Author Archives: Atul Rana

About Atul Rana

Private full time online tutor providing maths, Science and Guitar tuition at GCSE, iGCSE, A Level standard in the UK. Singer and guitarist in rock band DonkeyBox.

Maths Conference Sheffield (Penistone) #MathsConf19

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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.

Penistone Grammar School

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’.

Quadratic sequences using double sided counters.

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 first row of three separate groups rearranged to show both how factorising and finding the mean of yellow and red counters. Presentation slide by @studymaths

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!

The meaning of equals in the original language by Robert Recorde and its English translation. Presentation slide by @mathsjem

The meaning of equals in the original language by Robert Recorde and its English translation. Presentation slide by @mathsjem

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.



Maths Conference Bristol #MathsConf18

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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.

Rekenrek

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:

  • Build it
  • Say it
  • Write it

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.

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.

 

Bett 2019 Visit – Review

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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.

Going to Bett on a driverless DLR train, technology rocks 🙂

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.

Google at Bett 2019
Google at Bett 2019

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.

HUE HD and 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.

Soundtrap stand at BETT 2019
Soundtrap is a handy podcasting and online DAW browser based software.

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.

Back to the Future, EdTech and Virtual Reality. Right up my street!

Maths Conference Birmingham #mathsconf17

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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.

Maths Tutors UK with Mr Corbett

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 at #mathsconf17

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.

  1. Top Google Earth Objects
  2. Top Large Data Sets on the Web
  3. Top Uses of Excel
  4. Top Problem Solving Ideas
  5. Top Twitterers to Follow
  6. Top Maths Blogs
  7. Top YouTube Channels
  8. Top Mathematics Entertainment
  9. Top Dynamic Software for KS3-4
  10. Top Dynamic Software for KS5

Maths cakes #mathsconf17

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.

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 at the maths conference

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.

Maths Tutors UK Facebook group tutors

Maths Tutors UK unite.

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

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.

  • Deciding
  • Simplifying
  • Breaking
  • Repairing

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.

CGP free books for teachers #mathsconf17

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.

Summer Tutoring Break – Heatwave, Edinburgh and CPD

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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.

Local fair.

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 🙂

Stimulating CPD from #mathsconf15 Manchester

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It is hard to believe that I was on my first maths conference on this day exactly one year ago. Before that I had never been to a maths CPD event in my life. In just one year I have now been to five La Salle events, #mathsconf15 being my third maths conference.

Friday night – “Take life’s experiences when they come to you”

The timing for #mathsconf15 was perfect. I had just finished a very busy tutoring season of teaching that week and this was a good time to reflect and refresh. I went to Manchester early on the Friday and met up with Daniel of Peak Tuition (@PeakTuition) for lunch. We had connected on video calls and on twitter but this was the first time we were to meet in person. After lunch I met up with fellow tutor Austin (@Lazyrunner78). We roamed around Manchester central and found Alan Turing’s statue surrounded by flowers. It was his birthday on conference day and this set the mood perfectly for the next day.

Alan Turnin's statue in central Manchester.

Alan Turnin’s statue in central Manchester.

We eventually got to the pre-conference drinks which were again absolutely brilliant. I met speakers and various teachers in a relaxed informal environment. Conference day itself is a fast roller coaster, so this was the perfect way to ease into it and meet others beforehand. The clock struck midnight and drinks had us all a bit hazy and happy. The war cry rang out from Mr Mattock and Mr Smith. “We are in Manchester, you only get a few chances in life like these so let’s explore the famous city nightlife”. Only a little arm twisting was required to convince us and so we went club hopping in Canal Lane dancing away to cheesy music. Though sensibly we stopped after a couple of clubs and went off to get a bit of sleep.

#mathsisbeautiful

Maths is beautiful intro by Andrew Taylor of AQA #mathsconf15

Maths is beautiful intro by Andrew Taylor of AQA

So what was the actual day like? The opening talk by Andrew Taylor of AQA introduced the hashtag #mathsisbeautiful What a great idea! Using images and music I personally want to show the links between maths, science and art. It is easy for most to see the beauty in the arts but with maths that art is hidden and implicit. So I hope to bring my take on this with that hashtag.

Simon Singh’s satanic hell and Simpson-e stuff

Pop and rock music culture has references to cryptic messages by artists when their songs are played backwards. From the Beatles to the Eagles with Hotel California and plenty of others. Simon Singh’s talk showed how this works for Led Zeppelin’s Stairway to Heaven. Amazingly once we were told the lyrics backwards the mind had a curios way of getting meaning out of noise in a way that was really a surprise.

As Simon went through more of his stories and books, there was also mention of the term ‘Spherical bastards’ used by Swiss astronomer Fritz Zwicky as a term of insult to other astronomers in his field who he did not get along with. Someone who is a bastard no matter which way you look at them from. Zwicky was sure a grumpy one.

Simon showed a short video of Andrew Wile’s story on cracking Fermat’s last theorem. Maths can bring people to tears (the good type) and it is a passion we can all relate to. We’ve all missed meals as we were too busy solving maths problems. Andrew Wiles missed many and the moment he breaks down in tears to describe his journey was really authentic and touching.

Simon Singh talk at #mathsconf15 with The Simpsons

Euler and Lisa Simpson.

Simon Singh then moved to The Simpsons as well amongst some of the projects he is working on to help maths students. I know a lot of maths tutor friends who want to volunteer at schools. Simon has the perfect opportunity for that in his Top Top Set maths project that I would recommend you check out.

This is the second time I heard Simon talk. Simon is a superb and highly engaging speaker. La Salle put the guest speaker talk in the middle of the day rather than at the start of the day. This helped break up the day a lot better I think.

So what were the workshops I chose like? There were several workshops happening on the day but since many of them ran in parallel we were limited to 4 workshops. Tough choices had to be made and these are the ones I chose.

Workshop 1 : Indices and the importance of SLOP (Shed loads of practice)

Indices in Depth workshop in the main hall

This was the first time I heard Jo Morgan (@mathsjem) talk. She’s an excellent presenter and had a lot of invaluable things to share on indices. Megan (@MeganGuinan1) covered her talk very well in a series of tweets, so that is also one place to go for a summary and key slides. Jo was very thorough with her research. She covered the importance of the topic comprehensively from the correct use of language, history of teaching indices, SLOP, examples of indices that would easily be suitable for GCSE students and a whole load of other indices goodies.

What I took away is that one must really sit with the indices topic for a while, until the language, process and meaning of indices makes clear sense to students. Through, conscious, deliberate practice.  Rather than a one hour lesson, indices need more like 10 hours worth of lessons throughout the many years students have to get this one right. This could not be more true since I am finding that most of my A Level students get flummoxed when indices are inversed with Log operations.

It was also a relief for me that Jo confirmed what I thought all the time. Why don’t modern books have tons and tons of practice questions? 10 questions on one part of indices is not enough! I studied in the Indian system until the age of 15 and doing absolutely tons of questions per topic was the norm for me. It turned out that this was also done during the Victorian era in the UK as well. Jo called this simple idea SLOP – Shed loads of practice. Love that term.

There’s no way out of SLOP. SLOP is also needed in music practice, me and my ex-bandmate had a saying “Most of what happens in a band is so not rock ‘n roll”. What we meant was what every performing musician knows. At the start of learning a new cover (or original) song seemingly hours of mind-numbing practice have to be put in. We break down a song so meticulously into all its parts and slow the tempo down. At first this process kills the entire romance of the song. But once all the parts are nailed and put together a few times, at various tempos, the magic comes back to the song many folds. And that’s why maths feels so beautiful to mathematicians. The magic in maths happens after due diligence and practice has been given to it first.

Presentation slide by Jo Morgan on Indices at #mathsconf15

Conscious, deliberate practice of indices when students first introduced to it

There was a lot in Jo’s talk and to cover it all would take a more comprehensive blog post of its own. Her workshop was confirmation of some of the things I already do and it also gave me loads of brand new things to think about.

Workshop 2 : EdTech tools and making maths digital

This talk and interactive presentation was given by Patrick McGrath (@TH_PatrickM) of Texthelp. There is no getting away from it. I am a tech geek and this was tech talk heaven for me. When choosing my workshops I restrained myself to attend just two presentations with an EdTech flavour. Patrick was clear from the outset that technology is only an aid to learning and ultimately teachers make the real learning happen. It was great to be reminded of this again.

BitPaper as an EdTech collaborative tool

He started off the session with a pretty cool interactive where he could create a poll with 4 responses and delegates could answer with their mobile phones. As the data streamed in you could get a real time view of what everyone thought. This reminded me of the Plickers I saw at a Google EdTech conference.

There were a range of digital learning aids that Patrick went through. Too many to keep track of so I have a big list to explore. More digital toys to play with! What stuck in my head were a range of tools with interactive videos. Whiteboard type apps where students could answer questions without needing to talk, really good for quiet students. A way in which students could also record short audio and screencast snippets to show how they did the working out of questions.

With whiteboards talk there was one that was mentioned that put a mile long smile on my face. BitPaper is the tool I use all day for hours on end with my students. It was so cool to see it being shown on there. It has been an absolute game changer in my maths tutoring. It has bought colour and interactivity to my online lessons in ways I never thought were ever possible.

Many new things for me to explore after this talk which I am looking forward to.

Workshop 3 : Mind the Gap. Making Stats (even more) interesting

Statistics seems to have a terrible reputation both in popular culture (There’s lies, more lies etc) and even among maths educators.  Richard Tock (@TickTockMaths) took the challenge on to make it more interesting to us. I must admit that beyond S1 I find Stats pretty tricky too. As mathematicians we love the sense of having an exact, definitive, irrefutable answer. Stats seems to take us into new fuzzy land.

The winning maths cake

Florence Nightingale and her polar diagrams are an inspiration in the world of Stats. She bought clarity to how so much data can be crunched and presented in an elegant visual that can then be used to make real arguments based on data. Yet even I didn’t know about her commitment to Statistics until I saw the maths exhibition in London. There are no real modern Stats role models that I know of either except for the late Prof Hans Rosling. His visualisations blew me away when I first saw his talks on the BBC. And as someone who tutors both maths and Science, I really see that for Stats to have more meaning we must move it away from made up examples to real data.

One example is of normally distributed people living in a world of discrete sized t-shirts and never quite finding that perfect fit. It opens up a nice conversation on mass manufacturing methods vs tailor made clothes. Boltzmann first showed that gases have atoms shooting around at various speeds. With enough stats you can start making sense of it all and link the micro with the macro. Essentially the type of work I did in a software development team as an analyst helping build cost models of metal commodity prices. Both during my PhD and my job in commodities there was an enormous amount of data crunching, sorting and making sense of it all. So we can’t really escape Stats in the real world.

More winning. I won these books in a raffle!

Richard took us through a lot of the visualisations and examples that Prof Rosling used to have in his talks. I didn’t know you could download them from the gapminder site and have a play with them yourself. So this is something I will definitely explore.

Going back to visual stats displays, the other side of those displays are ones that are horribly inaccurate and completely misleading. Richard had plenty of examples of that from tabloids for example. He also went through the Large Data Set examples of various boards.

I am glad that I took a chance on this talk. Many of my friends work in data related jobs so I will prod them and get some ideas from them too.

Workshop 4 : Geogebra and the attack of the z axis dinasour

This workshop was given by Leona So (@lwyso). Choosing this one was a close call between choosing this one or the Desmos one. I am somewhat embarrassed to admit to all my techy tutor friends that I have never had a play with Geogebra. One reason for that is clear, it is not as intuitive as Desmos (for the simple stuff anyway). Geogebra is a complex tool with which you can do a phenomenal amount. I have used interactive tools made on it to explore circle theorems for example but have never actually made anything on it myself.

Geogebra presentation #mathsconf15

Surfing the curve with Geogebra

Leona took us through various examples live. Putting a gradient on a curve and surfing along the curve to see how the gradient changed. She extended that idea to show differentiation from first principles as well. Continuing with tangents, she showed how the derivative function can be plotted alongside the original function. Cubics lead to quadratics and quadratics lead to linear ones. All stuff that we know but to see it live gave new life to it. “Students like to see moving things” and that’s certainly true for me too.

To finish off the talk she got us all to wear 3D glasses and showed equations of lines and planes in 3D. It was like being at a 3D cinema. Instead of being attacked by dinosaurs I was being attacked by the z axis that seemed to be protruding out of the board and into the classroom. What a way to finish the last session of the last day! There was a lot to cover in the session and inevitably it was hard to replicate all the demos on our own computers at the same time. To do that would have taken a lot longer so I am glad there was a good snapshot of all the cool stuff compressed into a short workshop. Fluency in Geogebra will add a great tool to both my online A Level maths tutoring and for GCSE as well.

Now I have no excuse to explore Geogebra a lot more.

In Conclusion

I am in awe of some of the top teachers, resource makers and relentless hard workers who make these conferences happen. It gives me great hope that with such dedicated educators we do have control on how we deliver maths education in the UK and spread the knowledge of this beautiful subject.

The awesome tutors of the Maths Tutors UK collective

Thanks to La Salle for putting on the whole show. This was easily my most favorite conference of the three I have been to so far. I am a member of CompleteMaths and for the CPD alone it is worth it for me. The conference is very affordable thanks to some sponsorship from AQA. I cannot recommend these conferences to teacher and tutor friends enough. Get yourself booked up to the next maths conferences, they have dates all over the UK for the next two years. To echo what a wise man once said “Take life’s experiences when they come to you”.

Electrolysis Part 1 – Molten Compounds

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Electrolysis seems to be one of the topics that comes up top during my online Chemistry tutoring sessions. So I am starting a short series of blog posts just on this topic aimed at GCSE students. Firstly, we must ask what the meaning of Electrolysis is:

  • Electro – broadly speaking to do with electricity and the flow of electrons.
  • lysis – breaking down, decomposing, loosening etc.

What we did there was to break up the word into its components. Well, that is not too far from the very process of electrolysis itself! Thanks to electricity we were able to discover elements that we previously had no idea that existed. The periodic table grew pretty fast due to this.

So thinking in terms of simple metal -non metal compounds, electrolysis simply reverses the process of ionic bonding and breaks the compound into the original elements it was formed from. This is only possible through a flow of electrons in a circuit, which is provided by the cell.

Seeing is believing so here is a short video that shows solid lead bromide melted under some intense heat and then given the electrolysis treatment.

Year in Review 2017

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It has been a good 3 months since I posted a blog post about how my tutoring is going. To me the tutoring year ends in mid to late June when I am finishing off with the very last students of the year. I gather my thoughts then and sum up the academic year like I did for the 2015-2016 year.

But this summer I wasn’t able to post that summary. In July I was given notice to move out of my flat in central London so I had a frantic month of looking for a new place and packing. So now is a good time to reflect on all of 2017 covering the two academic years and everything in between.

On 22 November 2016 I attended The Profs Christmas party and #christmaths2016 on the same evening. Attending both these events set the scene up for me in 2017 like I would never have anticipated at the time.

Online tutoring – Here comes the world

I want to see some of that Californian sunshine, can you give me a tour of what it’s like around where you live?

The last student of my day was a 7pm one in San Francisco. It was still the morning for her and she was in good chirpy spirits. On a tall building in that city she showed me the view of San Francisco, a vast expanse soaked with glorious morning sunshine. It was cold and dark in London and somehow the bright vivid sunshine, even via camera really felt enlivening. Online tutoring really amazes when I connect to far flung reaches of the world in real time. I still can’t believe it sometimes! This year I have added even more exotic locations to my overseas tutoring. Indonesia, St. Kitts island, India and Bermuda come to mind straightaway.

A picture of the volcano in Bali sent to me by a client there.

The decision to go all online and cut out face to face tutoring was a real business gamble and in April this year I got proof that it well and truly paid off. With Dyscalculia and IB I am heading towards a more international and borderless type of tutoring.

Dyscalculia Tutoring

This year has seen me take on a lot more Dyscalculia students. I have now got two years of experience in this very special field. It turns out to be a really complex area of tutoring and I have learnt to treat it very differently to tutoring any other subject. The Dyscalculia spectrum is very wide and yet it has such little public awareness as a word.

Wacom Intuos Draw

My graphics tablet.

It is incredibly rewarding to tutor it as students make progress and do things they never previously thought was possible. I have invested a lot in learning about this more and more ; buying books, manipulatives, emailing the known experts, asking one of them to be my mentor and attending any training that I can afford to attend. To make my online tutoring even better I have invested in a document camera. I remain committed to tutoring for Dyscalculia and will be blogging specially on this in the coming months.

Tutoring younger children

Another big change this year is that I have started tutoring children as young as 9. Previously I would rarely tutor children younger than 12. But I felt I could make a big difference to children at a younger age and I wanted to learn how younger children learn, especially online.

It has been a really rewarding experience tutoring maths at that age and level. I can feel it is already making me a much better tutor and person. Younger children really love the vivid colours of BitPaper and they are so comfortable with technology online too.

A lovely Christmas message by a 9 year old student for me #drawnonbitpaper

BitPaper and The Profs

I don’t think anyone following me on any form of social media can escape my enthusiasm for BitPaper. Neither could  BitPaper, so they recently added me to their team and I now also work for them. BitPaper is virtual interactive paper. I can write paragraphs on BitPaper but will save that for when I am blogging for them.

BitPaper tutoring session.

Are you The Profs guy as well? Ahhh Richard has the same surname as you, that makes sense now!

I was chatting to Leo on Facebook messenger in March 2017 about BitPaper. Attending that Profs Christmas party in November 2016 I had met one of the founders of the company Richard. Leo and Richard shared incredible enthusiasm for tutoring communities such as the maths group, the global online tutors group and the empowerment of tutors and the tutoring industry in general. It really is going to be onwards and upwards as I collaborate ever deeper with their projects in 2018.

Tutor communities : Meetups, Facebook and video calls (Indie Tutors)

There was no independent community of tutors back in early 2016. By mid 2016 they exploded into existence and connected previously alone and isolated tutors for the for the time ever in history. I was given the Maths Tutors UK Facebook group to run in August 2016 and in 2017 it has spun off several groups including the two official sister groups Science Tutors UK and English Tutors UK.

Tutor meetup in London Hyde Park.

Networking and bringing people together has always been my thing and with these groups I got a lot more active on tutor meetups. I arranged more regular meetups in 2017, and the summer Hyde Park ones were a real hit. The one on this photo has us listening to legendary 80s band Tears for Fears playing literally next to us while we talk tutoring, bless.

Facebook has its limitations in terms of CPD and networking. And real life meetups aren’t practical for everyone purely due to geography. I found an elegant solution around this inspired by online tutoring. Weekly online meetings on group video calls! For all of 2017 me and my good friend Henry Dingle have been running highly focused one hour weekly video calls for tutors based on various tutoring issues. We have started up Indie Tutors to facilitate this more and as we get even more focused we really hope to help the tutoring industry in ways that has never happened before.

Maths training workshops and CPD

Thanks to the tutoring communities and the #christmaths2016 I attended late last year I found an incredible community of maths teacher training in the UK. Many tutors also teach at schools and I found a teaching community on twitter. The biggest discovery for me has to be La Salle Education. A really incredible maths training company.

Algebra tiles training at La Salle workshop.

I have attended two of their conferences and blogged about #mathsconf10 (my first ever maths conference) and #mathsconf13. I also attended two of their workshops in London. I have learnt so much from that community about teaching maths.

I got more CPD in 2017 than in the combined 10 years of solo tutoring I did before. And I have found a really supportive community of people in maths education in the UK. I plan to attend more events and encourage tutors to go to these too.

Other golden moments of 2017

I was awarded The Profs online tutors of 2017 award at their summer party. This came as a surprise to me as they have a few hundred tutors! I now have a physical tutoring award.

I didn’t know these even existed as a previously lonely tutor. I also got featured as a guest blogger on the How to Tutor Online site, and Joanne from the Ultimate Online Support Group awarded me with membership to one of her groups.

Winning the Online Tutor of 2017 award by The Profs

When 2017 started I couldn’t have dreamt of so much growth in my own personal tutoring career. And the opportunities bought about by networking with The Profs, various groups on Facebook, tutors I meet in real life, my clients themselves, maths teachers I have met and many others. I can’t wait for what 2018 has in store.

A cracking maths conference #mathsconf13

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Sheffield, maths teachers at the pub, stand-up maths, a calculator cake, lots of new connections and of course the invaluable CPD of the conference, #mathsconf13 did not disappoint.

I stumbled into La Salle by first going to the London #mathsconf10 earlier in the summer this year. I was mindblown by that first conference and ended up attending their MTN event in London and went to a workshop last week. The network of teachers, resource creators, examiners, speakers etc. they have got together is very impressive. And the value of such events is not just what you hear at the workshops but from meeting those in the front line of education.

Planning to go to the conference and making time for it
Unlike the London conference which was on my doorstep in East London this one needed more planning. I booked my train and hotel for the Friday night and I moved my Saturday students to Sunday instead. I even tutored my Friday evening students from the hotel room in Sheffield. I like to keep things rolling along as regularly as I can for students and lost hours are lost income for the self employed.

#mathsconf13 in Sheffield. Intro talk on two floors.

#mathsconf13 in Sheffield. Intro talk on two floors.

Pub time with teachers and two birthdays to celebrate!
Sometimes things just align in unexpected ways. The Friday night before the conference was my birthday. And the day before was the birthday of my good friend Richard Glasgodine (@RGMathsTutor) a fellow maths tutor and all round enthusiast of all things tech and Engineering. We had talked on video several times and known each other on social media so it was so cool to meet him in person. By coincidence it was his birthday the day before so we had lots to celebrate.

Pint of guiness

Double birthday celebration!

The theme of meeting real people from social media continued all through the night. Gone are the days of exchanging business cards, all the maths teachers there were on twitter. Seriously if you are not on twitter you must get on to it, it’s where pretty much where the maths teaching CPD action is.

I was glad to meet Jonathan Hall (@studymaths) who runs the mathsbot site. I have used his site extensively over the last months after I learnt how to use Algebra tiles at a short workshop that Mark McCourt (@emaths) ran in July this year. I was also nicknamed “Algebra Tiles Man”! I am nowhere near having that title as I have only just started using these and mostly with positive numbers.

Throughout the night I met more and more teachers, we chatted all sorts of things from my experience of online tutoring, to theirs of class teaching and exchanged teaching ideas. I got to know a lot of teachers before the Saturday in a relaxed setting and this really set the scene up for the all important conference the following day.

Intro by emaths, AQA, keynote stand up maths talk and speed dating
A packed school main hall with two floors of 400 maths teachers from all over the UK. Mark McCourt (@emaths) who runs La Salle introduced us all to the conference and set the scene. This was followed shortly by Andrew Taylor from AQA maths who gave us some insights on post 16 maths options. And then we had the keynote by Matt Parker (@standupmaths) who I had never heard of before but is clearly a really funny and smart maths speaker.

Superb at holding a large audience, keeping us all intrigued and with a quirky sense of comedy in maths he kept us all hooked to his every word. He showed a fair bit of maths magic to us, ranging from fractal cubes to all sorts of number trickery. The centerpiece of his talk was the thing us maths teachers love, spreadsheets! He zoomed out of a spreadsheet into a pixelated picture, and showed us how all RGB pictures are really just spreadsheets. He even took a picture of himself with the audience and then observed the phone screen under a microscope to reveal the RGB pixels. Not only that but he’s written code to transpose the image into an actual spreadsheet. Honestly, I loved spreadsheets before but now I see them in a different light 🙂

The speed dating was a quick 2 minute chat to exchange teaching ideas with teachers. I used folding paper with fractions and learnt some things about a functional skills volume exercise.

Maths Tutors UK group tutors unite and meet in person for the first time.

Workshop 1: Making Maths Work in Science
This workshop was given by Luke Graham (@bettermaths) who I have seen host maths chats on twitter. As I tutor the Sciences (up to GCSE and Physics A Level) I was curios to know what was going to come up on this. Luke had sat in many Science lessons at A level and GCSE to understand the maths content in there. We looked at some questions on estimating populations using quadrat sampling. An example being used was of white painted snails. Then to think beyond the simple assumptions to refine the model and getting students to ask “What if?” questions like what if the white painted snails are more likely to be eaten by predators. Punnet square genetic diagrams were shown to be essentially like quadratics. I’ve always likened them to grid multiplication so it was great to hear this.

And there was some great A level Chemistry content to do with Maxwell-Boltzmann distribution curves. These are essentially normal distribution curves in action. The cut off in the curves can be used to explain things like rates of reaction. This is a really great application of normal curves so this gives me a new idea to use in my teaching. All in all an inspiring talk for me, there was some elegant A Level Science/maths crossover that I had not thought about for a while.

Workshop 2: Richard Skemp: Relational Understanding & Instructional Understanding
I had met the speaker of this talk Gordon Brough (@gordon_brough) at a Bar Modelling workshop and had also been following him on twitter before. I first heard about the formalised idea of relational and instructional understanding through previous La Salle events. It was reassuring to confirm what has come naturally in tutoring. A lot of the time you just need to get students fluent in using certain techniques (a rote type of learning) and then later explain why it works. Or with some students you can start with the “why?” straightaway. The approach I take is customised to individual tutees and varies on a case by case basis.

Lots of food for thought after that talk and something I will think about in the coming few days.

NCETM guide on teaching scenarios

Different maths teaching scenarios

Workshop 3: Patterns, primes and purposeful practice
This talk was by Jonathan Hall aka @mathsbot He had already asked me what 8.5^2 was in the pub the night before so I was curios to know what shortcut he had. Turned out that (x+0.5)^2 can be used to make a simple rule to find this. This certainly looked like an impressive trick and had me hooked. I really liked his philosophy that it is important to spend a couple of minutes to do something interesting that will engage students before diving into content. There were plenty of other number tricks in there including prime diagonals and happy numbers. A visually impressive piece was the demo of a Serpinksi triangle animation followed by a “Chaos game” which would recreate the triangle with a multitude of dots.

Besides all the number stuff, he also went through his mathsbot site in some detail including all the virtual manipulatives that I use with my students. All in all a very impressive showcase of what he does, showing both breadth and depth in his material. I am a big fan of his site and I recommend others have a look at it too.

The resourceful Mr. Corbett.

Workshop 4: Interactive Problem-Solving Models
My last workshop was given by Matt Dunbar (@MathsDunbar). This involved us actually doing some maths as we were all given an A4 sheet with blank spaces as part of interactive problem solving questions from an interactive spreadsheet. There was linear algebra in more gneral form, probability using cuisenaire rods, a vector grid and finally an impressive exercise using a circle in 36 parts.

Matt Dunbar had a custom made interactive spreadsheet where inputs can be changed to see the output and the other way round. There’s even circle geometry possible on there. We all got a copy of his spreadsheets and I look forward to trialling them out and having a play. Even as the last talk of the day it sure kept us engaged, and on our toes!

In addition to the workshops there were plenty of stands by suppliers for books. I was most interested in some of the online book platforms so I will possibly sign up to even more online ebooks. I was also glad to meet Corbett who has produced some superb resources for GCSE maths. That was definitely a fan moment for me. One of many fan moments that day.

Casio Classwiz cake

Maths cake competition. The Classwiz calculator cake won.

Conclusion
New things I learn get passed on globally as a third of my students are currently in many countries, typically going to British schools in Asia, the middle East and mainland Europe. What I learn from La Salle gets beamed across the world and to my students. I am learning ever new ways of teaching things and being more aware of the methods gives me increased confidence in teaching new things. The maths teaching community is ever so supportive and diverse. Despite 7 days a week of maths during these last two weeks, I find the conference refreshing and a blast of inspiration. The next conference #mathsconf14 is all the way in March which seems like an eternity from now. I could certainly do with the time to start implementing more of the things I have taken away from the two conferences this year. So I wait eagerly for March 2018 and the next La Salle conference.

Indie Tutors Meetup – 23 September 2017 London

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The grassroots Indie tutors community in London is growing! Working for yourself as an independent tutor can be a lonely job and even if you put all your effort into providing the best possible service, it is always invaluable to know how others manage the teaching and business part of their tutoring.


Typically we discuss things like tutoring rates, how to get new work using The Tutor Pages or otherwise, websites, cancellation policies, the best agencies, and I am happy to offer my advice as a full time online tutor for those considering starting out in that market.

This is open to all tutors, independent or tutoring for an agency. The Larrik Pub is a well lit airy gasto pub which does snacks, food and drinks. Nearest tube Edgware Road, Marylebone or Baker Street.

Looking forward to meeting you and feel free to contact me if you want more info or to let me know you are coming 🙂