Over the last 2 years I have been mentoring Paul Morgan, an A Level Chemistry tutor on his move to tutoring Chemistry online. With Paul being based in Burnley and me in London, we are still yet to meet in person. We have been meeting on a video call every week which serves as part staffroom and part CPD. We discuss a range of things from the business side of tutoring, teaching techniques online and more recently I have been his test pupil for the Chemistry teaching videos he records while we are on a call. So in effect we are on a video call, an interactive canvas and online video recording studio.
I teach up to GCSE Chemistry and Paul being an A Level Chemistry specialist, I have learnt a lot from him. Particularly how what I am doing at GCSE and earlier stages links up with what comes up at A level. Always keeping a long term view of learning Chemistry and making sure that things are taught correctly the first time round in the learning journey. I did A Level Chemistry and did research in a multi-disciplinary Tribology lab at Imperial College. So Chemistry has always been of interest to me.
One of the great things about using interactive online whiteboard Bitpaper (disclaimer : I work for them as their social media rep) is that you can build a whole bunch of filled shapes. Both the tutor and tutee can move these shapes around. For maths teaching this has been excellent since I have made my own two coloured counters, algebra tiles and cuisenaire rods. A tutee can be thousands of miles away from me yet both tutor and tutee can move the manipulatives around on screen as if we they were on the same table.
I have started to use virtual counters in teaching Chemistry as well now. In Chemistry students may use ball and stick manipulatives at school to understand the basic formation of molecules, the relative arrangement of atoms in space in that molecule, bond breaking and bond breaking etc. Quite a lot of that movement and playing with things can be replicated online.
We have created a series of videos to show exactly this. This first video is the very first one that introduces virtual manipulatives. Some things to note:
The atoms sizes are relatively in proportion to each other approximately.
The subscript symbolism of what the molecule represents with a pictorial representation of the molecule needs to be explicitly practiced by students.
Embedding what monoatomic and diatomic means using a pictorial representation.
Common misconceptions are addressed using non-examples. For example, while Methane’s molecular formula is written with Carbon first and Hydrogen with a subscript of 4, that does not mean that the molecular representation has a carbon atom, followed by four Hydrogen ones in a row.
The whole process of forming a molecule from atoms is then animated by the tutee once they have manually formed the molecules. This is done while I keep silence. Silence from the tutor is key to reduce cognitive load on the tutees while they discover and make these molecules.
I have tested this with a number of pupils now online and Paul has started using it with his tutees as well. It has been really useful for me to consult Paul and together we are creating this new way of working with manipulatives for Chemistry when teaching online. Please do let us know in comments or on twitter/Facebook what you think of this.
26 November 2005 was a dark night for my family. I was in Budapest where my dad was on a posting and had lost his short struggle for life after a sudden brain hemorrhage. I had no idea what had just hit us as he was a perfectly healthy and fit person. In that state of shock it was inconceivable that he had left our lives forever.
As the eldest sibling of my family I took the call from embassy staff 36 hours earlier that he was in hospital. I left London with just a rucksack of some clothes. My brother and sister who I lived with at the time were at the flat in London. We were no strangers to talking to mum and dad on webcam every week, something we had done since around 1999. Dad liked calling us on video on MSN messenger. We were all university students at the time and were used to chat programs on those old desktop computers. Dad would always try to catch us online and call us on video two or three times a week. He was never to be online again on our MSN list.
For those last 36 hours I had held myself together for my mum and my siblings. I knew dad was in far more a serious condition than they all realised while me, mum and embassy staff were visiting hospital. I held hope, great hope that he will recover and that he would be in ICU for a few more days and then be out. He wasn’t even there for 2 days. At midnight we went to see dad as he had lost his last struggle for life. My mother was inconsolable at the hospital. I called my siblings on the phone as my brother and sister tried to console her. I was a student on a roaming pay as you go phone and my £50 top up ran out in minutes.
I reached our home in Budapest and started the MSN video call with my younger brother and sister. 2005 webcams were grainy but still we were able to see each other, see the sadness in our eyes, some of us cried and some were still in shock. This was the era in which the term 24/7 internet was coined as broadband was still in its infancy. It was about 2am and we decided to try and get some sleep. I told my brother in London to just keep the video call going, whether or not we were sleeping. I don’t know why I did this at the time, I needed to know that even if we were not talking to each other live that we were connected together.
I couldn’t sleep, the reality that my dad had just died hours ago and that I was the one now who had to inform his brothers and sister in rural India dawned on me. None of them had phones, they were too poor and mobile phones in India were expensive at the time.
I frantically looked around for phone numbers of relatives with a landline or mobile phones. I couldn’t do it, every time I saw a piece of paper with my dad’s writing I realised the writing is of my now dead father, and that I will never see any new writing from him again. Shock finally turned into mourning and I started wailing out loud, I turned into a screaming 5 year old again. My mum woke up and to my surprise even my brother who was on a live link to the MSN call woke up in London. We talked for a while and I calmed down. I then located the phone numbers and called various relatives in India all night. How can anyone ever be prepared to call up to tell the news of a brother’s death? You can’t. I did my best at the time and talked to them as long as I could. They didn’t know what to do either, mourn or console me? They consoled me and my mum who were at the flat in Budapest.
2 weeks later I travelled to India and met my family in India after 12 years of not having gone to India. In a suburban poor part of outer Delhi, my mother’s brother, my uncle found us four a small room. We were lucky to have running water near that room but my uncle’s flat didn’t. I helped my aunt in those next 3 months to bring buckets of water in the morning to her flat. It became a morning routine but never a chore as the temple blared out holy songs and India woke to life with that life energy of India that is hard to put in words. I even got used to cold showers in December. My aunt’s food was delicious, the Indian sun, Hindu philosophy and a sense of community in that suburb was nourishing to me.
My uncle’s grandchildren were three boys, the eldest of them was 13. The boys were amazed by the the tales of London and the Western world. They were inspired by what my dad had done for me and my siblings. Tales of how total dedication to education got my dad a school scholarship and eventually a job in the Indian diplomatic service. The prodigal son had escaped poverty, travelled the world and represented his nation. If he could do it, then so could they all.
I travelled to wrap up my dad’s paperwork, pension, bank accounts etc. from suburban Delhi to central Delhi for the next 3 months. It was such a trip, a tiny minibus that rattled through the rough suburban dusty roads with loud Bollywood music blaring. I had just finished my PhD and was in debt myself, so the 5 Rupees (~6 pence) journey suited me fine. I couldn’t afford a car or taxi either and was far from being a middle class Delhiite. So I ditched my GAP flares, bought clothes from local markets and just fit in with everyone else there.
The nearest cyber cafe with a webcam was about 45 mins bus ride from the suburb I lived in. I went to the cyber cafe to chat to my brother, sister who were now back in London after two weeks in India. I also got to keep in touch with my friends from Imperial College and catch up on the local student news, MSN was just about to be replaced by MySpace and Facebook. My nephews started to come along to the cyber cafe with me. I put two of my older nephews into an IT skills and English speaking course three mornings a week as that part of Delhi had more resources. The eldest ended up going to university, got a degree and is now working in an accountancy firm. He and his brothers got my uncle’s family new luxuries. 15 years later they have running water, plenty of appliances, a bigger house, a motorbike and more.
In those moments when I had left that video call on and continuously running shortly after my dad’s death, I felt that my flat in London was joined to my dad’s flat in Budapest virtually. It is as if the walls and boundaries had disappeared, as if that the room in London just became an extension to the room in Budapest. They were one. We could see each other and talk to each other. The quality of call didn’t matter, the fact that there was a live connection put us in a virtual space. That space is perceived and enhanced in our minds.
This idea of interconnected virtual spaces has never left me since that night in 2005. I started tutoring in 2006, fast forward to 2012 and I started tutoring online. Many of the things I learnt back then on how to stay connected with my family is what I now apply in my teaching. A vast part of that is forming very real and human connections with my tutees and their families. The tech has always been secondary, I just used whatever tech I had at the time to do the teaching I wanted to do. I turned the limitation of the tech into a strength, a pedagogical tool in itself. I made ‘remoteness’ a powerful tool. The engineer and problem solver in me has just learnt to adapt and innovate with whatever tools I have at any given moment of time.
Over the next weeks and months, I will try to open out from my head what these tools are. What it might mean to hold a space for someone online, to get them to articulate, to articulate myself, to value the silence and realise that perhaps the most important communication is happening in that silence between the talking. Once I have my own clarity on this, I will be able to convey it to the wider world.
Everything changed the day after I came back from the weekend #MathsConf22 trip to Manchester on 15th March 2020. The seriousness of the current pandemic truly hit home. It would still be another week before the government would stop politely asking people not to go out but to enforce a lockdown. I’ve been in my London flat ever since that weekend and have barely ventured a mile away from it during my daily walks. Avoiding the high street and tube station. It is bizarre as a Londoner not to have used the tube station for two and a half months.
In the immediate aftermath of lockdown I witnessed tutor colleagues lose their jobs, Bitpaper go from bust to survival and I threw myself into training friends to learn how to work online.
The constant attention to news, social media and the lack of being able to go out enough made for a cocktail of restlessness and being on edge. I have no garden in my small London flat so each outing was invaluable respite. As the clocks changed and spring arrived, the earlier sunrises further reduced sleep hours.
Nonetheless, given everything I am still extremely fortunate to not have had more serious family and work related stress. I was already working from home and in that aspect business continued for me as normal. Indeed, one of the few constants I was able to provide my tutees was our same tutoring slot at the same time of the week. That wasn’t to last long as like many tutor colleagues I too lost tutees for a myriad of reasons. I was having daily conversations with parents and realised the pressure that families are under. It made total sense that for some families tutoring would not be a priority at this point in time.
I was disappointed to see fake news that the tutoring industry was booming, a more detailed and comprehensive Sutton Trust report confirming that in the UK the amount of tutoring taking place was down overall. There are various global Facebook groups of tutors with thousands of tutors in them. We get a far more accurate and nuanced picture of the industry through hundreds of daily conversations between tutors. Almost every news story on the tutoring industry has an agenda.
Transferring my online teaching skills – Two to tango?
My job to transfer my skills had begun back on the train from Manchester to London already. I saw a Facebook message from my Argentine Tango dance instructor that they were offering free online trial lessons. The thing that was their life and works purely in the physical realm was seemingly going to be gone for months. I knew I held a part of the solution as I had pushed online tutoring a long way. I had chosen to stop tutoring in person altogether in 2016, so working from home and teaching was now the norm for me. While still on the train I got my instructor to install zoom and we made a video call while I was on a train going at more than 100 miles per hour.
After 2 months of running several group and 1-to-1 classes online my dance instructors are one of the few who have quickly adapted to the art of teaching online and done it well. I have a lot more to write about this but what they achieved is a truly rare event. There have been a few other exceptions, those tutors that were already adaptable and creative in their tutoring. But on the whole mass attempts to deliver online tutoring have been sub standard to say the least. Live online teaching is a highly sophisticated form of teaching requiring its own separate pedagogy and intersection of skills. Like learning anything worthwhile it requires consistent, deliberate effort and constant improving. Those who tutor well online, tutor all or mostly all online.
One of the most effective ways how online learning can work was for me to actually just live stream examples of this teaching. This happened in a CPD context and is mentioned later on this blog post.
Bitpaper or bust – further consequences of the rapid shift to online
The whiteboard company I work for called Bitpaper was facing an emergency. Tutors who previously either dabbled in online tutoring or were complete newbies were forced into online tutoring by the pressure to save their livelihoods. I am glad that the perceived quality of Bitpaper from existing users meant that so many people chose Bitpaper. The product was still in beta mode and therefore free at that stage. Nothing comes for free though as there were server costs amongst the other costs that included mine and other people’s time.
With a huge increase in user base, server and AV platform costs were escalating out of control. This was running the company and the team into the ground very quick. The levels of stress placed on the team and me as the social media community and PR person was immense. Plans to commercialise were brought forward by a few months and it was now imminent or we’d go bust. We made an announcement to commercialise which went down well with most but there was an inevitable backlash by a minority. After a live stream to a big facebook group to fully explain our reasons we could breathe easy. We commercialised and I went out of emergency mode to focus on other aspects of the product. I remember sleeping well that night for the first time in several days.
I had numerous messages and requests from tutors on training them to become online tutors. I was way too busy with my own tutoring, life and Bitpaper to do this. I had already prepared detailed guides on online tutoring a long while back. I can only think of maybe 10 tutors at most who are expert at tutoring maths online. Along with me, their voices got drowned in providing what is the correct and expert advice on online forums.
I offered free training to those who wanted it but on the condition that this training is live streamed so that others can see this too and a recording is kept. Not many signed up to this as one might imagine. But the few who did made it totally worthwhile. I then extended this to live streams with other experienced online tutors, something that had been on my to do list for a year already. Our voices were being drowned by constant panic and terrible mass novice to novice advice. The video platform was far better to present this expertise.
I now knew that live streaming was going to be the most valuable use of my time and expertise. Previous experience with tutors showed me that only a small minority of tutors put in the effort to take CPD or read books. The few that do value CPD turn up to meetups and events anyway. The next step for me was logical, I turned to the mainstream school teaching community which does actually care about CPD and has had well evolved networks formed over the years. I approached La Salle Education CEO Mark McCourt to live stream on twitter as I had known him from attending several CPD days and maths conferences. This would leverage on an already well formed network on twitter in a novel and more human way.
The #MathsChatLive live streams were born and took right off. I have learned a lot from this level of live streaming. They have around a thousand viewers on each live and more that view the recording later. In many ways all my experience of tutoring online, making tutees comfortable in a virtual environment, holding the space and using tools to teach online was preparing me for this. We are only a few live streams in and I’m keen for this to evolve and get better with time. I will write a separate blog post on multi live streaming for CPD as it has been a fascinating learning experience.
And then the rest of my life moved online too
On 1st March 2020 in a studio under a church on a sunny Sunday I took my first ever singing grading exam. Grade 3, Trinity Rock and Pop. I had been taking singing lessons consistently for about 2 years, every week in fact. It was all online. I had convinced my singing teacher to teach me online 3 years ago and we had found a way for it to work for me. The only part of the entire grading that took place in person was the actual grading exam itself. I am glad to say I passed with a distinction. Bring on grade 4.
But ultimately we exist in the real world and not in a virtual space. I take two dance classes a week and a pilates class as well. The reason I was doing this was to get out of my home and get out! With even these moving online, everything I do now is online. Now that it is no bad thing as I have made my room a practice space for dance classes and pilates, something I never thought was possible. I have also learned to live stream music performances from my room and have made an art form of that in itself. This will all come in useful even after lockdown.
With Gigabit internet, 5G, the internet of all things, video walls, autonomous cars, bio technology, data driven algorithms etc. all developing very fast we should expect a different world in the coming years. The American civil war propelled the use of the telegraph to the mainstream when it was a niche product for the railways initially. And so this global pandemic has also moved the use of video calls, cloud computing etc. more to the mainstream I hope. And we can truly now ask, which appointments need our physical presence and which do not? Something that I have tested for years now. I have formed fairly sophisticated relationships with tutor colleagues and families in other parts of the world that I have never met in person. A lot is possible online.
All the technology aside, I keep in mind the seriousness of the global pandemic we are in now and that there have been lives lost. I have a civic duty in playing the small part asked of me to minimise risks. And it has been fascinating to see what that means for my tutees in other countries and my extended family in India.
Video killed the mp3 star – my first video channel circa 2007
Back in 2007 I started a video channel on YouTube for my band followed by my own channel in 2008. Phone cameras were pretty rubbish back then, so for any decent videos you needed a video camcorder (remember those?!). I bought a mini DV camcorder and along with my grainy phone videos I started uploading videos.
My band used to be filmed nearly every gig so I had tons of footage to look at, upload, edit etc., It was a fascinating learning curve on video editing, compressing and uploading. But the real learning came after the video was already uploaded. From what people were commenting on, likes, dislikes and analytics data.
I found that mostly no one cared about my band’s music and it wasn’t ‘viral’ enough. I was surprised to find I was getting more views on my personal YouTube channel than my band’s channel. I was posting acoustic cover versions of songs and was one of the first of the video blogger generation, holiday videos mixed with concert outings and even random ramblings.
Video feedback – harsh, instant and very useful
Through YouTube I realised I could in effect ‘beta test’ my voice with cover versions of songs. This would help me gauge for how good I really was as a singer. The feedback was nearly instant and very clear. People respond to a good voice and a well played cover version. The harsh truth I realised is that most of my covers bombed but a few kept getting hundred or so views every month, not bad going but definitely nowhere near some of the top video song covers out there. I’ve been taking one on one singing lessons for a year now so at some point I will revive the song covers.
Starting my tutoring video channel at long last
After a little dabbling in tutoring videos over the years (I made about 3), I finally committed myself to making videos on a dedicated channel. Through my tutoring video channel I hope to present some of the teaching methods I have learnt over the years. Now that might not be unique but it is my own take on things, my voice and my style of communicating. Much like posting the music videos, I feel like I will find my audience, whoever that might consist of.
At the moment I have been sending the videos to other tutors, teachers and also to parents of tutees. In future, as I have more videos I can use them as a resource with my current tutees who are used to my voice, video and specific way of explaining things. Any method they want to know again in the way I taught it to them….well, the videos will all be there.
My tutoring YouTube channel is born
Making maths video course and finding other tutors keen on videos
Earlier this summer I went to a ‘Making maths videos workshop’ delivered by educ8all, which I must say has been really helpful in the whole process. The most important thing was finding another tutor who is keen on making videos. Taking action is what I value and only by taking action will I become a better ‘YouTuber’. The one single act of having an hour appointment with another tutor every week at the same time to work just on video has set the wheels in motion.
Currently I am making videos with Catherine and Paul who both jumped in with the idea of video. Working with both of them individually makes the videos more like a live tutoring session, keeping things more bouncy and with a real person on the other side it is just much easier to articulate. I find solo videos harder to do. But with the wheels set in motion that too becomes easier to do now.
Things I have learnt so far about making tutoring videos
It turns out that there is a LOT to making videos. Here are just a few aspects I am learning about:
Video planning and storyboarding – freestyling videos is actually pretty hard. Scripting them and having a plan is far better
Storyboarding – How one ‘scene’ flows into the next. E.g two tutors talking, cut, then to the whiteboard
Various scenes – There turns out to be many possibilities on what can be filmed. Eg. two tutors talking, switching to a second camera to show manipulatives, writing together on a digital paper canvas with both tutor headshot videos showing, sharing computer screen and other ‘scenes’
Looking presentable and natural on camera
Having a presentable background – i.e removing visual clutter and getting a nice background colour. A real background, none of those fake green screen ones that I have seen in too many tutoring videos
Lighting – Bad lighting can destroy a video. I mostly film in natural light and add some additional soft lighting. I have done this already for live online tutoring so this was easy to implement
Sound – Great sound quality is an under-rated part of getting a good quality video. I have a Rode NT USB microphone and a mic stand to close mic me. Laptop mics are terrible and they also pick up tapping sounds, best avoided
Delivery and video presentation – The energy has to be solid in the video intro. I felt stiff and robotic during the first few videos but now I am starting to relax and be more ‘myself’ on camera
Editing video – Smooth transition between intro and main body of video, fade out as we both say bye, overall flow of video should be good
Rendering – Compresses the edited video size down. Takes a surprisingly long time
Uploading and Publicising – Video must be described and tagged appropriately. And then I publicise the video on social media
Feedback – Comments, likes and video analytics along with any feedback by talking to others then helps me figure out how things are working, or not working
Reducing unnecessary cognitive load for the video viewer
Both myself and Catherine have carefully thought out how the video should work. We always want to make sure the videos are short, to the point but still feel organic and lively. We have taken on board the lessons learnt on the video training course. I.e not making rookie mistakes such as writing and talking at the same time all the time (a little bit is ok). This diverts the attention with the audience having to focus on the dynamic writing and also listening at the same time, split attention effect etc. We have kept in mind cognitive load theory and hope to make very clear, well flowing videos.
The peak of the academic year ends for me after around the second week of June. By then the exhaustion has really kicked in and I’ve been running on adrenaline with total commitment to helping my students. The demand on my hours is highest in the build up to exams as existing tutees (some who I have been working for many years) need that last minute support, reassurance and specific troubleshooting with exam questions or technique in general.
Things then gradually slow down but never really stop during the summer until I decide to block a week or two off and go on holiday. I am still to do this and definitely need to do take some time off completely from tutoring to refresh and re energise in doing the thing I enjoy.
Every academic year is unique and different. This year the highlights for me have been:
Taking Sundays off every week
At the start of this academic year back in September 2018 I made the decision to not tutor on Sundays. This is something I had done almost every year previously with tutoring 7 days a week being the norm. This seemed like a tough decision at the time but it has been the single best decision I made last year. Having one day off a week meant cramming my Saturdays as a result. Previously I’d like to keep Saturdays and Sundays light but now I felt I needed a full day off entirely. That one day off a week, spending time with family, doing music and relaxing has been priceless for my well being.
Taking time off for CPD and the value it provides
The biggest cost to me for taking CPD is taking the actual time off tutoring. Lost tutoring hours is lost income and disruption to the regular tutoring timetable. There are other costs like train, hotel, food etc. when travelling to conferences. The cost is well more than worth it, some of it helping reduce the tax bill a little and the rest is all about increased confidence and finding a community of teachers. CPD is a long term investment and like many things in life, taking a hit in the short term is necessary to play the long game. Besides, many teachers who deliver CPD often do so at their expense and two events I went to were free which I am grateful for.
There is absolutely no doubt that I have learnt more about teaching maths and developed more as a maths tutor this year than in any other year. I went to 3 maths conferences, #MathsConf17 near the start of the school year, #MathsConf18 just before Easter and then #MathsConf19 as a treat after exams. Last summer I attended a workshop on 11+ exam entry prep and a La Salle one on ‘Making maths memorable’. Continuing with the La Salle ones again with two phenomenal workshops in the autumn term (Multiple Representations and CPAL). This summer so far I’ve been to a making maths videos afternoon, Maths Teachers Network day and a Dyscalculia conference.
I am always excited to tell parents of tutees about all the new ways I learn about educating their child. And I have new self belief that I am becoming a much better online maths tutor for primary, Dyscalculia, GCSE, IGCSE and A Level.
CPD is not just about attending courses though, I am reading books (more on that below) and engaging in conversations with teachers and tutors on twitter + Facebook all the time. It is invaluable to learn from other teachers and to articulate what is on one’s mind.
Books, books, books, a microphone and a chair
These are the books I read during the last academic year. Some directly related to tutoring and some on general knowledge.
Sapiens: A Brief History of Humankind by Yuval Noah Harari
Why We Sleep by Matthew Walker
Homo Deus: A Brief History of Tomorrow by Yuval Noah Harari
Factfulness: Why Things Are Better Than You Think by Hans Rosling
Dyscalculia: from Science to Education by Brian Butterworth
Last year I spent all summer reading Craig Barton’s book ‘How I wish I’d taught maths‘ and this summer so far I have been getting well into Mark McCourt’s ‘Teaching for Mastery‘. I have a massive backlog of books after that still. I am addicted to reading about education.
Being a sound and music nerd I also bought a shiny new USB microphone to improve my online tutoring sound quality. The Rode NT USB gives crystal clear sound to my tutees. I can’t believe it took me so long to buy a high quality external mic!
Last June I bought the most important piece of hardware of all, a proper fully adjustable desk chair. Previously I was starting to get back pain and other back problems that I don’t even know of. Long days of online tutoring at home on rigid chairs was not good for my back. The new chair, together with taking plenty of standing breaks has helped my back recover back to normal this year.
Tutoring community of those showing up and an award!
I am so glad to see tutors showing up to the London Tutors meetups that I organise. And those who turn up to the maths conferences and CPD events. It is refreshing to see the same group of tutors regularly engaging in meeting each other and going to CPD events. The tutoring communities are relatively young and it is thanks to these that I found such a wide world of educators and teaching CPD.
At the end of year summer tutors party I was ecstatic to receive an award from The Profs for being an ambassador for them. In helping promote them and the work I have done with online tutoring communities. I am very grateful for the award and will treasure the trophy and speech that was given during the award.
Maturing as a SEN and teaching adults tutor
With a few years of teaching SEN students (Dyscalculia is really my specialism but it is often comorbid with other issues), I feel like I am starting to mature in teaching in this area. By tutoring in this area I am developing real sensitivity, good pedagogy, excellent communication skills and most of all thinking outside the box with constant innovation in online tutoring technology. There is always plenty to learn though so this maturity process has only really just started.
I also started teaching adult students this year on a regular basis. I always believed that maths can be learnt at any age and I now have my own proof of this from various case studies. I really look forward to developing more into an online maths tutor for adults as well.
BitPaper and TheWayUp! game
Work hasn’t been all tutoring though, I continued to keep pace with the rapid new developments and features being rolled out by BitPaper, the digital interactive paper I use for my tutoring. My job in the team has been to communicate, interact and get feedback from an online community of tutors.
TheWayUp! was another project this year that I was involved in. This required an entirely new way of thinking about digital PR. Much more planned, strategic and with a team involved. I learnt a ton about digital PR.
Both BitPaper and TheWayUp! game meant I was working with a group of people in a team. This has been really refreshing to me as a solo tutor.
Time to relax
My workload is the lowest now with just 2hrs of tutoring daily and all of Saturdays and Sundays off. I’ve been catching up with friends, going on day outs with family, doing a lot more music, more CPD courses and ticking away with reading books too. As I relax I can also ponder on some of the longer term things I want to do in life. And the summer is now the perfect opportunity for it all.
This blog post is a write up of my sixth maths conference. #MathsConf19 was held at Penistone Grammar School near Sheffield on 22 June 2019. Run by La Salle Education, the conferences are attended by around 400 maths teachers, trainers, publishers, suppliers, academics, tutors and others involved in maths education.
TLDR ; Both real and virtual double sided counters are very versatile, the term radius is a relatively new word to the circle party. Just a few alternative methods for constructions brings the topic alive.
A beautiful summer’s day for #MathsConf19 at the idyllic location of Penistone. Picture by @LaSalleEd
Pre-conference Friday night socialising
The Friday night pre-conference drinks are an invaluable opportunity for informal CPD in itself. Teachers have so many things they want to share and bounce their thoughts off others. This is the part I enjoy so much as a one man band online maths tutoring business who doesn’t get the opportunity to do much of this in person. Twitter is useful for these things but there really is no substitute to meeting in person.
I got to check in with teachers with the new A Levels for example and how teaching the first full first cohort has been. I was so impressed to meet a couple of teachers who teach everything from further A level maths to Year 7 students, from top to bottom sets. A lot of skill and versatility is needed for this which I need as well as a tutor. I am looking to teach further maths in the future so I asked some questions on the various modules for that.
Some of us were also doing maths games and puzzles. I was playing Albert’s insomnia bought in by Drew Foster. A game using mental maths and the order of operations. The beer, chatter, games and socialising continued through the evening. Unlike Bristol I took an early night after the bar closed this time. Thankfully there was no Atul’s insomnia after playing Albert’s insomnia and I was in good spirits for the following day of conferencing.
Introduction, twitter and a MacMillan award
La Salle CEO Mark McCourt kicked things off with an introduction to the maths conference. AQA maths head Andrew Taylor also gave a short talk with a “guess the year this question was set” slides showing how certain stylistic elements of questions go in an out of fashion from the 1940s to date. Mark also mentioned that there are about 300,000 maths teachers in the country and encouraged us to tweet about the event so others can get involved with the network and get out to know each other. I couldn’t agree more on the immense power gained from meeting and learning from other teachers. La Salle truly excel at creating this community; online and in person through these events. And you really can’t go wrong if the entire conference title is a hashtag itself!
Mark was pleasantly surprised by an announcement from the audience to receive the 2019 Douglas MacMillan award. All arranged and nominated for by Julia Smith. He always doubles the amount (with some generous rounding up) raised on the day from raffle ticket sales. Mark also has a new book out “Teaching for Mastery” which I really look forward to getting into. I’ve been to three of his full Complete Maths CPD days and continue to learn from his vast understanding of maths teaching.
Speed dating and some new ideas for teaching
Next up was speed dating, 4 ‘dates’ where each delegate gets 120 seconds to share their favourite teaching idea with another delegate. 120 seconds to share all my life’s knowledge on maths teaching and my greatest hits of ideas. This was going to be pretty difficult I thought. Coming out of it I learnt a lot from these dates about maths teaching; from goalless problem solving to a highly atomised approach in teaching some topics. I talked mainly about ‘backwards fading in example-problem pairs’ and the ‘pretest effect’ that I have been trialling out with some good success.
Workshop 1 : Double sided counters
This workshop was delivered by Jonathan Hall aka mathsbot. He has created a very rich resource of online manipulatives that I very highly recommend using. Double sided counters have been late to this manipulatives party for me as I still haven’t started using these with tutees. So this workshop would serve as the perfect intro to using them.
Double sided counters workshop.
It was certainly a lot more than just an intro. Jonathan showed how this simple and one of the cheapest manipulatives can be used to explain numbers, probability, algebra and proof. Each delegate had their own set of manipulatives to play with. To start off with we were given a hotel problem with 12 closed doors to try out in our heads. It was apparent very quickly that this would be pretty hard to do mentally. As soon as the counters came in, it was easy to solve the problem with the yellow side as a ‘door open’ and red as ‘door closed’.
Students can explore patterns using counters. Eventually coming to their own conclusions on the general formula of a pattern. Presentation slide by @studymaths
We then looked at sequences. Now I have seen these on 13+ papers a lot in picture form but there really is something else about having the actual counters in physical form and to actually build the patterns with your hands. There is something satisfying about the process of building the patterns by hand and there is no doubt this very act leads to richer understanding. We looked at a couple of sequence examples and while both examples were for quadratic sequences, the counters work very well with linear sequences as well. We were then shown some great examples of visual proof and probability questions using Venn diagrams. Everyone had an A4 sheet in which to make a Venn diagram and place the counters. Each application eventually leading to a generalised form where a total of n counters can be used. Probability being finished off by looking at a Simpson’s Paradox example case.
I was really impressed to see the counters being used for factorisation and finding the mean. In this example we had three separate groups of red and yellow counters (first row on image) then redistribute it all to get three identical rows of 2 yellows and 3 reds in each row, i.e 3(2y + 3r). The last row in the image showing elegantly how the mean is simply two yellows and three reds 2y + 3.
The presentation wrapped up showing the many uses of double sided counters. These being; Directed number, Ratio, Sequences and nth term, Proof, Averages, Collecting like terms, Factorising, Venn Diagrams, Probability, Tree Diagrams, Factors, Multiples and Primes, Square and Triangle numbers, Long Division and Modelling Problems.
I’ve already got myself a set of the counters and can’t wait to use these in my teaching.
Workshop 2 : Ratio and Proportion
The next talk was by David McEwan who is the Curriculum manager of Maths at AQA. Ratio, proportion, scaling, fractions, percentages are all of course linked topics. #MathsConf18 gave me a real appreciation of the idea of ‘scaling from unity’ so I was really looking forward to this particular workshop. Each one of us had a list of specification extracts and exam questions to accompany the workshop too.
We kicked things off by an open ended discussion on how one could define ratio (see image).
An open ended discussion on what ratio means.
David also mentioned that ratio and proportion appears in some form or other mostly on Foundation or Higher-Foundation content. Analysing the June 2018 series he mentioned that ratio and proportion questions appear almost at the start of the paper and are evenly distributed towards almost the end. And the proportion of proportion questions? Roughly 25% in Foundation and 20% in Higher. The pun here is unavoidable and bought some chuckles around the room.
David showed the equivalence of fractions with ratios leading on to equality of ratios. Finally linking it all up with a really neat cross multiplication method suitable for all ratio-equivalence calculations.
Using bar modelling as well each percentage problem could be solved using this cross multiplication technique once the problem was set up the right way. Find the percentage, finding the number, percentage changes, reverse percentages could all be done using the bar model. I really liked the idea of going for one consistent representation and following it through.
A neat bar modelling and ratio cross multiplying method that can be used to solve various types of percentage problems with the same consistent representation.
We were also shown some slides to remind us that an introduction to trigonometry is all about ratios as well and that students can essentially be introduced to trigonometry at earlier ages when introduced to right angled similar triangles. Also discussed were ratio tables showing the conversion factors for area and volume scaling and a few other concepts that showed the same thread of proportional relationships. It was really good to get such a clear reminder of this.
Workshop 3 : The Evolution of Vocabulary in Maths Education
Next up was Jo Morgan with a talk dedicated to the use of words in maths and how words change, evolve or fade out of use through time.
Words change in general over time because..
They become obsolete (e.g ‘cassette’)
Go out of fashion (‘groovy’ or that 90s word ‘naff’)
They get superseded by newer ways of speaking (‘telephone’ becomes just ‘phone’)
I was very relieved to hear that “thrice” was once indeed a word. I used it when I lived in India and other countries. I stopped using the word in Year 11 when I arrived in the UK as my classmates told me that no such word exists. It must have been faded out here in the UK by that time. And apparently “twice” is on its way out now too. Being gradually replaced by “two times”. The words ‘Evenly even’ (divisible by 2 and then 2 again) and ‘evenly odd’ (divisible by 2 just the once) were also mentioned.
Jo Morgan discusses “Evenly even” and “Evenly odd” numbers.
Jo then moved on to use of some words in the context of solving and simplifying equations. Transposition: “The act of transferring something to a different place.” and ‘concinnation‘ (simplifying in an equation) make a regular appearance. And so do terms such as ‘destroying‘, ‘clearing the fractions‘ and a verb in its own right ‘to vinculate‘.
The word ‘concinnation’ made me think of the word ‘concatenate‘ (link things together in a chain or series) that I vaguely remember using in computing. The ‘concatenate’ command is used to stitch up two or more files into one big one using the MS DOS command prompt.
On to circle geometry next. It is hard to believe now but the word radius is one of the youngest words to be used in circles and has only joined the circles party relatively recently. Mathematicians managed for a very long time without the word and using ‘semi-diameter‘ was enough. The earliest reference to radius as a mathematical term in English is Hobbes writing in 1656.
After that we got into some quadrilateral language. Rhombus “So called from the Greek word Rhombos, which signifies the Fish called a Turbot, and the Quarrels of Glass in a Window.” Rhomboids was also mentioned and discussed as what we call the modern parallelogram. And interestingly oblong is the old word used for a rectangle. The new oblong is a lot different to the old one in that way.
Jo finished off the workshop with a look at Welsh mathematician Robert Recorde‘s contribution to maths. His book The Grounde of Artes was written with a lovely tutor and student narrative with Recorde doing some tutoring to his imaginary student and the student responding back. Encouraging the scholar with “well said”. Good tutoring practice has remained unchanged all these centuries then!
One cannot mention Robert Recorde without referring to his most well known contribution, the use of the equals sign = After a little training on how to translate old English we were given the original text to translate to see if we could spot the mention of the equals sign. Recorde also invented new English mathematical words with many not surviving common usage today. Language is something that changes through time and perhaps in a 100 years some of the maths terms we use today will be obsolete too.
I really enjoyed this workshop, it flowed very well, was paced just right and left me with curiosity to go and explore more.
Workshop 4 : No gimmicks learning and teaching using Algebra tiles
This workshop was delivered by Bernie Westacott who I recently found out about after his video podcast with Craig Barton on manipulatives. I very highly recommend watching that video series. Bernie has an incredible depth of knowledge in the use of manipulatives and in particular getting the teaching for young children absolutely correct the first time round. Not only that but introduces algebra right at the start when children first start their maths journey without using the notations yet. I got to meet him the week before for the first time at another workshop in London and this week he had a packed audience ready to get into virtual manipulatives.
A packed hall for Bernie Westacott’s presentation. Picture by @LaSalleEd
The workshop was based around the use of virtual manipulatives app brainingcamp. We spent some time exploring the use of double sided counters and then algebra tiles. Bernie also uses real counters when teaching young children. Incredibly enough he does that without using any symbols or written work, yet he can start getting children to understand the ‘rules of negative numbers’ and even simple simultaneous equations. Young children are perfectly comfortable with the ‘upside down’ world of negative numbers for instance once they have had a play with the counters.
Algebra tiles in action on the Brainingcamp app.
Like Jonathan Hall he also started off with the field axiom of mathematics on the idea of there being an ‘additive inverse’ rather than ‘takeaway’ for the idea of subtraction. He stressed that there is no such thing as ‘takeaway’ at all. The app is a great way to show the additive inverse, the zero pairs can be greyed out when brought close to each other which is pretty neat. These zero pairs can also be used in teaching Chemistry as the positive and negative charges can be used to model electrons, protons etc. I use coloured dots in chemistry teaching as well. But that’s a seperate blog post altogether.
Bernie showed us very elegantly with the counters how a negative of a negative gets back to a positive. What it means to add a negative to a positive and to a negative. And the moment that got the biggest ahhh moment was a demonstration of how multiplying a negative with another negative gives a positive. The clarity and evidence given by this representation using the field axiom idea is irrefutable
And here you have it. Why multiplying two negative integers gives a positive integer. Very straightforward in the context of the ‘additive inverse’ field axiom.
There was a little demo of Alge disks then, which seem to be a halfway house between algebra tiles and place value counters. The difference being that instead of numbers the counters have x and y labels on them. Factorising using these disks seemed to tie in very well with the factorising I had seen earlier in Jonathan Hall’s workshop.
We then moved on to algebra tiles themselves. The tiles can be used for a number of things and I have been using them for nearly two years now. Though I only use them for showing the area model and how they can be used to factorise quadratic equations. There’s loads you can do with them, including zero pairs that disappear when merged together
Finally Bernie stressed the point made at the introduction once more that these representations are only there for students to slowly learn and get a feel and sense for what the abstract version of such representations should lead to. And that with time the use of manipulatives need to be faded out of use. They can of course always be bought back as and when necessary on a topic per topic basis in the non linear journey of learning maths as and when required. Which is exactly what I do as a tutor. Bernie now also has a video channel that I recommend watching.
Workshop 5 : Yes But Constructions
The final workshop of the event was delivered by Ed Southall, author of the books ‘Yes, but why?’ and ‘Geometry snacks’ fame. Constructions as a topic is really interesting to me, having done lots of constructions during my Mechanical Engineering degree. In first year drawings are all done on paper with proper equipment before moving on to CAD after that. And subsequently practical sheet metal requires the use of constructions with good equipment.
Ed Southall discusses other ways of bisecting a line.
Constructions for teaching school students is none of that however, it is mostly wobbly compasses, broken pencil leads and nothing ever quite lining up. And teaching it online is a pain as well with the document camera kinda getting in the way. Mathspad and Bitpaper help me though and are usually enough. But I just get the bare minimum done that way.
A sensible order of teaching constructions @solvemymaths
Before starting any construction work whatsoever it is important to make sure the very hardware students will use is in reasonable working order, fastening the compass screw tight so it is not wobbly and making sure the pencil is not very sharp. Keeping it a little blunt makes the lines a little thicker and gives scope for covering up a little when things don’t match. Just getting used to joining up two points into a line requires practice and fluency (this always seems to have some degree of randomness as the pencil may not follow the ruler track as we think it does) and getting used to drawing circles of various diameters.
We then moved to perpendicular bisectors, bisecting it the classic way. But making sure to draw the full circles so the symmetry and context behind it all is clear to see. In fact drawing full circles instead of arcs is always recommended. Except for when your line is at the bottom of the page, then what? Enter alternative forms of bisecting a line.
Another way of creating the perpendicular bisector of a line.
Next up was angle bisection “The Don” method and another one. We also did an exercise with circles and lines, eventually leading to something looking very pleasing to the eye in an islamic art type style.
“The Don” method of angle bisection
And I learnt about a special type of triangle called a Reuleaux triangle. I finally know what the shape of my guitar plectrum is called and why it rolls so nicely!
Reuleaux Triangle. Good design for guitar plectrums as well.
There was also drawing an incircle of a square, incircle of a triangle and a circumcircle of a triangle (see video).
While teaching and leaving a class to do the constructions Ed suggested having gifs of constructions on a loop so students can look at them if they missed a particular step during the presentation so they can go back to it and see the whole sequence. He does this very well indeed on his own twitter account with the gifs which I highly recommend looking at.
Overall another great workshop with loads of great ideas to take away and implement.
A superb experience from the Friday to conference day
The workshops and the entire day is very carefully planned to bring maximum benefit to the delegates and also to make sure as many teachers get to know each other as possible through the various tea breaks, lunch, tweetup event, exhibition, speed dating etc. Penistone was not an easy location to get to particularly for those like me who don’t drive but once you got there it was difficult not to be wowed by the idyllic location and the spacious school layout which made the day feel so much more relaxed despite so much going on.
I say it every time but quite genuinely this was again my most favourite maths conference. I learn so much from everyone, not just the workshops but from every conversation with a maths teacher. With so many new things to try out and full of inspiration I am ready and refreshed for some light summer tutoring followed by a brand new academic year.
This blog post is a write up of my fifth maths conference held on 9th March 2019 in Bristol. Run by La Salle Education, the conferences are attended by around 400 maths teachers, trainers, suppliers, academics, tutors and just about anyone who is passionately into maths education. The maths teaching ecosystem is very diverse indeed and I learn so much from fellow professionals who live and breathe maths teaching. In this post I cover my thoughts straight after the conference with some reflection on how I have used what I learnt nearly 3 months ago.
TLDR ; I got a deeper appreciation of the idea of unity, the unit, one.
Pre-conference Friday drinks
As on previous occasions I travelled up to conference city on the Friday afternoon to tutor my Friday evening students online from the hotel room. After tutoring I headed to the Friday night pre-conference drinks; one of my absolute favourite parts of the whole experience. Conference day on Saturday is an intense day so I really like the Friday to relax into it all over some drinks. At the bar I got a chance to check in and catch up with some of the teachers I’ve got to know through La Salle and I also made some new connections. Tutoring is an isolated profession and it is so useful to share experiences with other maths teachers.
When the bar closed there was only one thing to do, go to another bar. And like Manchester #mathsconf15, the last men standing ended up exploring the nightclub scene. An epic time was had dancing to 1990s tunes.
Onwards to conference day itself.
Workshop 1 : Rekenreks rock, the new manipulative on the block
This workshop was delivered by Amy How who has recently become the ambassador of this invaluable manipulative. I learned about this manipulative recently from the Bernie Westacott video podcast with Craig Barton and from Mark McCourt’s workshops on CPAL and Multiple representations. Since I work with a few Dyscalculia students I am always seeking new ways of developing number sense for students. The Rekenrek turned out to be a tool that can be used for far more than developing number sense alone.
The Rekenrek is an invaluable manipulative. This is a 10 row version.
I used the Rekenrek for about two months previous to this conference for number bond work, doubles and subtraction but nothing more than that so far. So frankly I was blown away by how much more is possible with this manipulative from Amy’s workshop. Starting from the very simple idea:
The building part is moving the red and white beads, saying affirms the language and writing it gets it into symbolic form. Amy showed us how to use the beads to show the times tables in action through various arrangements. The patterns that started to emerge by exploring the six times tables got some aha moments in the room.
The 100 bead rekenrek can be used to build fluency for the number bonds of 50, 100, rounding and working out the times tables. We moved to the idea that a 10-row 100 bead rekenrek could also just represent one. Meaning that the same manipulative can also be used to embed the idea of fractions, decimals and proportional thinking. It is so clear and obvious when two fifths of 30 is explored by selecting two rows (of 10 each) out of five. There is an elegance and clarity to using this manipulative and while I initially made the mistake of thinking they are suitable for just number bond work, I have started using these with older students for fractions, decimals, percentages and ratio work.
One other small but important thing I implemented straightaway after this workshop was the idea of “one finger one push” to move the beads. Previously if students were to count the beads out by touching them and moving them one by one then I would let them do that. I realised that for one of my tutees who counts in clusters of one, this had to be corrected immediately. 3 months on and I have used this manipulative with various tutees now, including a superb virtual version of it on the mathsbot site.
Amy’s workshop had primed me with the idea that we can make something ‘one’ and then work from there. This theme of one or the unit then ended up repeating in nearly all the workshops I attended.
Workshop 2 : Cuisenaire rods, Metallica and the one
This workshop was given by Drew Foster who is a big fan of puzzles, manipulatives and hosts #BrewEdPreston. I got a set of original Cuisenaire rods back in 2015 after my Dyscalculia training with Patricia Babtie. For a good three years I used them mostly for number bond and number sense work. I have become more drawn in and fascinated tutoring number bonds over the last 3 years, there is something very profound about them. A few months ago I got some training on how to use Cuisenaire rods from the La Salle CPAL and Multiple representations CPD courses which has accelerated my use of these to no end. I am starting to find so many ways in which you can use these, with students at various stages of their maths learning journey. They are so useful for secondary maths as well; from arithmetic sequences, linear equations, ratios, percentages, area scaling, volume scaling and surface area to volume ratio. I am merely at the tip of the iceberg in terms of their full application.
Drew gave each table a set of Cuisenaires to play around with and move about. He stressed the idea that we should try and see things from the children’s point of view. You have to move these around physically first until stumbling into the right answer through the right combination of the rods. I was making the mistake initially of trying to do things in my heads and then move the rods about. We did a bunch of basic exercises at first from setting up equations in colour, to staircases and a pyramid.
The moments that wowed us all were how a simple ‘up and down staircase’ which looks like a Stats distribution and is linked to square numbers as well. We were also shown how Quadratic factorisation could be shown using the rods. Although I have used Algebra tiles for quadratic factorisation I never linked it using it with cuisenaire rods.
We were shown the video below which is the ‘cuisenaire rods way of the zen’. All to the soundtrack of Enter Sandman by Metallica, my head was bobbing along for that one for sure or was that from the Macarena a few hours earlier at Popworld?
The fact that you can make one anything you like and then the other rods take on a different value is very profound. A couple of tutor colleagues who were at the workshop have now bought their own cuisenaire sets, remembering not to buy any sets with graduations or marks on them which Drew stressed are not the right type of rods. They must have no writing or markings on them. The beauty of these rods is that by keeping them free of any markings you can make them whatever value you want them to take. I was so inspired by this workshop to use this manipulative more and a few months on I have innovated their use in online tutoring ever more. I intend to write more about this in future blog posts.
Workshop 3 : Creativity and Curiosity, there’s more to maths than convergence
Even if creativity is not assessed it is important
As a tutor I often feel the pressure in helping a student prepare for an imminent high stakes exam, particularly for Year 11, 13 or 11+/13+ prep. Every tutoring hour has to count, not just the teaching itself but in supporting the tutee, communicating how the system works to the parents and showing the tutee how to revise by themselves in a structured way. Teaching for a test or exam is very ‘convergent’ in that way. There is a right answer to be got as quickly as possible.
Andrew Sharpe’s presentation reminded us why we really got into maths and how creative it can be. We started off with a number grid puzzle and a coordinate grid exercise. It was ok to fumble about and come to the solution, and in that fumbling process is the joy of discovery. Trial, improvement, iterative processes are all part and parcel of the overall learning process in maths. He encouraged us to make up our own puzzles and for students to do so as well.
An exercise in divergent thinking that I remember was of the ‘Alternative Uses Test’ where 10 alternative uses of a brick should be brainstormed. Highly successful people are creative thinkers and problem solving itself is a creative endeavour. Some students like to think divergently rather than convergently, which is certainly something I have encountered as well. Andrew gave plenty of examples using number maths and geometry for the Alternative uses.
This workshop has inspired me to bring that creativity to more of my students. I do some fairly divergent teaching to those who are homeschooled but there is no reason to have elements of it with other tutees. During preparation for an exam gears have to be switched completely but there’s always some scope for creative and explorative thinking. Most importantly this presentation helps me give myself permission that divergent teaching is all part and parcel of overall teaching and in getting the best out of students. Andrew’s presentation for this workshop with some very useful extra resources are on here.
Workshop 4 : Unit Conversions, metre rules and following the multiplicative arrow
Jo Morgan’s in depth series of presentations are invaluable and I often refer to her presentation notes on the other in depth series, all available on her site here. For this topic on unit conversions Jo started off by mentioning that while unit conversions is not a big topic like solving quadratics or angles, it is a topic that often carries a lot of easy marks and students miss out on these.
She mentioned that units are covered first in Year 3 and then consistently again every year until Year 6. In fact students see mixed units like 1 kg 200 grams very early on in their maths journey and often year 6 students can know their millilitre <–> litre conversions better than Year 11 students. I often teach Year 6/7 students back to back with Year 11 ones and have observed this too. Somewhere in the middle years students don’t see unit conversions as often and lose that fluency in this topic. Jo showed us several examples of GCSE students losing fairly straightforward marks on unit conversions, both in the higher and foundation tier from examiner reports and example scripts (AQA and Edexcel boards). Quite often students were losing marks in just getting the simple decision on whether to multiply or divide the conversion factor.
The presentation then followed the structure of following this strategy in converting units.
Step 1: Be fluent in multiplying and dividing by powers of 10
Step 2 : Memorise the conversions
Step 3 : Perform the conversions
Step 1 is a self evident prerequisite and so Jo covered the other two steps.
Step 2 is all about memorising and recalling the conversion factors. There are surprisingly few conversions to be memorised for GCSE maths in the full range of conversions and all these are given below from one of the slide presentations. I have highlighted in purple the ones that need to be memorised.
GCSE maths unit conversions (from presentation by Jo Morgan)
This then lead to the discussion and history on why the adoption of the metric system. One interesting fact that I didn’t know was that the prefixes for bigger units (kilo, hecto, deca etc.) are Greek and the smaller ones are Latin (centi, deci, milli etc.). Definitely very useful to know and a great point of discussion for A Level Physics students who need to be aware of the fuller spectrum of units.
To remember units using manipulatives Jo mentioned that an actual metre rule is essential to show to students and water bottles also help. I really like bottles of water in addition to how useful they are to get a feel for volumes. They have lots of lovely Chemistry stuff on the labels, including the ions present, the charge on them, the exact type of plastic (polymerisation) and the concentration of the ions (a compound unit in chemistry that GCSE students also need to know). Lots of Chemistry and maths in water bottles.
Step 3 is carrying out the strategy once students have memorised the actual conversions. There are a number of methods possible, from ratio tables to Don Steward type grids and for calculator papers it can all be done on the new Classwiz calculators. This is very useful to know as I have a few IGCSE students who would benefit from getting the new calculators as both their papers are calculators.
The method that really appealed to me was ratio tables. I have seen them appear on twitter but only during the talk I realised how invaluable a technique it is, a very simple layout with the arrows representing the direction of multiplication. Going against the arrow means to divide. This will be very handy indeed for many of my students. The method that was very popular amongst maths teachers was “Last man standing”. It is a neat method using the idea that (100cm/1m) can be expressed as 1 and then the units can be ‘cancelled down’. I’ll refer to the excellent interpretation of Last Man Standing by Mr. Bracewell and Jo’s presentation slides referenced earlier.
This presentation gave me plenty of thought on another interpretation of the unit as being one and how you can use it convert between units. I tutor the Sciences at GCSE as well and dimensional analysis is very useful indeed there. Ratio tables to convert between units is something I certainly want to implement and last man standing is a useful new technique to have in the teaching toolbox.
Nearly three months on the thing I have used most is the use of ratio tables with my two GCSE retake tutees, particularly the idea of ‘going against the arrow’ to divide. Teaching students for an imminent exam when time is short does require such shortcuts which I feel can be justified for the long term benefits it will bring to the student’s future chances. As for what division sense actually is and how to convey the idea to students over the long term, that was covered in the next workshop.
Workshop 5 : Time to revisit…Division, the beast of division tackled
This was the first time I attended one of Pete Mattock’s talks having chatted to him before about the use of Algebra tiles and other manipulatives. In the preview blog post for this workshop he mentioned that “Professor Emeritus in the department of education at the University of Oxford calls division ‘The Dragon’. Those pupils who slay ‘The Dragon’ tend to go on to do well in mathematics; whilst those who don’t tend to struggle from that point on.”
Cuisenaire rods and counters
There’s certainly a lot of truth in this. Making sense of division has many important implications further down the line, including unit conversions which I had just seen on the workshop before. By being able to make sense of the division process from the very outset using the appropriate concrete and pictorial methods as support, a long term framework can be built up for pupils to understand the process of division. Concrete and pictorial methods eventually being faded out. I am currently reading Pete’s book ‘Visible Maths’ that looks at a variety of topics from different representations of whole numbers, powers and roots, the laws of arithmetic to algebraic manipulations. Division being just one of the topics in that book that was presented during this workshop.
Double sided counters and cuisenaire rods were the two manipulatives used during this workshop with delegates having ample opportunity to move the manipulatives around on each table. Counters being used to show the discrete view of division. 12 ÷ 3 can be shown as 12 being put into groups with 3 counters in each group (creating 4 groups) or 12 being shared into 3 shares (with 4 counters in each share).
Left : 3 counters in each group (creating 4 groups) Right : 12 being shared into 3 ‘shares’
Using the other side of the counters can then be used to show division where negative integers are involved. The red side of the counter represents -1 while the yellow side represents +1. Putting a red and yellow counter together creates a zero pair. Having a line of 12 reds represents -12 which are then put into groups containing three -1 counters, representing -3 together. Thus creating 4 groups.
Red counters for demonstrating division with negative counters (see blog post)
300 ÷ 20 can be demonstrated by making the 20 as 1 (in the same way as shown in Drew’s earlier workshop). Once the cuisenaire train of 20 is 1 then it is easy to make a multiplicative comparison with 300. 15 multiples of the ‘1’ unit.
And how to tackle the beast of division itself? Division and fractions. Again a multiplicative comparison is used to compare part to “whole”. The part being assigned the value of 1. Pete talks about fraction division in his podcast with Mr Barton, which is an excellent and more comprehensive description of the idea.
We finished off with a practical context where a simple speed, distance, time context could be visualised using the idea of multiplicative comparison. Speed is the distance travelled in unit time, i.e the distance traveled in one hour, one minute, one second etc. The example used was finding the time when 75 miles are covered at an average speed of 20 miles per hour. Once again 20 is made into the unit, i.e one. There are 3 of those complete units of 1 hour time ‘blocks’ and a remainder. The remainder being 15 out of 20 = ¾.
75 miles covered at an average speed of 20 miles per hour. 20 is called the unit, i.e one. There are 3 of those complete units of 1 hour time ‘blocks’ and a remainder. The remainder (not drawn in) being 15 out of 20 = ¾
The idea that really stuck with me, from Pete, Jo, Amy and Drew’s workshops being that the ‘unit’ is of profound significance. Exactly what that means was summed up by a tutee of mine in the last days of GCSE exam preparation with the quote at the end of this blog post.
Summing up the whole experience, this was by far my most favourite MathsConf so far. I am grateful to all those teachers who put in so much effort to run these workshops for the rest of us. And big thanks to the La Salle team and visionary Mark McCourt for putting these together.
Nearly 3 months after this conference and just days before the final IGCSE paper, my retake tutee exclaimed with delight in that light bulb ‘aha’ moment that we teachers all live to experience.
Once you know one, you know everything!
Mission accomplished, so many things fell into place for my tutee in that moment of realisation. I can’t wait for #MathsConf19.
The Bett Show in London is an Educational Technology Exhibition held every year for four days. Companies that supply hardware, software and other educational technology related material to schools showcase their products. Additionally there are young EdTech startup companies also exhibiting there. This blog post covers a short review of my visit there this year.
Tutoring is a lonely profession and online tutoring is a niche within the tutoring profession itself. It is hard to judge the scale of the impact of technology on education when working alone. I have often felt like a lone voice of online tutoring and technology in tutoring in general. There are barely even a handful of tutors I know who tutor 100% online (though those who tutor a mix of online and in person are a lot larger in number). Over the years I have gone to great efforts to organise tutor meetups, find Facebook online communities and more recently attend the excellent maths conferences and CPD by the La Salle Education Network. The missing piece though has been something online tutoring/teaching related.
I am a tech geek at heart and my tutoring is based completely around technology. Technology has revolutionised the effectiveness, impact and business of tutoring for me. As such I am really passionate about it and need inspiration on that angle. So it was incredible to visit Bett Show and be wowed by a giant hall of all things EdTech. The world’s largest education technology show, 4 days, over 300 stands, many inspiring lectures, big names like Google, Microsoft, Apple putting in their weight behind EdTech products and lots of smaller EdTech companies.
Seeing the technology in action there in such a vast arena was like a dream for me. From Microsoft’s Minecraft games to Google’s lecture hall and classroom there were many toys to play with and see all sorts of great things. Most of the displays and products were angled at classroom teaching, though with some creativity I am sure I can adapt them to online tutoring.
Virtual Reality in teaching is much further along than I thought it was. I wore a headset and got to be in a world war 1 scene in the trenches. Thanks to some augmented reality I could see little dinosaurs on tables. Some of the smartboards out there are truly incredible, images, video, colourful drawing all on one large creative canvas. I had no idea that this was even possible. I am hoping that this type of technology can be implemented in the type of virtual whiteboards I use for my day to day tutoring.
I also saw lots of other stands, including one about Dyscalculia intervention teaching via a website. It looks pretty impressive as the exercises were well designed. The one stand I had booked an appointment for was the HUE HD document camera team. When I started tweeting about their camera last year and tagging them, their social media representative was very impressed with how I use the camera in my tutoring.
That camera is a classroom visualiser and they sell to schools, so online tutoring was very out of the box for them. I got invited to write a blog post on their teachers for teachers blog. And finally I got to meet the person I had been emailing all these months in person! On behalf of the Ultimate Support Group for Online Tutors Facebook group manager Joanne Kaminski, I awarded the HUE team with the tech resource of the month award.
I was there for a whole afternoon for about 4 hours. This is nowhere enough time to really go into the show in depth and only gives a taste of it all. I would like to plan a longer visit next year and see more of the lectures. I leave the show really inspired, energised and with so much more confidence knowing that I am not one of a few lone EdTech educators, I am in company of a whole educational technology revolution.
This blog post is a write up of my fourth maths conference. La Salle Education run the UK’s largest network of maths teachers’ professional development along with an online platform Complete Maths. Attended by around 400 maths teachers and a few tutors, the conferences are invaluable professional development, training and networking with fellow maths teaching professionals.
TLDR : All four workshops were phenomenal as standalone workshops. In the sequence I attended them, they compounded my learning even more.
Friday – Hotel tutoring and drinks
I have Friday tutees and Saturday is my busiest tutoring day. I wasn’t going to let that get in the way of going to #mathsconf17 though so I rescheduled many of my Saturday students well in advance. I took the train on Friday morning, checked into the hotel, set up my mobile online tutoring office (laptop + graphics tablet) and away I went tutoring until the evening.
Selfie time with Mr Corbett!
Fellow tutor friend and conference buddy Austin (@Lazyrunner78) arrived after a long evening of his own tutoring. We had a catch up and then made it to the bar late. The Friday drinks are always so welcoming, you can join anyone and instantly share your own enthusiasm of teaching amongst fellow teachers who understand the slightly crazy passion we have for teaching maths. I met some new teachers, both local to Birmingham and those who travelled. The friendly Mr Robert Smith was welcoming as always, introducing people to each other and keeping us all ticking socially.
Speed dating with some unexpected Science
The Saturday was buzzing and La Salle CEO Mark McCourt opened the conference with an intro. His story on how the conferences started and his passion of empowering and bringing together maths educators set the scene for the day. We kicked it all off with mathematical speed dating. This was missing at #mathsconf15 so it was good to see the return. A speed date is talking to a teacher for two minutes about your best teaching ideas then hearing the teacher for two minutes. That’s one speed date, next you find a random teacher and then rinse and repeat four more times. Mark reminded us all on how a mathematical speed date in Birmingham led to a wedding two years ago. Love that story!
Andrew Taylor from AQA.
I shared my own ideas on using manipulatives to teach from a mixture of algebra tiles to the meaning of pi experiment. Amongst my dates I met a teacher from Birmingham who was retraining from being a Chemistry teacher to teach maths. As it was his first conference he felt a bit out of place amongst so many seasoned maths teachers. I reassured him that I felt even more out of place at my first maths conference as a private tutor but now I know the community is super supportive. Since we both also taught Science it was so easy to go straight into common themes between the two. His speciality was Chemistry so we had plenty to talk about that. I had my big aha moment right at the end of the day too on maths and Chemistry. More on that later.
Workshop 1 : Tech, Tech, Tech from Steep Roads to CGI Films
This is the second time I went to Douglas Butler’s (@douglasbutler1) talk, previously seeing him at #mathsconf10. This second helping was with a different flavour. He gave an overview of some of the items on this list.
Top Google Earth Objects
Top Large Data Sets on the Web
Top Uses of Excel
Top Problem Solving Ideas
Top Twitterers to Follow
Top Maths Blogs
Top YouTube Channels
Top Mathematics Entertainment
Top Dynamic Software for KS3-4
Top Dynamic Software for KS5
Maths cakes. Perfect for sugar rush.
I have installed Google Earth pro on my computer after seeing it in action at this workshop. I use Google maps with tutees already to show them the similarity between New York’s grid layout and the x-y system. Google Earth Pro can do so so much more though. He showed the world’s largest equilateral triangle layout, parabolas, pentagon and the world’s steepest road. He also gave us all a hearing test. The airline industry is full of amazing data that can be used to show the perils of sampling data from a population. We also got a taster of Autograph and Excel. I am amazed by what those pieces of software can do. He finished off by making an animated version of the Starship enterprise from Star Trek to show 3D dynamic geometry in action, with music included!
Douglas tells great stories and delivers with such great enthusiasm that you are drawn into the world of maths he reveals with the help of simple technology. I’ve got such great ideas from this workshop which will no doubt help my online maths tutoring for KS3, GCSE and A Level students.
All that geometry and visual representation got me in the perfect mood for Singapore maths next.
Workshop 2 : Dyscalculia, Bar Modelling and the rise of Singapore
Dyscalculia and Singapore bar modelling are massive topics. I have been to day courses on both of them before. To deliver a concise idea of the two in one workshop was no small achievement by Judi Hornigold (@DyscalculiaInfo).
Counters are a powerful tool in learning maths.
I have totally immersed myself into tutoring and understanding Dyscalculia after going to a day workshop on it 3 years ago. Judi told us how we can better define Dyscalculia so that we can then address it. She also discussed that in many cases Dyscalculia might appear to be the issue when in fact it is maths anxiety. Anxiety triggers a fight or flight reflex shutting students down to learning maths. Again, maths anxiety is a huge topic on its own.
So how can Singapore maths help? Students and teachers in Singapore had never heard of maths anxiety to her surprise. Judi went through a brief history of Singapore maths and then we got to the fun bit! Using counters, cuisenaire rods, Singapore strips (of paper) – Singapore strips sure got some chuckles in the room. We looked at the bar model method itself for a range of situations from number bonds, ratio questions, linear equations in counters to the idea of metacognition for students. Metacognition is about building into students how and when to recognise when a problem can be reduced down and then solved in a different way, rather than applying an algorithm on autopilot. A quick example is on finding 12.5% of a large number without using a calculator. If students recognise 12.5% instantly as one eighth then they can divide the number by 8 instead.
Singapore maths and bar modelling is changing lives for children. Judi had some amazing stories of students cracking things in maths. She had stories of students in tears of joy when they figured out concepts. I can relate to that as I had a Year 11 tutee who had battled with ratios all his life. It made sense to him after just half an hour when I used the bar model with him as the very first tutoring session I ever had with him. The utter delight and sigh of relief he had at understanding ratios is something I still remember so clearly.
What an inspiring, well thought workshop. Inspiring low motivation students was just about to be covered in workshop 3.
Workshop 3 : Re-visioning success and the marigolds of multiplication
Julia Smith (@tessmaths) is a motivational power house, absolutely no doubt about it. She works with some of the least motivated students, those who have retaken GCSE maths and in some cases, are still retaking. She has found many ways of motivating students and has some excellent methods on how to help them revise and pass their exams.
Re-vision workshop in the school music room.
Julia started off the talk by clarifying that if students haven’t managed to figure a method out by the age of 15 and a high stakes retake exam is imminent, then it is time to re-visit the topic in a totally different way. If a method that works for them to give them the correct answer, then no matter how procedural or ‘quick fix’ the method seems, it is more than worth it to get the student to pass, gain confidence and go on to get a better paying career in life.
She broke down the word Re-vision into re and vision. I had never thought about it this way so this was very refreshing. We also discussed possible answers to the “I hate maths” line from demotivated students and a tea towel of her revision techniques was given to one of her favourite responses.
I am really torn when I have to teach to the test rather than teach for understanding. I will switch to teaching for the test in cases when I have to. To many of my students their dream might be to work in Veterinary Science, Sports Science, Nursing, Music Tech or something that requires that all important maths pass. I’ve got such students over the maths hurdle and it is truly satisfying.
Amongst her top tips was the idea of double marking past papers, one with the real mark and the other with what the mark could have been with all slip ups and silly errors were given. Getting students to visualise tough moments in exams and to work out strategies to overcome those tough moments and to continue. Her centrepiece was her toolbox, which amongst other methods uses the marigolds of multiplication. This helps students to instantly figure out the times tables of 6,7,8 and 9. It works and will get students out of jail when they most need it, I really liked it! The other technique that I learnt was Vedic multiplication using just line strokes and counting for long multiplication. Again, what a superb technique.
She also stressed that the way to do maths is to do lots of it, the importance of good exam technique and plugging gaps in the nine basics. Corbettmaths revision cards were mentioned amongst mathsbot and a few other great revision resources.
What came across so well is Julia’s energy and a can-do attitude to get her students over that line. I will take a lot away from this workshop and have new found courage to help my GCSE retake tutees.
On to workshop 4. I was already primed for linear equations from the bar modelling workshop earlier in the day.
Workshop 4 : Atomising Linear Equations and an aha moment with Chemistry
Choosing this fourth workshop was a tough decision indeed. Between Jo Morgan’s workshop on solving quadratics, this one by Kris Boulton (@Kris_Boulton) and Pete Mattock’s one I had to pick just one. The title of this talk “How to solve linear equations, 100%, guaranteed” and a compelling description is what really sold it to me in the end. Perhaps the biggest motivating factor for me was that solving linear algebra equations is one of those pivotal key skills that once cracked, really gets students a firm grounding for algebra in general. I keep having to revisit it with some students.
Kris started off with Al Khwarizmi. This is what I do when introducing linear algebra to students, so this struck a chord with me instantly. I ask students to google the origins of algebra and more on Al Khwarizmi’s book. We then talk about some of the words that come up, balancing, restoration, completion etc. Kris went into some detail about the appropriate use of the equivalent, equal signs and the word solve.
Atomising how to solve linear equations
He has ‘atomised’ the process of solving one step linear equations in some very fine detail indeed, 17 steps in fact. Breaking and repairing equations was the sort of language I have not heard in this context, so it really gave me food for thought. These steps could be put into component process pretty much independent of each other.
I was sitting next to Austin for this last talk of the day and we both tried to come to terms with the idea of breaking an equation. This careful ‘atomisation’ and the early Chemistry moment suddenly gave me a Eureka moment. At GCSE Chemistry students are given equations to balance. These are broken equations because atoms are quite literally in unbalanced numbers on both sides. Balancing equations is a nightmare topic in Chemistry and Kris’s talk has given me an idea on breaking the process down rather than teaching it as one big process from start to end.
There was a lot in this last talk of the day and by being forced to think in language I had previously not encountered I have taken a lot away from this workshop.
Fan moments, freebies and meeting other maths tutors
It is so refreshing to see more tutors turn up to these conferences. The Maths Tutors UK group has about five core members who attend these conferences and a new tutor local to the conference always joins in. It is vital that tutors get out there to such events as working in isolation has drawbacks.
Free books from CGP!
The rest of the conference was all about goodies from CGP, maths cakes, selfies with the legend that is Mr Corbett (we were in a long queue of selfie takers!) and all round socialising.
In summary this was the best maths conference for me yet. On its own each workshop was perfection. By design or sheer coincidence the order in which the workshops followed one another complimented each other so well. Compounding at its best. Einstein wasn’t kidding when he said it is the eighth wonder of the world!
The positive, supportive, can-do energy of these conferences is what bring me back to them each time. Endless thanks to the La Salle team and Mark McCourt for making this all possible.
With the new school year starting up I feel thoroughly refreshed and excited to start a new year again. My online tutoring has just grown and grown and with it so has the demand on my time, particularly now that I am involved in various other tutoring projects like Indie Tutors, BitPaper, various Facebook Tutor groups, EdTech stuff, maths CPD and general networking. In terms of growth, last year was really exciting indeed and I covered that a little in my end of 2017 blog post. However, more so than any year, I felt I overtutored last year. And so this year I have already limited the slots I will tutor.
Hanging out with Aniello at the end of year The Profs party.
Last summer I moved out of my flat in Old Street and have been living with my family for a year now. Since location does not really matter to me in terms of my job this worked out well while I am in an interim stage of my life before getting on to the property ladder.
The summer heatwave in the UK gave me and family a perfect excuse to go out to many day outs in and out of London. Southend on Sea is the nearest coastline to us so we went there and saw the world’s longest pier, Windsor got us some royal history and cream tea, lots of local fairs meant indulging in some great food and I explored the beautiful area around Hackney Wick which shows how much East London has developed.
Southend pier. A good day out on a hot summer day.
The Profs summer party was a real celebration of tutors and I got nominated for best online tutor of the year 2018. Away from London, a weekend outing in the countryside, jamming music in the open air with other musicians was absolutely divine. I played the open air Mint Street Music festival as a musician which was great on a hot day. The Summer is all about big gigs and I got to see my local band Iron Maiden at the O2. East London’s finest.
While the football World Cup was very enjoyable and we were all in awe of Southgate and his new team, the highlight for my family was watching the Ladies Hockey World Cup 2018. This World Cup really did come home, in fact just a couple or so miles from it where the London Olympics hockey games were played in Lee Valley stadium. We got autographs from the entire Indian team and watched the games on a big screen (tickets were sold out by the time we knew). We also went out on a cable car ride and the riverboat and the Farnborough Air Show on a very hot day.
Another escape from London in late August got me to catch up with my ex-bandmate and some other musician friends in Edinburgh. Edinburgh is a place that will always be close to my heart because of the time I spent there as a student. And going to Whistle Binkies music venue 20 years later was quite something.
I wasn’t completely away from tutoring and Science though, I had the odd student and true to spirit I organised a tutors meet-up at Hyde Park. I also showed a student and parent around the Science Museum in London and met my client in person after a whole year. To indulge myself in Science even more, I paid a visit to the Royal Society Summer Science Exhibition which. It is a really inspiring outing with various bits of new and cutting edge research. Very accessible as well.
The summer also gave me some invaluable CPD. I am totally committed to my own CPD and my two most important CPD events were #mathsconf15 which took me to Manchester. A few days later I went to a maths CPD day on maths and Cognitive Science in London. The perfect compliment to all that CPD has been reading Mr. Barton’s “How I Wish I’d Taught Maths”.
How Wish I’d Taught Maths started off with a pizza meal
It is a phenomenal book, the best one to do with education that I have ever read. I am just over half way over it and I have learnt so many new things. I will be blogging about how this CPD has changed some of my tutoring practice. Already I can tell how it will make me a much better online maths tutor for all levels, primary, GCSE and A Level maths.
I was at university for around 11 years and in my mind the academic year starts when summer ends at the end of September (which is also near my birthday). The way I see it there is a little bit of summer still left and I am going to make the most of it 🙂