The Joy of Planning

I had great fun planning a lesson on tessellation last week. Planning lessons is one of my favourite parts of the job.

This lesson certainly won't be everyone's cup of tea, but I enjoyed planning it so much I wanted to share it here. Tessellation is no longer on the GCSE specification but I think it helps students develop their knowledge of angles in polygons, plus it's interesting, so is worth looking at.

I started with a quick Don Steward question aimed at refreshing my students' memories on how to calculate angles in polygons, which I'd taught them the day before.

I then asked the class, "What is tessellation and where do we see it?". One or two students described it in terms of tiling, and some pointed out examples of tessellation around the room (the painted bricks on the wall, the square vinyl tiles on the floor). I gave them a definition, which they noted down, and we talked about the meaning of the word plane in this context.

I told them about the etymology of the word tessellated. In planning this lesson I was interested to find that the word derives from the word 'four', referring to four corners.

tessellated (adj.)
1690s, from Late Latin tessellatus "made of small square stones or tiles," past participle of tesselare, from tessella "small square stone or tile," diminutive of tessera "a cube or square of stone or wood," perhaps from Greek tessera, neuter of tesseres, Ionic variant of tessares "four", in reference to four corners.

I showed them some pictures of tessellations.

I spoke of The Alhambra. A student put up his hand and told me he'd been there. I told him I was very jealous - I long to visit.

I also talked about Escher. Having recently been to the Escher exhibition at Dulwich Picture Gallery I could have happily talked about Escher for the full hour, but alas - time is limited. My Year 10s were amused when I told them that in the 60s Escher's work was loved by both hippies and mathematicians. A student put up his hand and said he had a book full of Escher's artwork at home. This made me happy.

I showed some examples and non-examples of tessellation (when planning lessons I often do a quick trawl of google images for the pictures I need to illustrate a point).

They noticed that the angles around the point have to sum to 360^o if the polygons are to tessellate. 

I showed an example of a semi-regular tessellation, which can be created by using two or more regular polygons repeatedly to tile the plane (for example an octagon and a square).

I then showed them a series of animations from a Tumblr account called Skunk Bear. They were 'wowed' by these animations (one boy asked, "where do you get all this cool stuff, Miss?". "Mostly through Twitter" I replied.). I think these gifs will help my students remember what tessellation is. If not, the animations certainly help foster an enthusiasm for the beauty and complexity of mathematics.

Tessallating equilateral triangles

Non-tessellating pentagons

When I told them about the recent discovery of a new type of tessellating pentagon ("It's a really big deal", I said) - they laughed. "Miss, are there really people who spend their life looking for tessellating pentagons? Shouldn't they be trying to find the cure for cancer or something?".

Tessellating pentagons - as discovered in 2015

All of this chat about tessellation took a good 25 minutes. It was a bit longer than I normally talk, but that's ok. They listened intently, and their reactions suggested that they were interested. I could have gone on for longer - Mathigon has some great stuff on tessellation - but I was keen to get them working on some angle problems. So I set them a Don Steward exercise.

During this exercise some students asked about the names of a 20-sided and 15-sided polygon, and thankfully I had a list to hand (borrowed from a Don Steward slide) and we chatted about the words. I overheard some students trying to break the words down and make sense of them.

Some of my students completed the tessellation activity really quickly - others took a lot longer. I followed it up with two Don Steward activities (Regular Polygon Angle Compilation and Pentagon Angle Compilation) which were pretty challenging. These activities developed their fluency in calculating angles in polygons. Towards the end of the lesson I invited a couple of students to come up to the board and talk through their approaches to these problems.

In the final minute of the lesson I decided to bring everyone back together to tell them about platonic solids. One student kept referring to a dodecagon as a dodecahedron during the lesson so I wanted to pick up on the difference between ~gon and ~hedron. So I ended up with an unplanned tangential plenary...

This lesson may have been relatively light in 'exam content' but it was rich in mathematics. It might not have ticked all the 'good lesson' boxes, but I felt that it went well.

I don't write formal lesson plans. I create minimalist PowerPoints instead. I make no apologies for using slides - this is not 'death by PowerPoint' - it's just a bit of structure. Here's my slides for this lesson, feel free to borrow any bits that you like.

Do I sometimes spend too long planning lessons? Absolutely! Are my lessons the 'best possible way of teaching that topic'? Absolutely not. I have not perfected the art of teaching mathematics. This tessellation lesson is very 'me', and I doubt anyone would want to teach it in the same way I did.

I enjoy lesson planning. It allows me to explore my subject. It allows me to be creative. I wholly agree with Megan Guinan's recent tweet, "Planning lessons is my second favourite part of the job, after delivering a lesson I've planned well."

I'd love to hear all about a lesson you've taught recently that you particularly enjoyed planning and delivering.

Handwriting

At the age of 16 my older brother started writing in the style of the wording used on the cover of Siamese Dream by Smashing Pumpkins. I believe the font is Agatha.

He did it very well, with meticulous attention to detail, though it must have slowed him down considerably in his A level exams. He is now a 37 year old solicitor and I can still see the Smashing Pumpkins' influence in his handwriting.

In typical younger sister style, I attempted to copy his cool handwriting. I wasn't as dedicated as he was, but I did begin to put a hook on the top of the letter a. I hooked the letter a throughout my A levels, university and my career prior to teaching.

During my NQT year this hooked a started causing me problems. My handwriting on the board is messy, and my students were often confused when I wrote the letter a in algebra. They couldn't tell if it was a letter or a number. It looked like an ugly 2. Over the course of my NQT year I made a conscious effort to stop hooking the letter a, and as a result my students no longer asked me to interpret my handwriting. Well, until last week...

The crossed Z
I was going through a Normal Distribution example on the board when a Year 13 raised his hand.

'Miss, what does that symbol represent?'

I was flummoxed for a second. This class were studying S2 - they'd learnt the Standard Normal Distribution in Year 12, so the notation should be familiar. I looked at what I'd written on the board:

'What symbol? The Z?'
'Oh, is that a Z?'
'Yes, it's a Z.'
'Why does it have a line through it?'
'That's what Z looks like. Or perhaps it's just how I write it. I suppose it's so it doesn't get confused with a 2. Does anyone else here cross their Zs?'
All 11 students shake their heads.
'Oh. I thought everyone did. I'm not sure when I started doing it. But I always cross my Zs.'

I wrote the word lazy on the board to demonstrate my crossed z. They looked at me like I was crazy. Self doubt crept in.

I did a Twitter poll and thankfully it confirmed that the way I write the letter Z is totally normal (pardon the pun) amongst maths folk:

Most tweeters confirmed that they cross their Zs to avoid confusion with 2s, in the same way crossing 7s avoids confusion with 1s.

I had a fascinating tweet from air traffic controller @jlaa who has to make sure he doesn't cross his 7s because a crossed 7 has a very specific meaning. The picture below shows flight details written on strips - both show that the aircraft has been told to descend from 7000ft to 5000ft. In the bottom picture it is safe to issue 7000ft to another flight but in the top picture it isn't. He has to be very careful not to automatically cross his 7s.

Does handwriting matter?
I teach a Year 13 Further Maths class and most of them are going to study maths or engineering at university. I talked to them about mathematical handwriting for the first time last week. They were interested, and it led to discussions about notation such as the use of dots for multiplication and commas for decimal points. I felt like it was a discussion worth having.

When letters are unclear in words we can normally interpret the meaning by considering the context or looking at the other letters. But when letters and numbers are unclear in mathematics we might not have any clues. This can be a problem for exam markers, particularly if they are marking individual questions so can't refer to the rest of the paper for clarity. My colleague told me she has a Year 10 student who writes the numerals 9 and 4 in exactly the same way. He may well end up losing marks in his GCSE because of this.

Here's some pictures from my Year 13 students' mock C3 exams. The first student has trouble with his ones. He hooks the top and draws a line at the bottom so they sometimes look like twos. In this picture it's clear, but only because there are twos there for comparison.

Here's the same question answered by another of my Year 13s. This boy's brackets drive me crazy. Since September I've been complaining that his brackets are too much like modulus signs. He is clearly trying to fix this because the slight curve on the right bracket is an improvement on what I've seen previously.

Later in the paper his brackets become even straighter.

I will continue to berate him for this in the hope that he will shake the habit. 

Good practice
I think that guidance on mathematical handwriting should be delivered in Year 7. The importance of clear handwriting - and tips such as the crossing of the 7 and the Z - should be made explicit. This post Tips for mathematical handwriting is a good starting point (though teachers from outside the US won't be happy with the letter x here!).

Christian Perfect picked up on this international x discrepancy a few years ago - his article Let's talk about X is worth a read.

I have a student who does 'joined up' xs (ie he doesn't take his pen off the paper) - see picture below. They look like ns. Making x look like n is pretty unusual. Do your students have any unusual handwriting habits?

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Further Reading

• Old Pappus' Book of Mathematical Calligraphy
• A Guide to Writing Mathematics 
• Ten Simple Rules for Mathematical Writing (via Colleen Young's post Mathematical Handwriting)

New GCSE: Pythagoras Questions

This week my department took a detailed look at GCSE sample questions for topics that are coming up on our Year 10 Scheme of Work. This was the most useful thing we've ever done in a department meeting! We used Mel's (@Just_Maths) excellent Questions by Topic resources.

I worked through the Higher Pythagoras questions. Have you looked at these in detail? It's well worth doing. The questions are excellent. They will be challenging for even our highest attainers. I usually use a nice set Pythagoras problems when I teach Pythagoras at GCSE but I think I'm going to have to up my game.

Let's take a look at some of the new GCSE questions.

Here's a three mark question from OCR. Have a go. I think my students would find this pretty challenging. They need to know Pythagoras and how to work with surds 'backwards' (I don't do enough of this when I teach surds...).

Here's another question - this is a four marker from AQA. It's a great question... Again, a different level of challenge to what we're used to at GCSE level.

This question is from Edexcel - here we have bounds and Pythagoras:

And this question is from OCR. It's not quite as challenging as the others though there are a lot of steps.

Finally, here's another question from AQA. I particularly like this one.

All of these examples show that new GCSE questions will often combine two or more topics. Rightly so. Previous GCSE questions often treated topics in isolation.

When you're planning your Year 10 Pythagoras lessons I recommend that you try the rest of the sample questions. Even the 3D Pythagoras question has a spin on it. There's some really great problems here. These questions also remind us of the notable step up in challenge level that we're dealing with. I'm trying not to panic! We have our work cut out.

Seeking Generality with Don Steward

I'm very excited to announce that the legendary Don Steward will be presenting a workshop at my school on 19th March. And you're all invited!

Don's session, which is being held on a Saturday morning, will be on 'Seeking Generality'. Here's the description:

The second aim of the national curriculum is that students can reason mathematically.

What does it mean for your students to be able to follow a line of enquiry?

The intention of the session is to explore ways to engage students in conjecturing relationships, expressing a detected general rule and developing a notion of proof.

Examples will be offered from across standard curriculum topics and some tasks will illustrate how a range of new GCSE specimen exam questions contain seeds for growing generalities.

This workshop is free to attend. I'm very grateful to my headteacher for funding this event.

Afterwards we'll go for a pub lunch which you are very welcome to join us for.

In only one day 40 maths teachers have registered to attend! There's still places available so register now!

You'll find all the details here: mathsmeetglyn.weebly.com.

Hope to see you there.

Classroom Photos - #mathscpdchat

On Tuesday 26th January I will be hosting #mathscpdchat on behalf of the NCETM. During this chat I'll be calling on you to share photos of your classroom. Even better, take a wander around your department and take photos of absolutely anything interesting that you see - displays, student work, exercise books, resources, seating arrangements, equipment and so on. The idea is that we all get to have a peek into other maths departments.

Very cool... (source unknown)

I'm going to get things started by sharing some of my own photos in this post.

I have young children so I only work four days a week - this means I don't have a classroom to call my own. I never teach two lesson in a row in the same room - I'm always on the move, which means that at the start of my lessons I'm always frantically trying to login and sort out my equipment before my students arrive.

This is the classroom where I teach my Year 10 lessons - it's normally occupied by my colleague Jack:

I quite like teaching in here. It's not cramped - I can access all students fairly easily. Things to note include:

• the small whiteboard to the right of the IWB (far too small for long binomial expansions with Year 12!)
• the seating arrangement (in pairs - I like this)
• the lack of displays. 

I asked Jack about displays and he said he doesn't really see much value in them. He thinks they are too time consuming to create and have relatively little impact on learning. I'm inclined to agree - though I know that many of you would disagree (please share your views in #mathscpdchat!).

Displays of student work can be nice (though they often get tatty). I spotted these intriguing 'Piems' on the wall in another classroom - I believe they've been there since 2012, when blogger Paul Collins taught in this classroom.

Back to Jack's classroom... On his desk he has a trick calculator (a 'gagulator') which deserves a mention because I accidentally mistook it for a real calculator last week and used in front of my students (oops). This is such a good secret santa present for a maths teacher!

Jack has an expectations poster at the front of his classroom to help with behaviour management...

... although he admits that he never refers to it anymore. This is often the problem with posters and displays - after the initial impact, students stop noticing them.

Although many of our classrooms lack displays, we do have some displays around the department - for example the now classic Mr Men display by Ed Southall, which I sometimes see students looking at...

... and the popular growth mindset display that originated from Sarah Hagan.

Every maths classroom at my school has a literacy display including 'Greek Letter of the Month'. I love this idea but it certainly doesn't change once a month - delta has been in place for well over a year now! :)

This is where I teach my Year 11s:

It's a bit dismal, but put a passionate teacher and 30 enthusiastic students in there and I don't think it really matters what the classroom looks like.

This is my colleague Lizzie's lovely classroom, which is much more cheerful:

My worst experience this year was when I had to teach a Year 12 lesson in an English classroom which didn't have a proper whiteboard. It only had an interactive whiteboard, and the pens weren't working. Disaster. Maths teachers, probably more so than teachers in other subjects, need something to write on when they're teaching. So whiteboard size and accessibility are important.  At my previous school every maths classroom had two very large whiteboards on runners. They could be pulled apart to reveal an IWB behind them. That was fantastic.

In general, the classrooms at my school are not spectacular, but the maths teaching is very good and my colleagues are awesome people.

Now let's have a quick look at some other classroom photos and ideas.

Displays
I always enjoy reading Sarah Hagan's annual post where she shares her new displays. Her enthusiasm for teaching maths is very clear.

I'd quite like a large calculator poster by my whiteboard like Sarah has - I think it would be a useful teaching aid.

Sarah continues to share excellent displays and resources so if you're looking for inspiration and ideas, do follow her blog.

Desks
In Gems 39 I wrote about John Corbett's (@Corbettmaths) idea to put photo frames and baskets of equipment on desks. The contents of the frames can be changed regularly to display key dates, star students, reminders and so on.

Literacy
I like these sentence stems from @ExplainingMaths - I can see these being useful during class discussion.

Whiteboard walls
I long to have whiteboards on every wall of the classroom. Unfortunately this is not possible in most classrooms due to the locations of desks, windows, filing cabinets etc. If you want to know more about the use of vertical whiteboards, this post is a good place to start.

Inspirational quotes
At my previous school I briefly had my own classroom and I had just two displays:

1. My Year 10s created a circle theorems display during a lesson. I loved it but it was hard to ensure that students didn't look at it during assessments!

2. I also had a few quotes above the whiteboard - I was inspired by this tweet from @surreallyno.

There are hundreds of display ideas and posters for maths classrooms online. I'd love to hear what you use and why.

Hogwarts poster by Meg Craig via this post

Spotted on @sxpmaths' classroom wall - quote from Matt Parker

Please share your photos on Twitter at 7pm on Tuesday 26th January, using the hashtag #mathscpdchat (seriously, this chat will not work unless people take photos...!). Remember, I'm not just interested in displays. Equipment, books, resources - I'd love to see it all!

Classroom design from Andy Heffernan

Five things you might not know about the new GCSE content #2

I recently wrote a post about five changes to the content of maths GCSE. In today's post I list five more changes that may not be widely known.

1. Invariance

When teaching shape transformations to Higher Tier students, you'll now need to ensure that students are be able to identify invariant points. This is described in the specification as follows: "Describe the changes and invariance achieved by combinations of rotations, reflections and translations".

We are given this example question from AQA:

"Write down the coordinates of a point that is invariant when it is reflected in the line y = x".

Here, students will need to know that the points (1,1), (2,2) etc lie on the line y = x and would therefore be unchanged if reflected in this line.

There's a set of resources for this topic in the Mind the Gap Maths Toolbox and Peter Mattock has shared a resource 'Invariance activity sheet'.

2. Geometric Sequences
When I saw that geometric sequences now appear on the GCSE specification I assumed I'd be making use of my AS level (C2) resources. This is not the case.

In C2 we find the nth term of a geometric sequence using the formula U_n = ar^n-1.  This gives us a 'position-to-term' rule. For example if we have the sequence

3,  6,  12,  24,  48, ... 

then we have a = 3 (the first term) and r = 2 (the common ratio), so the nth term is U_n = 3(2^n-1).

Although geometric sequences do come up at GCSE, there's two points from the specification that are worth noting when teaching this content:

1. Geometric sequences will be in the form rⁿ , for example:

2,  4,  8,  16,  ...  

3,  9,  27,  81, ...

√5,  5,  5√5,  25,  ...  (Higher Tier only)

2. Students are not required to find expressions for the nth term of these sequences. They only have to do that for linear and quadratic sequences.

Examples of new GCSE questions include:

The nth term of a sequence is (√3)ⁿ. What is the 5^th term of this sequence?

and...

U_n = 2U_n-1     U₁ = 2     Write down the first four terms of this sequence.

In both examples students are using an nth term formula but not deriving the formula themselves. So when you teach this topic I suggest that you focus on:

• recognising geometric sequences
• finding a common ratio and using this to continue a sequence
• substituting into both position-to-term and term-to-term rules (including those using subscript notation). 

If you've spotted this question in OCR's Practice Paper 5 you may think that it contradicts what I've written here about geometric sequences:

Here is a sequence.

2,  2√7,  14,  14√7,  ... 

a) Work out the next term   (1)

b) Find the nth term   (3)

c) Find the value of the 21st term divided by the 17th term.   (2)

I asked OCR for clarification and they sent a helpful reply:

"...the Assessment Objectives around making deductions, inferences and problem solving mean that some questions may involve taking known elements of content and taking them that bit further, as seen in the question. Given that students at Higher tier have to know how to find the formula for the nth term of a quadratic sequence and also to 'recognise and use sequences of... geometric progressions (r^n where n is a... surd) and other sequences', the question is an example of how higher ability students might be expected to make a deduction from known content. I don't expect this to be a question we'd regularly examine in live assessment, but is the sort of thing we'd want to include in sample assessment to give an indication of how the content and Assessment Objectives are brought together in writing questions."

3. Scatter Graphs

There's a bit more to scatter graphs now, though some teachers may have already been covering these things. Students will need to know:

• that correlation does not necessarily indicate causation
• the difference between interpolation and extrapolation, and the dangers of extrapolation.

Although I will use the words interpolate and extrapolate in class, I doubt these words will be used in exams. Questions are likely to be in the form of this example from Edexcel:

You should not use a line of best fit to predict the number of units of electricity used for heating when the outside temperature is 30°C. Give one reason why. 

Students may also have to identify an outlier from a scatter graph (note that this is informal identification of outliers - ie by eye) and decide whether to ignore it when drawing a line of best fit.

The Scatter Graphs: True or False activity from MathsPad covers all of this content and is absolutely excellent.

Don't forget that some statistics content has been removed from the new GCSE, such as questionnaires and stratified sampling. It's worth looking at these exam questions and this OCR Check-In Test to get an idea of the new sampling content.

4. SUVAT

The early versions of the DfE’s new GCSE maths specification contained content relating to the 'suvat equations', but this content was removed from the final published draft. However the formulae were retained in the appendix (in the section entitled 'Formulae that candidates should be able to use, but need not memorise. These can be given in the exam, either in the relevant question, or in a list from which candidates select and apply as appropriate').

This means that the exam board might include these formulae in a question, but this will be no different to how a student would be expected to work with any formula or equation provided (for example, students may have to substitute into or rearrange a suvat formula).

In short: you don't need to teach this topic at GCSE in the way you would teach it in M1 at A level, but you might find it useful to use these formulae in your teaching of algebra - for example using this great resource from Christine Norledge.

5. Don't follow the textbooks... yet!
I've said before that if you plan to invest in textbooks for the new GCSE then it's best to wait for the second editions. I've already found a few inconsistencies between the specifications and first edition textbooks. For example a helpful conversation with @STABMaths confirmed that an Edexcel textbook contains graph stretches, as does a sample paper, but these won't be examined (as stated in my previous post).

Also, in my post about real life graphs, I said that I was surprised to see sketching cubics in my new GCSE textbook - including identifying roots from factorised expressions.

Cubic graphs from Edexcel GCSE (9 - 1) Mathematics: Higher Student Book 

This is what the specification says about cubic graphs:

recognise, sketch and interpret graphs of ... simple cubic functions ...

This is on both the Foundation and Higher Tier. The AQA Teaching Guidance provides further details, stating that students should be able to:

draw, sketch, recognise and interpret graphs of the form y = x³ + k where k is an integer

There's certainly no mention of the type of cubic graphs that feature in my textbook, and I think this is one of the things that will probably be removed from subsequent editions.

A few more clarifications
I asked OCR what they are frequently asked about the new GCSE. In addition to questions regarding grading and teaching time, they are often asked to clarify the following:

• whether students will be expected to differentiate to find the gradient of a curve (no, they will have to estimate gradient from a tangent at a point, or potentially a chord between two suitable points) - see my blog post about this. 
• whether Foundation Tier students are required to calculate turning points of quadratic graphs (no, at Foundation they’ll just need to read from the graph. At Higher they will find turning points by completing the square).
• if Higher Tier students have to know about the equations for any circle (no, only those centred around the origin).

This is really helpful information from OCR.

So that's it - I hope you're now feeling more informed about the new GCSE content. Do let me know your thoughts and questions.

Worries

A Twitter conversation about recruitment this week got me worrying. I went to bed that night feeling the weight of the world on my shoulders.

Being a maths teacher is wonderful, and if you ever doubt that then read Ed Southall's post 10 reasons why it's a great time to be a maths teacher. But it is the best of times and the worst of times. Let me tell you some of the things that are on my mind...

1. Recruitment
Undoubtedly the biggest challenge we face is a dire shortage of maths teachers. I don't trust any data in education so let's take a quick look at the anecdotal evidence. Have you seen the huge number of maths teacher vacancies being advertised on TES this week? That number is set to increase dramatically over the coming weeks as schools desperately try to win the race to recruit trainee teachers.

My school is planning to significantly increase the number of maths lessons for our students at both Key Stage 3 and 4 from September. This, coupled with the ever increasing uptake of maths at Key Stage 5, means that my school will be looking to recruit at least two new maths teachers over the coming year. Other schools are in the same position. This continued increasing demand against a backdrop of diminishing supply is a very serious concern.

The competition for maths teachers is fierce. There aren't enough of us to go round. Across the country, a whole generation of students will suffer dreadfully. I wrote about this in Schools Week last December and the situation has only worsened since then. Teachers are being driven out of the profession by utterly unsustainable workloads and we are simply unable to replace them.

What will happen if we can't fill our vacancies? Initially we will see an increase in class sizes. As most classrooms don't have the desk space for more than 34 students, this will have the greatest impact on low attainers whose classes may well double in size. Eventually we will start to see an absence of teachers in the classroom, with online delivery of content perhaps being the only option. This is hardly conducive to a good education. I strongly suspect that we will lose the 'global race' that the Government cares so much about.

One final thought regarding recruitment. School budgets are ridiculously tight - the financial situation horrifies me. Every spare penny should be spent on our students, not on extortionate fees for job adverts. Schools are spending serious amounts of money advertising for maths teachers for weeks on end. Precious education budget is sitting in the pockets of the TES. How very frustrating.

2. Curriculum Changes
Changes to the maths curriculum are coming thick and fast and it's down to teachers to try to make sense of huge amounts of information and mixed messages.

The new GCSE is going to be very challenging for the vast majority of students. Our current Year 10s are guinea pigs. At Year 10 Parents Evening this week I had to admit to parents that I wasn't entirely sure about gradings - my predictions are based on vague hunches rather than experience. Maths teachers are in the dark. And we're competing against each other for the top grades.

I'm doing all I possibly can to make sure I know the new specification, but it's much harder than it should be. The workload is huge. The process of implementing this new qualification has not run smoothly and we can only hope that the implementation of the new A level qualifications is a better experience for both teachers and students.

Another thing that worries me is the new Foundation GCSE. It contains topics that are in no way appropriate or necessary for Foundation students. Even more worrying though is that fact that so many more students will now sit Foundation papers when previously they would have been entered for the Higher Tier. I hate the low expectations associated with saying 'it is impossible for you to achieve higher than a Grade 5'. And at the same time many of the students who find maths difficult are in classes with badly behaved peers who hold them back even further. It breaks my heart.

Finally, the thinking behind the new Key Stage 2 resits is flawed in many ways. Mel sums up her concerns brilliantly in her post Year 7 resits ... genius idea. This is another poorly thought out policy that may end up being detrimental to both students and teachers. Yet another thing to worry about.

Solutions?
There's a simple long-term solution to many of these problems. Reduce contact time. If teachers spent less time in front of students then they would have the opportunity to plan effectively, mark well, collaborate with colleagues, implement new policies, enhance their subject knowledge and learn from best practice. The quality of maths education would improve and at the same time, recruitment and retention problems would diminish. The current workload is killing us. But how can the Government fix this? Reducing contact time across the board would require vast amounts of money and vast numbers of new teachers. Either that or less children... It's an impossible situation. This is what keeps me up at night. This is why I worry.

I must end this post on a positive note. I am a worrier, but I am also an optimist. I love being a maths teacher. I'm doing something really important. Fellow maths teachers, when faced with challenging times, do not turn your back on the profession - generations of children need you! Maths needs you! I need you! This is important, let's not give up. But let's support each other when things get tough and do everything we possibly can, in our own schools and our own classrooms, to make the very best of what we've got.

Mr Barton's Podcast

This is just a quick post to mention that Craig Barton interviewed me yesterday and, if you're interested, you can listen to the podcast below or via Craig's post. It's an hour and a half (chatterbox, me?!) and I talk about a range of topics including the new GCSE, Twitter, and my approach to teaching. Do have a listen if you get a chance. Let me know what you think. Also, can you spot the mathematical error? (it was a slip of the tongue, promise!).