## Thursday, 20 August 2015

### just a teacher, trying to be better

In the early hours of this year's 'GCSE results day' I found myself awake, unable to sleep, in anticipation of today's revelations. Now, this is not just down to the anxiety of finding out how my students have done, but also just because my holiday sleeping pattern doesn't even entertain starting until at least 2am!
So, without even knowing how my students had fared this year and having read copious amounts of tweets concerned about grade boundaries, I found myself thinking about next year...how next year's Year 11s will do, how I can make sure they do as best they can with their Mathematics and how they can get the grades they need for college/life after school.

I'm just a teacher, trying to be better and here are a few of the things that I will try to be better at this coming academic year...
(some of these are specific to teaching Mathematics, others are more general, but all are things I will either continue to do, improve upon or try)

Numeracy
As a Mathematics teacher it's kind of expected that I'd teach numeracy in every single Mathematics lesson, but I know there is more that I can do when teaching numeracy. I see gaps in students' basic numeracy all the time, regardless of whether they are in Y7 or Y11. Much like, for an English teacher, teaching spelling, punctuation and grammar in every English lesson, numeracy is a key part of my subject that needs approaching and discussing as it comes up in lessons. Even more so, it needs teaching as a separate part of lessons for the weaker students who's lack of basic numeracy stops them from accessing the more complex topics in Mathematics.
So, this year I will aim to, wherever possible, ask students how they have done their calculations - what strategies they used to do them and how else they could have approached them by comparing their method(s) with others in the class. For example, when having to subtract 17 from 42 how did they do that - did they take 10 away from the 40 and then 7 away from the remaining 32? Did they 'count on' from 17 until they got to 42 - and how did they do that? By adding 3 first to 17 to get to 20 and then a further 20 to 40 and then the final 2? Or did they group the numbers differently, and why? I still find ways of doing calculations that I hadn't considered before and possibly didn't use at school myself/weren't taught, so my students are bound to hear ways to do 'sums' that they hadn't used previously too.
This year I am only teaching Y9, 10 and 11, but I do have the lowest set in one of my Y9 classes. So, I'm planning on using @Maths_Master's 'Numeracy Ninjas' with this class. I aim to use this in the first term with this class to set the 'Mathematical building blocks' that they will need before attempting the more complex topics. Ideally, this skills will have been developed in Y7 and 8 and they'll already be numerate, but classes like these need to constantly go over the basics to retain them. So, I will run the Numeracy Ninjas as starters to our lessons and watch their progress, hopefully seeing them become more numerate and prepared for their GCSE course (we'll be doing the new GCSE over 3 years from Y9). I'll be showing my department the Numeracy Ninjas and seeing if any would like to trial it with their Y7/8 class(es) - or see if our HLTAs could use it in their intervention sessions with students. I think it's a great idea and can already see students aiming for a 'black belt' in Numeracy - I know I already want one!
Another resource I will use to develop students numeracy is the @Corbettmaths 5-a-day Numeracy questions. I believe in the 'little, often' approach and so these questions will be great for weekly homework(s) or as starters in computer room lessons/lessons.

Problem Solving in Mathematics
Similar to how I'll be asking students how they approach their numeracy I will be aiming to develop students' problem solving skills in Mathematics. Students will need to be able to approach problems when entering the big wide world and will need to think about them, come up with a suitable approach and apply their knowledge to them. Students will rarely leave school and need to use the quadratic formula or find the sum of the interior angles of a regular polygon, but what they will need are the problem solving skills needed to look at a problem, think about what it is they've been asked, what information they have been given and what they know that could help them with it. When I get the dreaded 'when am I ever going to need this' question I usually come back with a statement/suggestion that it is more the approach to the problem/topic they are studying that they'll use in their future as opposed to the explicit rule/theorem itself, therefore preparing them. Sometimes it works, sometimes it doesn't!
There is a greater emphasis on these types of questions in the GCSE examinations and as such, students need to be prepared for them. Questions that involve a scenario of some kind, various bits of vague information and a statement to prove right or wrong or 'show...'; those questions that are more implicit than explicit...they don't just say 'write this number in Standard Form', they have to work out what it is they need to do/use.
So, in order to develop these skills with my students I will use a 3-step approach similar to that on an AQA poster I received free at a recent #mathsconf.

I have this poster on display in my new classroom to refer to, and will, when students are presented with a question like I've described above.
I'll also be using AQA's 90 problem solving questions document wherever possible when teaching my GCSE classes (so all of my classes!) topics that these questions link to. Edexcel also have plenty of resources on the Emporium that I'll be using and I'm sure I'll find some resources on the TES too.

Dispelling the Mathematical Myths

'maths is difficult'
'maths is hard'
'maths is boring'
'I wasn't very good at maths when I was their age'
'I don't need maths for what I'm going to do'
'I hated maths when I was at school'
https://www.youtube.com/watch?v=3uYBoWH3nFk#action=share <--all these films Hollywood have produced (beware...some naughty words)! Thanks to @ddmeyer for this.

Oh and my current favourite comment from the #ChineseSchool
Teacher: 'What is Trigonometry'?

Some/all of the above phrases/comments are bound to have been heard by all Mathematics teachers, at some point, as our subject does have a stigma attached to it. Negativity. Students, parents and even our colleagues can be heard saying these phrases and we (as Mathematics teachers) need to do all we can to dispel these myths/statements. It may be too big a battle to face, but I'll try and we all should. It still seems people are happy to say they're 'bad at maths' or were 'rubbish at maths', whereas they'd be horrified to admit they couldn't read or write. So, whenever a negative comment is said towards my subject I will challenge this statement. Every day I will aim to make my lessons as relevant and as engaging as possible so students enjoy doing Maths, but even then it may not be enough...
...I saw, in the local supermarket, a student I taught last year. She was a very able student and left with an A* in her GCSE Mathematics. I asked her how college was and what she hoped for her AS results and then couldn't remember if she'd taken Mathematics or not, so I asked! Her response was 'Oh god no, I hated Maths'! Naturally, I was horrified by this comment as I had taught her in her Y11 year so swiftly replied with 'Really? But you did so well and seemed to enjoy our lessons?' She then, rather kindly, said that she did enjoy the lessons and that the only reason she liked it/did well was because I taught her, but other than that she just didn't really 'like' maths. So, I don't really know what else can be done in these instances - I suppose I'll have to conceded that unlike myself and the other eager teachers of Mathematics around the country, it may not be for everyone?
Nonetheless, I can do my best to dispel the negativity towards my subject - to ask colleagues to be as positive about Mathematics as is possible when students ask them for help in tutor time, etc. In the same way that, for example, when Y9 students ask what 'options' they should choose all I ever do is say what I chose and why (because of my personal preferences/goals, etc), but would never deter/direct them from/to taking a certain subject.
Last year, I did a Mathematics assembly to each year group loosely based on how they can be better at Mathematics, when/where they can get support from us and (for the older students) how they should/could be preparing for their exams/mocks. I will be doing an assembly to each year group this year too and will try and focus on their approach/attitudes to their Mathematics this year...more on this nearer the time.

Making Mistakes
I will continue to ensure students know that it is OK to make mistakes in Mathematics. That we learn from these mistakes and they're key to us improving and learning. I wrote a blog post about the @magicwhiteboard reusable notebooks we have got for this year and these will be used by students to do their workings in class. They'll use them to do their work, make mistakes, rub them out, try again, make mistakes, ask for help, try again, get the question right and then repeat. They'll learn throughout this process and the perseverance to get from stuck to unstuck will be key in them learning new skills and becoming better Mathematicians.
I have a 'growth mindset' display up in my room this year and I'm trying to develop this with my students. The word 'yet' will be used more regularly when students state they 'can't do it', I will retort with a 'yet'. I will focus on students having put in lots of effort and for having improved or having tried hard, as opposed to just praising those for having got the highest grades or having completed all the work/getting all questions correct.
I will get students to challenge each other and question whether something one student has said is correct or not. The phrase 'do you agree [name]...?' will be used more in class when using @TeacherToolkit's Pose Pause Pounce Bounce in my questioning.
I'll also be using my favourite starter 'My Favourite No' ( <-- click to read previous post where I mention this) in class a lot more this year to cover misconceptions, highlight the importance of making mistakes and learning from them and encouraging students to try and that they'll be rewarded for doing so.

the new GCSE content
Oh yes! These new topics will be covered/taught for the first time this year and for our department we'll have to discuss these together in our meetings as to how we'll teach them to different classes. Some of us, me included, will be teaching some topics for the first time and won't have come across them since our own A-Levels/schooling. I haven't taught Mathematics post-GCSE so there will be a fair amount of 'brushing up' on some of these new topics, which I'm not ashamed to admit - I don't know everything 'Mathematics' by any means and am still finding links with current GCSE topics and discovering things/ways of teaching topics I'd never considered before.
Luckily for me, in my NQT year I worked at a school that did Edexcel's Linked Pair Pilot qualification and I taught the 'Methods' part of this qualification in that year and so have experience with topics like Venn Diagrams and Set Notation. At #mathsconf4 I took part in a session on the new GCSE content and the linked pair pilot was highlighted as a good place to get resources/past questions for teaching and preparing students for these topics, so I'll be using these to collect questions for use in class.

Furthermore, we are all extremely lucky that there are amazing Mathematics teachers already putting together resources and support materials for teachers on the new GCSE content.
@JustMaths have a whole host of blog posts already aimed at teaching the new 1-9 topics. Here's an example of their 'Error Intervals' post. They also have posts on Frequency Trees, Binomials and the SAMs for each examining body, just go to their blog here.
@mathsjem has been collating resources for each of the new topics on a whole page on her website www.resourceaholic.com here and it will definitely be a 'go-to' resource when looking for ideas/help with the new content. Jo has spent so much time putting everything together on her site and will no doubt be saving me hours of time and probably countless of other Mathematics teachers time too. So thank you to both Jo and JustMaths for all the work they've been doing on these - you're lifesavers!

Getting the kids Mathematical equipped
Over the course of the last few years it's been a right pain nagging students to remember to bring their calculators and other Mathematical equipment (protractors, compasses, rulers, etc) to each of our lessons. Some students have them every lesson without fail, but others rarely come properly equipped and have to borrow equipment. We don't have class sets of calculators in our school, although we do now have 1 class set of calculators to use if/when needed, but if we're all teaching Y11 at the same time (well, half of them anyway) there's no logistical way of us all using them - so we're reliant on the kids getting themselves organised. However, that's the problem - some of them lack this organisation and constantly turn up without (mainly) their calculators. This then either means they get lent one of the few calculators I own personally, work with their partner and share a single calculator or don't use one altogether. This has a massive affect on their learning and their ability to familiarise themselves with a single calculator and be proficient in using it come their examinations.
So, in a bid to emphasise the need for students to have this equipment for their exams I will continue to dish out detentions for forgotten equipment, but I've also already sent a letter to all Y9 (going into Y10) students highlighting what equipment they'll need for their GCSE Mathematics and how to order them cheaper via the school shop. We had a fair amount of orders in before we broke for the Summer and so hopefully there will be more students this year that come properly equipped to lessons.
Today I saw the importance of this as one student in our Y11s, having got 32 marks on the non-calculator paper, only got 16 marks on the calculator paper, which seems very odd and was our only real 'shock' result in terms of what was expected. Now, the low mark could be down to other factors, but I'd be willing to bet it had something to do with them either not having a calculator in their exam (although I checked with our exam's officer and she couldn't recall anyone not having one) or they just didn't know how to use it properly?!

Homework & Cultivating Independent Learning - little, often?
As I've said above I do believe in the 'little, often' approach to learning and this applies with homework too. In the past year I've tried varying approaches to the type of homework I set. I'm a massive fan of @TeacherToolkit's #takeawayhomework approach and will be using this again this year. I've had some fantastic work back from students using this approach and being given the choice and freedom as to how much they do each week to accumulate the required amount of 'chillies' across a half term, say, has worked well with my students. Equally, I have used 10 question homework sheets (available in my free TES resources here and here) with my Y11s to go over those 'bread and butter' topics and these have worked well too.
This year I may try giving homework to one of my classes every lesson, but just give them a small amount each night - say 1 or 2 questions to attempt before our next lesson where we'd start the lesson by going over the question in class and addressing any issues. I got this idea from a colleague I did my GTP with (@andydcodling) who is doing this at his school (my old GTP school). I liked the idea and so will see how it works with one of my classes and reflect on its benefits.
I'm also aiming to use the PRET homeworks far more this year than I have previously as I like the format of them and they cover a broad range of skills. @mathsjem has collated all of these homeworks on a website for teachers to use. Check them out at http://prethomework.weebly.com/.

All of last year we offered our students after-school and lunchtime support with their Mathematics every Friday (and, of course, teachers did other sessions as and when students asked for help) and this has made a massive impact for those students that turned up every week - outperforming some of their peers who didn't want to take advantage of the support. We'll be continuing this this year and I've put together a poster advertising the support sessions that will be put on display in each of our classrooms. This will hopefully encourage students to come and seek the support when needed and also get them to take a more proactive approach with their learning.

Topics don't just appear as separate entities in the GCSE examinations and neither should they. There are so many links between the topics we teach in Mathematics and this is no better shown than in @Maths_Master's info-graphic/diagram on his website, which shows all the links between topics. Check it out here.
Wherever possible I will attempt to make these links in my teaching. Combining area of a rectangle with multiplying & simplifying surds by putting the length/width of the rectangle in surd form. Combining algebra with, well pretty much any topic - probability, similarity of shapes, volume of shapes, etc.
The most recent, quite controversial, example of this was of course...'Hannah's Sweets' (my ex-fiancé's name coming back in exam form to haunt me), a question that combined probability, forming expressions, fractions and forming and solving quadratic equations.

'There are n sweets in a bag.
6 of the sweets are orange.
The rest of the sweets are yellow.

Hannah takes at random a sweet from the bag.
She eats the sweet.

Hannah then takes at random another sweet from the bag.
She eats the sweet.

The probability that Hannah eats two orange sweets is 1/3
(a) Show that n^2 - n - 90 = 0

(b) Solve n^2 - n - 90 = 0 to find the value of n'

Our students clearly need training and exposure to these sorts of scenarios and being able to link topics/concepts together to answer questions. So, where possible I will look to create scenarios/questions similar to the ones recently seen in exam papers in order to prepare students as best I can. The linked pair pilot papers, additional mathematics papers and exam board resources should all be rich sources of these type of questions.

Assessments
Life without levels! This is one area that my school is a bit 'up in the air' about at present (with our KS3 that is). We will be adopting an 'EDSM' (Emerging, Developing, Securing, Mastery) model for assessing students progress in KS3 and so this will affect our Y7 and 8s. Our Y9-11 will be doing their GCSE Mathematics. Y11 on the outgoing spec, Y10 on the 2-year new 1-9 GCSE and Y9 the first year group to start the 3-year new 1-9 GCSE. So, there's a lot to keep track of, assess and review.
We have purchased Pearson's ActiveTeach and ActiveLearn product and so will be using their assessments for our Y9 and Y10. Our Y11s will continue with the outgoing spec as the last few years have done and they'll be 'past papered' up until their actual exams.
As for KS3, they'll also be using Pearson's assessments, but as to how we'll be reporting to parents I don't actually know as of yet - so this is one area I'll need to get my head around when going back and I'll trust it'll all be explained when we get back, if not - we'll 'Matherise' their assessments to what we need and ensure we know where the students are to prepare them for their GCSE Mathematics.
I do know that in KS4 our students will be doing termly/half termly assessments, these will all be tracked, students highlighted for interventions and our wonderful HLTAs involved. We fit all our assessments around the school calendar so we always have a set of 'results' to report to parents either via interim/full reports or parents' evening and this will continue next year.

Sharing best practice
The frequency of my blog posts has dropped over the past year or so due to me naturally picking up more responsibility with the day job. I like to think I still make time as much as I can to blog about my teaching of Mathematics and will look to do as much as I can this year, although I am minded that being Head of Department will bring its own pressures and this may affect my blogging.
However, I am keen to share my department's progress, ideas and struggles - there are plenty of you out there who have supported me in my teaching career so far and I know that over the next few years as I try to figure out what I'm doing I'll need the support and expertise of the Mathematics teachers on Twitter/in my local PLN. I consider myself very lucky to be able to communicate with so many fantastic people all over the country and it is no doubt that I have developed as a teacher as a result. I can't imagine having taught the past 3-4 years without the online support, guidance and resources that I have received/used, so thanks to everyone that has tweeted me, commented on my blog, spoken to me at #mathsconf or local maths meetings or TeachMeets, etc - you're all awesome!
My school is one of 3 in our local area that is linked together in what I like to call a 'Tri-Wizard Tournament'. We have joint INSETs at times in the school year and have (I think) 3 joint planning meetings after-school this year. I'm planning on using these as best we can to share good practice, but as they are not compulsory I'm hoping that the other 2 schools do want to meet up and share their ideas - perhaps in a TeachMeet sort of fashion with each of us sharing, say 2-3 ideas each, from as many of our Mathematics staff as possible - I think it could be really quite good. But, when thinking about the 'Tri-Wizard' meetings I'm thinking 'why stop there'?! Why not invite our other local schools, where I have contacts, to join us and collaborate together. I've been lucky enough to work in 3 other local schools in my time either on placements whilst training or as a full member of staff. I've also been very lucky to mentor some fantastic ITTs this year/last (you guys know who you are) and their schools aren't a million miles away from ours! So, if I can, I'll look to gather everyone together - just the Maths departments, talking about Maths!

So there you have it - the whirlwind of thoughts currently whizzing their way around my head. All of the above are the things I'm going to try and be better at this year, the things I'll try to improve on in order to provide the best Mathematics education I can to our students.
I hope this post (if you've stayed with me and have actually got this far) is of use to others - it'd be great to read/see the thoughts of others as the school year approaches, so drop me a comment below or a tweet @mrprcollins if you've written anything similar or have any 'golden nuggets'!