I’ve put together a list for my students of what came up on paper 1 and what hasn’t appeared so far. Health warning: mine are target 6 students, so there are some topics missed out, and I have done this having left the paper at school, so I may have forgotten something! However, as always, if you find it useful, use and adapt as you wish. Questions all taken from edexcel past papers, and using new spec questions as much as possible.
This warm up powerpoint is aimed at students targeting a grade 6. It’s a mixture of reminders and questions – it’s possibly got too much in, but as I was writing it I just kept thinking of something else I hoped they remembered! Feel free to use or adapt as you wish!
A quick overview of the mathsconf14 sessions I went to, with my takeaways and links to the blogs of the speakers, who obviously put it much more eloquently than I can, which is why they were presenting!
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.
Workshop 1: Naveen @naveenfrizvi – Engelmann Insights: Structuring Teaching for the Weakest Pupils
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!
Workshop 2: Danielle @piximaths – Scaffolding in Maths Education
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.
Workshop 3: Jemma @jemmaths – Building Effective Learning Strategies into a Maths Curriculum
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.
Workshop 4: Craig @MrBartonMaths – How I Wish I Taught Maths, 2 months on..
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.
My sixth mathsconf, so it’s about time I blogged about the fab day organised by @Emathsuk and his team at @lasalle.
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.
In September 2015 I inherited a foundation year 11 class. The class had previously had low achievement levels and included a few pupils (at least 50% if I remember correctly) with SEN. We struggled during the first half term, particularly with getting maths notes and examples written in books. I was printing out an awful lot of write on worksheets and gluing them into books. I then read @mathsjem’s post on resourceaholic.com about her foundation group in which she wrote about the folders she used to organise their work and study packs for each lesson. See her updates on this here and here. I thought this would be an ideal way of working with my year 11 group, particularly in supporting their note taking, so many thanks to Jo for introducing me to this plan.
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.
For the first time since starting my NQT year in 2008 I’m moving school. In 4 days I’ll be starting at a new school, with a role in Teaching and Learning across the curriculum. I know it’s the holidays, but for me I need to be prepared for my new school, so I’ve been spending some of the last couple of weeks getting myself ready (I did make sure to have a good break in the first four weeks of the holidays!!).
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!!
Eeek, I’d been all prepared and printed out resources I had thought to share for speed dating at #mathsconf6, only to leave them on the printer at home. So next best thing I could think of was to get hubbie to take a couple of pics, email them to me and post about them on here.
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.
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.