Farewell Blaze United

For the past two years I have seen 13 students, four times a week. They arrived as newbies in Yr7, I arrived as a newbie teacher. We grew up together in School 21.

I would have spent more time working 1:1 with opinion-forming students who sometimes disrupted the dynamic. Overall however, it was an unbridled joy to work with the group, and I look forward very much to seeing them about the school.

Mile End Park Run

Another heart-warming Parkrun with students from school. I ran with Abdul (24 minutes), encouraging him to push on through a stitch, which he nobly did for the majority of the run. Esther ran with the girls, and tried to explain to them what a PHD was. Heather coached Yasir, and other runners supported us all through our struggles.

Parkrun is an oustanding thing for students to get involved in:

  • Achievable (5km is accessible for all – nothing wrong with walking)
  • Free
  • Weekly
  • Friendly
  • Minimal admin from teachers – students just turn up and run!
The runners!

2 = 3

Inspired by the work of Julian Beever (whose work I learnt about at the Chicago Lab Summer School), we spent 6 weeks understanding how to use our knowledge of trigonometry, similar triangles and three-dimensional thinking to make pavement art.

Geogebra links to play with here (Elevation, Plan, and 3D)

A year later, I look back on this project as a turning point with this class – earning their trust and respect. Although some of the mathematical learning was insecure and needed to be revised, we came together as a group and thought hard about how to apply abstract concepts to tangible products.

Presenting to PHD students
Working with PHD students
Co-ordinates ready
An army of helpers
Last-minute calculations
Working hard

Spreading Green Kindness

On a swelteringly hot day in the final week of school, I took my coaching group out of London for the day, to Epping Forest. (There is evidence of human history in the forest from 2,7000 years ago. It is the size of 3,300 football pitches. There are 50,000 ancient trees. Henry VIII hunted here. The ponds dotted around were born of bomb craters from WW2).

Aims Reflections
Understand why people use green spaces, by conducting a questionnaire  Interacting with members of the public is always great. Especially when they are from a different walk of life – the old lady who had walked in the Forest every day for 50 years…
 Have fun outdoors!  Once the kids got past their fear of dogpoo and bugs, finished playing games about who fancies who, then the beauty of their environment flourished. Climbing trees, throwing a ball about, excitedly watching birds, running to stroke a dog…
Spread kindness in the forest, by picking up litter We became detectives, imagining the past life of the wrapper/can/condom that we were picking up. Who had dropped it? Why?

By far the highlight (for me at least – the students’ highlight was lunch) was ploughing through the forest, navigating our way to Connaught Water by our shadows alone. Jaydan constantly checked that his shadow was behind and to the left, as Sophie had told us to do. We dived off the path, over streams, under branches, through bushes. Great teamwork, helping each other through difficult patches. Finally shades of blue spotted through the trees, and we emerged, joyous, on the lakeside.

At times I was frustrated at the hilarious fear with which they approached walking through a few brambles. It is useful to remember that over a three day weekend earlier in the year 7 of 15 students in the group had spent less than 1 hour outdoors.

Edit: wisdom from Kate on how to deal with negativity

(Kids are strange beasts: those who were most vocally against the idea of tramping around a forest told me two days later that it was the highlight of their two years with the coaching group…)

  • Go bold on games, when tiredness is an issue
  • Everyone is experiencing the same rain/hills/tiredness. There are two types of people. Drains only are interested in talking about the problems, focussing on the bad stuff. Nobody likes to be around a drain. Radiators focus on the good things, they recognise that some things are difficult but they think of solutions
  • Completely ignore negativity
  • Quiet words with ringleaders

All good advice for any groupwork. Somehow it becomes more amplified when outdoors. Just as students struggle to transfer learning from science to maths, teachers struggle to transfer techniques from the classroom to the forest?

Reading a map
Utterly and happily lost in the forest
Learning why people spend time outdoors
Happy Paul
Beautiful oak tree
Group pic up a tree (the floor is lava?)
Giving back to the forest

Wrestling with Infinity, in Newham

I spent an enjoyable if busy week thinking with a bunch of prospective A level students about Infinity. We chose the topic of the endless because it is not explicitly A level content, but is beautiful, important, broad and relatively accessible.


Key reflections

  • The problems we gave the students were challenging, probably slightly too much so. At the beginning of the week they were struggling to cope, but by the end we had noticed a significant improvement in problem-solving skills. Students were able to stick with a problem for more time (2.5 hrs on the second day, on one problem, was maybe too much of an ask), and were more comfortable collaborating with each other.
  • I noticed (as did other teachers) a shift in my teacher personna. No longer requiring to behaviour-manage (or maybe that is wishful thinking – a few were misusing their phones for example), I was able to focus more on the mathematical concepts.
  • There are two types of problem-solving. The sniffing dog follows his nose, working forwards (sometimes haphazardly), doing what he can do, until a pattern forms. The wise elephant thinks carefully about what she wants to achieve, and then works backwards from this. The students picked up this language from the week, and agreed that excellent problem-solvers were able to use a synthesis of the two approachesjzMNRoVrqUq7gSJsRVv-wam4Qm7bS56dzbSF8-3q3vxMVbYKrNnIl2m7ZWhUaL37nbX2xFYOtuP42T4DJDVBGlsteEN3doEoaiM0hn8YdZN2Zg4cm9TExA42vka_Hh1_PnvlG2Wg
  • All maths teachers descended into an afternoon session for the Festival of Problems. We used some outstanding questions (from Westminster School, curated by Kings Maths School), and had a grand time. If the questions are good enough, then minimal structures are needed.

Feedback from students:

  • Long open problem-solving sessions were amazing (contrary to my perception that the students were burnt out by the end of it, most of them said they loved being able to spend so much time on one thing).
  • Don’t ask us to read chapters on things we haven’t learnt about yet (almost all said this)
  • Introduce more practical hands-on sessions


A few pics of the week:

We had an entire floor to work with, which was amazing.

The lecture theatre
The Problem-solving Lab
KS talking about types of numbers
Organic flurry to a whiteboard when Ashwin discovers a pattern


Understanding why infinity squared is still infinity…
Getting to know each other…
Independent study: harnessing the power of Youtube.



Wrestling with Infinity, at Cambridge.

After spending the the week at School 21, KS and I took the remaining students (large rate of attrition in the buyer’s market of sixth forms) to Cambridge, to present what they have thought about to professional mathematicians (or, my friends and brother all who studied Part 3 and mostly are in the middle of PHDs). Tabitha, from Underground Maths, then led a problem-solving session, on this problem about the difference of two squares.

The students presented on:

  1. A problem I grappled with
  2. A story that resonated with me
  3. A question for my audience

Key Reflections



Tabitha would carefully listen to a group, before adding optional questions – “I have an idea. You don’t need to follow it, but you could”

Look before you leap. Too often I jump straight in, possibly repeating thoughts the students have already have, or derailing their thought process.

Nina did not know how to use a calculator, one of the students (much to their amazement), had to teach her.

Professional mathematics is not about calculation. Constantly remind students about this

Several of the PHD students had to struggle to understand the ideas being spoken about. “Wait, what even is an infinite fraction?” one asked.

Everyone, when meeting new Maths for the first time, struggles.

“It feels like it will be finite, because it is not very wiggly” said Tom.

Professional mathematicians use intuition much more than students. Nurture intuition more explicitly.

The session was the highlight of the week, because the professional Mathematicians were instinctively and continually asking excellent questions and providing incredible explanations. All students were hooked.

A reinforcement in the belief that content knowledge should never be underestimated…

One student had never eaten a raspberry. Another had never seen a tennis court. Several spoke about Hogwarts.

Do not forget the “side”-effects of trips to contrasting places.

Last minute preparation on the train. (The iphone is being used to learn about Hilbert’s Hotel, not to play games…)
Harry (16 yrs old) teaches Hugh (Masters in Maths) a proof he has never seen before (Banach-Tarski Paradox)



Examples of work

Lecture notes
Briefly mentioned once, and this student went away and researched it
Banach-Tarski. Deep thinking here!
She taught herself integration…
She has internalised the sniffing dog and the wise elephant

Brains worked so hard that sleep was necessary…

In John’s…
On the train…

A Technophobe’s Blogging

Guyan, self-confessed technophobe, spent ten years of his life as a professional writer before becoming a teacher.

He has spent the past year immersing himself in the use of technology in the classroom – hurling himself in at the deep end as an experiment.


Students write and curate blogs, instead of using exercise books. Inspired by edutronic, he created spaces for Yr7, Yr8 and Yr9.



  • The only person to read exercise books is the teacher. If your work is published to a wide audience (online) then you  are more likely to care, and to ensure your work is of high quality.
  • To provide a need to teach digital literacy. Students should be equipped with the skills of email writing, they should be aware of where to place a full stop or comma when typing.
  • To enable students to critique each others’ work easily
  • To make redrafting more efficient. There is something heartbreaking about having to re-write a four page story by hand, mindlessly repeating the same words… Why not drag around the paragraphs and tweak a word here and there online?

Guyan’s observations

  • A sign of success is when students start to use the technology without being told to. One student wrote a poem, “Injustice”, about being unfairly asked to stay behind after one lesson. The teacher had provided a space for creative writing, and the student felt comfortable enough to use it independently. I have seen similar things within my practice – I taught some students how to use OneNote. A few have started to use it in other subjects.

    Untitled picture.png
    Students using technology well, without being asked to.
  • It is utterly false to think that students, since they are “digital natives”, will be effective users of technology for education. They require training. This takes time at the beginning, a somewhat slow and painful process.
  • Regardless of your views on technology and education, there will be a study out there somewhere that backs you up.  Playing video games before exams can improve your scores. But playing video games can lead to addiction. Using technology ruins your memory.     Using technology improves your memory.  Use research cautiously – it is muddled. Beware the echo chamber.
  • The handwriting of a few students drastically deteriorated over the year (2 out of 70). Whether this was due to lack of practice or increasing lack of care is unclear.

Next time…

  • Ensure blogs are able to include multimedia. Students should be able to post photographs of written work, rather than always typing it up.
  • Provide students with blog templates, rather than asking them to start from scratch. Tagging, for example, is useful to use, but unwieldy for a student to build themselves.
  • Hand more ownership over content to students. Celebrate their freedom and allow them to write about what they want. The teacher cares about content, but does not prescribe the content.




Technology is a Tool for Learning

I have been collaborating with Rosie, who thinks about the coaching and well-being curriculum for the school. We summarised the ways in which we see students using technology, using six archetypes. The following two posters are now up in every classroom in the school, and serve to provide students and staff with a common language. This enables students to be able to self-reflect more productively on how to ensure that they use their iPads as tools for learning.

The six Tech-Types
Reminders of how to use technology well

Flipped Learning at School 21

Following a visit to Shireland School to learn about Flipped Learning, a few departments at School 21 have started to use flipped learning within their practice. In this post I will focus on Spanish and Humanities. The following screenshots are taken from Google Classrooms (virtual spaces where students and teachers can post, share work, critique, refer to the scheme of work).

history 1
Providing students with topical references
history 2
Creating student independence by giving them the structure of the project from the beginning
spanish 3
Students upload their work for the class to critique
spansih 1
Students watch videos as homework and comment to summarise their learning. Classic flipped learning, effective in motivating the students to want to arrive at the lesson pre-prepared.
spansih 4
Google Classroom used as an online store of key materials
spasnih 2
Google Classroom used as a gateway to other forms of technology – using quizzes to improve vocabulary.

From Play to Proof

Maths teachers, from across the school, sat down for a morning’s reflection on what Maths education should be, from 4 – 18, at School 21.

  • Broadly, by the end of Yr4 students should be broadly numerate, comfortable with place value and any number.
  • By the end of Yr6 they should be equipped with all the practical numeracy they are likely to need to use in their lives.
  • Secondary maths, therefore, is broadly about enlarging brains for the sake of it, rather than teaching practical applications of maths. This shift could be the cause of the change in attitudes that students have about maths – from unadulterated joy in Yr3 to dread in Yr8.






Familiarity with basic number

Exploration and play


1 – 100, add and subtract

Concrete and visual strategies


1 – 100, add and subtract

Concrete and visual strategies


1 – 10,000, multiply and divide

Efficient methods of tackling two-step problems


1 – , multiply and divide

Efficient methods of tackling two-step problems


Fractions, decimals, negatives

Introduction to formal problem-solving toolkit


Fractions, decimals, negatives

Introduction to formal problem-solving toolkit


Summary of number

Relight the fire after SATS

Problem-solving in more complex scenarios

Move from concrete –> visual –> abstract


Links to outside maths (through projects)

Focus on the hand – crafting beautiful products

Answering the question “Why study maths?)


Links within maths

Understanding algebra deeply

Being comfortable with using technology to graph, to analyse data on spreadsheets


Clarity of communication

Independent work

Sophisticated open Problems


A GCSE is an example of beautiful and deep understanding


Understanding infinity, limits, calculus…

Proof, rigour

The Modelling cycle



Lifelong learners of Mathematics