Clever Lands: A first-class education insight


To put it simply, I cannot think of a person I would not recommend this book to. Educators, parents, leaders should absolutely read it but I will push students and others to read too. Everyone can learn something from Lucy Crehan’s fantastically researched, objective account on the ‘world’s education superpowers’.

Upon opening this book, I was interested in other schools, particularly internationally but now I would go so far as to say I am fascinated. Crehan manages to subtly compare and contrast education systems without putting one above another and without her own opinion coming through. The reader is encouraged to imagine themselves in these different scenarios and imagine whether they would send their own children, or work, there.

Backing up all of Lucy Crehan’s findings is an immense amount of research. Indeed there are more than 250 studies, journals, books referenced – all contributing to a stellar discussion on how students learn all over the world.

To finish, I will not go into details about the book – you must buy it to see that – but I will push the author’s clear fascination with motivations. She is adamant that culture is not the be all and end all but there is a theme throughout that motivation lies at the heart of solid education. This is the take-home message for me and one in which we can all act on. Parents can help. Teachers can help. Leaders can help. Students can help.

All in all, a fantastic book and one I hope to read into more and more in the new year. A great way to finish the year. Here’s to reading and learning more!



Clever Lands: A first-class education insight

How to Harkness (a maths teacher’s view)

Before you carry on reading this, it is imperative you read Sarah Donarski’s blog about Harkness and how to implement it in the classroom. I aim to discuss the ways in which our Harkness experience is similar and how it is different in the mathematics department. I hope to open eyes to the creativity allowed and debunk the myth that it means the teacher does nothing but turn up, sit down and listen.

What is the motivation for responding to the previous blog written by an English teacher? Having observed a handful of Harkness lessons in different subjects, I can say that Harkness takes different forms depending on the teacher and on the subject. In particular, mathematics through Harkness learning looks and feels remarkedly different to  a Harkness lesson on Macbeth or a translation of a text etc. I therefore aim to try and mimic Sarah’s plan to bottom-line Harkness teaching particularly from  a maths teacher’s point of view. I encourage you to make the links between the two and see how it can be linked to your own subject, classes and environment.

Sarah highlighted when Harkness can be most effective – I don’t think this changes much regardless of subject. I am absolutely fascinated however by whether or not we need as much teacher-led time as was suggested. With no research to confirm nor deny, I am merely hypothesising but particularly in STEM subjects, I propose that with clever scaffolding of the resource, students can cope without being explicitly led down a path by a teacher’s voice. Instinctively, I feel that this could happen in English, for example, too but would require a different look to Sarah’s outline. In my head, it would take the form of a short worksheet asking students to a) find quotations and then b) find historical context and then c) … etc. I would like to push this subject further and research a little more. Sarah then went on to push the three pr’s of Harkness learning in her subject: preparation, practice and praise.

In mathematics, Harkness learning looks slightly different than that outlined in the blog. In lesson one, a student takes home a booklet of problem sets and gets asked to spend [insert time period here – 45 mins for me] on the first problem set before coming back to the next lesson. In the next lesson, we spend 15 minutes or so with students putting solutions on the board  before talking through these and asking questions about where mistakes occurred or why things work. This would then continue for 4 problem sets. After this, the students have a short test on the material covered so far which is marked and given back to the students. This process is then repeated. For larger groups, we are slightly more creative – less time spent on problems to bring to class and some class time dedicated to problems involving the skills being learnt at the time.



The skill from the educator’s point of view, then, comes from creating a resource which means the students can tackle problem sheet 2 after discussing problem sheet 1 and seeing correct solutions to those. This has been the toughest challenge for our department. The head of department has written most of the problems and the resource (the book of problem sets) is constantly evolving. An example for sheet 1 to sheet 2 would be:

“Compare three quadratics in how difficult they are to solve” in sheet 1


“Explain why [quadratic with imaginary roots] can’t be solved with the quadratic formula” in sheet 2.

We do not discuss the word ‘discriminant’ until sheet 5 but by then students are very comfortable with the idea that sometimes a quadratic equation will not have real solutions. Each problem set has multiple topics so students will look at quadratic equations, trigonometry, sequences, areas of a circle and much more in almost every sheet.

This is where the ‘preparation’ aspect is not aimed at the students but at the educators. Teachers must be prepared – indeed the resource has taken our department a long time to put together and it is changing all the time – and they must look forward to where each question leads. My advice for any maths teacher using this philosophy is to plan for concepts not for lessons. For example, I would like all of my students to understand a sequence which increases by a constant amount each term can be summed by finding an average and multiplying by the end of the first 4 sheets. When that happens does not matter but as long as it happens in that time frame, I am happy. This means teachers can probe individuals who may not be there yet and can let others lead who grab the ideas really quickly.


I have purposely re-ordered Sarah’s three because this is an area of mathematics learning which has to be at the top of every teacher’s list. Success breeds success and students are more likely to engage in the premise if they feel successful. Our job as the teacher in this environment is to ensure every student is successful and understands when they have been. Success in a maths discussion takes many different forms. It may be that a student has a correct solution, another student may have a more efficient solution and another student may ask a really good question about that solution. All three of these should be heralded by the teacher. The third student may have walked in without a solution to offer but by asking that question and being praised on it, they may well have enough knowledge now to have a go at the next sheet.

Success also takes the form of giving things a go. ‘Maths anxiety’ is very real and particularly in lower school the fear of getting something wrong will hold some students back from putting things on the board for all to see. Teachers must create a culture whereby everything that is up on the board is a chance for us to learn from. If it is not correct, let this be a chance for someone else to feel success by finding where the solution breaks down. It is then important, in my opinion, to let the original student have another go at trying to get the right solution with that mistake pointed out. You then have two people feeling successful and learning has taken place.

Praise in the Harkness classroom works very much in the same way as any maths classroom but you can create a genuine team-orientated classroom when praise comes at the right moment.



This happens less in mathematics. The practice element is more about refining their abilities to talk through solutions, which questions to ask, when to ask questions etc. This practice comes through each individual lesson. If we get through a sheet particularly quickly, I would actively reflect with the group on the lessons and talk about when learning takes place in the most effective way. Usually, students will bring up ideas of ‘good explanations’ or ‘clear diagrams’ and we will talk about the importance of these. Students are then held accountable and I would use these phrases with students as they are explaining or showing a solution.


Just give it a go!

Finally, I would encourage everyone to try this idea at some point. If you are trying to get students talking about maths, actively engage with challenging problems and have the chance to ask some real open-ended questions about mathematics, this gives you a fantastic springboard for that.

Harkness teaching relies on empowering students and letting them be in charge. Teachers can throw in probing questions when the time is right but trust the students and trust your worksheets to bring out the skills required. Don’t be afraid to let them run with a discussion and see where it goes. What’s the worst that can happen in one maths lesson?

The resource created at Wellington College is available. Please tweet me @jk_mcd or @AidanSproat [head of department and creator] for details. As always, if anyone wants to learn more, come and see it in action!













How to Harkness (a maths teacher’s view)

`Today I will just observe’

Today was a pretty important day in my approach as a teacher of lower sixth mathematics. It was the first time where I can genuinely say I planned for and observed for learning.

I have blogged previously about our approach at Wellington to Sixth Form Maths – following the Harkness philosophy where students come in with questions done and we talk about their solutions in class.

Usually these lessons involve me chairing a discussion and letting student A talk through his/her solution before the odd pupil chimes in. I then proceed to ask some question to try and touch on the conceptual ideas. “Why is it important to write the equation in this way?” “What does this mean we can now do?” “Why do we care how many roots this quadratic has?” etc.

This morning, however, I decided to remove myself from the lesson and watch. I told the class this was my intention and I would only intervene when they had confirmed they were happy with the discussion that took place and I had spotted some mistake.

What then followed was some brilliant student leadership – a couple instantly took it upon themselves to dictate pace and timings of the lesson. They decided to focus on 4 questions and the atmosphere was far less judgmental than it feels when I am involved. The students seemed far happier to interject and offer slight changes to solutions than when I am leading the discussion. I think this was probably because they are waiting for me to jump in sometimes.

I only had to step in on two occasions. One was to be slightly more rigorous with a proof and the other when a conversation was going round and round in circles. The second in particular was a valuable learning point for all about how to bring yourself back to basics when finding a problem with a mathematical question.

The problems with this lesson were that the conversations were very procedural. “I did this and then I did this” “But how have you got from that line to that line?” “Yes I got that answer too” “Did you do that on the calculator?” “Is my answer the same?” and so my challenge for them was that next time I want to listen to some conceptual conversation.

This is something I will almost certainly try with all my classes in the near future. I felt like an empowerment happened and the students surprised me in the quality of the discussion. I have since learnt that “this won’t work in maths – the teacher is too important” was an egotistical feeling more than a fact.




`Today I will just observe’


Edfest Thursday, Edfest Friday morning and then a train up to Leeds for my third straight day of CPD can only mean one thing…it must be time for a maths conference! My third of the year (and ever incidentally) and I still have the same emotions leaving this one as I did after leaving Sheffield in September last year. Getting to Leeds from Crowthorne isn’t the easiest journey but 5 hours after departing, we landed in the hotel, had some food and prepared for the day ahead.

The day itself began with the usual coffee and chats with a couple of stands and I was particularly impressed with the number and quality of the stands present at this conference. A very good representation from all exam boards and some new exhibits that I hadn’t seen before – I am particularly intrigued by how Brix can benefit our students. We arrived quite late so there wasn’t much time before Mark McCourt opened up.

As a semi-experienced #MathsConf goer, I knew the routine of Mark introducing the keynote and then speed dating before starting the first session but this was slightly different in that the keynote speaker, Professor Mike Askew (@mikeaskew26), really captured my attention. I would listen to him speak all day.

Research into problem solving techniques

I will be as brief as possible but in short, Mike was discussing the current research into how students solve problems, what does and doesn’t work, ways in which we can incorporate this into our teaching and the journey between abstract and concrete and back again.

Some superb things came out of this talk. He emphasised the idea of testing students on topics they have learnt previously (not necessarily the ones being studied right now) before discussing, with evidence, the ideas behind ‘sleeping on’ a thought and remembering it better. His final introductory point looked at the impact of asking ‘deep explanatory questions’ and their impact on student learning. This was profound and if I take anything away from today, it will be that “we are a problem solving species”. It is in our nature!

Mike had us thinking about the questions we ask and the tasks that we set against an “indirect” criteria: is it improving fluency; is it improving problem solving or is it improving mathematical reasoning? What a brilliant checklist for every question you ask of a student. If you can answer yes to one of those, I believe it is worthwhile. If not, why are you asking it?

Shortly after, we look at Kahnemann and his ideas behind quick and slow thinking. There is research proving we are a little sad when we don’t get something quickly, is this why students push back? How can we fight this in the classroom? Teachers must think about the culture in their classroom and how they can aid their students in coping with this sadness that comes.

Mike finished talking about the ABC’s of problems (Burkhardt) and highlighted a key point. “The real skill of an educator is when it comes to facilitating the discussion of solutions”. I cannot agree more with a statement and his idea of private vs. public talk is one that anyone should talk to him about if you get a chance. Mike offered some really simple advice to further understanding when students are speaking in a public domain – repeat, rephrase, revoice, agree. In that order.

A great way to start the conference before a little speed dating!


Speed Dating and Mark McCourt


The speed dating is one of the highlights of the conference, always, and it did not disappoint this year. I picked up a couple of valuable teaching ideas and hopefully shared our Harkness resource with others to see how we are going about teaching A Level maths at Wellington. The excitement is palpable between all when this happens.


Mark (@emathsuk) then spoke himself. This was the first time I have heard Mark speak but after the reviews of his researchEd chat, I was not missing this. He always talks so passionately when hosting and the same love was evident this morning. He discussed the amount of hours teachers spend not teaching and ineffective ‘working’ hours. I could almost copy and paste his transcript but the major messages that hit home were that “every lesson has been taught before” and “if something isn’t working, stop it!”. This actually resonated a lot with me after listening to Clive Woodward say that we must put enjoyment at the top of our priorities and Mark is trying to encourage the same message.

We listened to Mark talk about the Singapore approach of teaching less and discussing teaching more. This strikes me as an ideal we will not quite reach in England but it does leave me thinking, how often do I sit and talk about teaching? What worked and what didn’t? Was it effective? How could it have been more effective? Mark showed us how Complete Mathematics is trying to help address the balance and regain some of that enjoyment which was exciting and showed that maths teaching does not need to be reinvented every year.

The overriding question Mark has burnt into my brain is “Am I being impactful?” This can be transferred to a whole spectrum of teaching. Marking. Resource design. Questioning. Testing. Is what I am planning going to impact the students’ learning? If not, why am I doing it?


16 Things about the new A-Levels

Straight after Mark, we went off to listen to Andrew Taylor (@aqamaths), Gary Wing from Hills Road VIth Form and Christine Andrews from AQA talk about the new A Level. This was fascinating and I always find it interesting to get inside the exam board’s head. We were given answers to the most common questions asked of AQA and were  advised on topics such as large data sets, calculators and which papers to enter. All in all, a very helpful and important session to attend.

All 3 spoke excitedly about the new reforms and showed the positive side to the new specifications and how they will benefit students. I enjoyed listening to this side and I can certainly see the benefit myself now. Well done, all.


We then scooted off for lunch and enjoyed a more relaxed hour or so before the last two sessions with Danny Brown and Craig Barton.


Be aware of being aware

Danny Brown (@dannytybrown) really impressed me. I have followed him on twitter for a while now but listening to him speak showed me that this is an educator who cares. His students can count themselves very lucky.

This was one of the few workshops I have been at where not one person is tweeting about it or taking notes/photos. The whole message was about being present and recognising whether or not you are present when listening/talking/reading aloud. Danny is obviously well informed and he was a pleasure to listen to and discuss mathematics teaching with – I would certainly like to do so again some day. I took a lot from his session and I certainly want to implement a values-based teaching philosophy of my own moving forwards. What do I care about? How does that affect my decision making as a teacher?

Incidentally here, a discussion came about into how 1-2 year olds count and whether or not they know they are counting. Why do kids say “one, seven, two, six, three” before they know that these are numbers and why do they eventually work out the order in which these go? Truly fascinating and I look forward to reading more!


Guess the misconception

Craig Barton(@mrbartonmaths) closed the day for me with a fabulously engaging talk about students’ misconceptions. Craig’s website is fantastic and offers students a chance to give an explanation for why they selected the answer they chose. This offers tremendous insight to us as teachers and should be something that is seen more in classrooms across the country. Very rarely are students just plucking a number out; they have some sort of thought process. It is our job to find this out and act on it.

Craig showed us some data analysis from around the world – the Americans can’t do lower or upper bounds – and then looked at our own children’s issues. We were shown 5 questions that students struggle with (in the easier parts of the syllabus) and discussed why we thought these students had misconceptions.

This was a great, light hearted way to finish the day and it left me thinking about how often we delve into wrong answers and how often do I really probe and discuss why a student made a mistake. I should be asking more about what it is that made a student give a particular answer.


Overall, this was a superbly impactful day and, as always, left me excited about being part of the greatest profession in the world. This is a profession, we all care and we can all help each other. I will keep going to these events as long as time and means allow and I will always recommend them to others. Everything went smoothly and La Salle should be complimented on their part in this as I am sure it is not easy to organise something on such a scale while keeping the quality that high.

Well done all on a great day. See you all at #MathsConf8







Let’s have an argument!

Through recent re-watching of “The History Boys” and “Dead Poet’s Society”, I came to realise that I am far too conservative in my approach to lesson planning and, more importantly, resource writing. The two films, for those that haven’t seen them, centre on eccentric History and English teachers who employ a teaching methodology inspired by argument and free thinking.

I wonder how often we, as maths educators, write a resource or ask a question with the answer we want in mind vs. not having anything but the beauty of the subject in mind. What happens in both of these films is that the teacher conveys a complete love of the subject – their faces light up when a pupil starts arguing about Hardy’s use of adjective, for example. I wonder whether that happens enough in our mathematics classrooms. Do the educators truly convey a passion for the subject? Do all your pupils really know that you love maths? This shouldn’t just come up when you talk about irrational numbers or proofs or the real top end of your interest but it should come up when talking about similar shapes and scatter graphs and everything else.

It is with this in mind that I have gone about writing my latest set of resources for next year’s Year 9. With Year 11 and two upper sixth form sets gone, I have some time this Summer term to really knuckle down and concentrate on creating a quality resource. I have taken our Scheme of Work and gone through the relevant things I have to cover before half term. This gives about 10 different areas to go through. The general pattern I am following is to have all the topics combined on each sheet and teach them all incrementally. To carry out this process, we write 10 different problem streams and then combine the questions as we see fit ensuring that things are not introduced too quickly nor too early.

What does all that have to do with arguing and promoting passion? Well, when putting together the sheets, I have tried to include at least one question where all the students in the class will have an opinion. This is not an easy goal and has truly had me thinking about the “low threshold, high ceiling” idea that Craig Barton (his rich maths tasks do this fantastically) first instilled in me. The brilliant thing about this will be that when the students are having their discussions from these questions, I can embrace it and I will be a part of it. I will just be another part of the discussion, hopefully a truly passionate part. With the questions included (for example, should we include 0 as a counting number?), I don’t know any more than a 14 year old, we can have a live discussion.

I also hope to achieve the dream goal of getting away from “is this right?” or “will this be in an exam?” by asking questions on each worksheet which are so obviously not examinable that the students can just try. Robin Williams in “Dead Poet’s Society” has a wonderful phrase whenever a students answers of “Thanks for playing!” and rings an imaginary bell. It doesn’t matter what the answer was, the positive feedback is for answering the question. This is the sort of thing that I hope will push the students to truly love the subject and it is nothing to do with the methods they learn or the numbers they meet. It is do with the subject itself and the history of maths and all the things that are constantly changing. For example, how would Deep Blue the Computer write “100” in comparison to Tutankhamun…which is more intuitive? Which is easier to understand? What problems are there with these number systems?

I encourage all to argue more and let your students discuss stuff. It might be complete rubbish but there will be one statement from one student that may just remind you why you love the subject so much. Here’s hoping!








Let’s have an argument!

Mr. McDonald the English teacher?

‘A music teacher, an English teacher and a maths teacher walk into a staffroom.’ No this isn’t some corny joke – we did and we sat down and planned an English lesson. The lesson was going to be delivered by the maths teacher – me! We are seeking to understand the effectiveness of coaching within a classroom environment and what happens to pupils’ learning if led by a non-specialist. Later on in the term, Sarah Donarski, the English teacher aforementioned, will teach Music and Sean Farrell will lead a cricket session. The three of us outside of our comfort zone and relying on the expertise of the children to drive the lesson in the right direction.

I walked into the English classroom this morning very excited by the prospect but also incredibly nervous. The aim of the lesson was to discuss “how to write a perfect 40-mark response to the 2-part English literature question” in particular to do with Macbeth. After some planning as a triple, the other two teachers sat back and observed how well the coaching methodology was working in progressing the students’ learning.

First up, we broke into groups and the students analysed someone else’s response to a similar question. This was the first chance I had to walk around and talk to the students, who by now realised this wasn’t a joke and a maths guy was trying to teach English. It was remarkable to have a handful of conversations with students and never correct them once. I hope the students felt empowered by the process and it will be interesting to hear their feedback. I offered nearly no advice and I learnt a lot myself about how the students think and what they get from such exercises.

After this activity, we came back together as a whole group (my basic premise was to break into small groups and come back as a whole cohort – akin to my sports coaching) to discuss the essays. Together, we came up with a criteria for a perfect essay before we would go away and have a go at planning. This whole group discussion took 10 minutes and my goal was to always try and bottom-line exactly what students were saying. I was not going to write anything up until I had been told explicitly what they meant by “write good sentences” or “use clever words”. This was an important exercise from a teaching point of view and I think it will affect how I go about teaching my own subject. Far too often, we do the bottom-lining ourselves, I feel. It is a very important part of a conversation and a coachee must be able to succinctly say what they have learnt or what they will do from now on.

This was used to then go and have a go at writing/planning a response before coming back as a group and having a similar conversation. While they were doing this activity, I walked around and asked more questions and had more conversations with students. As an aside, it was fantastic to talk to children about Shakespeare and what they think of the play. Well done, Miss Donarski on instilling a genuine enthusiasm towards the story and Shakespeare’s writing!

The highlight, from my point of view, of what coaching can offer happened when a student said “I don’t anything about the play”. This is the absolute nightmare for a teacher who actually doesn’t know anything about the play! What can I offer? I can’t lead him to think about the question asked because I have no idea, myself. The solution was to just talk about the story (which I know a little) and the student proceeded, with help from his pals, to tell me the abridged version of the story. From this, he convinced himself he did know a little more than he thought and he now had an idea of where to start his work…absolutely the end goal we were looking for. The student found a roadblock and just from talking to someone, found a solution and “taught himself”.

Coaching is something I have spoken about in the past and I cannot thank Graydin and Iain Henderson enough for the training we have received here at Wellington College. This whole experience showed what a powerful tool it can be and for the first time, I really saw how it can be implemented in the classroom. I hope the pupils enjoyed themselves and I hope the English teachers observing me don’t think I desecrated the subject or Shakespeare too much! I had a lot of fun throughout and I am looking forward to seeing how the rest of this term pans out!


Mr. McDonald the English teacher?

Maths Conf 6

Yesterday saw my pursuit of getting better travel through the East of England and into Peterborough for the first time in my life. It was my second Maths Conference and I am still of the same belief that it should be a constant in every maths teacher’s calendar. The best CPD never feels like you have to be there and it feels like every conversation you have will improve your teaching. The two maths conferences I have attended have certainly felt like that. I met some of the guys I idolise on twitter and spoke to many more both about my own practice and what we do at our school and listening to their new ideas and how they approach mathematics teaching.

I headed up on Friday night and wanted to head out for a drink beforehand but timings didn’t allow – I resolve to make these drinks at one of the events!! After a hotel dinner for one and a good night’s sleep – kudos to The Bull Hotel – we were off to Kingsgate Conference Centre for #MathsConf6.

Almost as soon as you walk through the door at these events, you are astounded at the quality and quantity of things that people are producing to help mathematics education. We had stalls ranging from the awarding bodies, resource producers right through to one-to-one tutoring and feedback specialists. These are almost worth the entrance fee alone – the people who work on the stalls are as passionate about education as the teachers who are there as punters and this comes across fantastically when talking to the staff working here. I was particularly impressed with what Complete Mathematics could offer any school and the “All About Maths” opportunities through AQA. I will spend some time looking into these two things this week. Both will give the chance for teachers to spend their time loving the subject and engaging wholly with it as they take away the time-consuming aspects of lesson planning.

After a few too many cups of coffee, the day begun:

Mark McCourt and Andrew Taylor (AQA)

Mark opened up with a great 30 minute introduction. It was both funny and welcoming and although I’d been to one before, I was instantly excited about the day ahead and what I might learn. The take home message for me was a very simply one: we should expect every single child to be able to master maths. Very succintly, Mark put it this way:

“From counting to calculus, there are 320 topics to learn. Children have 1200 hours of mathematics learning. Why can’t every child achieve this?”

We then had a live demo of what Complete Mathematics can do for us and I think a lot of teachers (particularly those like myself at the start of the career) can learn a lot from the ideas on there all backed up by research and shared by people who have tried the resources themselves.

Andrew Taylor then came on to talk about assessment and there were so many quotables I could relate to. Andrew conveyed an absolute passion for mathematics and the line that summed it up for me was:

“Nobody ever got taller by being measured; nobody ever got cleverer by sitting an exam.”

Andrew was reinforcing the point that exams should not be the end in themselves – they are a good feedback tool for what the next step should be in a child’s development. This falls exactly in line with our school’s ethos and Andrew also proposed that “teachers go back to teaching and enjoying it”. Absolutely! There are far too many that don’t fall into that category which is a shame – this is the best profession in the world when we’re enjoying it!

Following on from this, we had a 20 minute speed dating session which is a great opportunity to talk to others about what they do to benefit their students. I picked up on  lots of ideas and it was nice that there seemed to be a common theme that we are all trying to promote independence and problem solving. This was also my first opportunity to really talk to people about Harkness teaching and what we are doing in our department. I’ve blogged about this but everybody I spoke to seemed interested in the idea and rather excitingly, a number said that they would like to come and see it in action. Please do – we’d love to have you!


Technology should not get in the way

Douglas Butler (@douglasbutler01) delivered the first workshop I attended and he was awesome! The man clearly loves technology but the point is that we have to use it in the right way. We found the world’s largest hexagon, pentagon and the world’s largest parabola with nothing more than some clever googling. We also looked at how poweful Autograph can be and how children can engage with things when it’s something they see so often.

Douglas conveyed great energy about mathematics and given the title I was a little anxious that it may have been a “let’s get back to talking” discussion but it certainly wasn’t that. Douglas was showing us all how we can use technology to engage pupils and enhance understanding. The latter in particular was personified by a tremendous Autograph demonstration to look at why we find imaginary roots of quadratics.

By far and away though, the best thing that Douglas did was generate lots of similar sharks and get them to eat each other (all with the Jaws theme tune in the background)! He followed this with an awesome showing of how 3d shapes are created in the cinema – it’s just triangles and enlargements after all!

I enjoyed the first 45 minutes of workshop and it left me wanting to learn more about the capabilities of Autograph, Desmos and the other applications I am supposedly using in my teaching.


Using Software and Games to help A-Level

Next up, Tom Bennison (@drbennison) and Jazmina Lazic carried on the theme about the power of computers and how we can use this to help our students. Firstly, Tom exclaimed that he has cheated on every Sudoku ever and had a computer solve it; secondly, Jazmina live-coded a solution to the Monty Hall Problem that would convince even the most quizzical of students!

This session opened my eyes to what MatLab could do and similar to the session before, left me wanting to learn more about this particular bit of kit. Jazmina and Tom delivered very well and it was exciting to see yet more presenters trying to excite their students. The Monty Hall idea was proved mathematically and shown using the power of computers. Students can see both and if you time it correctly, you’ve excited them enough by the solution that they are interested in the proof and the key mathematical ideas.

All of the first two sessions followed this pattern and technology was the common denominator behind these presenters’ desire to excite and inspire their students.


Lunch time called and this was my chance to catch up with a few people on Twitter and in particular I got to catch Tom Bennison and talk to him about our Harkness style teaching at Wellington College. After watching him work and listening to him speak, it was an honour to have him listen to me and discuss the profession.


How to approach tricky topics at GCSE and improve problem solving

Luke Graham(@bettermaths) was delivering this talk and this was a name I had never come across. The session was superb – messy planning was the order of the day.

‘Messy planning’ is a great concept where we start with some big question and let the kids try and find the answer. The lesson also comes with a starter which aims to get the students talking about mathematics. One of the examples given was “here are 10 ‘facts’…which ones are true?” let the children have an argument and debate. Yes, you are right it does depend or why do you think that is true sometimes and not at others?

I loved the idea of this and it is one of the examples of how I will almost certainly change my practice immediately in the classroom.

The second part of this session I really picked up on was that his school have a policy where SLT will not observe a lesson if the teacher is trying something new (such as this planning method). Any teacher is allowed to come in and watch but it’s not a formal observation. I love this idea as I am wholly of the opinion that observation is one of the best learning tools for a teacher if it wasn’t filled with such dread about not meeting the requirements every lesson should. We should all be happy to let our colleagues come in and let us know what they think and we should be happy to go and watch others too.

Well done everyone at Luke’s school!


AQA vs Edexcel vs OCR

The last session of the day was a Q+A session with the three exam boards and funnily enough, it was mainly centred on the new GCSE grading system and what the exams will be like, what a grade 5 means and which paper should we send our children to. Some of this was above my current position but it was insightful nonetheless. All 3 boards have the same issues and the truth is nobody knows what a level 4 looks like nor a level 7 nor anything else.

All three advised we focus our attention on the new question styles – 4/5 markers with not as many parts. Children have to unpick the writing to work out what the question is and then pinpoint the critical information from the question. We must get our students talking about maths in order to be able to tackle the proofs and discuss the importance of significant figures when it comes up in an exam.

The interesting thing towards the end was a question from Jo Morgan about their opinions on the new A-Level reform and Andrew Taylor made a point I’d not thought about that it will definitely impact on the numbers of people selecting to take Maths (in particular Further Maths). I’m undecided on my own opinion yet but I think it is a better assessment system in terms of ensuring the best candidates perform better than weaker student.


That was the end of the day. What a brilliant Saturday it was too. I must say it again but I would heartily recommend to everyone and it has absolutely reinforced to me that I need to present myself one day. For those interested in the resources I shared or for anyone who spoke to me about Harkness, please see my other blog posts or go to the following sites:


We will be running our own course in this teaching style in the first week of July. This was a fantastic 4-day course last year – a chance both to learn with and socialise with other great maths teachers.


Well done everyone at Maths Conf and thanks once again to LaSalle and Mark McCourt for putting on an amazing event.












Maths Conf 6