Feedback should improve the student, not the work

This week I've been thinking about marking, feedback, and corrections. Marking books is one of my least favourite teacher tasks, and it's probably the one that takes up the most of my free time. I also believe it has the least impact on my students' learning, but only because the way I do it is pretty rubbish. And spending hours and hours of your free time doing something that you know is rubbish, makes you feel like rubbish. I decided it was time for a change.

Let me first explain the marking policy in my department, which I think is a pretty good one. Our students in years 7 to 10 have two books: a normal exercise book and an assessment book. They use the exercise book every lesson for writing notes, copying examples, answering questions, and doing homework. We teachers never mark this book, but students are expected to self-mark and correct when we go through answers in class. The assessment books are kept in the cupboard until the end of each chapter (roughly every 2-3 weeks) when students complete a semi-formal (silence, closed-book) assessment in them. We then collect these books in and mark them formatively and provide detailed feedback. The next lesson (ideally) we give these books out and the students have DIRT time where they respond to the feedback and do corrections and maybe follow-up questions. These are the books that we will show to the Ofsted inspectors when they come, and we make sure to impress upon our students the importance of upholding high standards of presentation in these.

This policy means that I only have to spend around three hours per week marking, which from what I've heard is pretty low compared to other schools, and is certainly low compared to teachers from other faculties within my school. I shouldn't look a gift horse in the mouth, and I should just get on with it and not complain. However, my questioner personality means I find it hard to follow policies, even ones that I was a part of creating.

Last weekend I was planning my lessons for the week ahead and I thought about the fact that my year 10s would be doing an assessment on the Tuesday. I knew they would generally struggle with the assessment because the questions were hard (it's a higher tier test and my students have targets of grade 5) and I knew exactly which questions they would be able to do and which they wouldn't, and why that is. That's when I started to question: what actually is the purpose of this assessment? And what will be the purpose of my feedback?

If you ask a load of teachers what the purpose of end-of-topic assessments is, you might get the following responses:

1. so teachers can see how much students understand
2. so teachers can see which bits they've taught well and which bits they haven't
3. to inform the teacher's planning of the next unit
4. so students know how much they understand
5. so students can practise exam-style questions in an exam-style situation

Some of these purposes are good, some of them are bad. Some of them are being fulfilled by my assessments and feedback and some of them aren't. I can immediately eliminate purposes one and two. I already know both of these things, through my use of assessment in lessons throughout the chapter. Purpose three is also irrelevant in my case, because the units are usually disparate and unrelated. Chapter 5 might link to chapter 11, but by the time that comes around I would have forgotten this information anyway. Purpose number four sounds decent, but the assessment I was going to give them doesn't fulfil this purpose, as students could get every question wrong but still have 80% understanding of the unit. They could finish the assessment feeling like a failure when they might be close to getting it. Purpose number five is the only-non problematic purpose on the list, in my opinion. I could also add to that a sixth purpose, one that doesn't often get mentioned, which is to make use of the benefits of the Testing Effect, where being forced to retrieve information improves a student's long-term memory of that information. 

Now that I've decided my purpose of the assessment is actually just to expose students to exam-style questions, what should be the purpose of my feedback?

Some common responses:

1. so students can see how much they understand
2. so students can see areas they need to improve in
3. to let the students know you care about them and build a relationship
4. so the parents can see that you care
5. so the school knows you are doing your job
6. so Ofsted know you are doing your job
7. so students can correct their work

Purpose number one we have already touched on when I said that students can't always gauge their own level of understanding. I could address this in my feedback, by RAGing each sub-topic for them, but what will students do with this information? If Ali is an amber in finding the surface area of a prism, how does knowing he's amber help him? Perhaps in year 11 this would be helpful, as he can add it to his revision timetable. This is also the problem with purpose number two. Yes maybe they need to improve their understanding of surface area, but when will they have the opportunity to do this, and how? I don't think setting them a video to watch at home is really sufficient here. They didn't understand it when you, an expert teacher, explained it first time round and gave examples and independent practice. They're not going to suddenly get it (and crucially, embed it in their long-term memory) when Mr Corbett or the Maths Watch lady explain it to them. Purpose number three is debatable. Surely there are other ways to show you care? Surely planning well-thought out and effective lessons shows students you care about their learning? Surely talking to the students in person is the best way to build a relationship? But I do kind of get it. Students definitely do like it when you write stuff on their work, and I know that I liked it when I was a student. It's almost like when someone "like"s or comments on your social media post. You ticking their work probably gives them a similar feeling of validation that the little heart in Instagram gives them. So fine, I'll accept that one. And then purpose four, whether important or not, is easily fulfilled in the same way. Purposes five and six can piss right off. I spend enough hours in the evenings and on weekends planning high-quality lessons and honing my craft through engaging with books, blogs, podcasts and academic research. Let them try and tell me I'm not doing my job.

And then there's purpose seven: so students can correct their work. This is what my written feedback has always been geared towards. I would circle bits that were wrong, correct little slips, give some scaffolding, write some hints (try factorising!) and then leave a nice highlighted box for them to do their correction in. The more I think about this, the sillier this seems. What is the point in a student correcting their maths work? If it's a small arithmetic mistake or little error (the equivalent of a typo), then correcting that mistake doesn't improve the student's understanding of the topic at all. If it's a conceptual error, then is a correction really appropriate, or would a do-over be better? And how can the student really do that without being re-taught that concept? Your cleverly written hints and scaffolding can allow them to produce the correct answer, but will that have a long-term impact on the child? Even if you have gone so far as to provide a follow-up question for everyone who got question seven wrong, won't it take more than just that to embed the concept that they failed to learn the first time round? And what if they've got five out of the ten questions wrong? Do you really want them to re-learn five concepts or skills in one DIRT session?

Marking students' books to allow them to do corrections individually takes absolutely ages. This careful hinting and scaffolding and follow-up questioning is extremely labour-intensive, especially when it's a challenging assessment. For this reason, many teachers opt to simply tick and cross the students' work, and then spend DIRT time guiding the students through every single question so the students can copy the correct answers down. This is much more efficient but seems kind of like cheating. It also makes you wonder what was the point of taking the books in at all? And if there's not much green pen in the book then how are we fulfilling purposes four and five of the second list?

After thinking about all of this I felt like there was absolutely no point giving this assessment and no point marking it. However, that just felt wrong and also I would get into trouble. So I tried to define for myself some new purposes that I could get on board with. And then I saw a Twitter comment that was linked from a thread that was linked from a thread that was linked from a thread about marking and feedback, and it was a lightbulb moment for me.

"Feedback should improve the student, not the work."

I think this is so powerful. Improving a piece of maths work has no long-term impact. It's kind of satisfying to do and it looks impressive to book-flickers, especially when you've done that thing where you go back and mark the corrections, so there are multiple layers of feedback and it becomes like a written dialogue. But this isn't improving the student. Going through the whole assessment as a class and copying down the correct answers probably has a small impact but it's probably not the best way of achieving the same effect. Going through one question at a time with extra practice in between, or even just re-teaching that sub-topic without referring to the assessment until afterwards may be better. 

However, I do want to do the assessment (because I have to, and because of purpose five from list one) and I do want to give written feedback (because I have to, and because of purposes three and four from list two) and ideally this feedback would do what @EduCaiti suggests and improve my students. But how? 

I did come up with something, but I don't think it's particularly great. I do think it's an improvement on what I'm doing before though. I decided that rather than focusing on improving the work that the students had done in the assessment, I would focus on improving something that would apply to other areas of maths, inside and outside assessments. I came up with the idea of having a specific "feedback focus" - one thing that I would focus on when marking their work. I would give the students specific and actionable feedback about that focus and that focus only (although I would also tick and cross their answers). The feedback focus I chose for this unit was "organising working out in a way that facilitates problem solving". I shared this with my students just before they started the assessment. I took their books in, and I marked for accuracy, and then I wrote a comment at the end, on a stuck-in sheet stating the feedback focus. I wrote things like, "The way you laid out question 4 was really good because you worked out each face separately and wrote these on separate lines. It would have been even more clear though if you had labelled these, e.g. front, back, top etc. This would have helped in question 7, when the top of the shape wasn't required as it's an open box." or "You write out the formula you're using at the start of each question which is great, but if you include the start of the formula too you would have less confusion (e.g. writing circumference = π x d is more helpful than just writing down π x d because then you're less likely to get mixed up with the area)." This might seem like it would take longer than my old style of marking but trust me it was much much faster. When I gave the books back, we spent DIRT time looking at photos I had taken of work that demonstrated good practice related to the feedback focus, then reading the comments I had written, and writing an action step based on my feedback. We didn't bother doing corrections.

Next time my students do an assessment I can remind them to look at their action step from last time and make sure they put it into practice. I can then comment on the new feedback focus as well as whether they have carried out their previous action step or not.

It's not anything amazing but at least I feel better about it. I think that whenever we spend a lot of time doing something we should always make sure to ask ourselves what our purpose is, and consider whether we are actually fulfilling that purpose. And if you can't find a good enough purpose for something, that probably means you shouldn't do it.

Emma
x x x

Rules First, Exceptions Later

I know that we as modern, innovative maths teachers like to say that maths isn't about rules and that it's about relationships and reasoning and all that stuff. But there are some mathematical processes that students have to be able to carry out in a fairly standard way and for the sake of this discussion, we're going to call them rules.

Just so you know what I'm talking about it, here are a few examples of processes that involve rules:
-adding fractions
-finding the area of a sector
-finding the volume of a prism
-solving equations of the form 5(x+3)=7.

When we teach these processes, I think the most obvious way to do it is to start off with easy examples that students can work out without having to use a formal rule, and then extrapolate their reasoning to apply to more complex situations, which is used to develop the rule that is then eventually used. But it's occurred to me that this intuitive approach may actually be inefficient and even detrimental to long term ability to recall these processes.

Let's take adding fractions as our first example. I'm guessing you probably teach this in the same order I've always taught it in:
1) adding fractions that have the same denominators
2) adding fractions with similar denominators (like 5/8 +3/4)
3) adding fractions with denominators that share common factors (like 5/6 + 3/8)
4) adding fractions with denominators that are coprime (like 3/8 + 5/7)

The logic behind this sequencing is obvious: number 1) requires a one-step process, number 2) requires a two- or three-step process, and number 3) requires a three- or four-step process, so this suggests a kind of hierarchy. Number 4) involves applying a rule that you have to use when no other option is available, so it makes sense it goes last.

Students often intuitively understand the rule for number 1), so they can master it within seconds. They are then pretty accepting of the rule for number 2), as it's easy to see that writing 3/4 as 6/8 will allow you to apply the rule from number 1). This then logically leads to a rule for number 3). Number 4) is technically the same rule as number 3) because you are still finding a common multiple, but in practice your approach to these questions is slightly different.

In summary, the rules students need to learn are:
1) Since the denominators are the same, just add the numerators.
2) The denominators are kind of the same, so change one fraction so that it matches the other, and then apply rule 1).
3) The denominators are similar, so identify what the lowest common multiple (or any common multiple) of the two denominators is, and then change both fractions so that the denominators match, and then apply rule 1).
4) Spend a while trying to find a common multiple using your times tables facts, realise you can't think of one, multiply the two numbers together to create a common multiple, then change both fractions to make that denominator. Then apply rule 1).

This is quite a lot of rules to remember just for one process.

Now consider an alternative (still referring to the original four cases):
1) Since the denominators are the same, just add the numerators.
2) Multiply the numerator and denominator of each fraction by the opposite denominator to make the denominators the same. Then apply rule 1).
3) Multiply the numerator and denominator of each fraction by the opposite denominator to make the denominators the same. Then apply rule 1).
4) Multiply the numerator and denominator of each fraction by the opposite denominator to make the denominators the same. Then apply rule 1).

In this version, there's only two rules to remember. Doesn't that sound so much nicer? The standard rule that works for case 4) works for cases 2) and 3) too, so why not just use this rule for all three?

Now I know a lot of you are feeling very upset about the fact that I am endorsing the idea of students adding 3/4 and 5/8 by making an unnecessarily large denominator of 32. You may also point out that this way would involve a lot more simplifying at the end. But hear me out!

I'm suggesting that we treat fractions with dissimilar denominators as the rule and the fractions with similar denominators as the exceptions. We teach the students the rule, we make sure they're super-duper confident with this process, let them feel really successful in doing this, give them lots of drills in this so that they're well practised and then teach them the exceptions. Say to the class, "of course with question e) there is a slightly easier way to do it, can anyone spot it?" and then discuss this and identify a few more exceptions like this and then do some practice with these. Of course, it's not really an exception because the other rule will still work, but it's exceptional in that there is another method you could use.

Let me give you another example: finding the area of a sector. I've always started out by finding the area of a semicircle, because students know straight away that this involves halving the area of the whole circle. They'll also get how to do quarter circles straight away. Then I would throw in a 120 degree angle or a 60 degree angle, and with a bit of thought they'd be able to tell me that you need to divide the area by 3 or 6. And then I'll put up a 24 degree angle and watch them struggle. They might eventually do 360 divided by 24 to get 15 and then tell me we need to divide by 15. And then finally I'll go to a 37 degree angle and they wouldn't be able to do it. At that point I would tell them, well the fraction that's shaded is 37 out of 360, so we do blah blah blah.

Now consider an alternative: start off with the 37 degree angle. Ask the class what fraction of the circle is shaded. Eventually they'll get that it's 37 out of 360. Then simply show them the correct calculation. And that's it. No faff. If they come across a question with a 24 degree angle, they can still do the same calculation, there's absolutely no need to work out that you can divide the circle area by 15. And even if you have a semicircle, the same calculation will work, and it won't exactly take much longer that halving (especially if it's a calculator question). Feel free to teach semicircles and quarter circles and even third circles as exceptions afterwards, as a little bonus shortcut that students will grasp easily. But I don't really see how starting with that will help students understand the process of finding the area of the 37 degree sector.

Another example: finding the volume of a prism. Isn't it weird that we learn how to find the volume of a cuboid separately from finding the volume of a prism, despite a cuboid being a prism and the prism rule working perfectly well for a cuboid? Why not just teach how to find the volume of a prism, and throw in cuboids, triangular prisms, trapezoidal prisms and compound prisms altogether (assuming they are all fluent in finding the area of rectangles, triangles, trapezia and compound shapes)? I would love to add cylinders to that list too but I found out embarrassingly recently that a cylinder is not, as I always believed it to be, a prism. Who knew?

One final example: solving equations that look like 4(x+2) = 8. Now there are two obvious methods to solving this equation. You could divide both sides by 4 or you could expand the bracket first. Dividing by 4 is a nicer method in this case and gets you the answer faster. However, what about the equation 4(x+2)=7? In this case, it would be unwise to divide by 4 first, so you should really expand the bracket. But there are no examples where expanding the bracket first doesn't work, so why don't we just teach our students to always expand first? (I have a feeling a lot of you do teach them this actually!) There are a lot more numbers that don't divide nicely by 4 than numbers that do (although Hilbert might disagree...) so most of the time the dividing method won't work, but the expanding method always will. It's nice to show the dividing shortcut as a little aside, once the students are really secure in the process of solving other equations with brackets. But I believe fluency in the rule should take precedence over the ability to identify exceptions.

I hope I've managed to explain my point well enough in this post. It would have been much easier if I could scribble stuff onto a whiteboard at times! Maybe that's the push I need to finally start the NotJustSums YouTube channel...

Oh and I should mention that this post was inspired by things I heard in Craig Barton's podcast which is excellent. My favourite episodes have been his interviews with Dani Quinn and with Tom Francome, and I strongly recommend that you check them out.

Emma x x x

I Was Wrong

That's right, I'm still here!

It's been a long time since my last confession.

I've been wanting to get back into blog writing for a while now but for some reason no particular topic really seemed interesting enough to write about (and let's face it, I've set the bar pretty low with some of my previous topics - "is zero a factor of zero?", anyone?) However, this week I've been inspired to crack open the ol' blog and do something with my spare time that doesn't involve my Nintendo Switch.

The reason for this sudden burst of inspiration? Reading Craig Barton's wonderful book, How I Wish I'd Taught Maths. If you've not heard of Mr Barton, you're missing out. He's a UK Maths teacher whose resources website has got me through many a Tuesday afternoon double lesson. His book is part memoir and part how-to guide, with lots of lovely academic references to back up his claims. I'd definitely recommend getting yourself a copy.

Mr Barton (why does it feel wrong to use his first name, like he's my teacher or something?) talks in his introductory chapters about how his opinion of what good maths teaching looks like has changed dramatically over recent years, and I've experienced something similar. When I was in my PGCE training year back in 2010/11, there was a belief held by many cutting edge maths teachers that maths lessons should be all about exploring, discovering, and open-ended problem solving. The suggestion that a traditional "chalk and talk" lesson which was teacher-led and full of repetitive exercises may be effective was met with haughty derision by us (wise beyond our years) trainees and may have even elicited an "OK boomer" type eye roll. We knew that the way forward was rich tasks from NRICH and a hands-on activity involving spaghetti and marshmallows. We quoted Piaget and Skemp as if they were old friends and bragged to our colleagues "oh I never use textbooks". I think we were rebelling against our own education, which might have involved those SMP booklet thingies or OHP slides covered in hundreds of near-identical quadratic equations. And the fact that we were really rather successful under that system was irrelevant; we knew that we could do better, and better must mean different. So clutching a copy of Jo Boaler's latest with our paper-cut (bloody Tarsias!) fingers, we marched into our classrooms determined to teach our students nothing and yet have them learn everything and when things didn't quite go the way we planned (although the marshmallow came unstuck from the ceiling eventually), we blamed the Primary school teaches for raising our students to have fixed mindsets and no independent learning skills. We pulled off Outstanding (capital O) lessons and wowed our observers whilst managing to cover remarkably little content. Those were the glory years, the halcyon days of group work and bits of string and "what do you notice?". But somewhere along the road I think we all started to realise that not only was this approach not anywhere near as much fun as we thought it would be, it also just didn't seem to work.

I'm in my ninth year of teaching now and my pedagogical beliefs have definitely changed. Here is a summary of how:

I used to think:
You couldn't tell students anything explicitly, you had to let them discover it for themselves, otherwise it wouldn't be meaningful.

Now I think:
Mathematical concepts don't become meaningful when you discover them, they become meaningful when you use them to solve a problem. Think about the circle theorems. Discovering the "angle at the centre is twice the angle at the circumference subtended by the same chord" rule by drawing a lot of random lines inside circles is very unlikely to happen without significant scaffolding (is it really discovering if you were given a guided tour?) and students may well discover something completely different (or "discover" something that's not even true!) along the way. And would they even know they've discovered it when they discover it? Would they even see its value? How about instead, we give students a circle with some angles in it and ask them to find the missing angle. They will try to apply the rules they already know, but will eventually get stuck. We can then say, "hmmm, you need a rule that's going to help you solve this easily. Luckily, I have just the thing!" and then the circle theorem saves the day and makes a difficult looking question dead easy. Much more meaningful, in my opinion.

I used to think:
You must show students the proof of rules or theorems before you let them use them. This includes basic rules like the laws of indices, up to more complex ones like differentiation.

Now I think:
Proofs should only ever be shown after students are fully comfortable with using and applying the rule or theorem. When I was shown proofs of Pythagoras' theorem as an adult, I thought they were amazing and interesting and beautiful, and I thought, why didn't my year 9 teacher show me this? So then I decided I would always show my students these proofs when introducing Pythagoras. It turns out, the only reason I found these proofs so fascinating is because I had already been using Pythagoras for eight years and was pretty intellectually invested in it. Why should students who have never heard of or used the theorem to solve any problems care about how the theorem is derived or why it works? I'm even starting to question my approach to teaching differentiation: I usually demonstrate graphically using a concrete first principles approach to find the derivatives of x² and x³. Along the way I generally lose the interest of 50% of my class, and the other 50% finish the lesson believing that differentiation is the most difficult topic EVER and they should drop A Level Maths before it's too late. Wouldn't it be better to teach them the quick little "lower the power" rule, get them used to it, and then show them where it all comes from? And then the sudden appearance of the 3x² out of nowhere may be met with a chorus of satisfied "ahhhhh"s rather than a sea of bewildered faces.

I used to think:
Slower methods are better than quick ones if it means that students understand how and why the method works.

Now I think:
The best method is whichever one has the lowest cognitive burden, as this frees up valuable thinking space for other aspects of the question at hand. Problem solving questions can sometimes involve five different mathematical processes to be carried out, wrapped in a "real life" situation that involves unpicking. The problem solving aspect of the question takes up a considerable amount of brain power, so being able to carry out the mathematical processes efficiently is really beneficial. I would say, however, that for students with certain SEND needs, sometimes the memorability of the method is more important than the cognitive burden, which means that slower methods can sometimes be favourable. But for students with a decent long term memory, the quickest method is usually the best.

I could probably list another ten beliefs that have changed, but I've written an awful lot today and I want to save some material for future posts. Stay tuned!

Have your beliefs about teaching changed since your training year? Let me know in the comments.

Emma x x x

How and Why I Decided to Become a Maths Teacher

If you've been reading my blog for a while and are a hardcore fan, you will know that one really annoying question that I get asked all the time is "Why are you just a maths teacher?" I've written two blog posts on the topic already (part one and part two) but what I've never written about is what made me decide to become a maths teacher. Someone asked me this question the other day and I realised I had to think quite carefully before I answered. I don't think I'd ever really thought about it until then. I wasn't completely happy with the answer I gave, so I made a mental note to think about it again properly when I wasn't in the middle of a chess match. 

I know that when I was 7 years old I wanted to be a teacher. I know this because it's written in my first holy communion booklet (yes, I'm a recovering Catholic). I remember that I used to play schools with my dolls and teddies. My dad has always worked in education, as a teacher and as a consultant. My mum also trained as a teacher, and has done some teaching. But the reason I wanted to be a teacher was probably because I really liked my teachers, and I loved school. It wasn't until year 4 that I met a teacher who I didn't like, for reasons that are obviously far too scandalous to disclose on this blog (OK, it was because she made me stay in at lunch once for talking even though I was just trying to explain to another pupil what they had to do. What a bitch.)

Anyway, I remember fairly clearly that in year 7 my ambition was to be an English teacher. English was my favourite subject, because all I remember doing in lessons was reading, writing stories, and performing. Those three things were and still are pretty much my favorite three things to do in the entire world.  I don't think, however, I'd actually thought much about what teaching really involves. 

I started hating English as soon as I moved into year 8. Although we still spent a lot of time reading (and we were reading Holes which is one of my all-time favourite books) and writing stories and performing, I didn't like my English teacher, and I found the lessons boring. I remember sneakily taking Holes home with me instead of handing it back in, and staying up all night reading the whole thing. I then had to spend the next 8 weeks of lessons totally bored whilst we read it as a class. You know a brilliant way of ruining an amazing book? Read one paragraph per lesson, and thoroughly analyse all of the linguistic devices as you go along. Urgh. 

I think that for the rest of key stage 3 and 4, the careers I had in mind were a bit more interesting. I read a book about stock brokers and decided I wanted to be one. I considered acting and dancing professionally. I considered being an author (actually I still am considering that) and I also really liked the idea of working for a magazine. But mostly, I just wasn't thinking about my career. I was too busy thinking about important teenager things like will my boobs ever grow and does that boy like me back? (Spoiler: the answer was no to both). 

The first time I remember considering studying maths at university was in year 10 when I first read the Curious Incident of the Dog in the Nighttime. If you haven't read it, you should. It was the first time I read about maths. I'd always enjoyed doing maths and I'd always enjoyed reading, but I'd never put the two together before. It was a revelation! It made me definitely want to pick maths and further maths A Levels. I chose French and Economics too, because I still wanted to be something to do with finance and trading. I was never really that bothered about being rich, but I liked the idea of working in such a challenging and stressful industry.  I also picked Psychology because, and I'm sorry if I'm insulting all psychologists around the world by saying this, I liked doing those personality test things in Cosmopolitan magazine. 

In year 12 I got really into maths. I started reading maths books for fun (not just for my UCAS personal statement). I was especially into codes, and I decided I wanted to be a cryptographer for the government. I loved all of my teachers for all of my A Levels, and being a Maths teacher was my back-up plan. I did briefly consider studying Psychology at university though. The main reason I didn't was because I thought that there were fewer people who were good at maths than were good at psychology, which made maths superior somehow. I know that's a load of rubbish. 

During my first year at university I wasn't thinking too much about what I would do after graduating. I think I had vague ideas about going into banking. In second year, we were offered the opportunity to do the Student Associate Scheme which is a three week paid teaching placement in a local secondary school. I wasn't intending to do it (too much effort) but then at the last minute I decided that if I did want to go into teaching, it would be really useful to me. I think that's what sealed the deal. I wasn't totally passionate about being a teacher, but it kind of felt right. Well, it felt safe and it felt comfortable. Also, this was around the time when there was a big problem with unemployment and the credit crunch and I knew that maths teachers were in short supply, so I'd basically be guaranteed a job. And applying for a PGCE was much easier than doing internships and work experience and appling for a job. So basically, I became a Maths teacher because it was the easy option. 

I applied for a place on a PGCE course, and was pretty happy with my decision. Once the course started, I really began to fall in love with teaching. Not the actual standing in front of a class bit, but the thinking that goes into planning lessons, and the psychology behind learning and understanding. The actual teaching lessons bit of it was my least favourite. It was really hard! But I loved talking about teaching and I loved talking about maths. By the time I finished my training year and got my first job, I was a fully-dedicated and very passionate maths teacher. And I was 100% confident that I had made the right decision.

I've been teaching for six years now. It's had its ups and downs. I've considered changing careers quite a few times. I'm generally happy, but I still can't help but feel I might be missing out on something. And I do still want to write a novel. And write non-fiction too. And part of me still believes my youtube channel will really take off one day. Part of me would like to work for the DfE. Part of me wants to work for Ofqual. Part of me would like to write textbooks and resources. Part of me wants to stay in school and be the head of sixth form. And a very small part of me wants to live in a cabin next to a lake filled with baby swans and play chess all day and not interact with humans.

I suppose the question of "what do I want to do when I grow up?" never leaves you. Or maybe we never stop growing up?  

Emma x x x 

Why We Should Get Rid of the Long Summer Holiday

I'm about to say something that all teachers are going to hate me for.

I think we should abolish the summer holiday.

It's my third proper day of the holiday, and I'll admit I'm enjoying myself a lot, with Pokémon Go and late night chess and sitting in IKEA writing blogs (free coffee on weekdays!) And of course there's also the fact that I don't have to be around children. But as much as I love my six weeks of freedom, I think British society in general would be better off without it.

Why do we have a long summer holiday anyway? It's not unique to the UK, in fact all countries seem to have at least 6 weeks off school in the summer, and some have much longer. For example, in the US they have a glorious 3 month holiday every year! This is because, back in the day, farm children would have to help out with the harvest during those months so they would miss school, and state schools in America were almost entirely populated by farm children, so they influenced a lot of the developments of the free education system there. In Japan, where they only have 6 weeks off like us, the farm children that made up the state schools did not have to stay home to help with the harvest, because rice, the main crop of Japan, does not have an intense harvest period like corn, the main crop of the US, and is instead harvested more regularly throughout the year. In the UK, our summer holiday is shorter because our farm children didn't have much influence on the development of our school system.

But even though our summer holiday is relatively short in comparison to other countries, I still think it should be shorter. I would keep the number of school weeks the same (39 weeks on, and 13 weeks off) but I would redistribute them. I'd have smaller breaks more often. (I would also make sure there was always a week off for both Eids, but that's a separate issue).

Why do I think the summer holiday is so bad? Well for one thing, it's bad for children's health. According to a recent study by ukactive, children lose 80% of their fitness (ability to run a certain distance) over the summer holiday. This effect is apparently much more pronounced in less well-off families. Low levels of activity are not just linked to poor physical health, but also to a lower attention span and worse social skills, both of which affect a children's ability to learn and progress academically.

“Our research with Premier Sport suggests deprived children are being plonked in front of screens for hours on end, while their more affluent peers are able to maintain their fitness levels through summer camps and other activities." Dr Steven Mann, ukactive

In my opinion, anything that causes such a huge gap between children of different socio-economic backgrounds should immediately be thrown into question. How can we justify such an injustice?

In addition, students who usually receive free school meals during term time may find themselves not eating as much, or not as much high-quality food during the summer holidays, leading to worse health, and hence lower educational outcomes overall. If we distributed the holiday weeks more evenly, the continuous length of time a child may have to go without decent food would be shorter.

Another thing is students forget stuff during the holiday. They forget how to write (I remember experiencing that myself), they forget how to do maths. But some students are affected more than others. There is evidence suggesting that two-thirds of the achievement gap between disadvantaged students and well-off students can be explained by the long summer holiday, although this research is mostly American, where the summer holiday is twice as long as ours. There are plenty of studies that have measured the achievement gap over many years and found that the summer holiday appears to be mostly to blame. The reason for this seems to be that middle-class children are more likely to be taken on educational trips (like to the zoo, a museum, or on holiday abroad), are more likely to be encouraged to read and be members of the library, less likely to watch TV, and less likely to be left without parental supervision. Whilst we can create summer programmes for deprived children to give them all of these experiences, attendance would still be optional and self-selecting, so the students who need it the most would probably be those least likely to get it.

Now, I reckon the summer holiday is particularly damaging in terms of maths. I doubt that many parents, whether middle class or not, consider enriching their children's maths skills during the summer holidays. They'll happily encourage their kids to read, to visit museums, to observe nature, to experience different cultures, and so on, but are they encouraging anything mathematical? How many children out there get a bedtime maths session? Exactly. And yet a bedtime story is synonymous with good parenting. There are actually loads of opportunities for parents to keep their children's maths strong over the summer, and none of them involve filling in a workbook (side note: I used to love filling in maths workbooks during my childhood summer holidays. I also used to make my dolls and teddies do them too. In fact I'm kind of in the mood to do one now...) For example, baking requires lots of measuring and scaling, and also involves eating baked goods, so that's a win all round. Whilst driving to the seaside, talk about speed, distance and time. Play board games that involve calculations like Monopoly and Yahtzee, or geometric reasoning like chess (no blog post is complete without me mentioning the benefits of chess). Construct some pretty geometric patterns like mandalas with compasses and colour them in. This book has got lots of nice mathematical art activities.

I just realised that the above paragraph looks like I'm telling parents how to parent and that's always a very dangerous thing to do, especially for a committed child-free person like myself. Parents: I bow to your superior knowledge and expertise. These are just ideas! Please don't roast me. Thanks.

The long summer holiday is also bad for teachers. You don't believe me, do you? You probably think that the summer holiday is the only reason you're still alive. But think about this: do you ever find yourself, during term time, putting off doing something because you're too busy, and telling yourself you'll do it in the summer holiday? Or feeling tired/anxious/depressed, and telling yourself you'll feel better in the summer holiday? Or feeling like you have way too much work to do, but telling yourself you'll catch up during the summer holiday? When do you start counting down to the summer holiday? Seven weeks before? Do you ever stop to think that this focus on the summer holiday is unhealthy, and that as teachers we're actually wishing our lives away? During my phase where I was really into researching happiness, I came across the idea of the "arrival fallacy", a term coined by Tal Ben-Shahar in his book Happier. It's the way we always think "I'll be happy when...". For example, I'll be happy when I've lost 5kg, I'll be happy when I get that promotion, I'll be happy once I've got a boyfriend, and so on. It's a fallacy because by the time you arrive at that state, you have already expected to reach it, and you've already got used to it, so it doesn't actually make you feel any happier.

If we constantly chase after the summer holidays, we will never actually experience proper happiness. And even if the summer holidays do make us happy, is it really OK to only be happy six weeks out of every fifty-two? If we had more holidays but shorter ones, less emphasis would be put on the summer holiday and maybe we'd be able to enjoy ourselves a bit more throughout the year. Then again, maybe we'd just end up doing more revision classes.

Additionally, everything I wrote earlier about children becoming unhealthy over the summer is probably true to some extent for teachers too. I know that my health has already suffered this summer due to poor sleep patterns, not eating regularly, and spending way too long slumped on the sofa watching anime. If it weren't for Pokemon Go I probably wouldn't leave the house. When September comes back around it will be really difficult to get my circadian rhythms back in place and it will be a huge shock to the system. The entire first half term always feels like an uphill battle.

So, should we get rid of the long summer holiday and make it just two weeks? Let me know what you think!

Emma x x x

Why Getting Rid of AS Maths Could Be Good for My Students

September 2017 sees the launch of the new Maths A Level course. All the other A Level courses changed a year or two ago, but the Maths changes were delayed because Maths teachers were already getting to grips with the new GCSE course (how considerate of the government, giving us two whole years to cope with the overhaul of two massive and important qualifications). The content has changed a little bit in some areas and hugely in other areas, but what I really want to talk about in this post are the implications of de-coupling the AS from the A Level.

Up until now, our students have sat 3 AS Maths exams in year 12, then 3 A2 exams in year 13, and then the two sets of results are added together and used to produce an overall A Level grade. The AS exams are obviously easier, but they are equally weighted. You can resit as many of the AS exams as you like in year 13, and your best grades count. From next year, students can take the AS Maths exams, and bank an AS in Maths. But if they decide to carry on and do the full A Level, the AS exam grades will not count for anything. 

The first cohort of students I managed as Key Stage 5 Coodinator produced a very surprising (to me) set of results. Their AS results were, on the whole, pretty bad. I felt like I had failed completely as a teacher and as a leader. Most of my students were below target, and our ALPS grade was really low. Some difficult conversations were had between me and the head. Then, one year later, those same students miraculously gave me our best set of A Level results ever. Is it because that talk with the head inspired me to turn my life around and become an amazing teacher and relentless pursuer of added value? No (I respond badly to criticism, anyways). I didn't really do anything different. So why did my students do so much better in the end? 

One possible explanation is that when my students take their exams at the end of year 13, they are much more mature, both emotionally and mathematically, than they were at the end of year 12. Most of my students resit at least at least one of their AS modules, and they usually improve their grades massively (S1 by 30 UMS on average - 3 grades, C1 and C2 by about 20 UMS on average - 2 grades). Everything they found difficult in AS just seems to automatically become easier to understand after learning the A2 course. I sort of expected this with C1 and C2, as C3 and C4 are mostly extensions of those. But it really surprised me that my students managed to improve S1 by so much, as S2 is very different and could probably be learnt without having learnt S1. I didn't do any S1 lessons in year 13, the students re-learnt it and revised it all in their own time. There isn't any reason they would do better in it after a year of self-teaching compared to a year of professional teaching, other than the fact that they are more mathematically mature. 

With the new system, there will be no such thing as resits. But I don't think it was the fact that they had two chances at a module that helped my students, I think it was the fact that they were able to do AS modules as older and wiser year 13s. As all of the content will now be assessed at the end of two years, it's a bit like retaking all three AS modules in year 13, but without having 4.5 hours of extra exams. This means my students' performance should really be better. 

Another benefit of the new system is having a much longer and more flexible period of time to teach all of the content. Every year, we struggle to squeeze in all of the AS content, often having to teach some of it during May half term, and every year we finish the A2 course around Easter and spend the last term doing revision, which students steadily become less and less engaged in as it drags on. With a two-year course and no half-way exams, we will have the flexibility to spend longer on the first year course if we need to. We could also choose to leave all of the mechanics and stats until the second year, or teach all the course in topic blocks with no distinction between what's year one and what's year two content. If you only have one maths teacher in the entire school who understands mechanics (and I know there are a lot of schools in this situation), but you have two groups of students, you could get her to teach one group one year and the other group the next year. It makes planning your scheme of learning a lot easier because of the added flexibility.

For this particular cohort of students, if they had not had AS results, that might have helped them get into university. Almost all of my students achieved a higher grade in their overall A Level Maths than they did in their AS. I had a student go from an E to a B, I had a student go from a C to an A*, and only two students out of nineteen went down. Their low AS grades stopped them from applying to some of the top universities or caused the universities to reject them. Our UCAS predicted grades (which I've complained about already here) were mostly the same as the AS grades, because we had no reason to believe their A Level grades would be any higher (although we know better now). It's not really a good thing that almost all of our students beat their UCAS grades, because it means we have limited their choices and decreased their chances of a Russell Group education unnecessarily.


One benefit of the old system was that the AS exams acted as a filter, weeding out the students who were never going to make it through the full A Level. This is good for those students, because it means they waste only one year of their life rather than two. It's good for teachers too, because it means that in year 13 the spread of understanding is usually less wide, which makes the class easier to teach. At that point the less motivated, lazier, and more disruptive students have usually left.

However, as someone who has a growth mindset, and as someone who strives to be inclusive, there's something about the paragraph above that just doesn't sit well with me. It sounds like I'm saying that the purpose of AS exams is to eliminate the students that we don't want, which almost sounds like we want a certain number of our students to fail. Also, a student failing (or doing badly in) their AS does not necessarily mean they are incapable of succeeding in A Level maths. It might just be that they have a differently curved progress trajectory.

For some students, adjusting to the demands of post-sixteen education is challenging and can mean that their progress is slow at first. These students would benefit from a two-year course because it allows more time to find their feet. Therefore I'm not completely sure that the "weeding out the weak" argument is fair or valid.

Another argument for having AS exams is that it can serve as a wake up call for some of the less motivated and more lazy students. There are always students (usually boys) who do well in their GCSEs with minimal effort, and assume they can get away with a similar level of effort at A Level. When they do their AS levels and inevitably get a lower grade than they were hoping for, this can be the kick up the arse they need to step up their game. One of my favourite manga series, Assassination Classroom, references this: (it's Japanese so read right to left)

I think this particular argument is quite a strong one, as I've seen it happen with many of my students. That student who got a C in his AS and an A* by the end is one example. He's extremely stubborn by nature, and after being disappointed with all of his AS results, he started working ridiculously hard. Without this lightbulb moment on results day, who knows what grade he would have ended up with in the end? And he wasn't the only one: I reckon around half of the class experienced something similar, just maybe not as strongly. 

Some schools have decided to enter their students for AS exams for this very reason. However, I worry that now that the AS exams don't actually contribute towards the final grade, students will treat them as mock exams, and not give it their all. Then, when their AS grades are below target, they will just say "yeah, well, I didn't really try that hard, I'll try harder in next year's exams and I'll be fine" which means they haven't received the full benefit of failing. I am also concerned that entering students for exams that don't even count is a big waste of money, in a time when education is critically underfunded. 

What we really need is a way to give our students that wake up call in a genuine way. Most students do not care about mock exam grades. Most students do not care about class assessment results, or working at grades or teacher predicted grades. They think they know better. 

Unfortunately, I haven't worked out a solution yet! Sorry if your were hoping for one! I've always been more of a questioner than an answerer. 

Emma X X X 

PS OMG I didn't mention chess for this entire blog! 

Thanks

After school today we had the first round of this year's 26 leaving speeches. They were entertaining as usual, and mercifully short, and, like every year, I found myself coming away feeling a little bit inpired. Inspired to be a better teacher, to be a better colleague, to drink more, and to write a blog post.

One thing that one of my colleagues said that really stood out to me was about saying thank you. I've thought for a long time now that teachers don't get thanked enough. Senior leaders don't thank us enough, parents don't thank us enough, and the government certainly doesn't thank us enough (a pay cut every year for 7 years!) Occasionally students thank us. However, what I never considered until today was that senior leaders in school get thanked much, much less often than regular teachers like me. 

Not being a senior leader, I can't really confirm that it's true, but I feel like it probably is, because I honestly can't think of any time in my six years as a teacher when I have gone out of my way to thank anyone who is above me in the food chain. 

As much as I love to complain about some of the policies they thrust upon me, I have to admit the senior leaders at my school do their jobs very, very well. And although I would love to take the credit for every Maths GCSE and A Level grade that my students receive, I should remember that without the systems and the structure and the environment of the school being as they are, those grades might have been impossible for me to achieve. I'm also willing to bet that a lot of hard work goes on behind the scenes that I'm completely unaware of. I have to remember that, although they may get paid significantly more than me, senior leaders are not fat cat CEOs. They're teachers like me and they are driven by the same things as me: getting the best outcomes for our students to ensure the best possible futures for them. 

So my new school year resolution is to remember to thank those above me. This will be difficult, because I'm too scared to talk to a lot of them (yay for social anxiety!) but it will get easier the more I do it.

If you're a teacher, I urge you to do the same!

Let's all spread some love around the staffroom next year. 

Emma x x x

PS thank you for reading! :)