasoning, and don't let it go. Don't give students an easy way out because they want it.

The next part of his presentation centred around the ABC of problems. Authentic (problems and solutions), Believable or Curious Challenges. Problems should be something that students might encounter or that they might never encounter, but is interesting (If Bolt's latest race was ran against his world record time, how far behind his record setting self would he finish?). Problems should also never have an image that contradicts a narrative, or a narrative that doesn't add to the picture, and we looked at an open problem using a box wrapped up with string (1m of string, a 300mm bow, dimensions of the cuboid?) - a low threshold/high ceiling activity - differentiated through the use of prompts and supporting materials and stretch materials, with an opportunity at the end for consolidation (How much string would I need for a 20cm by 15cm by 100mm box with a 300mm bow?).

Teaching for problem solving is something I do, but don't do well and don't really have a real plan for. Here's my new one:

Choose the task (with a particularly skill in mind).

Set it up (tell a story, show a picture).

Orchestrate the discussion of solutions (the bit I struggle with). I need to give 'private talk time' and 'public talk time', a chance for students to talk in pairs, and then with others, before asking them to share their solutions publicly. Students need to repeat, revoice, rephrase, build on and agree/disagree with each other's statements, and I'm thinking that I should invest in a visualiser to aid my lessons here. I'll choose the solutions that move the discussion on and show great understanding and a variety of methods.

Above all, my largest take away here was '

**Teachers need to select tasks so that over time students experiences add up to something important**'. It might be that small tasks don't seem beneficial, but it's important that over time the diet that students receive develops their fluency and reasoning skills.**01 - Mark McCourt - Reducing non-teaching activity workload and improving subject knowledge and pedagogy.**I signed up for this session with our department in mind, and it dawned on me prior to Mark starting his presentation that I'd basically signed up for an advert for Complete Mathematics. That said, I have a few takeways.

The

**DfE expectation**for the coming academic year is that:A fully resourced, collaboratively produced, scheme of work should be in place for all teachers from September.

Teachers should consider the use of externally produced and quality assured textbooks and teachers guides. This one has always bothered me. I know teachers who look down on other teachers for handing our textbooks, and advocate the use of worksheets. Well, I hate to break to this to those people, but textbooks are just worksheets glued together. If you have a selection of worksheets collated for use, and an exercise is appropriate for your learners, go ahead and use it!

Staff should engage in collaborative planning instead of spending a great deal of time planning individual lessons. We've done that this year, and the results are mixed. We started this to support our Year 7 and 8 teachers, of which I am not one, but became a part of the joint planning. I spent a good hour putting together a worksheet on perimeter that increased in difficulty between questions 1, 2 and 3 and within questions 1, 2 and 3, suiting the lesson I had planned perfectly. Unfortunately, another (number of) colleague(s) had thrown something together and added a CorbettMaths workbook as the worksheet. The objective was the area of triangles (if I recall correctly) and if you've seen the area of triangles workbook from CorbettMaths, it's not just area of triangles for Year 7! Joint planning is wonderful in theory, but when two people are asked to plan a lesson together, and they each plan half and throw it together it isn't collaboratively planned, and when teachers teach 20 hours a week and can't find the time to plan collaboratively, they go back to the same routine that they find themselves in day-to-day, and their collaborative planning matches the issues that we're trying to avoid.

The DfE has said that 'if your current approach is unmanageable, stop. If you're spending hours every night marking books, you need to ask yourself what the marking needs to achieve for the pupils and strip that back'.

The bit that made me laugh was how Mark has been in to schools and seen schemes of work where Year 7s always study position-to-term rules for sequences first. He knows that that SOW isn't fit for the students in that school because he wrote it, years ago, for the year 7 cohort he had that year. Your schemes of learning need to suit the students in front of you, and quoted a school that has 40 schemes of work in place. Of course, all that means is that they have 40 classes and each class works on different things at a different pace, probably because they have different abilities and starting points.

**02 - Kris Boulton - The genius of Siegfried Engelman: a comprehensive theory of how to teach pretty much everything.**This session made my head swim, a bit. It was very dense, but useful and may well transform how I approach some things in lessons.

The session was about the difference between facts, processes and concepts, and how many facts require a good grounding in many concepts. Learning that '2 is the smallest prime number' requires you to understand the concept of the number 2, the concept of something being the smallest, and the concept of a prime number. Knowing that 'the Earth is a sphere' requires conceptual understanding of the Earth, and what a sphere is.

These concepts need to be taught well in order for students to understand facts and develop fluency. We've all had that student who has seen an irregular 5-sided shape and responded with 'What shape is this?!' 'Well, count the sides' 'That's a pentagon?!' They know what a few pentagons look like, but don't really understand what a pentagon is. As an aside, the L-shape, that compound shapes typically look like, is a hexagon. Tell this to your classes and observe their responses - confusion and realisation that they've been lied to, probably.

'Everybody can learn what we need them to learn, if we find the find the right way to teach it to them'. This reminded me of a film released in the early 2000s (I think) called Road Trip. They travel to see one of the character's girlfriends, or something, and find that she's traveled to see him (I think!). They find out that one of them has been lied to about a final assessment at college and he becomes concerned that he doesn't know anything about the subject as they make their way back. One of the characters claims that he can teach Japanese to a monkey in 46 hours, and that the key is just finding a way to relate the material to that monkey. In this case, he compares ancient philosophy to the WWF (wrestling, not World Wildlife Fund) and he goes on to pass.

Concepts were put into five categories. For

**categorical**concepts, Kris showed a rectangle and said 'This is not a triangle', a quadrilateral which was almost a triangle and said 'This is not a triangle', a right-angled triangle 'This is a triangle', an equilateral triangle 'This is a triangle', a scalene triangle 'This is a triangle', and another quadrilateral less like a triangle 'This is not a triangle'. By showing these, students are now considering what a triangle is and what the shapes have in common, how can they be categorised? This can be followed by an activity on saying whether shapes are triangles or not, and in his experience, this has been largely productive and positive in results. The same can be done with surds, showing root 3 (a surd), root 4 (not a surd), root 5 (a surd), root 14 (a surd), root 15 (a surd), root 16 (not a surd), before asking students what surds are and whether certain numbers are surds. When approaching 'What is a prism?' this way, Kris realised that he had made a mistake when learners identified a sphere as a prism, and quickly realised that he hadn't given a non-example where the shape was convex or concave between the congruent ends and students had assumed that a prism only needed congruent ends, and didn't need to have a congruency cross-section throughout the shape.The basis is, begin with a 'non-example', then show a minimally different non-example, an example, a maximally different example, a different non-example and a different example. Give students a chance to show their understanding, and orchestrate a discussion allowing students to articulate their learning. Just because a student can't articulate their understanding, doesn't mean they don't understand, and lower ability students in particular may not understand worded descriptions, but will develop understanding based on the non-examples and examples, even though they can't get the words out.

**Fuzzagorical**concepts are not exactly applicable to me, but**comparative**ones are. Kris started with the understanding of the word 'gradient', which was defined as 'It's how steep the line is' and carried on, before realising that students had no idea what the word 'steep' means. 5 images, one after the other, showing a line with a fractional gradient (no information, just the line), a line with a greater gradient, a line with the same gradient, a line with a greater gradient, and a line with a lower gradient. As you flash the images up, 'This line has a gradient', (next image) 'Did the gradient go up?' or 'Did the gradient change?' or, for higher attainers, 'What happened to the gradient?'. Do the same with the area of shapes - images with (and my own example) 2 squares next to each other, 4 squares in a row, 4 squares in a 2x2 grid. 'Did the area go up?', 'Did the area change?' or 'What happened to the area?'. The diagrams, and particularly the change between the second and third are important, as the area doesn't change, but the perimeter does, and it's important that students know the difference. How about showing two shapes and asking 'Which shape has the greatest area?', to check that we are indeed understanding what area is and not looking for perimeter.**Transformative**concepts will change, and the best examples here were showing 2(5x + 7) = 10x + 14 and 3(-5x + 7) = -15x + 21, saying 'This is factorised, and this is expanded' and having students realise the link, but this will only work simple procedures and probably wouldn't work for (2x + 1)(5x + 17) = 10x^2 + 19x + 7, but potentially could for (2x + 1)(5x + 17) = 2x(5x + 7) + 1(5x + 7)The final category was

**correlated**concepts. Show an image with a blue, red, green on, and then an image with two blues, a red and a green. 'The probability of picking a blue has increased because the relative frequency has increased'. Show an image with two blues, a red and two greens. 'The probability of picking a blue has decreased, because the relative frequency has decreased'. Show an image with four blues, two reds and four greens. 'The probability of picking a blue has not changed, because the relative frequency has not changed'. Do the same with different images and ask 'Has the probability changed? How do I know?' and ask students to echo your wording to develop an understanding of relative frequency and its link to probability.I left with a lot to think about and enough to share with others. But having typed that up, I think I have more questions than answers.

**03 - Ben Ward - Developing Leadership Potential**I've never considered going into leadership roles before this year. I have a TLR, but it's more classroom based, and I didn't like the idea of being too involved and knowing too much. This year has changed that, though, and I'm hoping for greater responsibilities within the department sooner rather than later. I attended this session in the hope of getting some ideas about what I may need to do over the summer should the opportunity arise. The following are just sub-headings and some thoughts...

**Vision**- What do I want? What's important to me? How do I do that? Where do I want this go? What is not important? What doesn't NEED doing? What needs prioritising? What can wait? Is there a timeline?**Character**- How do I want to be perceived? How am I perceived? How do I respond to others? How am I spoken about? How do I speak about others? Do others trust me? Do I do what I expect others to? Do I behave with consistency, or does my mood affect my leadership, the way I communicate and the way I make decisions? What do I stand for? What matters?**Skills**- What am I good at? This is what I should lead on. What am I not good at? This is what I should seek help with and seek to improve. I took a personality test late last night to help with this, and to find out where I could start.**Delegation**- Allow others to own their work. Delegate tasks well - be open and clear with expectations, select who to give jobs to based on their competency and capacity to do that job, communicate expected outcomes, how will it be fed back to me? is there an first draft in the interim?, have more patience - others work in different ways and at different paces, give reasons for delegation, share decision-making power if applicable, provide the resources required for the task (time, people, a support network, physical resources?). Do not delegrate your responsibilities - for example, results lie with a HoD, and that conversation if results tank is your responsibility, and blame should not be passed on.**Stretch and challenge**- In the same way that you challenge your students, find a place where you and your staff are challenged, starting to gain expertise and experience, and that their fears disappear.**Look after yourself**- Pace yourself, make smart decisions, what needs doing? what can wait?, your workload needs to be sustainable and so does that of your team. What will give the most impact for the least effort?**Appraisal**- Make sure this is not a tick-box exercise, that objectives are useful, productive and meaningful. What are you proud of? What do you want to improve? What do you want to work on?**Coaching**- Have people around you who will challenge you, who you trust and who want you (and you want) to improve. Be that person to somebody else.**Read widely, and read well**- Here is a reading list shared by Ben yesterday.Again, my head is swimming and I think I'll have to park this until I have a role to work in!

**04 - Beth Smith (White Rose Maths Hub) - Teaching for Depth**I've had much of this training before, in school, when the Maths Hub visited us to do a bit of training to support out department, so my notes may be a little lacking.

The session centred around the increase in challenge and expectation of students as we move towards the new GCSE and how this filters down to younger year groups and the requirement around their learning.

The first key point was how our classrooms are centred around memorising and not around fluency and reasoning. A UK text book might have 16 questions focused on the same skill, with the same level of challenge throughout, and the idea is that we need to move away from this to a model seen in Shanghai in recent exchanges, whereby their exercises increase in challenge with almost every question. 16 questions with the same skill, or 10 questions challenging students? Their example was adding fractions with the same denominator, and where the UK text book stuck to solutions with proper fractions, the improved activity started simple, then moved on to having answers as 1, then using this fact in subtracting, and then using this to add fractions with different denominators (in pairs, so that their sum is 1). This is followed by a quick consolidation task of the same ilk, with 5 seconds on each question, with a negative fraction as an answer. At this time, a 'check list' was mentioned on our table, to make sure that exercises can be extended by introducing decimals, fractions, negatives and algebra to most tasks and concepts to extend students understanding.

The next part of the session was about how we can support all learners in the classroom with open-ended questioning. Consider three pandas eating bamboo, 51 pieces altogether, they all eat an odd number of pieces. How many do they eat each? Get as many answers as you can. As an extension, how can you be sure that you have all the answers? To support others - give them a strategy, pick an odd number and half the rest. Is that one answer? Can you find another? Try another question - using the digits 0 - 9, write a sum showing a 3-digit number and a 3-digit number resulting in a 4-digit number. To extend, is this the only answer? To support, make it 2-digit and 2-digit to make 3-digit, or provide digit cards so that they have something to hold on to. For those frustrated learners, who try to give up, give the answers (1089, 1098), and fill in the rest.

We finished by discussing the need to teach for depth and understanding, and how our teaching needs to allow students to apply their learning to problems, and how being able to memorise is great (knowing your times tables, for instance), but can't apply this (like my Year 10 student).

A good day, energising, and great to be a part of that energy despite my unwillingness to move from my seat and become involved in a greater way. I hope my notes are of use to others.

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