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.
Edexcel Paper 2/3 Prep
Edexcel Higher Warm Up
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.
GCSE Foundation Maths Folders
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.
Preparations for starting a new school
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!!
Sharing good practice #mathsconf6 resources
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.
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.
Sharing Good Practice: Marking for Feedback and Improvement
We had one of the best, if not The Best department meeting last night. There was one item on the agenda, which lasted for the whole hour: marking for feedback and improvement. And the reason why it was the best was that we spent the hour looking at all sorts of examples of our own practice, identifying the good practice and discussing how we could improve. The collaborative approach meant we could share the difficulties we found, and suggest ways together of overcoming these, so that our feedback became productive for pupils improvement. The photos shown on here are just mine, but attempt to cover the areas of discussion we had. I know I haven’t got it right yet, so by the end of the meeting, had an armful of strategies to try.
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.
Two Lessons, Two Year Groups: Translation and BIDMAS
The final #MTBoS blogging challenge is about a lesson taught this week. I couldn’t decide between two of them, so thought I’d write about both, being two quite contrasting groups. Firstly, year 10 (14-15 year olds), who find maths quite challenging and haven’t had much success in their achievement over the years, but are working extremely hard and hopefully becoming more confident, learning about translation and then year 7 (11-12 year olds) learning order of operations, a group full of high achieving pupils.
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.
Year 10 Translation
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.
Year 7 Order of Operations
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.
With week 3 of the #MTBoS blogging challenge we are thinking about questioning. And this did get me thinking, as verbally I know how I question pupils, but with written questions, whether it is class work, home learning or assessment, I hadn’t reflected much on the process. Yet as I got thinking about it, I realise I do have my particular ways, developed through experience and doing my best to read around other teacher’s practice and experience, as well as latest education news.
Starting with verbal questioning, it’s fairly staright forward to me. I want to find out what pupils know, facts and processes, and why they know that. When working through a problem whole class, I direct questios to pupils, and different pupils will get different questions from me, depending where they are in the learning process. I might ask one pupil a closed question to see whether they can recall certain aspects, whereas another pupil I might want to elicit further understanding from them. My favourite question is probably “why?”.
Onto classwork, I begin with the objective of the lesson and what I want students to be able to do by the end with their learning. I don’t often make up my own questions – quick practice questions I will do, but the deeper, thoughtful questions I search around my usual haunts until I find the questions which suit. We have electronic text books, so I may select questions from these, or use websites such as Don Steward’s Median, Resourceaholic, Teachitmaths (subscription) or Mathspad (subscription), and not forgetting TES resources.
I also keep in mind the SOLO taxonomy, so that the questions I give the students can develop from single knowledge questions, bringing in extra skills, through to problem solving questions, which may link to other areas of maths. Take area of shapes, for example. Questions would start with practising using the formula to find the area of the shape, then it might be finding a length, given the area, fidning the area of compound shapes, developing through to a problem solving question, which involves other areas of maths, for example fractions. I use a bronze, silver, gold, platinum system to identify the level of difficulty in the questions. Bronze would start with the basics we covered in whole class work, and each new section would involve something extra the pupils would have to think about. I often give a minimum number of questions to answer from each section, depending on whether it is a totally new topic to the group or not. The Plotting graphs example attached starts with the basic y = mx + c graphs that we worked through as a class, and develops into different forms of the equation, where pupils have to think about what the equation is saying.
For home learning, I section my questions into the three areas of the new curriculum, fluency (I call it skills practice on the home learning), reasoning and problem solving. There are more questions on the fluency section, as a primary focus, but I think it’s important that students are exposed to the reasoning and problem solving questions. My question choices are by no means perfect, and the reasoning and problem solving do cross over, but it’s a starting point I am developing from. The example is a home learning for Metric and Imperial Measures. For reasoning questions, one of @mrbartonmaths diagnostic-questions is good for pupils to explain their choice from the multiple answers on offer. These questions are carefully set by Mr Barton to help reveal misconceptions.
Finally, when it comes to assessments, for KS3 (11-13 yr olds), we have bought into a scheme that provides the assessments. With the quick change over of the curriculum, and no permanent head of department, it seemed best to start from something already written, and tweak as we go along. And oh how I’ve tweaked. I’m a devil for looking through assessments and thinking, that’s not what I want! I believe our end of unit assessments (a 20-30 minute assessment every 2 weeks), should be assessing what the pupils have learnt. At a previous #mathsconf, I attended a session on assessment by @kris_boulton, which was very informative, particularly about defining the domain of what your teaching – the assessment should then cover, as much as possible, this domain. Although teaching should focus on the domain, it isn’t restricted, so can go further. Assessment goes in the same categorise as the home learning for me, but not explicitly split into sections. There needs to be some knowledge and skills questions, and there also needs to be the questions that use the skills in more implicit ways.
I think I have changed all my spellings of questioning, as I’m very much inclined to put a double n into the word! Please forgive any I missed!