“How you are tackling problem solving? Our learners and staff are finding it a challenge and I feel the key is to ensure it is right lower down in the school so that pupils have more skills to tackle problems when they are at KS4.”

And my response, copied here in case it’s useful…

My problem solving strategy would be, as frequently and as early as possible, to give students questions/problems that meld two or more topics together. For example in year 7 when you’re doing algebra, bring in angle problems that require some collecting of like terms. When you’re doing fractions bring in an area question where the side lengths are mixed numbers. With indices make the powers an algebraic expression.

As you get up to year 11, you’ll have to be creative and often invent random maths concoctions. It’s a worthwhile team planning exercise to write out things like: vectors, transformations, probability, trig, quadratics, volume, speed, angles in polygons, bearings, etc. on separate cards and then choose two at random to make a question from. For example if you choose speed and probability, can you and your partner invent a mash-up question?

I’m saying this because there aren’t enough of these combo problems to draw on at GCSE yet but that’s the direction they’re going. So for the time being we’re going to have to make them up and force ourselves (i.e. the teachers) to make the connections in the maths.

On the more reasoning type of problems, the total AO3 questions, you’ve got to make sure your school is prioritising English and reading in a big way from year 7. I mean like 8 hours of English a week plus 40 minutes of silent reading a day, plus any interventions required for the weakest.

Language is a pre-requisite for thought. The better your language skills the better your ability to think. You simply can’t reason without language. So until their literacy is supreme, their reasoning is going to suffer and no amount of highlighting keywords is going to really tackle the issue.

Every school should be a big reading school. Speak to your HoD, the English HoD, the school librarian, your HoY or even your Headteacher to find out how to give English and reading more prominence in year 7.

Just my thoughts quickly cobbled together. Discussions welcome in the comments.

]]>In my first lesson with a new class I have two things I want to achieve: visioneering and routineering. This post is about visioneering, the act of sharing the Big Vision with your students and imbuing them with a Sense of Possibility.

For clarity, the reason I think visioneering is essential is that to date, my students haven’t arrived with an idea of what they’re really capable of and without a SOPO, their effort, resilience and satisfaction plummet. So as early as possible during our time together, I want them to appreciate what is waiting for them at the end. I want their mental picture of their own future to be vivid, enticing and potent because it’s going to give them the driving force they’ll need to work hard over the coming year(s) and deal with setbacks.

The Big Vision is simple: I think you deserve to be happy. A lot of unhappiness comes from not having choices in life or not being able to choose the things that make you happy. So, in contrast, the route to happiness that I’m suggesting is one that keeps your life full of choices, particularly the choices that make you happy.

There are many things that will give you choices in life and it’s not simply money. Your virtues and personality probably count for more. One of the virtues that probably gets the best results is that of being diligent…hard-working. Everyone appreciates a hard-worker and generally speaking the more hard-working you are, the more choices you’ll have.

The thing about being hard-working though is not to leave it too late. Don’t wait until you’re 25 to start working hard because you’ll miss out on the good things that have gone to those who started younger. Don’t wait until you’re 16 either because a lot of doors will have closed by then. In fact, the time to start working hard is from the beginning.

Let me show you a video of some students who started working hard when they were your age. These students go/went to *this* school. Not a private school. Not a school 100 miles away or even down the road. They went to your school and 5 years ago they were sat in *your* chairs.

At this point, I play a video I’ve recorded on GCSE results day of our highest achievers.

When the video finishes, I carry on…

What were the students in the video feeling? How could you tell? Why do you think they had those feelings? Can you imagine what it would be like to feel the same way?

Let’s see if we can feel the same way today.

Close your eyes, I want to tell you a story…

They listen attentively as I tell them a fairly drawn out story about the 5 year emotional rollercoaster from year 7 to 11, paying particular attention to the nerves they’ll experience on results day morning. As I build towards the final Envelope moment I slip a piece of paper on the desk in front of each of them. Printed on each sheet is a fake GCSE certificate that I’ve mail-merged with their name and date of birth to make it look marginally more authentic – as any illusionist will tell you, the details are key!

During the course of the storytelling, they’ve become immersed. They believe they are the protagonists and for a blissful minute when they open their eyes and read their results over and over (I’ve given them all grades that are slightly better than the ones they saw the students in the video getting) they feel a personal pride they’ve never felt before. They know they haven’t genuinely earned it but now that they’ve felt it, they want more of it. They *want* to earn it for real and they’re willing to believe it really will be them in 5 years.

Full of a sense of possibility, we can now begin the hard work.

>>Update

Carl Morris from Purbeck School has written this script.

With the hope of getting some feedback in the comments, here’s what I try to do consistently with modelling.

- I start with “empty hands and look this way”. I wait until hands are empty and eyes are looking this way. Every time. I don’t begin modelling until that’s done. I stay on top of low level distraction throughout. From lesson one.
- Where it makes sense I use physical resources to represent the concept. If I’ve got enough sets I try to put these resources in front of every pair of pupils and do some whole-class, quick-fire show-me stuff.
- Show me 98 (on an abacus, for example), add on 1 more, 1 more.
- Show me division using place value blocks.
- Show me a parallelogram (using lollipop sticks). Now change it to a rectangle (I’m aware of the overlap between parallelogram and rectangle but that’s usually for another lesson). Show me a square.
- Show me a clockwise rotation (with a ruler or pencil)
- Show me negative 5 (on an air number line)

- If it’s a procedure that has a step in it that I-know-they-can-do-in-isolation-but-they-might-get-stuck-on-because-it’s-now-in-a-new-context, we’ll practice that step as a warm up.
For example…

- Simplifying fractions requires finding a common factor. So we’ll warm up by finding common factors.
- Multiplying a pair of brackets requires ability to multiply a variable by a number. So before tackling pairs of brackets we’ll just do y × 3, y × y, -2 × y, etc.
- Working out a scale factor requires some mental or written division. So we’ll practice working out how many times bigger one number is than another.

- If it’s a procedure that has some unfamiliar steps that I know will hold them up, we’ll take out those out and work on them in isolation.
- Determining opp, adj and hyp on a right angle triangle
- Choosing whether to add or subtract equations when solving simultaneous equations by elimination
- Working out frequency density for a histogram
- Working out b² – 4ac for the quadratic formula
- Deciding whether the line should be solid or dashed for graphing inequalities

- After understanding and becoming successful at each step, we’ll then glue the steps back together. For example, if they’ve got the hang of step 1 and step 2 in isolation of each other, then we’ll do step 1 followed by step 2.
- When choosing examples to demonstrate I think about the following:
- Will the sequence of examples lead them to a false generalisation? For example, if I choose a series of fractions to simplify that are all made up of even numbers, will they assume that simplifying only involves dividing by 2?
- How can I make example 2 very similar but slightly different to example 1 so that they can see the impact of changing one thing? Maybe I’ll change one of the signs, one of the numbers, one of the variables, one of the powers, the order, the orientation of the shape, involve special cases using 0 or 1, introduce a fraction.
- Are them some non-examples that will help to make the point. If I’m trying to exemplify what a polygon, a difference of two squares, an improper fraction, a Pythagorean triple…what counter examples would help my pupils understand the required features of a true example?
- As the series of examples goes on, I’ll tend to leave gaps in the steps or what I’m writing to get their help filling it in.

- When checking how well they’re following the maths, I don’t ask “Does everyone understand?”, I target questions at pupils and lure the less confident into giving me an answer to a gap fill or another easy question.
Or…

- I make the most of whole class responses (“Class, after 3, what is the highest common factor of 12 and 16? 1…2…3…!”) or showing me answers on their fingers or on a mini whiteboard.
- I use 10 second bursts of tell-your-partner
- I use true or false questions, is this right/wrong questions, the awesome question stems from Thinkers (by John Mason and Anne Watson).

- If there’s another adult in the room, I like to get some dialogue with them in front of the pupils. For example, I might get them to explain the steps on the board while I pretend to be a student with lots of questions. If it’s a TA I regularly work with then I insist they chip in with a question when they think I’ve missed something in my explanation.

Comments welcome.

]]>My interest in Shanghai maths teaching is an intellectual matter not a political one.

We should definitely be wanting to know more about their pedagogy given we are rarely in a position in our busy, chaotic, highly emotional school lives to engage with it. They’re the ones who have the chance to rigorously pull apart and reconstruct maths teaching.

The fact that they come out on top consistently is of interest to me. If I was a manager of a mid-tier football team, I’d be wanting to find out what the managers of the top teams were doing. If I was a trainee surgeon, I’d want to know what the best surgeons do. If I was a maths teacher, I’d want to know what the best maths teaching might look like (and PISA would give me an indication as to where to look).

Shanghai is humble enough to claim they don’t have the monopoly on good ideas and I’ve been more than happy to find out how they do what they do.

As 60 Shanghai teachers prepare to teach in our schools next month, I am excited about what we’ll see that’s transerable.

]]>If you come away with one thing it should be…

Ofsted don’t have a preferred lesson style, marking approach, differentiation approach, pupil grouping arrangement, textbook, lesson activity, assessment system or curriculum. So long as you can evidence how your school’s choices on all of these impacts your students’ learning, there is no need to “do it for Ofsted”.

Quick! Get that message to all headteachers and SLT!

On…

**Next-step marking**– school policy needn’t stipulate next-step marking in maths.**Differentiation**– it may be subtle in maths.**Verbal feedback**– it needn’t be recorded unless you think it’s going to benefit your pupils.**Lesson plans**– not required by Ofsted.

Download all the responses to the pre-chat questions you submitted, including ones we didn’t have time for.

Please bear in mind that #OfstedMaths was not able to comment on individual inspections nor able to give advice on which textbooks to use, whether to opt for mixed attainment groups, how to assess without levels, etc. For that reason you may find your question was not included in this document.

It’s fantastic that Sean and Jane are so open and common sensical but a small number of you has shared with me instances where you felt the current inspectors had given feedback that was almost in contradiction with the maths part of the handbook and possibly in contradiction to what you’re reading on this page.

That is a problem and Ofsted knows this, none moreso than Sean and Jane. To address the issue of consistency Ofsted is letting go 1200 inspectors, they have put in place compulsory additional training of the remaining inspectors (more to come on this soon) and they are making the move towards bringing more practicing headteachers on to the inspection teams.

We have a role to play during inspections too – Jane made it clear to me in a conversation that inspectors are “not to be feared”. Go and speak to them, she said, their evidence is only as good as what the school provides so if there’s something you feel they should know about what the school/department does then tell them.

If, during an inspection, you start getting feedback that is contrary to what you read in this summary post, ask for clarifiation. Without sounding defensive, bring this post to the inspectors’ attention. Schools will be the sharpest way we can calibrate inspectors’ views with the handbook across schools.

**Please do not bombard the comments section with cynicsim, rants, specific cases and finger-pointing.
If there is a complaint to Ofsted to be made, use their formal procedures.
Instead, share the constructive ways you’re going to bring this to the attention of your SLT or department.**

This post may have stirred some strong reactions – more than anything, I hope it provides some reassurance and a direction of travel.

#Don’tDoItForOfsted!

For the full run-down of the chat, you should read the #OfstedMaths hashtag but for convenience I’ve summarised it using Storify, below:

**Essential Reading**

Ofsted and mastery of maths – direct from Jane Jones

Ofsted handbook maths section

Ofsted does not expect…myth-busting doc from schools watchdog

Changes to education inspection from September 2015

Characteristics of a mastery approach in maths (NCETM)

This is the chance to ask two prominent Ofsted inspectors for answers to our questions on maths as it relates to inspections.

Send your questions in advance and/or vote for questions that others are already posing, by clicking here: http://tinyurl.com/OfstedMaths

And then remember to follow the #OfstedMaths hashtag on Thursday between 8 and 9pm.

We want primary teachers, headteachers, secondary and FE maths teachers, education organisations (particularly ones involved in maths) to be involved or in the ‘audience’.

Over the last 12 months or so, we’ve seen some key shifts with Ofsted, particularly with their openness and willingness to listen, e.g. Mike Cladingbowl hosting eminent bloggers and tweeters, publication of the Myths document, bringing all inspectors in-house and doing away with lesson gradings. They’ve even got a pretty reasonable set of guidelines in the inspection handbook.

Despite this, at times and possibly for good reasons, Ofsted and the maths community can seem far apart, both with their back turned on the other. So I approached Ofsted and said I thought something needed to be done to bring the maths community and Ofsted closer together. To be fair to Ofsted, without hesitation they agreed to take part. Now it’s your turn to step forward.

Thursday’s chat is a great opportunity to engage positively with two very approachable inspectors and ask your questions. So that everyone can get more from the discussions, please refrain from using cynicism and general Ofsted-bashing-language. This is as close as you get to peace talks in education so enter into conversations with an open hand, ready to appreciate the work they do well. You can assume that Jane and Sean already hold you in high regard.

Ofsted and mastery of maths – direct from Jane Jones

Ofsted handbook maths section

Training of inspectors on changes in maths

Mastery approaches to maths

Maths in primary, in secondary and in FE

What else? It’s up to you!

The link, again, to submit a question by 4pm on Thursday is http://tinyurl.com/OfstedMaths

Please help to get as many people there by sending a short email, Facebook update or tweet. Suggestions as follows:

**Email**

Hi [name],

I thought you might be interested in the #OfstedMaths twitter chat happening this Thursday (18th June) between 8 and 9pm. Hosted by Bruno Reddy (@mrreddymaths), the chat will involve two Ofsted inspectors (@harfordsean and @janejoneshmi) answering questions on maths as it relates to school inspections.

You can submit your question by 4pm on 18th June (by clicking here: http://tinyurl.com/OfstedMaths) or you can simply vote for the questions that others have already submitted.

To find out more, visit Bruno Reddy’s post: http://mrreddy.com/blog/2015/06/twitterchat-ofstedmaths-with-sean-harford-and-jane-jones

There will be a summary of the chat posted on the same page by Sunday 21st.

Please forward this email on to anyone you think may be interested.

Many thanks,

[Your name]

**Facebook**

This Thursday (18th June, 8-9pm) @MrReddyMaths is hosting a twitter chat with two prominent Ofsted inspectors on maths as it relates to inspections. Submit your questions by Thursday 4pm and find out more here http://mrreddy.com/blog/2015/06/twitterchat-ofstedmaths-with-sean-harford-and-jane-jones

Please share with all your education friends.

**Tweet**

Submit #OfstedMaths questions to @harfordsean & @janejoneshmi by 4pm Thurs. http://tinyurl.com/OfstedMaths More info http://mrreddy.com/blog/2015/06/twitterchat-ofstedmaths-with-sean-harford-and-jane-jones Pls RT

(School inspection handbook January 2015, No. 120101, page 19, para 55.)

55. When evaluating the effectiveness of a school’s work in mathematics through the analysis of performance data, observations in lessons and scrutiny of pupils’ work, inspectors will consider:

- how well the school is identifying and tackling inconsistency in the quality of mathematics teaching between different groups of pupils, key stages, sets and classes, including those taught by non-specialist teachers of mathematics in secondary schools.
- how well teaching, in the mathematics lessons observed, through discussions with pupils and scrutiny of their work and by reviewing curriculum plans:
- fosters mathematical understanding of new concepts and methods, including teachers’ explanations and the way they require pupils to think and reason mathematically for themselves
- ensures that pupils acquire mathematical knowledge appropriate to their age and starting points, and enables them to recall it rapidly and apply it fluently and accurately, including when calculating efficiently and in applying arithmetic algorithms.
- uses resources and approaches to enable pupils in the class to understand and master the mathematics they are learning. The national curriculum for mathematics24 specifies the aims and then states, ‘The expectation is that the majority of pupils will move through the programmes of study at the same pace.’
- develops depth of understanding and readiness for the next stage. The national curriculum states, ‘Decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concept rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on
- enables pupils to solve a variety of mathematical problems, applying the mathematical knowledge and skills they have been taught.

- how well pupils apply their mathematical knowledge and skills in other subjects in the curriculum, where appropriate.

I find it hard to disagree with any of the above. In fact, if I was writing a handbook for my maths department, it would draw heavily from this. Not because I want to please anyone but because it’s absolutely on the money for what a good department should be doing.

]]>Centering on the **what** of early mathematical schooling, Helen talks about the emergency, reactive shortcuts that end up being used as a result of pupils not learning the basics by age 8.

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The question is, “What is better for the child’s mathematical development in the long run?”

What is it going to be best for (her) to learn and consolidate now so that (she) is best prepared to make the most progress in the remaining 5 years before she does GCSE Maths and so be prepared for the Maths she needs in life.For your own performance management, your own schools’ data and in turn to get a good/outstanding Ofsted, it would be to intensely teach tricks on a one-to-one basis or in a small intervention group – go through loads of past papers and explicitly ‘teach’ her how to get enough marks for a 4b. (Probably avoiding fractions, ratio and algebra questions that require a sound understanding of times tables), This is what most of good/outstanding Y6 teachers do!

What you should really do, is prepare the children for secondary school by making sure they have mastered these basic skills:

1. Can they instantly recall the 221 addition facts to 20 without counting on fingers and recall related subtraction facts?

2. Do they instantly recall and understand times tables and related division facts?

3. Can they quickly and reliably perform written methods of the 4 operations with understanding?

In terms of the new curriculum, they should have come into Y5 (let alone Y6) being able to perform all 3 in order to ‘do well in National Curriculum Tests’.

When as Y6 teachers, on management’s demand, we push struggling Y6 children through to a 4b, we are saying to the rest of the teachers in the school is, “No problem – you have fun in maths, forget about the progress of the basic skills for those who are struggling and we will make sure all children in this school make the ‘progress’ In Y6!”No problem – you have fun in maths, forget about the progress of the basic skills for those who are struggling

The struggling children get a 4b but aren’t really a Level 4 at all. So in Y7, teachers are asking, “How on earth did this child get a Level 4?”. The answer is the same as when employers ask, “How did this 16 year old get C in maths at GCSE?”. When we get annoyed by this question, we should ask ourselves, “Would she get a Level 4b or get a C at GCSE if we left them over the summer, and they did the exam in September?”

The long term answer is to make sure that children have mastered the basic skills by the time they leave Y4. If they are not mastering these skills – you should be asking, “Why not?” so you are not worrying about a child ‘getting a Level 4b’ with only 22 days to go before the Year 6 Paper A.

For future children in the school, don’t be inadvertently saying to the rest of the staff, “Leave progress to me!” Put some of your energy into helping the Head/Maths Co-ordinator make sure there are systems in place for children to master the basic skills before they get to Y6. It will be hard to begin and take years to feel the difference with but will pay off in the end – and you will never be in this position again – it’s horrible.

It’s not good for your health!

It’s not fair on the child.

The only positive for a child struggling at Maths going through intervention to get a Level 4, is that they don’t feel like a Level 3 failure. The negatives are that there has been a total waste of time in maths during their last 6 months at primary school and they will struggle at secondary school as they still don’t have the basic skills.

I have 30 Y5/6 children – 18 Year 6s. I did have this problem – but don’t anymore – except when children come to us from other schools. At the moment I am happily teaching fractions, percentages, decimals ratios and algebra to Y5/6 and they love it (only because they have already mastered the basic skills).This is because there is a now firm focus on basic skills in Y3 and Y4 – especially for those children who are beginning to struggle – not just for those who quickly grasp it.

Helen

*********************************

So the key messages are:

- Aim for mastery of the basics by the end of year 4.
- Support the person in charge of maths to make this happen.
- Year 5 and 6 take care of themselves when pupils have a secure mathematical grounding.

If you teach maths or numeracy in years 1 to 4 or you’re a primary headteacher who recognises this problem in your school then a good next step is to get in touch with your local Maths Hub as they have been spending a lot of time on teaching for mastery of maths. If there isn’t a Hub near you then start by reading these three articles:

Charlie Stripp, NCETM

Jo Morgan, Resourceaholic

Paul Broadbent, Broadbent Maths

I had the opportunity to listen to Jane Jones HMI speak at the Maths Hubs Primary Conference today and did my best to capture what Jane was saying. You’ll see from the notes below, how positive Ofsted are about a mastery approach to maths.

**It’s important to mention that Jane has reviewed and okayed these notes.**

********************* NOTES BEGIN **************************

You might not expect to see ‘synergy’, ‘Ofsted’ and ‘mastery’ in the same sentence but that is how we see it.

Ofsted believe there needs to be a marriage of knowing the basic facts with deeper understanding (not pursuing either in the absence of the other.)

Under the previous curriculum, pupils have tended to very quickly be put on to a particular track. If they are ‘rapid graspers’ (rather than ‘high attainers’) they go a higher/faster track but if they’re not, they go on to a lower/slower track. In both cases that’s where they stay.

Instead Ofsted are of the belief that *all* pupils should achieve including and especially pupils from disadvantaged backgrounds. A mastery of maths approach is a vehicle for catching pupils up and keeping them caught up.

**On inspections**

When watching a mastery lesson, and Jane’s inspectors know this, whole class teaching could look slower than usual. What’s important is that learning is deeper.

“Deepening understanding” is in the Ofsted handbook, not “accelerating teaching”.

On the matter of the Ofsted handbook, paragraph 55 is a good place to look as it is on inspecting maths.

Things inspectors are looking forward to considering how well:

- Pupils are thinking and reasoning.
- Pupils are applying skills fluently and efficiently, arriving at accurate answers.
- Pupils are using resources to aid their understanding.

There is nothing in the Ofsted handbook that conflicts with the principles of mastery of maths.

If Jane was a primary headteacher and she knew Ofsted were coming in she would prepare a single side document (or shorter) for the inspectors that said:- What the school is trying to do to take maths forward from where they were/are to a mastery of maths approach.
- What an inspector might typically see in the lessons.
- What you are doing to address interventions quickly so that pupils can keep up and what you are doing to stretch the rapid graspers.
- How far you have got in developing systems to help you track attainment and progress in maths – focusing on the most important things ready for the next stage/year/term.

Jane concluded her talk with a call for everyone in the room to “Go for it! Do the right thing for your pupils!”

********************* NOTES END **************************

It seems Ofsted are taking great strides to ensure there is internal consistency amongst the inspectors, who are currently having to reapply to keep their jobs in September. As part of the re-recruitment process, inspectors must receive training on the mastery approach and certainly one HMI who I met this week was telling me, with convincing conviction, about what he was hoping to see in maths lessons with regards to ‘section 55’.

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