Sort of Rethinking Card Sorts

During my ITT and NQT year, my colleague (a science teacher) and I just couldn’t get our heads around the idea of ‘card sorts’ which were pushed on us by our university tutors in particular. Why use them when, even then, we realised there are more time efficient and yet equally effective ways of encouraging students to think about and sort information.

Eventually we started using the term ‘card sort’ as a term of derision used to describe a particular type of teacher who insists on using ‘card sorts’ (and any other activity where the input didn’t seem to justify the output). “Oh that Mr Jones, he’s a bit of a card sort him” or “Ms Khan has got six different coloured worksheets out again, what a card sort”. Furthermore, as a teacher, nothing irks me more and immediately switches me off than having to undertake a ‘card sort’ in an inset session  as part of an attempt to disseminate and drip-feed staff ‘good’ classroom practice and I always imagined many students think similar things when faced with one in the classroom.

And that was that. No card sorts for me ever. Or so I thought….

I was recently given a ‘card sort’ activity by a colleague on classifying data and I threw caution to the wind and gave it a go thinking of it as a substitute for a large number of textbook style questions which I didn’t have to hand on this particular topic.

The activity was, to misquote Obi-Wan Kenobi, (it was Star Wars Day this week after all) “more powerful than I could have possibly imagined” and far more effective than textbook style questions could have been. The activity allowed students to appreciate that not all categories of data are mutually exclusive and that data can for instance be both primary and continuous.

Perhaps this is an obvious point and but too often I have seen card sorts used, and indeed been ‘subject’ to, card sort activities which just get students to consider and debate whether something belongs to one of a number of categories or just as a substitute for getting students to write things down in oder. A quick search on TES yielded the following card sorts:

  • A Geography card sort-‘Reasons for population control vs. reasons against population control’;
  • A card sort in which students had to order chronologically the events and personalities leading to the discovery of the structure of the atom;
  • A card sort of the chronology of the events leading to the outbreak of the Second World War;
  • A card sort on the positives and negatives of nuclear power.

In such cases I just think teachers can use their and their students’ time far more efficiently than preparing and doing such an activity. If you want students to learn and put things in chronological order, just get them to write the damn things in chronological order. There is only one answer here- moving cards around on a page won’t change that. You want students to debate the positives and negatives of nuclear power? Great- get them to draw out a table (a skill in itself), or better yet, get them to write about the issue. If you want to encourage students to consider all sides of the argument or decide between the importance of various factors and are worried writing things down will lead them to keep one opinion rather than consider changing it, then perhaps a card sort does have more value. Although I still think there ways of doing this that won’t require the preparation, cutting and sorting that could instead be used planning, teaching, learning and thinking (mini whiteboards that can quickly be erased spring to mind here).

However, in cases such as the one above, where students have to consider non-mutually exclusive overlapping categories, I found that it genuinely contributed to learning in a way that I don’t think could have been done by other means.

Card sorts shouldn’t be used to order things chronologically. They shouldn’t be used to sort things into simple, exclusive categories ‘chemical change vs. physical change’ for instance. They probably shouldn’t be used to encourage students to debate issues where there is no right answer, although there is perhaps some merit to this. Where card sorts do have a use is in encouraging students to appreciate that things can fit into multiple categories at once (sorting shapes is another area that could lend itself to this sort of activity). I wonder how many of the card sorts used at INSET sessions fulfil this criterion!

Traditional doesn’t equal boring

Making my lessons enjoyable isn’t my number one priority when teaching in the classroom. Or my number two. I’m not even sure it is third on the list. However, despite teaching in a fairly traditional and ‘boring’ way, I think it would be fair to say that most students I teach do enjoy the majority of their maths lessons.

I teach in a traditional and consistent style. Most of my lessons look the same- a starter or quiz lasting 10-15 minutes recapping a range of previous topics that have been covered so far in the year, an introduction or reintroduction as appropriate of the concepts being learnt and practised in the lesson, some modelling, independent practise (often in silence) with me circulating and discussing answers with students and identifying any common misconceptions, more modelling if required, and possibly a final question to check what students can do at the end of the lesson (note I write what they can do, not what they have learnt). The lessons feature lots of mini whiteboard work so that students can’t ‘opt-out of thinking’ and lots of questioning. I don’t use many of the ‘gimmicks’ or ‘hooks’ that some teachers choose to and I believe in the value of didatic teaching methods. I am unashamedly strict with my classes whilst simultaneously being warm with them. I rely on my personality and ‘humour’ (very much of the cringeworthy/dad variety) and try to inject a lot of energy and life into most of my lessons.

I am by no means perfect at any of this and, some days I am certainly not as good as I want to be. However, this is what I strive towards each lesson of each day.

I am not claiming this is a better or worse style of teaching than other methods (in terms of content learnt over time). My aim is to argue that this fairly traditional style of teaching isn’t ‘boring’ or ‘unenjoyable’ for students (though, even if it was I would still be inclined to teach this way as I do consider it to be the optimal method).

Some thoughts about why this is the case:

  • Progress– students enjoy making progress. They enjoy being able to do things they couldn’t previously do and gaining confidence as they begin to master their subject. Genuine and precise praise is clearly important for this, as is reminding them of how far they have come.
  • Relationships- these are one of the keys to to any teacher’s success. Building up strong relationships, getting ‘buy in’ and gaining the trust from students, whatever the teaching methods used will lead to students enjoying lessons, irrespective of the style of teaching used, whether ‘traditional’, ‘progressive’ or anything in between.
  • Enthusiasm– same as above- if a teacher is suitably enthusiastic, the style of teaching and the structure of lessons fades into insignificance. Students enjoy having enthusiastic teachers, however they teach.
  • Structure-having taught in both a ‘challenging’ inner city school in the UK and an extremely high performing international school, I believe that despite protestations that some students might make, almost all students prefer structure and clear boundaries (in my experience this is especially the case with boys but this is both a generalisation and purely anecdotal). A ‘traditional’ teaching style goes hand in hand with such an approach and provides students with an environment in which they can thrive.

Again, I am not arguing that jazzy lessons filled with group work, technology and discovery are worse than the approach to teaching I personally favour. Indeed, some traditional lessons certainly are boring- I know that sometimes mine are (to my discredit). Rather, I am claiming that ‘traditional’ style teaching can be just as enjoyable for students as any other method of teaching and ultimately, might even be more likely to lead to the most desirable form of enjoyment- the intrinsic enjoyment that comes with the challenge and mastery of a subject.

‘Think Aloud’- Reflections on a metacognitive strategy

Last week I attended an in-house training session led by a number of my colleagues in the MFL Department including Louise Miller, Dr. Gianfranco Conti and Dylan Viñales.The focus was on developing students’ metacognitive skills. I was particularly taken by an activity which they suggested that they called ‘Think Aloud’.

On paper this was identical to a Kagan ‘Rally Coach’ activity that I have seen elsewhere numerous times before. Students work in pairs and talk through a particular question while their partner quizzes them on what they are doing. This always felt like something of a gimmick in the past- a case of getting students to talk for its own sake or perhaps because it checks a box for an observation. At best I have heard some generic comment about how somehow, as if by magic, student learning is enhanced by working cooperatively with no explanation of the mechanism behind this .

It was refreshing to hear some research and rationale justifying this strategy (that it improves metacognition) and some advice as to how best to implement it. Modelling a constant stream of discussion worked well, but what was most useful was asking students to model the sorts of ‘coaching questions’ they could ask as I made deliberate mistakes on the board. Initial comments such as ‘you’ve got it wrong there sir’ or ‘you need to square root at the end’ were corrected and improvements such as ‘have you considered what is happening between lines three and four?’ or ‘what have you found here, does it make sense?’, ‘could a different diagram help you here’ quickly came to the fore.

Students then worked through a fairly difficulty Pythagoras’ Theorem problem set that I had put together for them. I circulated listening for good coaching questions and periodically asking students to share with the class good questions they had been asked.

Screen Shot 2016-01-29 at 12.08.40 PM Questions courtesy of http://corbettmaths.com/

Problems with the questions included students ‘getting lazy’ and neglecting to talk their way through the problem (vigilance is key here) and students not speaking when they become unsure of how to proceed (convince them that just saying exactly what they are thinking is a good strategy and often leads to a ‘lightbulb moment’ of how to proceed.)

Did the students find completing the problem set any easier using these strategies? Probably not. Were the students stretched in other ways and becoming more aware of the ‘voice in their head’- probably. Were the students being forced to think like a mathematician to frame questions that supported students but didn’t involve just telling them the answers? Definitely. Indeed it was refreshing, if a little spooky, to notice that some of the questions students asked each other sounded remarkably like something I would ask.

The key with any metacognitive improvement strategy is progressing slowly over time. Rome wasn’t built in a day and effective metacognition is not developed in one lesson (or even one year- it’s a lifetime skill). Crucially a proportion of the training session focused on a neglected aspect of metacognitive strategies- that of developing automation. In Maths terms, this should include students reviewing their own solutions, drawing diagrams and ‘sense checking’ answers without prompting (though I think I could soon end up out of a job were this to become the norm!).

To recap:

  • Model, model and model again. This was the most important part of the process.
  • Encourage students to share good examples periodically.
  • Be aware of pitfalls, particularly student reluctance to speak when struggling- nip these in the bud by modelling what to do in these situations.
  • Don’t expect improvements to happen straight away, progress in any aspect of learning is not predictable or linear (or even monotonic) and indeed should not be rapid despite what many observers and school leaders might have you believe. Metacognition is no different

In some cases students may find completing the problems more difficult using these strategies. Good. Difficulty in learning is beneficial for students and is an indicator that they are being stretched.

One further point- a good proportion of the work I do at my school is with students to students applying to Oxbridge. Oxbridge interviews require students to talk a lot. Indeed, any interview for any mathematics or science interview will almost certainly involve students having to talk their way through a number of problems. Many impressive mathematics students lack the ability to do this. Like anything, practice is crucial and activities aimed at developing metacognition like this one are an excellent way of developing students for these intellectual challenges.

"What does the word ‘percentage’ mean?"

Note: Originally posted on Betterqs


I love asking low-ability students or students whose first language is not English questions like this. Unpicking the etymology of words is something that can benefit all students but for low-ability or English as an additional language (EAL) groups this is of the utmost importance as they had anywhere near the same level of exposure to the subtleties, nuance and conventions of the English language. It is the job of educators to increase the level of exposure beyond what they would otherwise encounter.

IMG_7112
For young students especially I really ham it up when I reveal that ‘percentage’ means ‘of 100’ and let them know that they are part of a small secretive club that will refuse to use the word ‘percentage’ willy-nilly but will stick to its strict definition.
I usually then go on to tell students that they would now be able to have an educated guess as to the meaning of any word with the word ‘cent’ in and I ask for a number of suggestions. Again for younger students a touch of the theatrics can be useful here (think Sherlock Holmes references).
When I asked this question last week it was with a Year 7 group, most of whom hadn’t encountered percentages yet but who were beginning to gain confidence with fractions of amounts and equivalent fractions. They quickly cottoned onto the idea that 25%=25/100=¼ and were then able to find percentages of amounts.
Focusing on the fact that percentages mean ‘out of 100’ and treating percentages as a special instance of the fractions work they had already encountered was something of a long way round. However, initially and in subsequent lessons students seemed to ‘get it’ and were far better able to explain some of the intuition behind percentages. Additionally, it made subsequent work on converting between fractions, decimals and percentages far easier.
Also posted @NWMaths

In praise of video self-analysis

I had been delaying it, putting it off, avoiding it and making excuses but the time had finally come…it was time to film myself teaching.
 


I made a private resolution at the start of the school year that before the half term was out I would film and watch myself teaching. There was only one rule- the filming had to be as ‘no notice’ (or as ‘no-notice as it is possible to be when filming oneself) in order to capture an authentic lesson.


Come the last week of the half term, I still hadn’t taken the plung myself so right before the penultimate lesson on Friday (year 9, four operations with standard form) I grabbed my iPad, propped it up against a set of textbooks and set it filming.


The results were…not as cringe inducing as expected. On the contrary, they were (quite) reassuring. It didn’t set the world ablaze with it’s cutting edge teaching and learning techniques or whizz-bang resources but it was a ‘tight’

lesson with great learning gains for almost all of the students. After the inevitable discomfort that comes with hearing one’s own recorded voice which subsided after the first five minutes I was pretty pleased with what I saw. As someone who has observed a fair few lessons in my time, I was relieved that my ‘bog standard’ lesson without all the out of the ordinary ‘oofle dust’ that (some) people put into their observations was reassuringly ‘solid’.

However, the tape doesn’t lie and did pick up on a few things that I should definitely work on which I don’t think would have been picked up on by an external observer. The inevitable self-consciousness and tendency to be self-critical that inevitably comes with watching oneself worked in my favour. I was that bit ‘harsher’ than some observers might be and thus picked up on things that might have been unchecked by others.


Habits and Body Language- This was the real eye-opener and it is something that no amount of introspection and reflection was likely to identify and something that hasn’t been commented on by those observing my lessons. On more than one occasion when explaining a particularly difficult concept to students I made a strange movement with my hands (picture the ‘whole thing’ gesture from charades but with your elbows touching your sides). Whilst not an issue in itself, I imagine that I would have picked up on this were I was one of the students I teach (and I probably would had a good laugh about it to boot) so it is worth eliminating. I also have a particularly annoying habit of throwing pens up and catch them when circulating the room. This didn’t look particularly professional and I wouldn’t stand for my students doing it. Again this isn’t something that either myself or others have been identified as an aspect of my practice that I should improve.


Choosing Students-I rarely allow hands up when answering questions and instead choose students and differentiate my questioning accordingly. However, I noticed that I seemed to have three or four ‘go to’ students from across the ability range that I called upon more than the others. So much so that when watching the video a week later I was quickly able to predict fairly accurately the students that I was going to call upon after I heard the question I was asking. Whilst an external observer may have noted and perhaps praised the fact that I was moving the questioning around the room to include a range of students, my knowledge of the class and students showed that this wasn’t as inclusive as first appeared.


Video analysis isn’t a complete solution for developing one’s practice and has it’s downsides. Notably, my video analysis was time consuming-I watched a few minutes of video at 10 minute intervals throughout the lesson and made a few notes but this was still a process that took over half as long as the lesson itself. I’d be really interested to hear how others have analysed videos of themselves teaching. However, it was definitely worthwhile and is something I will do again.


I know that many schools use IRIS Connect and other similar systems which I’m sure are great and even include the teacher being ‘miked up’ and technology to ‘follow’ the teacher around the room. However, I managed with an iPad propped against a stack of textbooks. Given the near-ubiquity of tablets (and indeed textbooks) it shouldn’t be too hard to beg or borrow one. Probably best to avoid stealing however.


Take control of your own development and try filming yourself teaching a lesson. You don’t need to share the results or even tell anyone else about it. If my experience is anything to go by, you will notice things that you might never have, it will improve your practice and it might even be reassuring.

Perhaps, like me, the video will even remind you to stay clean shaven unless you are capable of growing designer stubble or an impressive beard!

Comments welcome either here or @NWMaths.

Reflective Journals and Developing Metacognition in Maths


In my school’s dedicated professional learning time on Friday afternoons, I recently read about the techniques that Gianfranco Conti plans on using over the coming year in order to enhance and develop his students’ metacognitive abilities.. The original article is a must read and can be found here but I was particularly taken by two of his strategies which I think have could prove particularly powerful in the Maths classroom.

The first of these is an error log. The idea is simple and one I have used (inconsistently and sporadically) before. When students get back a marked piece of work they read through their feedback and pick out the errors made. They then record these and make a note of their mistake, along with an explanation. When using this with my classes this year, I will not sum up their ‘WWWs’ and ‘EBIs’ for students and will only mark on a question by question basis to ensure that students have to engage in the process of working out their mistakes for themselves. To do otherwise may turn a cognitive exercise into a copying exercise.
The second of these techniques is encouraging students to keep a reflective journal in which students are presented with a stimulus question each week (e.g. ‘which aspects of Maths do you think are causing you the most worry?’) and are then encouraged to respond with a short paragraph.
I have decided to combine these strategies. Students will always be required to produce a written log of errors on each piece of marked work and will be given a stimulus question less frequently (perhaps every other week).
In addition to the metacognitive benefits that Gianfranco mentions, the error log in particular will hopefully have other positive impacts. Specifically it will ensure that students have read in detail the marking and corrections that I have made to their work. Students will therefore gain the benefits of acting upon individualised feedback as well as the metacognitive benefits of reflection.
I plan on introducing this to my Year 10 ‘core’ IGCSE class who I believe will benefit significantly from the increased confidence these metacognitive strategies will have and my Year 12 A-Level group, many of whom achieved a grade B or a low grade A at IGCSE.
All the journals will entries will be made on a Google Document that both myself and the student have access to and upon which I can comment directly. Here is a verbatim entry from two of my year 12 students.
Student 1
“I have to be more careful when multiplying with negatives because one of my first mistakes was that I had multiplied √2 by -√2 and said it equaled to 2 which is wrong. The right answer was negative √2. Moreover, when dealing with surds that are in fractions, and finding the value of P and Q which are numbers in front of the surd, I should not times the denominator by the numerator because the fraction would no longer be equivalent. I should continue to draw a graph when dealing with quadratic inequalities because they helped me a lot in finding which part of the graph is needed. When using difference of squares, I can times back to see if the equation is exactly the same as how it started. If it’s different, then I know that something must have gone wrong which I can then check through the working again.”
This student has clearly given a considerable amount of thought to his journal entry and has picked up on my feedback. I think that by ‘difference of squares’ he means ‘completing the square’ and I added a note to the document highlighting this. The student is using the language that I would expect from an A Level student and this has been a useful way of confirming that the student is responding to my feedback and ensuring the time I spent marking wasn’t wasted!


Student 2
“I feel that the the effort grade you gave me was a fair one as I actually spent quite a bit of time on this homework. Overall I felt that most of my homework was well done by me as I got the marks I felt I deserved however about the marks I didn’t get, I understand how I did not get those marks. I need to work on the discriminant questions that include inequalities in them as well as having to remember to draw the graph when working with inequalities.”


This student has commented on the effort grade I have given him as well as mentioning some of the topic areas he has lost marks on and how he can improve (drawing a graph to help solve quadratic inequalities). However, he doesn’t seem to have engaged with the reflective process in as much depth as he is capable of and the quality of his written English could be much better. Given this was his first entry I responded very positively and thanked him for his reflections so as not to put him off the reflective process. In future I will encourage him to be more reflective than he has been on this occasion, but that is a job for another day.
Key to the whole process will be consistency on my part in keeping this up over a long period of time, as well as ensuring that students really ‘buy into’ the idea of a reflective journal. Initially I expect the journal to be focused on the errors made rather than student perceptions of their Mathematical education. However, with some well-placed stimulus questions, I envisage this becoming will become more and more reflexive over time. I have also made a point of periodically checking the documents and as soon as I have read a completed entry emailed the student thanking them for their contributions and giving personalised feedback on their entry (perhaps encouraging meta-meta-cognition?!).


I really look forward to reading the reflections of my students, especially my low-confidence year 10 group. As always, comments welcome either below or @NWMaths

Direct instruction and inquiry…thoughts on starting at a new school

 
Starting teaching at a new school (inevitably) has its challenges. New systems, new colleagues, new parents and a different context all combine to produce an intense and challenging first couple of weeks.
My previous role was teaching mathematics in a state school in inner-city Manchester- a world away from my new position at a prestigious fee-paying international school in Kuala Lumpur. One particular challenge that I have encountered during the first few weeks is in adjusting my classroom ‘style’.
The students I taught in Manchester were, by and large, incredibly positive, motivated and hardworking. However, due to a range of factors, I found that the students responded best to a fairly traditional and heavily disciplinarian style of teaching. I have always been keen to embrace best practice from colleagues both in my school and across social media in terms of pedagogy and assessment, but this has until now been coupled with a fairly ‘old-school’ approach to behaviour and discipline. Students would line up in silence before entering the class, would wait silently behind their chair before being allowed to sit down and would be expected to work for periods of time each lesson completely individually in silence.
 
A range of strategies to encourage collaboration and communication between students were of course used (the latter being particularly important due to the exceptionally high number of EAL students at the school). In particular cooperative approaches were used in problem-solving activities which I increasingly used with Key Stage 3 classes in order to best prepare students for the new style GCSEs. Students were also never spoonfed and were encouraged to persevere on difficult problems, find their own solutions and make their own mistakes. However, the metaphorical leash was firmly kept on students at all times. In order to maximise mathematical learning gains, I created and sustained an environment in which me as the teacher exercised considerable influence and control over all aspects of the class at all times and students had relatively limited control over the macro-direction of their learning.


John Hattie’s oft-quoted work Visible Learning appears at first glance to vindicate this approach. High quality ‘direct instruction’ (NB this is distinct from didacticism) in which the teacher specifies the learning outcomes, engages students, models, checks for understanding and provides opportunities for both guided and independent practice has an effect size of 0.59. This was very much the aim back in Manchester and was predicated on my complete control of the classroom environment at all times. Inquiry-based teaching, in which students pose their own problems, ask their own questions, observe phenomena, form and test hypotheses and and have far more influence over the direction of their learning than under direct instruction has a much lower effect size- 0.31. Without going into the nuts and bolts of Hattie’s meta-analysis it is worth noting anything above 0.4 is considered effective whilst a negative effect size has a regressive impact upon a student’s learning.


My initial impressions of my new workplace is that ‘inquiry’ within the classroom plays more of a role than I have yet encountered in my (fairly short) career. That is not to say that in each and every lesson students are completely independent inquiriers, exercising ultimate control over the direction that their learning takes. Far from it. Rather, it is just the case that there is more inquiry-based learning taking place and more discussion of inquiry than I have been exposed to until now.
Two questions about this have been occupying my reflections on this. Firstly, what are the merits of an inquiry-based approach to learning given that Hattie’s meta-analysis suggests its impact is limited? Secondly, how can I adapt my current practice to allow students to benefit from the positive aspects of inquiry-based learning?


A few initial thoughts about Hattie’s findings regarding inquiry (a full critique of inquiry-based teaching is far too broad a topic for a Friday afternoon):


  • Most teacher training courses that I am aware of tend to develop a ‘direct-instruction’ approach to teaching. Coupled with the fact that it is reasonable to assume that there exists a pedagogy specific to inquiry-based teaching, direct instruction is likely to have a greater impact than inquiry-based approaches simply because more teachers are better at it, rather than it being an inherently better approach.
  • Some topics and subjects are better taught in different ways. Indeed Hattie suggested that pre-teaching core content in order that inquiry can be focused more on process will enhance the effectiveness of any inquiry. Learning times-tables through an inquiry-based approach for instance would not perhaps be the best way for students to learn.
  • Inquiry may or may not lead to subject-based learning taking place at as quick a rate but it is reasonable to assume that the transferrable skills developed are greater than those developed through an approach focused primarily on developing mathematical learning.


So to what extent will my classroom practice be influenced by a more inquiry-based (and some would say progressive) approach to teaching?


Firstly, it will be a useful personal reminder for me to avoid one of my own flaws as a teacher: the tendency to talk too much. ‘Chalk and talk’ isn’t what Hattie meant by direct instruction. Knowing the premium that many around me place upon inquiry-based education and that the students I am teaching are used to this approach will help remind me to reduce this aspect of my teaching.


Secondly, it will encourage me to leave my comfort zone, something which can only be a good thing. I frequently remind my students that they should find the work ‘slightly too difficult’ as that means that they are learning. I see no reason as to why this shouldn’t apply to my teaching. Having been trained and indeed immersed in a system in which ‘direct instruction’ is at a premium, any initial foray into inquiry based approaches will likely be met with limited success. By persevering and developing this part of my teaching, at worst I will have another ‘string to my bow’, whilst at best I will have found a new and exciting way of engaging students in Mathematics and encouraging them to excel.


Thirdly, it will encourage me to think about what I want the students that I teach to be good at (examinations aside). I want students who are being taught by me to develop into good mathematicians and good people. The inquiry approach can certainly play a role in the latter through the development of excellent social and interpersonal skills and it seems reasonable to suggest that there is more scope for doing this through inquiry than direct instruction. But what about the former?


I tentatively (and perhaps rather boringly) contend that a combination of both approaches is likely to result in the best mathematicians. A good grasp of mathematical methods is vital for a mathematician and instinctively I feel that amongst most students that I teach, this is best achieved by direct instruction. However, effective mathematicians look for their own patterns, ask their own questions, and pursue their own routes of learning. This is something that is not just developed by inquiry, this is inquiry.


I currently believe that the more able students that I teach will be more able to benefit from a greater number of inquiry-based lessons than the less able ones. Maybe this is because of I have less confidence in my ability to provide scaffolding and support for inquiry-based approaches at the lower end or perhaps because some of the students that I teach lack the requisite skills to gain as much from an inquiry lesson as from direct instruction.


One thing is for certain- I won’t be stopping old fashioned regular ‘rolling numbers’ style practise of multiplication tables anytime soon!

Any comments, thoughts or criticisms welcome either below or on Twitter @NWMaths