Split groups

One of the things I love about my job is the building of relationships between me and my classes.  I love the shared learning journey, the discovery of how one concept links to another, the ability to be able to freely reference topics we have covered together in the past and link it to what we are doing now.  I love seeing my classes regularly, marking their books and getting a really good idea of who they are as mathematicians, what it is that is stopping them improve and working through how I can help them address those barriers.

If I had to come up with one reason why this may not happen with a group – my top reason – it would be split groups.  If I share a teaching group with another member of staff then a few things happen.  Here are four issues that I face and what I try to do to minimise them.

1. Split groups don’t feel like a priority

Firstly, if I’m the minor partner in the split, I struggle to make the marking and planning for that class a priority.  I know I have less teaching groups than say an Art or Music teacher but it’s hard not to prioritise the students I’m going to be working with 8 times a fortnight over those I’m going to see 3 times.  Knowing that this is a temptation of mine lets me check in with myself to see if it is happening.  When planning a 5 or 6 lesson day, I’ll try to plan them first.  I also aim to reflect much more in writing about these lessons so I can remember how they went and what I need to do next.  I probably should do this for all my classes but find I carry lots of those details around in my head for groups I see most days.

2. Struggling with names

Secondly, I struggle to learn names in split groups in ways that I don’t have with groups that are ‘mine’.  I pride myself in knowing the names of all my students by the end of the first week in term but when there are 9 or 10 days between seeing my students I can find it difficult to keep the names straight in my head.  By January, students are insulted when you can’t remember their names, especially if you’ve seen them once a month since September.  To help with this I rely much more heavily on seating plans, the photos on SIMS when I’m taking the register and the use of lollypop sticks.  When the class are working independently, I’ll often run my eye across the room and test myself on the names, using the seating plan to help me out when I get stuck.

3. Lack on continuity

Thirdly, I feel the students get a jerky experience potentially lurching from one topic to another with little reference to what has come before and what the class has been thinking about together.  If you carve up the topics for that term with your co-teacher, they can have two lessons in a day on different topics.  Our year 7s are following a shared curriculum this year which means that shared groups know what has come before and after – that solves one problem but creates a new one, namely that content has to be covered in a lesson – it can’t spill over very easily.  I know of another school that aims to split groups over style of delivery rather than content – students get the same topics but delivered in different ways.  I haven’t heard yet how that’s going.

4. Increased potential discipline problems

Fourth, if there is a discipline issue it can take longer to work out with a split group.  It takes longer for relationships to develop and there is greater space between the repair and rebuild conversation following a behaviour incident and the next lesson.  This can allow that conversation to be forgotten and a potentially challenging relationship to take longer to mend.  It can also mean that students with challenging behaviour can forget about their own successes from one lesson to the next.  After I see split groups, I will often jot down some notes to remind myself about successes and issues that appeared during the lesson.  When I’m planning the next lesson, I’ll look back at these notes and try to find ways to reinforce those successes next time.  “Steve asked an awesome question last lesson … let’s see if we can answer it!”  “Sarah, your work last lesson showed amazing effort, let’s try to see that again this lesson.”  Helping our students feel known is so important but hard work in this particular context.

It can be a good thing to be in a split group – experiencing two different teachers, a different environment, a different classroom culture – but I think to make it work requires a lot of effort for each of the teachers.  Probably as much work as the group you teach all the time!

Are there any issues or solutions I’ve missed?

Illustration from Jason Ramasami, check out his work at saamvisual.com


(Re)reading this summer

I haven’t done quite as much professional reading this summer as normal. Mainly that’s because of a certain toddler who had urgent games to play in time periods when I’d normally be able to do some. I’m not complaining, just recognising the difference.

On top of that, most of my reading this year has been re-reading things I’d skimmed or read during the year. I wanted to make sure that I’d really understood the messages and that I was going to be in a better position to embed what I’d been reading.
First up is a book I read in early 2012 that lots of people have been talking about but that I wanted to revisit. Mindset by Carol Dweck is a really interesting and engaging book. We have been talking a lot about Growth Mindsets vs Fixed Mindsets over the past year and it was helpful to revisit her work and be reminded of the fundamental thinking on the topic straight from the horse’s mouth. It’s reminded me again and again, as a parent and teacher, to make sure that I praise the process and the aspects that are under personal control rather than innate qualities. Still picking myself up on this!
Second, is a book I reviewed last summer here. 5 Practices for Orchestrating Productive Mathematics Discussions – I really love this book and like the structure for making the most of discussions. I like the way it encourages the building of the narrative and how the responsibility for this lies with the teacher. I was also challenged by a short section on how to make a permanent record of the lesson and loved the phrase ‘learning residue’. David Didau and others have been talking a lot about learning what you think about and effective Mathematics discussions definitely facilitate deep and meaningful thinking. Having students write down a key thought or sentence as a discussion ends would be a great plenary!
I know that this book is very American and some people don’t find it applies well in a British context but I really enjoy Teach Like a Champion by Doug Lemov. Harry Fletcher Wood got to visit some KIPP schools in action last year and I was fascinated to hear about what it looks like in action when viewed from a British perspective. When I reread this book, I was reminded of key things that I can improve on and really value recapping on those as we go in to the new school year.
The Together Teacher by Maia Heyck-Merlin is a book which I was surprised to enjoy reading last year and recapping on this summer. I’m a bit of a productivity geek but as a husband with (almost) two small boys, a busy classroom, lots of shared classes and whole school responsibilities, those skills become more and more important to nail down. I really like the structures to make sure you don’t forget things and to have systems set up that you can trust so you don’t panic that you have forgotten. I’m keeping these systems going and trying to find the best tools for those that don’t involve paper.
Lastly then, Key Ideas in Teaching Mathematics by Anne Watson, Keith Jones and Dave Pratt. If you haven’t picked up a copy of this book, I’d highly recommend it. For each of the key ideas that it covers it explores the progression from age 9 to 16, the relevant research and teaching approaches. I’ve found that the quality of my explanations on some of the topics covered has definitely picked up and my links between some of the different areas have been reinforced as I’ve read. There is a great website that has most of the content covered in the book here.

That’s about it. I’ve been in my classroom today trying to get it sorted – all of my display boards had been stripped over the summer and I was trying to get those back up again. Frustratingly, my staple gun ran out and I couldn’t find recharges that fit anywhere in the school. Ah well, I’ll keep going next week. For now, I’m going to enjoy the last few days of the summer holidays including a camping trip this weekend with 5 almost 2 year olds – what could go wrong with that?


Am I addicted to Khan academy?

When Khan Academy launched a few years ago, I read a lot of blogs that were not very positive.  The main contention seemed to be that the best way for students to learn was not through disembodied videos but through constructive, social engagement in the classroom.  At the time I looked at some of the videos but, given that the curriculum didn’t exactly map to the UK one, I didn’t give it much attention.

Sarah Montague finished a three part series on Radio 4 this week entitled, ‘My Teacher is an App’.  Having listened to the first episode of that, I returned to Khan academy and realised there was plenty to do without necessarily having to engage with the videos.  While I try to work out how to make technology a force for good in my classroom I thought it would be silly not to give this a go – it’s free after all.  I made the decision to trial this with my Year 7 and Year 10 classes.  I am also trying something different with my Year 8s which I’ll blog about later.

To be able to set up your class, you have to create your own account.  I did this, invited my classes, had a lesson in a computer room to launch it and then asked each student to spend a minimum of 45 minutes working on Khan over the course of a week.

All my Year 7s have managed that – some of them have spent upwards of 4 hours practising Maths outside of lessons.  Those in my Year 10 class who have done it, have all spent more time on it than I asked.  But, the strange thing is, I seem to be spending time on there every day – I check on how my students have been doing and then end up doing some of the challenges myself.

What is it that gets me to complete the work?  I think it is because it feels like a computer game – it is compulsive.  For students, each year group is being presented with work on and below where they are at but this helps them demonstrate and practice knowledge that they may not have seen in class for a while.  The progress map on the side spurs a student on – they want to get it all dark blue (or at least I do!).  They want the points so they can update their avatar.  As far as I can see, the gamification has worked.

With my students, the videos haven’t yet been watched, but the questions have been engaged with.  I’m not getting many skills that students are struggling with in the coach menu but that could because they are self-selecting the topics they can answer.  As they spend longer working on the site, I reckon that could begin to increase.

I’m enjoying this experiment with Khan and I think my students are too.

Oh, it’s time to do another mastery challenge – I’m off!


Perusing my book shelf – Opening up closed problems


Over the years, I’ve collected a pretty large set of books related to teaching and Maths teaching in particular. I’ve decided to try to read through a book a week to glean any interesting ideas that might be useful and decide if I should keep or kick it.

Today I’ve picked up a thin pamphlet (have to start somewhere) called ‘The Delholm Fun Book of Mathematical Puzzles’. I have no idea where I picked this up from but I think it’s followed me around two schools now so I figured I’d take a look.

This is an old book which has 34 puzzles that may be useful as starters to lessons – probably why I picked it up!  There are quite a few vocabulary based puzzles and most of the Maths involved could be usefully tackled by late KS2 and early KS3 students, focusing primarily on the four operations.

The puzzles themselves are quite closed but I could see how working backwards may provide a more open problem that makes it a high ceiling problem.

The hidden picture problem is a good example:


The initial problem would be to complete the puzzle but then, with new copies of the grid, students could firstly design their own picture and then create questions to go alongside it. One idea could be to use this as a revision lesson – creating a list of topics that need to appear in your question list.  These could be exchanged with someone else and then students will have practiced creating and doing the questions.

I’ve created a Word version of this here.

Lots of these puzzles feel a bit like busy work – I can see them being used as a launch pad to check basic vocabulary or understanding but I’m not particularly impressed with the depth of thinking that any of these tasks involve.

Looking through this book I realise my metric for deciding if a problem is worth bringing into my classroom has changed a lot since I began teaching. Before I would be interested if this covered a part of a learning objective, now I want to know can this be used to enhance the quality of thinking my students engage in. I think when tired or busy I slip back into busy work and keeping kids active – I actually need to always keep them challenged and thinking which is a wholly different and more difficult problem.

So, decision time – keep or kick …. I think it has to be a kick. The quality is pretty poor and I don’t think I’ll struggle to find resources that would fill this gap. I haven’t used any of these in the 6 years I’ve had the book and, apart from the hidden picture idea there isn’t anything that excites me at all.


#MBToS Challenge 3: Collaboration Nation

This weeks challenge on the Math(s) Twitter Blog ‘o’ Sphere is to check into one of the collaboration projects set up by Maths educators around the world (mostly in the US but at least one of which comes out of the UK), to explore a bit and reflect on what we find.

I’ve been lurking around the edges of Maths education blogs for a long time, so I remember a lot of these projects starting up.  I’ve dropped in but for whatever reason I haven’t contributed much – I thought I’d use this as an opportunity to drop back in on one of them, namely 101questions which is a project of Dan Meyer.

Dan has done a lot of work thinking through 3 Act lessons.  When I describe that work to others I talk about trying to get a picture or video that poses one key and interesting question that could be used as the launching point for a lesson or series of lessons.  I talk about seeing lessons as stories with a beginning, middle and end, with possible sequels.  I talk about using the digital projectors in our rooms to share digitally rich materials.  I talk about having something beyond the answer key or my decision being the measure of correctness or success.

101questions is an online community set to pose videos and pictures to see what questions come up – to see if other people intuitively jump to the question you have in mind.  The people posting the pictures or videos and the people suggesting questions are mostly Maths teachers but given that level of homogeneity, there is a great diversity in the types of answers that are given.  You still get different questions in the classroom but this gives a good starting point to make sure you aren’t completely blindsided.

I have taken some of these and used them in the classroom.  We’ve watched the video or examined the picture, come up with our questions, asked what information we might need to begin to solve that question and get stuck in doing some mathematics.  It takes work to find an Act 2 (the information) or Act 3 for some of these problems which is where I have greatly appreciated the work of others doing this (I’ve benefited a lot from Dan and Andrew Stadel in particular).  The site now has functionality to search for those resources that have lessons associated with them.  I’m pretty sure this is new and will make it much more likely for me to use these in my lessons more often.

I find  that these problems are very engaging but not often fully mathematically rich.   They do present problems that can be solved in a variety of ways but as we are aiming toward one key question most students are working to try find out the same thing.  Maybe the sequels is where the juicy richness comes in – we could encourage pattern spotting and generalisations as students develop their own problems in our context.

Do you think 3 Act lessons are mathematically rich?  Am I way off base here?  Are there ways to make them more rich?


Thinking about indices …

Okay, maybe I’m a bit slow but I said and thought something today that I’ve never thought about before.

We’re looking at indices & surds in my Year 11 class.  Today we were looking at the rules of indices: multiplying and dividing indices was “insultingly easy”.  Negative indices seemed to push it over the edge … some very confused faces.  We struggled with it and I think most people managed to get an instrumental understanding but not a relational one.  We’re working on that!

I was trying to explain that 6^{-3} was equal to \frac{1}{6^3}.

Now, in explaining this I said it was 1 divided by 6 three times.  Seems fine but where does the one come from?  We talked about reciprocals, we talked about the pattern that follows as we look at 6^3 6^2 6^1 6^0 6^{-1} … and we talked about a few more bits and pieces.

I then thought about 6^3 could be thought of as 1 x 6 x 6 x 6.  This adds a bit of consistency to the system and made me think of an inaccuracy that I sometimes hear myself making or confirming.

“What does 6^3 mean?”

“6 times by itself 3 times”

But does it? 6 times by itself three times could be 6 x (itself three times) or 6 x (6 x 6 x 6).  I suddenly thought surely this could be 1 times by 6 three times.  This helps with consistency in two ways.

Firstly, with our negative powers – we can say that it is 1 divided by 6 three times.  This has internal consistency and I like it.

Secondly, raising something to the power of 0 makes sense – 1 times by 6 zero times is obviously 1.

I’ve never seen or heard this anywhere before – am I wrong?  Does this break down somewhere that I’m not aware of?  Do you think this could be a helpful way to see it?

Also, is there a richer way to introduce this apart from pattern spotting?  Any ideas gladly received.


Level 6 Maths in Year 6 – what’s going on?

I recently gave some input at a primary Maths training event in my local area.  As more and more schools need to move students on to level 6 at the end of primary to hit their league table targets, there is a training need to enable our teachers to be able to teach the content effectively.

I think primary teachers are great – I’m pretty sure I could not deal with planning for subjects that are not my specialism.  I love Maths – I get a buzz from planning for Maths lessons – I have taught Maths at P-Level and A-Level – I can plan engaging lessons with background and context and extension and support really well in Maths.  I’m confident with the vocabulary, the progression, the pitch and can address misconceptions well.  All that being said, ask me to teach history and I’d flounder.  Last year, I had to teach some science – it wasn’t difficult stuff – but I really struggled to know enough to make the lessons meaningful and useful.

Primary practitioners are expected to do this for every area of the curriculum every day!  No way I could do that!  Now, with the expectation that Level 6 is achieved by some students, there is a danger of slipping into old ways of working – teaching verbatim from a textbook, not knowing where this goes, not fully understanding where a concept has come from.  I have observed some amazing Maths lessons in primary – using concrete resources and visualisations, pair talk and problem solving – all of which were used excellently to help their learners learn and make progress.  But, if the content is something unfamiliar, if you’re worried about being ‘good’ at Maths or that your students might be ‘better’ than you, if you are being pressured to get the magical level 6 – then it would be easy to forget about all the excellent practice you do and slip into something from a box.

In my input, I wanted to encourage primary teachers to keep doing what they are doing.  I’ve embedded the Prezi I used below.  Saying all that, there is a training need that is there.  How can these teachers plan effectively if they haven’t made these connections themselves in a number of years, if ever?  With the demise of the National Strategies, I think it is the responsibility of local schools to help each other.  Effective secondary Maths departments that have the capacity to do so, should be helping to develop and equip our primary colleagues to know the content well, to make the connections more easily so that when our students arrive with level 6, we believe it.  Surely, a secure Level 6 rather than one coached for a test is a benefit to the secondary school who receives that student and is then judged upon their progress?

What do you think?  Is this the responsibility of local cluster groups to source funding and time to deal with?  If not them, then who?

Answers on a postcard please.


#MTBoS Mission 2: Coping with the Steam

I think teaching Maths is the best job ever – I love doing it and I love improving at it.  I actively seek out ways to do that and the #MTBOS has given me some great ideas over the years I’ve been lurking.  I’ve a full twitter feed and a bulging blog-reader.  I also have a full-time job, a family, a church and (though I haven’t been there in a while) an allotment.  Getting the balance is something I find tough.

There are times of the year when I am on top of my blog and twitter feed – I think I sometimes see it as a competition and if I can get everything down to zero then that’ll be great.   But, this is unsustainable – there is so much great stuff out there that I don’t want to be left behind.  When I see something I like, I add that blog to my blog feed – on average that clocks up 100+ posts a day. I need some survival techniques and I’ve come up with two.

For twitter, it’s using notifications.  I found out about this over the summer and I’ve loved it since.  If you use an iPhone or similar device, you can select particular users to get notifications for.  Then, when they tweet, it pops up on your screen.  I use this to make sure I don’t miss tweets from friends and people I’m finding interesting.  If I find someone tweets too much for me, I can switch them off.  If there is something I want to respond to, it is there straight away.  Occasionally, I turn them all off if I want a break.  This has helped me not open twitter like a nervous tick which I like a lot.

For blogs, it’s quality over quantity.  I’m still struggling with how to do this well – but I want to read blogs until I find a post I find interesting, stop and engage with it.  Too often, I find myself skimming and racing to get to the end, to get to the next post, to get to the end, to get to the next post, …..  That’s probably a sign I shouldn’t be reading that post, right?  Or do you persevere with the hope there might be a great idea coming up?  I want to allow what I read to affect what I do.  Otherwise, what is the point?  I love reading but skimming blogs sometimes leaves me feeling a bit morose – either overwhelmed because there is no way I can implement all those great ideas or numb because there are so many ideas I haven’t engaged with any of them.

Do you feel my pain here?  Do you have any award winning strategies to help make the deluge of information manageable and useful?  How do you make sure that your engagement with the #MBToS changes your practice?


#MTBoS Mission 1: Rich Task – Painted Cube

I really wanted to be involved in the MTBOS (Matho Twitto Blogo Sphere) challenges this year – I was a bit lame last year and never got off my bum to do anything about it.  I’ve been a bit late on last week’s Exploring the MTBOS challenge but I thought I could catch up today.

I wanted to talk about a problem that my Year 8s have been working on this past week – The Painted Cube.  Now, this used to be one option for GCSE coursework and I’ve used it for that in the past.  I think it is a pretty good example of a ‘Low Threshold, High Ceiling’ task – the problem is easy to pose, everyone can do something and the students can run with it, extending it to the limit of the their Mathematical ability.

Here’s the problem:

3x3x3Imagine a large cube made up from 27 small black cubes.

Imagine dipping the large cube into a pot of yellow paint so the whole outer surface is covered, and then breaking the cube up into its small cubes.

How many of the small cubes will have yellow paint on their faces?
Will they all look the same?

nRich have a nice animation to help with the launch here.

There were a number of skills that I wanted to be used during the few hours that we were looking at this task.  I wanted students to collect results systematically, I wanted them to look for and spot patterns, to come up with general rules, draw isometrically, consider the volume of cubes and cuboids and to relate their rules to the physical reality of the problem.  I knew I could encourage some to look at graphs to summarise and present their results, to begin thinking about algebraic proof, expansion of quadratic and cubic brackets and, potentially, propose results in 4D (sadly, none of my 12 year olds got that far this time round).

I had students working in pairs or individually – I gave them access to some cubes but encouraged them to move towards visualising using diagrams because we didn’t have enough cubes for a 10x10x10 example. Lots of discussion and lots of excellent thinking ensured.  The quality of the questions was superb and the student support for each other was excellent.  Some students weren’t clear on drawing isometrically, so a student expert demonstrated with the visualiser while another narrated and answered questions.  There was some tussling over the multilink cubes but that calmed down after a while.

We spent two hours of lesson time looking at this problem.  We looked at finding nth terms earlier in the term and are about the begin a section on volume, so I thought this was a good place to drop this problem in.

I’ve asked every student to spend another hour on their own for homework to take the problem further, so I’m looking forward to see what they bring back after the weekend.

I love that from a simple problem we can get so much Maths that connects to everything else – when they come back on Monday we’re going to mindmap all of the Maths we used in this one simple problem and marvel at the wonder of Mathematics.


Marking is Planning

We are about to start the next cycle of Teaching and Learning Communities at my school. Each community or group is looking at a different aspect of teaching and will help inform the future policy and practice around that area by carrying out small scale action research projects. They are mostly based around what we believe are the non-negotiables of a lesson (learning intentions, differentiation, questioning, AFL for in lesson intervention and plenaries), alongside two broader topics, namely Progress over Time and Marking is Planning. It is this last one that I’m facilitating and that I want to explore a bit.

I first came across the phrase in a post from David Didau – I think he coined it – and it hangs on the premise that marking to which students respond not only informs you and the student but also plans a chunk or entirety of a lesson. David talks about Dedicated Improvement and Reflection (DIRT) wherein students work on individually assigned and focussed questions and tasks. This helps reduce the problem of feedback that is never acted on by students, gives meaningful differentiation for every student in our classes and reduces the time involved in the feedback loop.

Most of the bloggers that have explored this are teachers of written subjects and for them the individually assigned task can be about redrafting based on feedback. I’m not sure that works in the same way in Maths – redo this problem based on my feedback? Maybe sometimes. Mostly though, I think it is about giving a directed, probing question that helps push my students thinking further and that begins a dialogue over time. There must be time built into lessons for students to respond to this feedback otherwise I have wasted time for no meaningful reason.

Possible ideas to support marking

Over the past few years, we have tried various methods to make our marking more effective. Some of these are great for certain topics and some don’t work as well for others. The marking needs to be speedy and, a concept I read about on this blog, needs to follow the x10 rule – it needs to produce a task for students that should take at least 10 times the amount of time I took to mark it.


I love my highlighter, almost as much as I love my post-its. Graphs, calculations, constructions … highlight errors and have students identify and correct them. This could be the scales on an axis or a sign error in a calculation. If it is repeated error then you could do one worked example and highlight the other occasions this error crops up. Having students to write what the error was and how they can avoid doing it in future has been really powerful for my students.

Probing Questions

While my department never really bought into APP as a way to continually assess our students – at least in so far as the A3 grids and tracking was concerned – the collections of probing questions are invaluable in my marking. I collect the ones on the unit we’ve been working on at the start of the unit and then when I’m marking use these as prompts to set a probing question for the student. I want a probing question to explore the thinking behind a concept, to address a misconception or to drill down to an issue that needs to be addressed. I want a student to have to think about it – it shouldn’t be something they can answer off pat – and it should be something that helps them move their understanding forward.

Screen cast

If there is an issue that I’m seeing appearing in several books then I start to think about other ways to help support these students. One method I have found working well is a screen cast. I simply use my iPad to talk and write my way through a problem, explaining my thinking and reasoning, asking questions and pausing. I aim to make the videos 2 minutes or less. The students then watch these as homework and then error spot some sample work or try some examples themselves.

I’m always searching for feedback and marking strategies that minimize on my workload while maximising on student engagement and progress.

Are there any corkers I’m missing?