Ben Rapley took us on a a tour of how they have included a focus on improving core skills alongside their scheme of work in his department. Through departmental discussions, they selected 7 key topics that are essential, and regularly used in multistep problems: Fractions, decimals, percentages, ratio, negative numbers, brackets and equations (this was stage 2; stage 1 topics were: addition, subtraction, multiplication, division, number properties, place value and collection like terms).

Already, I’m liking this workshop! I’m currently working on building more number sense into our scheme of learning from year 7, and the stage 1 topics, except for collecting like terms, were pretty much the same as what I had!

Ben’s department created a core skills development ladder for each of the 7 topics. Looking at brackets on our table, you realise how quickly the ladder could be enormous! But as Ben said, these are organic creations which change as you use and need to tweak them.

The next part was about the assessments. For Ben’s department, they do 1 assessment per half term, and everyone on stage 2 (from year 7 to 11) do the same assessment. This is an interesting idea, and the question was asked about motivation for some students who may score poorly on it.

The assessment lasts 1 and a half hours and has 15-20 questions per topic – a question for each sub-part of the ladder. The 2nd half of the lesson is self-assessment, and here Dylan William’s quote about the research comes into play, where students that self-assessed progressed more than those that peer assessed or had their work teach assessed. The next lesson was feedback, often whole class verbal and modelling target questions. Every lesson after that had starters related to the targets.

The assessment set up is a big step away from ‘normal’ termly assessments, being one mark per skill, and total fluency without context or multisteps. The big takeaway for me here though, is the excel spreadsheet used to generate the questions! I need to do a bit of work, but currently I have weekly quizzes for years 7 and 9 (I don’t currently teach 8) and daily starters for year 10, which if I could press F9 and do some of the amazing things the spreadsheet does, then it would be such a time saver!!! I was almost drooling when Ben explained that you choose your click on the questions and they appear in a worksheet, which could also be changed to a project view. Might be watching a few ‘Excel how to’ videos over the holidays.

Ben finished with talking about interleaving the core skills throughout the scheme of work; again something that I am looking at with the number sense work for Year 7, with the example of using fractions when calculating perimeter or area. This is something I also want to think more about within my teaching, so that it’s not just the weekly quizzes or daily starters that cover topics taught, but they’re intertwined throughout future learning.

I hadn’t realised when I went to Andy Elwell’s workshop that he was the creator of Method Maths. I hadn’t come across it before this year, but have been very impressed with how the year 11 were using it to practise, practise, practise this year!

Andy started with a tour of how multiplication is taught from year 1 to year 6. The stand out point of this was the journey from concrete, with lots of manipulative, to more abstract (ie just written) in Year 6. Andy then demonstrated the number of steps needed to complete a column method multiplication, compared to the lattice method.

The immediate murmuring was about how the lattice method does not help students understand the place value in multiplication and it was just learning a procedure. However, Andy was ready for this, and showed a neat justification of why the lattice method works, by rotating a multiplication grid. The question to consider is, why don’t we let students use easier methods, as long as we keep it conceptually connected justifiying why they work? So my first takeaway – should we teach our year 7s the lattice method when they arrive, alongside why it works?

The next idea was a game changer for Andy, and I love it! I wouldn’t even call it a procedure, but more making Pythagoras’ Theorem a bit more concrete, rather than the abstract algebra workings. I (and I’m sure many do) introduce Pythagoras looking at the square of the sides of the right angled triangle. Well why not draw squares next to each side and put the square value in?

We were now starting to get, on what Andy believed to be, more controversial ground. The DM method! And I’d agree, if it was introduced as a process with no understanding, it would be controversial. So what is it?! The DM method is basically a procedure to use for any maths that can be set up in proportional grids From ratios, to map scales, equivalent fractions to even inverse proportion.

And all it is is “divide, multiply”. But of course there is a justification – dividing establishes scale factor and multiplying applies the scale factor. This is definitely something that I want to explore.

The final idea we unfortunately didn’t get to explore as much as was possible in the workshop, but again is something I’d like to revisit, even if just for my interest. Andy has stopped starting trigonometry with SOHCAHTOA, but introducing trig using the Sine Rule.

How amazing to have Simon Singh, mathematician (background is mainly Physics), author, and one of the writers of The Simpsons to deliver a midday plenary session. Simon talked to us about some of his books: The Bible Code (and how for every prediction found in the Bible Code, one is also found in The Moby Dick Code!); Fermat’s Last Theorem; The Simpsons and their Mathematical Secrets (which I’ve read and enjoyed). It was a pleasure just to listen to Simon and his enthusiasm about his work.

Simon also mentioned some of the maths projects that he’s running for schools. For post 16s there is “Who wants to be a mathematician” – more can be found at http://goodthinkingsociety.org; and for KS4 Top-Top Set and Parallel https://parallel.org.uk, which is well worth an investigation.

Claire took us on a tour of problem solving and some of the research around it. She looked at some of the definitions that have been given about problem solving and shared what what I thought was a great summary: challenging for individual learners; involves a strategy for solving that is not immediate or obvious and involve independent thought and creativity. Problem solving is another of my projects in our department, as we develop our SHAPED problem solving (taking the SHAPED genius of my HOD to implement it effectively to improve problem solving – hopefully more on this to come).

Claire looked at the why of problem solving and what we have to consider when problem solving with out students – some really useful considerations: cognitive load of the students; surface and deep structures (I really like the idea of trying to sort problems into similar groups, where there are multiple groups possible); growth mindset; generic problem solving skills (and whether there are any??!! but also identified the work of Polya’s 4 stages, which is what we’ve also used in our SHAPED problem solving) and topic specific problem solving skills.

“Reflect, Expect, Check”

A treat of a workshop to finish, with Craig Barton, Jess Prior and Ben Gordon doing a triple act on how they’ve used variation theory in their teaching. Craig began, introducing 4 ways in which he uses variation theory: by example, by rule, by pattern and by demonstration. Then it was over to Jess to explain how she uses variation by example as an intelligent practice exercise. I love these!! I’ve started using them with some of my classes after reading Craig’s book, but without the full “reflect, expect, check” experience. However, they have already allowed questions and discussions about what is happening. The point is, instead of having unrelated practice questions, change one thing each time, so that the students have the opportunity to think about what’s changed and what effect this will have. At this point, it’s worth pointing out that from Craig’s point of view, this is one tool to use whilst giving student a wide diet of maths. I was so engrossed, I didn’t even get any pics! But Jess has very helpfully written in far more detail on her blog here at minimallydifferent.wordpress.com.

Ben then took the baton to talk about variation by rule, and how he introduces concepts through examples and non-examples, but by varying one thing at a time in his examples. Again, I’ve done some of this, but not to the extent of only changing one thing! And it was hard to come up with the examples and non-examples as my list. Ben’s example of mode from a table was seamless, and his demonstrations of actually how to do it with the class were very useful. A silent introduction whilst students concentrate on the examples, cold calling for reasoning, insisting on correct language, and then class calling!

Both Jess and Ben came across as if they’d been hosting workshops to a packed lecture theatre alongside “famous” maths teachers for years, and not that it was their mathsconf debut! Craig then finished off with the other two variation methods, firstly making sure that if you are to use a pattern that to make sure it doesn’t become a pattern filling exercise, you leave a “gap of understanding” for students to identify the pattern, see what is happening, and use to predict the results. Finally with regards to variation by demonstration, the key point was to keep the initial diagram for a reference point. I really need to learn how to use geogabra!

Of course, Craig these days does not finish a workshop without an announcement, and true to form, there was an announcement at the end of this one. Craig, Jess and Ben have created a new website called variation theory.com. This will become a collaborative website with all things variation!

If you haven’t been yet, you must go to a mathsconf. The CPD for maths teaching is amazing and the willingness to share in second to none. I was very excited to hear that mathsconf17 will be in my home town of Sutton Coldfield! Asking Mark whereabouts, he couldn’t remember but suggested I do a workshop. I had the intention before, but expressed how all that I know is what I’ve read about and heard about from other more expert people than me! Yet the kind Kris Boulton suggested to make that the basis of my workshop, as many other teachers won’t have read these, or heard about them. So, watch this space!

]]>

First though, a little aside about the night before and the friendships formed over the conference. I started going to mathsconfs by myself, and still do. However, I do not feel like I am by myself when I attend as the good folks of mathsconfs are always very welcoming, and I hope I am now passing that on to new folks. As well as wonderful CPD, mathsconf brings together maths teachers who are passionate about their subject and want to talk about it (amongst other things of course!).

Andrew Taylor delivered another informative key note message at the start of the day, and following some speed dating, during which @AMercerMaths shared with me the Teach Like a Champion mat. I’m part way through TLAC 2.0, and have listened to @MrBartonMaths podcast with Doug Lemov and it is always good to be reminded of the many ideas that Doug has seen and written about.

As I have the pleasure of teaching 2 nurture groups (and 1 almost nurture group) this year, it was a no brainer for me to go to Naveen’s workshop. I’ve heard Naveen present a few times before, and I really like the thought she puts into the maths pedagogy she presents about. This presentation was about her experience using Engelmann’s book Connecting Maths Concepts, using an example of teaching fractions and how Engelmann breaks it down into small, well structured and sequence steps. The books are targetted for intervention groups, which is how Naveen has used it, but I did ask Naveen if the ideas could be used for whole class teaching of weaker students, to which she did say that the principles could be applied to whole class teaching. Naveen is blogging about her presentation here.

Connecting Maths Concepts uses scripts (remember it’s for an intervention group), but even without a script I should think more about the language I use and be careful about not using redundant language. Say more in less words.

“Future learning never contradicts prior learning”. My immediate thought of this was about division with remainders. For example, when first learning 5÷4, a student may be taught to write 1 r1. Then later on, they are taught not to write this any more, but 1 1/4. It may depend on sequencing of teaching, but why not teach 1 1/4 to begin with?

Pre-empt future misconceptions by thinking carefully about how you introduce earlier parts of the topics, as in the very first example of writing a fraction of a shape. Use more than one whole unit to emphasise the denominator is the number of parts in one unit.

Show that equivalent fractions is actually multiplying by 1, but replacing the 1 with, for example, 3/3 instead of using arrows!

Anybody who looks online for maths resources should already know about @piximaths and her wonderful collection of resources that she’s built up over the years. Danielle has also blogged about mathsconf14 here, and has included her slides for her presentation. It was good to have discussions on the table on how we would scaffold certain topics. We went off on a tangent from the directed topic (adding fractions), but that just gave us more insights. It was interesting how between us we thought of different ways to scaffold.

Danielle shared Alibali’s ideas for scaffolding, which reminds me not to always use the same method.

The most important part of scaffolding is to take it away.

To think about whole class scaffolding vs individual scaffolding – i.e. 1 worksheet which begins scaffolded and students can start at the appropriate point vs 3 worksheets with the same questions, where 1 is very scaffolded, then second has some scaffolding and the third is without scaffold (and the first two gradually take the scaffold away).

To further review the difference between scaffolding and differentiating by time.

The wonderful @MrMattock had got a few of us organised to run some puzzles and games at lunch time. I kind of overran eating my lunch and chatting with Jo and Craig, but I finally arrived with the puzzle I first discovered on @mathequalslove blog here, Petals Around A Rose. I’m sorry to Jess and @sheena2907, amongst others, who I annoyed with it, using it as an example of needing resilience. Unfortunately it meant I didn’t get to see other Tweet-up puzzles, but it was lovely chatting to new people.

I chose to go to Jemma’s workshop as this is what maths pedagogy is all about to me – using the most effective learning strategies. In this session, Jemma elaborated on the article that she wrote for Learning Scientists here, which explains how she is embedding the six strategies of effective learning from the Learning Scientists into her maths curriculum at her school.

Spaced practice: I love using Numeracy Ninjas every lesson for my Year 9 nurture group. They’re all building up stickers on the front of their books and I’ve been really impressed with the progress some have made. I also use BBQs (Bread and Butter Quizzes) for my year 10 and 11 groups, which means it’s never too long between returning to previous topics.

Interleaving: This is definitely an area I want to work on – bringing previous learning into next topics. At the moment this only occurs on an ad-hoc basis, but it would be far more ideal if previous learning was planned into new topics. Jemma describes beautifully how it works in her curriculum, which has the advantage that she designed the curriculum so that she could interleave.

Retrieval Practice: This is something I’ve started working on recently. The BBQs, which I’ve been using for a few years now can be seen as a type of retrieval practice as well as spaced practice. However, this term I’ve introduced weekly quizzes for my year 7 and year 9 groups. They have a homework with “last week, last topic, a previous topic” questions, which we self assess and review in lesson every Thursday. On the Friday they then do a quiz, with same questions, different numbers, and an added “this week” section. They must attempt if first of all without their books, but after about 10 minutes, if they have got to the end and have gaps, I allow them to look in their books. I can definitely see improvements for some students, but we’re still early in its infancy, and I know for some I need to help develop their resilience and pride in their work as well.

Elaboration: As Jemma says, “sweat the small stuff”!

Concrete Examples: A given!

Dual Coding: Another area I want to read more into. I’m aware that it’s representing with images or diagrams and not using additional text, but also that an image or diagram in conjunction with the spoken work is processed better than text that is read out. It is definitely an area I need to develop.

Initially I wasn’t going to go to Craig’s workshop. Not that I didn’t want to hear what he said, but more that I had already vacuumed up his book in a weekend of frenzied reading, and have listened to many of his podcasts with the experts from which Craig’s reading into the research had originated. How glad I am I changed my mind! Craig is a fantastic speaker and his depth of thought into maths teaching is inspiring. I have no problem in recommending any maths teacher, new or experienced, read Craig’s book. Craig chose 5 areas of his book to talk about, elaborating on what he wrote in the book, and adding some special little nuggets in for us.

I’ve got to try some goal free problems, especially with my year 11. Get a problem, take away the actual question part (the goal) and replace it with “what can you find out”.

I’ve already started using example pair problems, but what I want to improve is the “show-call” part of the “Your Turn”, using my visualiser to show student responses and discuss the best parts of them and if there can be improvements.

Intelligent practice is something else I am striving towards. At the moment, I attempt it rarely, but it is something that can become a powerful tool in students initial learning and understanding of a concept. Craig’s example with product of prime factors blew my mind! I thought it was genius how the questions develop so students can start to expect a certain answer, and then check it with their learning. And then every now and again a cognitive shock is thrown in when the answer isn’t what they expect and they look to see why, involving the hypercorrection affect (learning is more powerful when you are wrong about something you thought was correct).

Purposeful practice is another area that I’m trying to develop. This is for when students have learned the concept, but need more practice, and is trying to get away from just having questions to practice and towards practicing with a purpose (surprisingly!). I have already started looking at @colinfoster77 etudes which are ideal for purposeful practice. This was where Craig introduced the first of his golden nuggets, as he announced that he had collated and added to his collection of venn diagram problems, which are great for purposeful practice, on a new website www.mathsvenns.com, and I’m really pleased to say it came with a lot of venn puns!

Same structure, different deep problems (SSDD problems) were something else Craig introduced in his book and has since developed. These are problems which look the same, or are in the same context, but have different mathematical requirements for them, as on the example shown (this is one of mine!!). In this case they are different types of percentage questions, but the mathematical concepts in each question does not have to be related. Time for Craig’s second golden nugget – he has set up another website www.ssddproblems.com, to collate and share these problems. All he asks is that you submit one (or more) of your own, based on a shape, an image or a context.

From the bottom of my pedagogical maths teaching heart, I cannot thank the presenters enough for all that they do sharing their experience and response to research, and of course to Mark McCourt, @LaSalleEd for bringing it altogether and enabling such an event.

On a personal note, it was wonderful to meet up yet again with some twitter and mathsconf acquaintances who I hope I can now call friends. And it was in discussion with these friends that I am starting to believe in myself and my pedagogy again after recently experiencing feedback from a 15 minute observation which left me crushed and devastated when told what I was doing was “wrong”, despite (but not being allowed to) being able to justify why I did each part. Speaking with far more experienced maths teachers than me has given me my confidence back that I can keep developing my practice in order to help student learn maths in the most effective and long lasting manner that research is currently pointing towards. I know I still have a lot to learn and to implement and I hope I can continue doing this to impact positively on my students.

]]>

As often as possible I try to start mathsconf with the Friday night meet up. It’s a great time to catch up with maths teachers we’ve met along the way and through Twitter, as well as meet new folks. Despite a mix up with Julia, @Tesmaths, trying to meet in the foyer of the hotel, then realising we were in different ones, I made it up to All Bar One with Jo, @jolocke1. We’d both started new schools in September, so lots to chat about. At the bar I was chatting with @rach_2210 who was in Sheffield on her first mathsconf, and through our “where about do you teach” introductions, discovered we lived in the same town a couple of miles apart, and Rachel teaches at the school my 10 year old has put down as his preferred choice! Small world! It was lovely to catch up with Jo, @mathsjem, and hear of her experience so far as head of maths.

So onto the mathsconf. After introductions from Mark and Andrew Taylor of AQA, who talked about post 16, it was over to Matt Parker, @standupmaths, who as you can imagine, was an instant hit. Not only was there lots of laughing out loud, but some neat maths too:

Choose a random 2 digit number, cube it and Matt will tell you the original number. It’s all to do with expanding a trinomial and the affect on the 10a and b when cubing. Going to have to explore this one a little more – but isn’t that the point – creating a hook to explore some maths.

Then Matt introduced us to his favourite spreadsheet. Just a spreadsheet with cells coloured in red, green or blue, but when you zoom out it’s a picture of Matt! Here’s mine, created from Matt’s pixel spreadsheet downloader on his excellent website think-maths.co.uk. Amongst other things there are downloads for building 3d fractals, including a festive fractal Christmas tree, and if you visit megamenger.com, you’ll find details on building the world’s largest menger sponge from business cards, along with all downloads and instructions.

Matt finished off with a round up of websites and events. I’m particularly hoping we’ll be able to take some year 11s to the mathsinspiration.com event in Birmingham in November. Fingers crossed!

During speed dating I met Jack from Nottingham Uni Samworth Academy who showed me the spreadsheet they had made to support strategies for rewarding positive behaviour and effort. It was just the thing to implement with a couple of my groups, as I was looking for ideas of how to record all the positiveness in the classroom. Pete, @MrMattock showed us BBC Skillswise, the adults learning site, and the resources it had for older children who needed further support on the basics. Clear resources without the gumpf! I was also able to have a catch up with Bruno, @MrReddy, and was happy to share that one of my first responsibilities in my new department is to get TTRockstars properly up and running!

This was my contribution – at the end of school on Friday, a year 8 lad was excitedly telling his form tutor all about the probability tree he created and what each of the parts meant. He was in the nurture group, and the hook to get him engaged in probability trees was making it! All from my colleague Emily next door.

Onto the sessions, and first it was Sarah, @Schamings28, with Developing Resilient and Confident Mathematicians. Perfect, as 3 out of my 4 teaching groups are nurture groups, and resilience and confidence are in short measure. Sarah gave an inspiring workshop, clearly addressing the issues and giving excellent practical advice for taking back into the classroom straight away. She gave some excellent phrases to use to support confidence and resilience, as well as ideas for resources that get pupils practising resilience in low entry challenges which can then be used as a starting point to praise the process of resilience. I would highly recommend Sarah’s workshop if she were to do another one.

Next was an overview of Richard Skemp’s work: Relational Understanding and Instrumental Understanding from Gordon, @gordon-brough. I thought the effects of instrumental and relational teaching and learning was very pertinent. I have downloaded a copy of the paper so I can read through it again.

Jonny’s, @studymaths session on Primes, Patterns and Purposeful Practice was a whirlwind of ideas to engage students in their maths learning.

From “tricks” for squaring n+0.5 two digit numbers, based on expanding brackets like earlier, to factor skyscrapers, HCF/LCM pyramids, the Ulan Sprial, Goldbach’s conjecture, happy numbers, Kaprekar’s routine, Sierpinksi triangle and Chaos Game to name a few, Johnny provided us with many ideas, with quite a few being being enable from his excellent mathsbot.com site. It’s always great when you get an “aha, that’s perfect for when I teach …. next week” moment in a session, as well as a collective “wow” that came with the Chaos Game. Jonny’s session slides can be found here.

Finally I went to see Amir, @workedgechaos, and was treated to a review of how he would and does implement turning research and “current thinking” into practice with his staff. Amir has been a head of department and is now an assistant vice principal. It is very true that there is so much out there at the moment that it can easily become overwhelming. Amir took his big 3 – Bloom’s Mastery, Englemann’s Direct Instruction and Cognitive Load Theory and looked at the common themes. He then boiled it down to Question, Model, Check, Praise and Retrieve. It is, of course, a bit more detailed than that! You can find Amir’s slides and handout here. Amir shared with us an overview of a year’s scheme and how this was delivered each week. For spacing and retrieval, I loved how a topic was spread over several weeks (but not taught over several weeks):

Week 1: Topic A

Week 2: Mini test on topic A

Week 3: DIRT on topic A

Week 7: Review lesson on content A

But it’s not only the speakers and workshops which give great ideas. I happened to bump into Naveen and Dani, @Naveenfrizvi and @danicquinn, and got to ask a couple of questions I was intrigued about. Firstly rolling the timetables and implementing it with a group, and secondly from Dani’s podcast with Craig Barton @Mrbartonmaths, where she said they differentiated by time, so lower groups went slower. I just couldn’t fathom how these groups could have the same expectations if they went slower. The answer is obvious really – they have more time; more lessons!

I know I can’t do justice to some excellent workshops in such a short summary, but if it means that it interests someone to attend the next mathsconf14 in Kettering, March 10, then that’s great. A huge thank you to Mark and his team for another fantastic day of maths teaching CPD, and all the speakers who gave up their time to prepare and deliver such wonderful sessions.

Next for me is to give back and deliver a workshop myself, but for that I need to know I have something to offer that will be of interest to others and that’s worthwhile for teachers to give up their time for.

Oh, and I almost forgot, I need to do a bit of shameless plugging of our #TMBrownhills on Saturday 18th November, featuring @teachertoolkit Ross McGill, author of Teaching Backwards @oteacher Mark Burns and many local teachers presenting on classroom practice.

]]>

The ring binders were such a fab idea, and it just so happened that at the very point I was thinking about this, a friends workplace were closing down and skipping a load of lever arch ringbinders, which she kindly collected for me. Perfect!

Two years on, and it appeared so successful after the first year, that I repeated it last year with a similar year 11 group.

I’ve added a page with the folder sheets I have used over the last couple of years. I’ll admit I’m quite anxious about putting them all on as I know I’ve used resources that others have kindly shared. I’ve gone through and deleted resources that are from subscription or prominent sites. I’ve linked to TES resources I’ve used from there, but I’m still worried I’ve missed something that someone else took their time to create, so please accept apologies in advance and let me know if I need to credit you.

The first benefit of the folders is the organisation of the students work. We had 5 sections: Classwork, Homework, Assessments, Practice Papers and BBQs (more on those later!). It’s great to sling the assessments and past papers into after the follow up work.

For the classwork, I prepared a page, usually double sided, for each lesson, with the learning question already written on. I also decided to number the sheets with unit and lesson number on!

The real bonus of these sheets is that notes can be laid out for better referral back to them, and all the questions are already on there, so no glueing in! They tended to get a pattern of boxes for facts and speech bubbles to annotate examples.

Although it took time to make these sheets, these were the resource for the lesson. I didn’t make a powerpoint to go with them, as I used the visualiser I was lucky to have in my classroom. It wasn’t just a “copy these notes down”; as I was filling them in the same time as the students, it was all about the questioning too.

The BBQs are my starters I use. They stand for bread and butter questions; I first used Just Math’s bread and butter questions here, but then I wanted to use certain questions for my group, so developed my own. At the start of the year, I chose a selection of questions and then for four lessons in a row they would do the same set of questions (different numbers!). However, once we started doing papers, whether in class or for homework, I would choose mostly fluency questions which most of the class had got wrong, so the first session has more guided questions and then the next 3 would allow for further practice on these areas. Next job is to upload these!

I would totally recommend using folders for GCSE work. I would imagine if I were to do these with a higher foundation group, or a higher group, then I would leave more blank spaces for the students to make their notes, rather than the prescriptive layout I’ve been using with the groups I’ve had.

]]>Most of my preparation has been about familiarisation. I’ve popped into my new school a few times for short periods so I am familiar with my surroundings. I know my way much better along the corridors; essential so I’m not looking like a lost puppy during my first week. When logging onto the email system I was greeted by 120 emails! I had been added in early July, so I did spend some time reading through some of the emails that helped me get a better feel for the school and leadership.

It’s been good to meet some of the people working at the school during the holidays. I’ve met (and had a quite a bit of help from) the network manager, two of the caretakers and a couple of the student services team.

And of course there’s my classroom. I was lucky that the notice boards were left with displays on, and that the classroom had been painted over the holidays, but I also wanted to make my own mark on the classroom, and put up displays that would both be useful and interesting. Ideas and resources have come from Artfulmaths.com (flow chart, squares and cubes, mistakes quotes, faces behind the formula), Missbsresources.com (vertical number line, shape and formula bunting), and solvemymaths.com (Mr Men). I don’t know where the prime number caterpillar originated as my job share colleague put it up in our old room, and after she retired, I had to bring it with me. The fractions, decimals and percentages were an idea I saw at my son’s school.

Pride of place above the whiteboard is my maths clock, a present from my maths department at my old school.

EDIT: Twitter and @MrReddyMaths have linked in where I’ve seen the “Be Kind, Work Hard” mantra before. It’s from King Solomon’s Academy, “Work Hard, Be Nice”, taken from KIPP schools in the US, who got it from Race Esquith (Teach Like Your Hair’s on Fire).

The (almost) final part of my preparation has of course been for the students and their lessons. Although I know my timetable, I do not yet have any information about the students I’ll be teaching. This will be a priority during the first couple of days, to get as knowledgeable as I can about these students, both from their previous teachers and from the data that is available for them. Until we meet as a department, I also do not know the full expectation of the first lesson; whether I’m to go straight into the scheme of learning or can have an introduction lesson. Ideally I’d like a lesson where I can set an easy access but high ceiling challenge as part of some time to get to know the students and for them to learn about my expectations and routines.

I have viewed as much of the scheme of learning as possible for my classes and started to prepare lessons for the first week. I always like to prepare for the week ahead, with the flexibility to adapt when necessary as the week goes through. As well as looking through resources I’ve used to teach these topics before, I’ll be visiting my favourite websites for any inspiring resources that cover the learning objectives: www.resourceaholic.com, don steward.blogspot.co.uk, mathspad.co.uk to name a few.

Summer reading this year has been The Confident Teacher by Alex Quigley. It was a book used by my new school last year. I’ve still got a bit of it to go (the first four weeks I took the opportunity to read novels, something I don’t get much time for), but so far there are some great nuggets to take away from it. I’ve also continued listening to Mr Barton’s podcasts, and have just finished the interview with Robert and Elizabeth Bjork on Memory, Forgetting, Testing and Desirable Difficulties. Again, fascinating! One of my objectives for this year has to be to put to practical use the research about interleaving and spacing. I need to reread Damien Benny’s blogpost on this as a starting point.

And finally there was Summaths! Meeting up with twitter maths teachers for a summer social was both a great way to relax and motivate for the upcoming year. Jo Morgan (@mathsjem) had arranged an excellent day out with Tom Briggs (@teakayb) at Bletchley Park. Tom ran four different sessions about cryptography, and the two I went to reminded me of the Turing Cryptography challenge we did a couple of years ago for some year 7 and 8 students, which would be great to do again. My absolute favourite part was finding out more about the Enigma machine, and I actually got to have a go on it too! It fascinates me both how it works and how the codes were broken. It was great to meet some more maths twitter folk (@arithmaticks, @mrsmathematica, @emmaemma53, @amercertbs and @travellingblue to name a few) as well as catch up with those I’ve met a few times (@rjs2212, @ejmaths, @solvemymaths). The quiz was, as always, hard but fun and I was kicking myself on the cryptarithm as I was just 2 numbers away from solving it but forgot about 0!!! My husband and boys met us for the evening meal as they were staying over too ready for a bank holiday day trip to Gullivers!!

]]>

What I was thinking of sharing was a resources from another maths teacher that I had found extremely useful, and had shared with my department, for tackling problem solving, and the difficulties students have sometimes in getting started on a problem.

Back in July I read this post from @mrlyonsmaths on his blog mrlyonsmaths.wordpress.com about problem solving and the lack of resilience in even starting at solving a problem. Mr Lyons suggestion was inspiring and I’ve used his resource as a basis for problem solving with my groups this year.

This is Mr Lyons’ problem solving scaffold, with descriptors of each section. He’s generously made it available to use it/tweak as required on his blog, following link above.

It’s a fab way of getting students started on a problem as to begin with they are rewriting the key points of the question. Highlighting is good when you recognise where you’re going to go next, but for the less confident pupils, thus actually gets them started on writing something, and then some maths just seems to lead on from there.

These are just three examples of questions I’ve used the format for, for different year groups and abilities of students.

So a big thank you and shout out to @mrlyonsmaths for giving some of my students an entry way into problem solving.

]]>The school policy is for a comment mark using http://www.ebi.com (what went well, even better if, comment), and in maths the regularity of this is once a fortnight in years 7-9 and once a week in years 10-11. Assessment feedback is included in the comment marking, and most of our team use home work as a comment mark, with occasional class work being comment marked. Using home work creates its own issues with pupils not completing it, or handing in late etc, but the focus here is purely on the feedback and improvement.

The biggest thing we noticed was that in a good chunk of the samples, the teacher was working harder than the pupil, or the amount of teacher feedback compared to pupil response. We were doing our best to give quality feedback, but the resulting effort of the pupil was minimal and meant our feedback wasn’t doing it’s job in helping pupils improve. So as well as dealing with the pupils’ effort, we went on to discuss methods of giving concise and effective feedback. We discussed giving target or question codes, and then projecting the questions for each code for the pupils to complete, as suggested by @shaun_allison in his blog classteaching and in his book with @atharby Making Every Lesson Count (great book – I’m really enjoying reading). A second idea was to use @Missbsresources Dirt Bank, and start creating our own to share, where pupils have a guided question, followed by a similar question without scaffold. Again, these could be projected, or printed out for the pupils. This would also help with the pupils who immediately put up their hand to say they don’t understand, and give some of the responsibility back to them to read through and think about what they are doing.

The quality of the improvement comment by the pupil was discussed. Clearly saying that they were going revise a topic by a certain method does not mean they actually will, so did we follow up? And then there were the pupils who didn’t even complete the .com (could this have been because they were absent) and how do we follow up with this? It was discussed about training pupils how to use the ebi.com process, and this must involve both modelling to them and providing examples and good improvement work.

We talked about our assessment feedback sheets, and who should write the http://www. Normally, the teacher does, but as we give the pupils the question level analysis, should pupils be scrutinising the objectives and picking out what went well themselves, rather than the teacher repeating writing them out.

For home work marking, an idea from a teach meet was to have a printed out list of the objectives you were assessing, and to tick those that went well, again to save the teaching keep writing them out, thus giving more time to focus on the even better if.

There was the question of signposting the .com as well. We do use green pens for this, but there were several examples where it wasn’t clear where the .com was, for example when a green pen hadn’t been used and improvement work was on the initial piece and not underneath.

We looked at examples where improvement work had been highlighted to guide pupils to what they need to improve, with guidance in the ebi. There were also examples where the ebi might just have been a question number, but when you look at that question, further guidance was given at that point, rather than in the official ebi part.

Another part of the discussion we had was when was the best time in the lesson to do the feedback and the .com. I’ve always done it at the start of the lesson, but it does cause an issue of getting drawn out and having to provide further work for those that complete it, before we’ve even begun the lesson. The argument for using the start of the lesson is that pupils need the feedback and improvement time before they can move onto the next part of the learning. We have agreed to try the .com at the end of the lesson instead. I’m still getting my head round how this will work with the flow of learning, for example when feeding back on an assessment, I wouldn’t like to start the new topic first, then return to the previous topic to do some improvement work. However, the idea is to improve the focus of the response, and having a limited amount of time should spur pupils on, especially if it is before a break or lunch time!

So we ended up with a list of good practice in an attempt to improve how pupils respond to our feedback. It may seem really obvious to other teachers, but it gives a boundary of consistency across the department:

- When marking, go back to previous .com to ensure follow-up
- In ebis, highlight when pupils are being told what to do in their .com e.g. correct Q2 etc.
- Ensure students signpost in .com when they have done follow-up work elsewhere.
- Put a selection of questions on board and use a code in pupil’s book so they then complete the correct question in their book.
- Follow-up questions to complete as part of .com
- Make sure work is dated (either start of piece of work or in the feedback).
- Use 10 mins at end of lesson for .coms to increase pace and ensure completion to high enough quality before they pack away.
- Use mini post-its in books where .coms are not completed so pupils can be kept behind to do so.
- Give detentions were pupils refuse to complete .coms.

Both lessons started in exactly the same way, with the brilliant Numeracy Ninjas by @maths_master William Emeny (greatmathsteachingideas). I do some sort mental arithmetic or skills practice at the start of every lesson, as not only does it set the routine for the pupils, it settles them into thinking right from the start of the lesson, and ensures their numeracy skills are regularly practised to support with the fluency when tackling tougher topics. For the year 10s, they are focussing on the first two sections, mental numeracy and timestables, whereas year 7 whizz through these two sections and focus on the key skills section. We then pick out a question that pupils struggled with to review, before launcing into the topic for the lesson.

I knew when planning this lesson that the year 10 group studied translation last year, so they should know what it is. However, they wouldn’t have used vectors before, so this was the focus of the lesson.

We started with a quick reminder of translation, then headed straight into what a vector was. An explanation from me, some note taking and a few vectors for the pupils to think about what they mean.

We then spent a chunk of time identifying the vectors that would move the points, and then shapes.

This was whole class questioning, and they weren’t allowed to use the words left, right, up or down, just the two numbers in the vector. I, of course, threw in a question where there was only movement in one direction, and pupils discussed how they would give the vector for that. Then pupils had their own practice time in their books. As I circulated, I caught a couple of pupils writing their vector as a co-ordinate pair, and we stopped and discussed the different between a co-ordinates being a position and a vector being a movement, and therefore had to be written in the correct notation.

Once pupils were more secure in their vector writing, they then had a lovely translation activity from @just_maths (as a school we subscribe to Just Maths Online). We discussed the importance of identifying a vertex to complete the translation from, and to check they are completing the translation correctly, they could choose another vertex and repeat the translation.

And that’s it! I don’t really do bells and whistles in my lessons, I just aim to teach the pupils as best I can and give them the time and support to practise and hone their learning. In a few lessons time, we’ll be bringing all the learning on transformation together, where pupils will have to carry out or identify the correct transformation, including combinations.

Before I taught this, I knew that most, if not all, of this group would have been taught about order of operations at primary school, so this would be a revision and stretch lesson. I had to ensure they knew and understood the basics, but be ready to give them a bit of a challenge.

I love foldables as an alternative to note taking, and I have a BIDMAS Foldable I created for this topic. I teach order of operations as BIDMAS, being careful to keep DM and AS on the same level. The only sticking point was that pupils had been taught BODMAS previously. We discussed what order and indices mean, and I explained why we use indices at secondary school (in the mathematical vocabularly they are excpected to know).

The skills practise involved 3 levels of questions. Pupils could choose the level to start at, and several went straight for the gold challenge, whereas others wanted a bit of practise on the more straightforward silver questions first.

The challenge activity was a calculation square from Don Stewards Median website. I really liked this activiy, as it did make the pupils think. Not only did they have to remember the order of operations, but they had to think about where to start and what each calculation was asking. Pupils who found the gold questions starightforward minutes ago, were feeling quite puzzled about this one.

We finished the lesson with another Don Steward activiy, bracketed, from which I chose 5 equations for the pupils to decide if they were correct, or if they needed brackets in. Although mostly identified correctly, the biggie that came out of this was pupils thinking the 5 x 6 needed brackets in 2 + 5 x 6 = 32.

Unfortunatley I don’t have any photos of these pupil’s work as they have their books for revision! The powerpoint is attached BIDMAS.

You can probably tell that I have go to places for resources and activities in my lessons. When there is so many quality resources around, thanks to the generosity of so many maths teachers sharing their work, there’s no point reinventing the wheel! I do plan my lessons thinking of the outcome first, and then looking for activities which will enable this outcome for the pupils.

I hope you’ve enjoyed these lessons. I’m looking forward to reading and being inspired by others in the #MTBoS challenge who have shared their lessons too.

]]>