The world is getting smaller

Throughout my life I have always heard people say that the world is getting smaller. As time progresses that statement changes in its meaning.

I remember the Concorde plane flying across the Atlantic Ocean at supersonic speed. There were the first planes to fly from London to Australia non stop. Television broadcasts from Australia stopped having six second delays in between people speaking. All of these have contributed towards ‘The world getting smaller’ and I am sure that you may have your own examples.

My own experience of the world getting smaller has to be one of communication. It is around five years ago that I had a Facetime call to Thailand and there was no time delay. Since then I have used Skype but I tended to be frustrated by the quality of the audio. The next step was to use Line for video calls, but now I have something different.

Last month I was introduced to Zoom. This is for video conferencing and I have taken part in a video conference this week. I was at home in Surbiton in the UK and we had people in Bristol, Tyneside in the North East of the UK and Poland. That was my first video conference and it amazes me. I know that other people have conferences with colleagues in the USA, such as my son, but this was my first.

I am using Zoom to connect with the son of some friends in Wrexham. He is currently in Year 11 and I am tutoring him for his GCSE Mathematics exam. We connect once a week at the same time and I also use Bitpaper, which is best described as an electronic sheet of paper. I open Bitpaper in Chrome and when I share the URL for my sheet with my student we can both write on it. I can paste questions onto the Bitpaper for my student to do and I can see his every move as he works it out. It is just as if we are sitting in the same room. He is 200 miles away so I am thinking that the world is getting smaller.

This means that I can now tutor anyone in the world in Mathematics. They need a computer, audio, preferably a webcam, a mouse (to write with) and a decent internet connection. That is exactly what I intend to do: Global Online Mathematics Tuition. The internet has made my world much smaller and my market place has just expanded tremendously.

In the ‘old days’ teachers would advertise on a card in the window of the local newsagent for tuition and they would travel to their students. Some still do that, but not anymore for me. If you live in New Zealand, Australia, China, Thailand, India, The Middle East, Europe, Africa, USA, Russia or anywhere on this globe then I can tutor you in Mathematics. Isn’t that exciting? If you really want me to travel to you then we could come to an arrangement, but all that we have to do is connect on Zoom.

Now that is powerful and my reason for saying that the world is getting smaller.


The return of a blogger

This is the post excerpt.

This may be the first blog of many.

I am at the point where I have decided to blog again but it has been quite arduous deciding who I want to use as a host and which medium I want to write in.

So I have rediscovered WordPress and it has been relatively simple getting up to this point. I have registered and am writing this on my Samsung S6 Edge Plus which is coming up to 2 years old. I want to use my phone for blogging and I am happy with the ease with which I can do everything so far. Note that I have gone for the free option.

A few weeks ago I registered a blog using my Lenovo laptop with Wix but I wasn’t happy. It just seemed like hard work. The route to a blog was to have a website and I really didn’t want that. Maybe I was missing something but it prompted me to look for an alternative.

As I wrote on my Wix blog I was blogging a couple of years ago until one day when I logged on and saw a Turkish flag with the message ‘You’ve been hacked’. It was playing some awful music just to make things worse. I was paying for my blog to be hosted and so I contacted my provider. Nothing in return and I kept sending messages. I suppose this is one reason why I don’t really want to pay for a blog again.

The host finally contacted me when my subscription was due and finally I was able to unleash my feelings towards them. The result was that we parted without any apology from them.

So here it is: possibly my return.

How to develop maths resources that challenge students to think

This blog originally appeared via EdComs Teachers.

How to develop maths resources that challenge students to think

By Guest blogger: Gordon Brough

Thursday October 19, 2017

When I first started out as a teacher, I always made my own resources and that’s a habit I have continued throughout my teaching career.

From 1990 onwards, I worked full-time as a maths teacher in comprehensive schools around the country. My roles have included maths teacher, Head of Mathematics and Assistant Head, with experience of schools in Essex, Havering, Knowsley, Liverpool and Thurrock. I have always managed to improve results in maths at each of these schools, often achieving the best ever results in that school’s history.

Nowadays I author maths materials and deliver training courses for teachers nationally. I try to apply all of that experience when developing new resources, particularly focusing on how maths can do more to challenge students.

Since I started teaching, my approach to developing resources has changed quite a bit! In the early days my worksheets were produced using a spirit duplicating machine, also known as a Banda machine. The technology we have now is incredible, and much better for producing good-looking worksheets. Of course, that experience has also helped to improve the quality of my resources over time.

I have noticed that some maths teachers will make the work difficult by using larger numbers or decimals when producing worksheets. I used to do that years ago, but I have progressed to focus more on the promotion of thinking skills.

This isn’t necessarily an easy task – not least because some students do not want to think! They may want to simply get the correct answer and then move on. But the educational benefit of that approach can be limited.

Teaching with a purpose

I believe maths teachers must make an important decision about the resources they are going to produce. Please pause and ask yourself: What is the aim of this resource? Is it to enable learning, teach a topic or practice a technique? Every resource that you produce needs a strong answer to that age-old conundrum: Why?

There is also a question about familiarity and repetition when producing resources. Most teachers will use worksheets to supplement textbooks, which is good because pupils will quickly get fed up with one particular resource. However, you need to make sure there’s variety to your own supplementary materials. In the same way you can ruin your favourite meal by eating it every day, teachers can face falling engagement if they’re over-reliant on a single textbook, resource or worksheet.

The same can be said about work that is repetitious in general. This can be a common objection when teaching maths, so it’s important to ensure variety and relatability of your resources. That objection is also one of the reasons why I have shifted towards promoting thinking skills.

Teach pupils to think beyond the right answer

Here are some examples I use when training teachers about how to diversify their maths problems.

When I’m writing a resource about time, I use a clock face and ask for the time shown. The clock face can be used to challenge students’ ability in different ways.

  • First the clock face has just four numbers: 3, 6, 9, 12. This would be a standard setup.
  • The next clock face does not have any numerals, or it’s reflected in a mirror or a shop window.
  • Can students respond to the same challenge, but without the additional information?
  • For example, can they tell me the correct time when the minute hand is missing, and only the hour hand is showing the time?

Often children are asked questions such as 4 x 3 = ? Or they may be asked to find the factors of 12. However, from a different angle we can ask:

  • Using the numbers 1 to 4 only once, find the largest possible answer to oo x o
  • Find how many numbers under 30 there are with exactly six factors.

This process can be applied to lots of different scenarios. By removing information, we’re illustrating how you can arrive at the correct answer using different methods. These are problem-solving skills that may seem simple, but they are vital life skills for a range of subjects and careers.

By re-focusing on the process you go through to get the correct answer, rather than the correct answer in isolation, I believe we can better support students in developing vital problem solving-skills.


Gordon Brough is a business coach, trainer, entrepreneur and maths teacher. With 25 years of teaching experience, he has trained PGCE students, been a tutor for The Open University and gained degrees in Mathematics, Mathematics & Economics and Education Leadership & Management.

Follow Gordon on Twitter @gordon_brough

This blog originally appeared via EdComs Teachers.

Instrumental and Relational Understanding

One week ago I gave a presentation at the maths conference in Sheffield. 400 maths teachers signed up for the event and over 90 of these were in my presentation. There were of course other presentations on at the same time.

The focus for my presentation was Instrumental Understanding and Relational Understanding by Richard Skemp. In order to cover what I wanted I only discussed his article from 1976 and my aim was to provoke thinking amongst my audience. This was a time for reflection on how we teach with reference to an article from 41 years ago.

Instrumental Understanding can be thought of as ‘Rules without reasons’. An example of this is when a quick fix is given so that the pupil is able to get the correct answers. The problem with this is that they don’t always know why it works and they can’t apply the rule to different situations. I gave examples involving multiplying two digits by two digits, the addition of fractions and solving equations.

When I was at school I remember that I was taught a whole bunch of rules but I didn’t know why they worked and I couldn’t apply them if the questions were slightly different. Yes, I was the product of Instumental teaching and I admitted that I have used this in my teaching. I have used it to get results when time is short, especially when an exam is imminent.

I gave a meaning to ‘Relational Understanding’ as ‘Knowing what to do and why’. My examples of multiplication, adding fractions and solving equations were taken right back to basics and I offered ‘concrete ways of teaching these. I used Dienes Blocks, Cuisenaire Rods and Algebra Tiles to illustrate relational understanding. In an ideal world this is great but do the pressures of having to get through the curriculum stop us doing this?

The objective of the presentation was to get the teachers to think about what they are doing and the learning that is taking place in their classrooms. I had quite a few conversations with teachers afterwards and I believe that the objective was achieved.

Challenge for Chef Brough

It is just over 3 years ago that this photograph was taken.

Second from the left is Gordon Brough who was the visiting chef for the evening. Yes that was me and I was cooking Thai food for my friend Darius, in his restaurant.

Each dish that I cooked was fresh. I could have just made big pots of food and ladelled it out but the result would have been awful. The food would have been mushy just like I have seen in some cafeterias or one of the ‘Sunday Roasts’ that some pubs do very badly. My food has to be fresh and authentic when I cook Thai. The Thai’s that I know are very fussy about their food and so it has to be to a high standard.

I used only the freshest vegetables, which I bought from a Thai supermarket in Chiswick, London. I was so pleased to be able to get both Thai aubergines, kaffir lime leaves and Thai sweet basil. They didn’t have holy basil but I didn’t need it for my food. My Thai food has to be authentic. That is the philosophy of the chefs who train me.

I have worked with Darius in his kitchen before but that has been with him in charge and he is amazing. He creates a high energy just like so many chefs and if the food is not up to his standard then it doesn’t go out. This time I am the chef and Darius switched roles brilliantly. He showed a keen interest in everything that I was doing; from the prep to service.

The evening went so well and one of the diners who was a Thai lady commented on how authentic the food was. Some people came to the kitchen to say how much they had enjoyed their meals which was really nice. It is strange how I find compliments difficult to take even though I am flattered by them.

Before I became busy in the kitchen I managed to get out into the restaurant and speak to some of the diners. I was able to introduce myself and it gave me the chance to explain the food to the customers. I also welcomed the opportunity to get to know some of the people personally. This is something that I encourage restaurant owners to do when I have coached them.

The photograph was taken at the end of the evening and we were exhausted. I always am at the end of a service but this was different. I had cooked 86 individual Thai meals and it was great. I love challenges, especially when it involves working outside my comfort zone. I am constantly telling people that their next success lies outside their comfort zone and I do my best to help them.

I love the feeling when I have achieved something and I am thinking about what my next challenge will be. Watch this space to find out.

Customer Service

Yesterday I was in Holland and Barrett in Chelmsford. As I walked in a male member of staff said hello to me. I responded because I think that it is rude not to do so and really – why should I be rude?

As I was looking at the jars of vitamins etc the same male came up to me and asked me in a really unobtrusive way if he could help me. Well actually he could and I asked my question. He tried his best and then he got a lady who could have been the manager to help me.

I was made to feel important in this store and I thanked everyone individually. I also told the lady that the man was so helpful.

Furthermore, I tweeted using #customerservice and I got a lovely reply.

This is not the first time that I have commented on excellent customer service. I have tweeted about Enterprise in Warrington and Homebase in Chelmsford.

For me customer service is paramount for the success of a business. The people who come into contact with customers actually hold the future of the company in their hands and every business should realise this and invest in their people.

I will go back to the companies that I have mentioned above because of the way that I was made to feel and I will praise other people who show great customer service.

What is the customer service like in your business? What do you do to make your customers return?


I travel to work in London on a South West train from Surbiton to London Waterloo. During August half of the platforms at Waterloo Station have been closed for upgrading and they gave us commuters plenty of warning that there would be 50% fewer trains. There were announcements on every train journey prior to August and there were posters all over the stations.

On my first day of work in August I decided to get up 15 minutes earlier so that I could catch an earlier train. This train would arrive in Waterloo just before the time of my ‘normal’ train. Everything worked well during the first week and there were no problems getting home either. There were a lot more staff on platforms and they guided people where to go. They were so helpful that I tweeted a good comment. Yes, I got a reply.

The second week … Tuesday …

I arrived on the platform and there was talk of cancelling trains or stopping them because of a points failure. As I leave my flat I always check my Trainline app. No mention of it there. We got on the train and it set off. It stopped at Berrylands. We were being held there. The guard apologised. Eventually we arrived at Wimbledon and we were told very apologetically by the guard that the train was going no further. The platform was packed and most of us made our way to the District line. Two tube rides and I got to work for 08:30.

I then found out that it was actually a derailment that happened at 05:40 which caused the problems. Thankfully no one was hurt.

Throughout the rest of the day South West Trains advised people not to travel that day and the following day. Well how did I get home? Levitate? I got home using the tube to Wimbledon then two buses. It tok just over two hours.

On Wednesday I was going to go to work despite the ‘advice’. I got up ten minutes earlier and found an earlier train from Surbiton. My surprise was that it was going to Waterloo and we arrived before 07:00. I caught my usual bus and I was in work at 07:30. The journey home was smooth and uneventful.

When I travel to work I have always had contingency plans for problems with transport. That is my nature. I will try different routes because I am always looking for a faster route. The one thing about me is that I cannot be late. I hate lateness and I would rather be one hour early than one minute late.

So I have contingency plans. Do South West Trains have contingency plans? Points failure, Derailment and anything gets else. Do they actually plan for these? Where I am standing on that packed platform they appear to be in disarray. They don’t believe in good Customer Service because they don’t tell us what is happening. The poor people on their twitter feed take a lot of flack and do their best to placate individuals.

Where are the leaders and the managers at the top? They are being paid large salaries and yet to us people on the ground they appear inept. Surely there are risk assessments carried out regularly and plans of action in the event of a derailment. I actually wonder if the plan is to hide.

Ok leaders at South West trains, you should have reassured the people who pay your wages. Tell us the situation as it is and what you are going to do about it. You must know what you plan to do, surely.

Customer service is everything and you need to treat them better. It is in times such as Tuesday that you earn respect and it just did not happen. Customers pay a lot for their season tickets and they expect a decent service.

Perhaps the end of the franchise had a role to play in the way that this was handled, but I would like to think that they were professionals or am I a misguided fool.

Here’s to the next franchise …