Challenge for all

You know the feeling when you return in September, feeling prepared, lessons ready, imagining your groups, beautiful 5 minute lesson plans for the first 12 weeks that took an hour each all ready….smug! Then day 1 you are hit with...right so today we thought we could spend some time planning the first few weeks of term given our new lesson plan and scheme of work structure….Argh!!!! It’s all changed! Into the bin goes your summer work and rapidly you pray to get through at least the first 4 weeks worth of work in a day. No idea what I am on about, then you are very fortunate as this happens to me every year! Thankfully every year’s change or tweak to the lesson plans or schemes of work are positive and eventually I am pleased they have changed but those first few weeks are gruelling!

A few years ago I was introduced to the 'challenge for all'. (Cue images of Tower of Terror ride at Disneyland and the Twilight zone music!) As part of the team responsible for coaching and mentoring staff to meet standards it was quite complex to get across to staff what the 'challenge for all' is. I can take no credit it was all the work of my amazing teaching and learning colleagues but I am more than happy to share it!

To be clear, this is not stretch and challenge in the sense that you plan for the HATs (oldie but a goodie term!) top end of the group some extension activities. There is an element of that but it is actually about challenging all learners no matter where they sit in your group. What often comes up as good ideas for challenging all are, design a tweet, create a mnemonic, promote a discussion with deeper probing questions. Some of these techniques are useful and appropriate to maths lessons but often they are not. Discussions and opinions about who is right and wrong are very limited in their applicability in maths in my opinion. 

Imagine we are teaching expanding brackets, something like 2(x+5). 

Traditionally to stretch and challenge the high attainers we might ask them to move onto expanding double brackets, for example (x+5) (x+3). This stretches their skills to a new level. However it can be argued that they are actually learning a new skill in moving on to double brackets. In my experience of doing this, more teacher input is required meaning that the learner isn’t being stretched but that the teacher is guiding them to the next activity. Yes you can set them off with scaffolded worksheets to relieve this but I always have Dylan Wiliam ringing in my ears at this point. Wiliam (on the amazing Mr Barton Maths Blog) talks about a hysteria of a few years ago which came from observations where teachers, observers and OFSTED all wanted to see more activities to evidence the learning. Thankfully this is less so now, we recognise it’s not the busyness of the learner it’s the engagement that tells us if learning is taking place. This is why I like the 'challenge for all' element. It’s not about keeping them busy with the next thing, it’s not about more teacher input, it’s about deepening the learners understanding of the topic covered in that lesson.

So let’s return to our expanding brackets of 2(x+5). We could ask learners to create a tweet, a diagram of the stages or a cheat sheet (see next blog). However, if we could apply their knowledge to new concept we could evidence a deeper understanding. Asking them to move onto double brackets wouldn’t necessarily achieve this. We could take expanding brackets to solving a worded problem, an AO3 style question.  We could ask the learners how old Millie is if Billie is 5 years older than Ellie and Millie is twice as old as Billie.  For the lower attainers we could form the expressions as Billie is (x+5) and Millie then is 2(x+5). For the middle attainers we could give them the problem without the expressions. For the high attainers we could ask them how old Millie is if Billie is 12 and they could solve the expressions. We could ask all of them the age difference between the oldest and youngest and see if they can work this out algebraically rather than by solving. This got me thinking, would this work with any AO3 style question? Could we give a 'challenge for all' opportunity for all just by looking at the AO3 style problems. 

I am a big fan of doing something well once and it will save you time in the long run. I created a lucky dip box and cut up AO3 questions and put them in the box. The 'challenge for all' then became about learners applying their knowledge to an AO3 style question. It started off as random and they could pick a number AO3 question out and we had been learning data but it worked as a nice retrieval element as well. Reflecting on this,  I created an algebra AO3 lucky dip, a shape AO3, a number one, data and finally the really tricky crossover problems box lucky dip. Depending on the topic would depend on which lucky dip box we used. The beauty of this was high attainers could pull their own AO3 out. Mid and low attainers we could work on as groups and collaboratively solve. 

As with anything once it becomes routine it is expected. Learners would race through activities to get to the lucky dip. There was a leader board of who answered which question quickest. We would discuss if one question was harder than the other, and if so why. Given that we think one is harder than the other, should they be worth the same amount of points for the leaderboard. This then got learners thinking about the design on the question. One healthcare student said “the maths isn’t any harder in that one it’s just spotting what it’s asking” I think if we are aiming for learners to deepen their knowledge that quote sums it up beautifully. If learners know why they are doing something and can explain what the aim of the task is they have begun to understand the topic. We will cover understanding another time….

Retrieval Practice

I love to read, and I read widely around education, teaching. Maths, anything that interests me. However, no matter how much I love to read the amount of time I am able to spend reading is significantly less than I would like it to be. Prior to my current position, unfortunately the only real time I devoted to reading was when there was an urgent need. I was preparing for interview for my previous position I was trying to find some research that was relevant to what I was discussing in my presentation. 

I know this is the wrong way round to do things the research should have informed what I was doing beforehand but we were where we were and the interview was in 2 days. I am pleased that I now allocate myself coffee and reading time once a week to keep up with the latest blogs and developments. I love my coffee and reading time and it is sacred, I need it to be so. That doesn’t mean that if work is busy and I don’t get time to read at work I will make time to sit at home with a coffee and read, point is I read weekly! Whilst preparing for my  interview I came across retrieval practice. Retrieval practice had nothing to do with what I was presenting in interview but it instantly sparked my interest. 

I ended up spending all my interview talking about retrieval practice and openly admitted that I haven't used it yet because I just found it but since I got the job and have begun using retrieval practice. I am not an expert but am happy to signpost you to the experts here: https://www.retrievalpractice.org/

Retrieval practice works on the basis that if you regularly retrieve small bits of information you will deepen your understanding. It was really nice to finally find something that was current, relevant to my teaching and unusually appropriate to a maths lesson. Too many times as a maths teacher I have felt left behind. Whilst other subjects make huge strides in questioning and feedback I find myself trying my hardest to make it work in maths but most of the time answers are right or wrong. The guys at https://www.retrievalpractice.org/ shared a retrieval practice grid where the topics that have been covered previously were colour-coded by how far in the past they had been. This was easily replicated into my lessons and it looks a little bit like this. 

Share £60 in the ratio 7:5	Find the nth term of this sequence: 32, 26, 20, 14, 8	Simplify: f + f -f +2f -2f + e	Multiply: 5.4 x 3.2
What is the 100th term of the sequence 5n-6?	Tickets cost £3.50, we need 18 tickets in total.  Calculate the total cost.	Share £125 in the ratio 18:7	Simplify: d x d x d
Simplify: 2k - 3g + 5g + 4k	The next term in a sequence is 15. The start number is 9. What is the nth term rule?	Multiply:  2.5 x 1.2	Aliaa and Steve share £45 in the ratio 5:4. How much do they each get?
Multiply: 4.4 x 3.2	Gray and Teag share some money in the ratio 2:3. Teag gets £45. How much was the total amount shared?	Simplify: e x j x j x e x e	Is the term 54 in the sequence 6n-6?

Red is 4 lessons ago, orange is 3 lessons ago, green is 2 lessons ago and blue is last lesson. This replaced my bellwork. Students arrive and these are on their desks already they sit down and begin working through the grid. Every lesson I would change the questions and colours. It really wasn’t an onerous task. The aim of it being a little reminder a little refresher and in total would take less than 5 minutes to go through the board. So I would give the learner's 5 minutes to come in and do it and then 5 minutes to run through at the board I felt that it was worth the sacrifice in my lesson time but I appreciate not everyone has 90 minute lessons like we have. (We only have 1 90 minute lesson a week though!)

My adult resit learners would sit and discuss the questions. You would overhear questions about when to use ADAM or DINO. I would spend the 5 minutes catching up with any absentees from the previous week or any messages that I needed to pass on to my learners. The next time when I would look up the powerful maths discussions that were taking place were jaw dropping. The collaboration and cooperation of learners in reminding and refreshing each other with how to answer the questions was lovely to see. Age gaps disappeared and mature adult learners were working at the same pace and stage collaboratively with teenage adult learners. Over time our little routine expanded into each table being responsible for sharing the answers rather than me standing at the board. My application of the grids also evolved in that the red section became a place for poorly answered topics to be repeated and recovered. For example nth term would be in the red section for one class for a few weeks whereas for another class it was factorising. Using these grids I was able to personalise the retrieval practice that each group needed.

Having taught resit groups for a number of years the impact in my results was significant. The topics that have been regularly and consistently answered correctly on my retrieval practice grids were regularly and consistently answered correctly in my mock exam papers. It was evident that those 5 minutes made all the difference in keeping topics ticking over. When we came to the actual exam one learner asked me for a copy of all the previous retrieval practice grids to revise from. This was a Eureka moment. Thanks to Google Docs I had a bank of sheets that I could print off and issue meaning we had instant revision packs ready to go! Google docs is brilliant for this because it has version history allowing you to revert to previous versions. If you would like to know more about Google docs I will talk about this at a later date. 

Not only did retrieval practice improve my in class testing, it helped create an empowering collaborative working environment which was an outcome I wasn’t expecting. It also enabled me to have a class specific time relevant revision pack for learners appropriate to their stage and ability. I am a big fan of curating revision collections for my learners based on the topics and how well they have done in them. Retrieval practice did this for me! 

Nth Term Sequences

I love teaching nth term! I am not going to lie it is one of my favourite favourite lessons. 

I follow a great guy on TES called alutwyche https://www.tes.com/teaching-resources/shop/alutwyche  (he is also on Twitter https://twitter.com/andylutwyche) from the very beginning of my teaching career his resources have saved me from dreary worksheets consistently. When you are teaching mixed ability groups his bank of lessons of grade A to G of the old GCSEs are a lifesaver. His explanation of the nth term was completely different to how I had been taught it how I've seen it before when I was training and how my department taught it when I qualified. I love seeing something taught in a different way.

I was taught, and I saw be taught and my colleagues were teaching, nth term as you work out the difference and then you write that in front of the n and then you work out what you would do to get to the 0th term, like this:

This guy introduced me to the times table method you may have seen it before but it blew my mind. You work out the difference then you write the times table of that number above the sequence then you calculate the difference and you end up with the nth term rule. Have a look at this example.

Learner's really respond to this because if they have been taught a way that hasn’t worked before for them, it's nice to give them something different. But like I always say if you have a way that works for you you use that way. I only offer alternatives when you don't have your own way of working things out consistently correctly. 

Thinking about the working out the difference and what would the 0 term be I began to think about the steps that we were doing. We work out the difference you put that in front of the n and then you work out what the 0 term would be I wonder if there was a way we could make an acronym or a mnemonic for this and I thought Dino. A quick Google later and nth term with Dino is a thing and there are loads of resources out there! Phew I’m not going mad, others are thinking the same as me! So just like at famous Adams and famous Terry's appearing my lessons the amazing Rex the dinosaur from toy story also appears in my lessons. And it works like this 

D is for difference 

I in front of 

N 

and then the letter o is actually a number

0

This really helps learner's remember the steps they often know how to work out the difference and they know it goes in front of an it's just what are they adding or subtracting it's the final stages. With my famous Adams my famous Terry's my female mathematicians and now Rex the dinosaur from Toy Story on my walls hopefully now you can picture what my classroom looks like. 

Transformation Terry

So I have introduced you to ADAM, my SASSYLASS, and my magic triangles you can imagine what my walls are full of in my classroom along with my equality and diversity posters my safeguarding policy and my famous mathematicians through time. I only ever pick female mathematicians it provides an interesting discussion point for those that take notice of my boards. I recently walked past the pub with an a board outside it that said my manager told me to write something good on here to get customers to come in but nobody reads these anyway. This is true of my teaching boards I spend ages making them look wonderful and I really enjoy it when they ask questions about my famous female mathematicians. 

Let me introduce you to Terry, famous Terry’s are also on my walls! I've just mentioned before about a teaching transformations and how the learner's missed me and my experience and what I say and do when I teach transformations. I think this may be something to do with Terry. Terry is one of those lessons where learner's leave laughing and I mean genuinely laughing about a maths lesson and then can apply it straight away into an exam style question. So nothing difficult nothing tricky and I can't remember where it came from, it may even have come from me but I've been using Terry for years now. As well as famous Adams who appear in my lessons famous Terry's, Terry Pratchett, Terry from The Word (if you are as old enough as I am to remember The Word) Terry Butcher... all sorts of Terry's randomly appearing my lessons when it is a transformation question to remind them that they need a Terry. 

Terry applies to the “describe a single transformation” question that has been a mainstay throughout all the incarnations of GSCE specifications in my teaching career. How often do we see “it was flipped and then rotated”? (One of my favourite always incorrect answers!) No matter how I teach transformations someone always tells me a shape has been flipped!!!!! So to avoid the flipped and rotated or it was moved and turned or it was made bigger and turned round I decided to talk about Terry. 

Terry is Translation Enlargement Rotation Reflection whY? you only need one Terry in your life. 

Lessons have been completed on transformations. We are looking at completed transformations now so we have an understanding of the fundamentals of transformations. We look at a completed transformation and I will ask the class what has happened here?

I then follow it up with, pick a Terry and stick with a Terry, don’t ever change your Terry. It's the opposite of Bruce Forsyth's play your cards right, there’s no swapping your base card here! You can see how the students start to laugh. The learners enjoy the humour of talking about Terry and how you pick a Terry, you stick with a Terry and be loyal to your Terry. I have found this a useful way to ensure the correct language is used in answering these questions and thankfully the number of times I have read “it has been flipped” as been significantly reduced!