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?

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?

A New Year!


Woohoo!! Happy New Year!  Hear the party poppers and experience the joy!


I’m imagining that the night before coming back to school wasn’t as raucous as 31st December can be but I also imagine there were a few unsettled bellies.

I always feel nervous before the new term starts – thinking I’ve forgotten how to teach and plan and remember names and all the other things we have to do in a day to day basis.  But, I also know it’s never as scary as I imagine.  To start of this year, here are my 5 New Year’s resolutions!

1. I will stay organised.

I can be quite messy at work and this can distract from my thinking and students learning.  With this in mind, every day will start and end with a clear desk and a tidy classroom.  I’ve been trying to use a digital markbook and so I’ll be curious to see if that is as seamless as my old paper one.

2. I will make the most of every work day.

I can spend a lot of time faffing, even (or maybe especially) if I have lots of work to do.  With this in mind, I will continue my practice from last year and assign every free lesson a job but this time stick to it.  I’ll try to start jobs when I get them and make the effort to discern the important from the urgent.  I’ll try to keep my email inbox low and respond sooner rather than later.

3. I will post here once a week.

I’ve had this blog thing for a while but I’ve had no discipline with keeping it up-to-date – posting at least one idea or thought or reflection every week should be easy and I’m going to try my best to stick to it.

4. I will try to follow a marking is planning routine.

David Didau has been talking about this for a while and I’m leading a research group at school based around it.  I’m determined to shorten the feedback cycle and make meaningful marking an integral part of all I do.  I imagine I’ll be posting about this soon!

5. I will keep on top of my phone calls.

Since I first started teaching I’ve always made positive phone calls home and I know they make a difference.  But, they often slip away as time becomes more pressured – so I’ll aim to phone home to one student from each class, each week.  From experience, Friday afternoons are a great time for this – awesome way to start the weekend.

Those are my work resolutions – I hope they don’t fail to materialise like so many others or end in disappointment a week or a month from now.  I think each of them are important and am keen to give them the time they need.

How about you?  Any resolutions as you start the new year?

What do Mathematicians look like?

Today, I ran two one hour sessions as part of a transition summer school being run with pupil premium money for upcoming Year 7s (11 year olds).  I wanted to get stuck into some problem solving activities first though, I wanted to dig into attitudes about Maths and Mathematicians.  So, I pulled out an old classic I’ve been using for years that I got from the amazing @PaulineMGaston.

I had students draw a picture of a Mathematician. I was really careful with my language here – I said “Draw a picture of a Mathematician and try to label it … for example your Mathematician may have a furrowed brow because they think really hard.”  (the labelling didn’t really happen this time)

We stuck them up with commentary from the artists and looked at them together:


Some interesting things:  All these people are well dressed, wear glasses and are slim (when I asked one student whether all mathematicians were slim, she responded “Well, you are”).  I wasn’t wearing a suit – I was wearing jeans and t-shirt because it’s the summer holidays – but the other aspects could have been from me.

There was only one girl – @missradders and @JusSumChick reckon the second to last one is a girl, the student assured me it wasn’t but it is quite ambiguous.

Having chatted about the pictures, I asked them a series of questions and hit them with a cut up version of this so I could reveal it one at a time:


We referred back to this at the end of the two problem solving activities to check which of these skills and attributes we used – helping them to realise that, yes, they are Mathematicians!

I really like this activity and do it at the start of the year with some of my classes.  I already have added @Rathematician ‘s suggestion of ‘Persist people’.

What else did I miss?  Mathematicians are ….

Strategies to help all learners think Mathematically

This is a response to #blogsync topic of “A Teaching and Learning strategy intended to elicit the highest levels of student motivation in my subject”. See more at http://share.edutronic.net/

I’ve always worked in comprehensive schools, mostly 11-18, which means I can move in one hour from supporting a student who has difficult with number bonds up to 10 to helping support a small group of students for Cambridge entrance exams. I love this variety and I love the opportunities it gives me to see links that I might otherwise miss. I think this has helped improve my thinking as a Mathematician and has forced me to find and use strategies to allow all students to develop these skills as well.

I’ve drawn a lot on the work of Malcolm Swan, David Wright, Sally Taverner, Jo Boaler and Andrew Blair.

I’ve split this into two parts – strategies that help thinking and tasks that helps thinking. I’m working on gathering together a more comprehensive list – if you have any obvious ones I’m missing, please let me know!



This is a strategy that is used so much that it almost isn’t worth talking about. Having students think about an answer, share with their partner and then share more broadly helps everyone have a chance to articulate their answers. I find it is a good way of emphasising the use of Mathematical language and the importance of quality explanations.

Self-regulation Cards (inspired by Andrew Blair of http://www.inquirymaths.com)

I’ve recently had some of Andrew’s cards made up that students have on their desks – these provide prompts to help them self-direct their learning. They give ideas like ‘Draw a picture’, ‘What easier problem could help?’, ‘What other information might you need?’, ‘Ask a partner’ and ‘Ask the teacher’. Now, when I drop in to chat to a student I’ll ask them which strategy they are using. This has helped them become more independent and self-motivated.

Mini whiteboards

I don’t know what I’d do without these – how else can I quickly ask a question and process 32 responses instantly? I can quickly identify which students need more support and which concepts need more explanation. My only problem is, I keep running out of pens – do others have better organisational strategies for these?


Odd One Out

This is one of the easiest tasks to implement. Students are given a set of 3 numbers, shapes, functions or whatever and explain why each one might be considered the odd one out.

Using two-way tables or Venn Diagrams

For this task, students are given a large set of objects and then have to categorise them. This helps to pull out similarities and differences, developing Mathematical language and explanations. They then can design a two-way table or be given on to complete. I’ve used this for topics as varied as trigonometric graphs and rotational symmetry of 2D objects.

Multiple representations

To try to avoid focusing on technique rather than understanding, interpreting different representations of the same information can help make links that otherwise go unnoticed. This might be matching numbers (fractions, decimals, percentages, number lines), algebraic expressions (words, symbols, area diagrams) or statistical diagrams (frequency table, cumulative frequency curve).

Always, Sometimes, Never

When helping students to evaluate the veracity of their claims, it is helpful to ask is that always true? Sometimes? Providing provocative statements and having students develop their arguments is a really helpful task to identify key errors and misconceptions (eg multiplying always makes a number bigger, continuous graphs are differentiable, if you double the lengths of the sides you double the area).

These are some of my key moves – what are yours?