Maths, 'maths circles', Kolmogorov, Westminster's centralisation & vandalism
When it comes to education, the majority of parents think the school has 80% responsibility and the parents have 20%. This is sort of written into our social contract with the state.
But in my opinion (and people are free to disagree) the parents have 80% and the school has 20% responsibility when it comes to a child's education. The main benefit of school is social adjustment and social grounding.
My kids (13, 14) do their schoolwork and also have approx 8 hours of online 1v1 tutoring per week, typically one hour per evening and a Saturday morning session (both play for football teams, two night training and a weekend game, I find there is plenty of time to do stuff).
I don't follow the national curriculum for this tutoring. Standardised test results are Fool's Gold.
Usually I set up a 6 - 9 month block for a topic and we pick things like Singapore maths, python, AWS certificates, a language, architectural drawing.
I had a Microsoft SysAdmin teach my 14 year old python.
I had a teacher from Hwa Chong Institute teach my kids math.
Anything they express any kind of interest in, we just lean right into that. I think I've definitely had the most value when following / rewarding their curiosity. If the whole thing is a bit alien to you then do it yourself in the beginning, pick something you want to learn about and then hire an online tutor to teach you the skill. Try and learn some next level maths or an entry level coding language, or whatever you're interested in.
I will go and scout the internet for someone who is already in that space to do some 1v1 tutoring. Sweet spot is typically a young professional in their mid / late 20's who is likely underpaid at the coalface and is saving for first house, someone who still has a fresh memory of school. "Hey my kid is interested in this space? Would you mentor them 1 hour per week after dinner on a Tuesday? I'll pay you."
£25/hr on the international market, gets you excellent people (maybe £1,000/yr per topic). Maybe £5 - 10k a year for the whole budget, if you are considering public school and the fees are the main concern I would 100% recommend this path instead. It's a bit of work for you to manage their calendar and recruit folks, but these are either skills you already have or should probably practice.
In my mind, classrooms are 19th century social constructs and are really obsolete for their original purpose of education, they remain a good vehicle for the authorities to undertake social engineering, and for kids to socially adjust to groups and teams. But then again team sports are much better vehicles for learning teamwork than classrooms. Classrooms are useful for primary school, where it's mostly free daycare and social learning and classrooms are also valuable once you get to university and the people in the room have been filtered for interests and capability. But the part in the middle where teenagers are compelled to do things they have no real interest in, honestly it's just a huge waste of everyone's time. It's a system that rewards cognitive obedience and kills curiosity stone dead.
I think secondary schools, as a model, are probably a net negative in terms of socioeconomic value, they just generate a bland human soup of resource, as an employer for difficult things I find it deeply irritating that we put teenagers through this. I think what we are really missing is genuine diversity of models for developing people. The standardised everything education is meh. It is gamed to the point that the qualifications are actually worthless to hiring managers.
My experience of secondary school was that I learnt very little for 4 years, it was nowhere near challenging enough and spent most of my time playing sports and strategy video games and socialising and still walked away with top marks.
Tertiary education is better, but has too much filler. It acts more like a class filter than a value adding system. Listen to the job market, we need more people studying medicine, science and engineering and a lot fewer people studying humanities. Sorry, but we all know it's true.
I think we should take Oxbridge, put it online and export it as a service whilst in the opposite direction we should recruit young upward professionals from all around the world to mentor our early/middle teens 1v1.
I think this could be a centrepiece for creating a competitive strategic advantage for UK PLC and making the UK a global epicentre of human capital and soft power. But I doubt it would work as a public service. Probably doesn't scale beyond 20,000 kids before your drop off the cliff in terms of quality of tutors.
If you want your kids to offer extremely high value add in the 21st century, is paying a high fee for a stuffy Victorian education model really much of an investment? As someone who has hired dozens of phd folk for very difficult jobs, I would argue no. Public school might get your kids above the water line of the iceberg, but they are still stranded and adrift in the 21st century. Get them off the iceberg, it's going to melt they are going to drown.
I have a plan to sideline the school education system - make it all irrelevant - for which I'm trying to get traction. I've been corresponding with Tyler Cowen about it - it's partly Bryan Caplan influenced. Tyler thought it was a good plan but that I needed better allies over here. I come from a sink school where my lazy teachers blocked me from applying to Oxbridge, but ended up a Cambridge fellow by 25 anyway. Not many people have the luck to get through the system so as to see if from both sides and understand what is and isn't needed to fix the problems - as shown by the terrible design and predictable, measurable failure of schemes like Uni Connect from the OfS.
I just got my super-bright home schooled kid through A levels at 16. They're a disaster, with mark schemes that now penalise the exceptionally smart in favour of helping posh midwits get A*s. The only exam prep I could think to give my child was to regularly hit her over the head with a rock. We have to make the whole thing irrelevant, and I have a cheap and quick way of doing so.
I would love to pick your brains about this. Could I send you what I sent Tyler?
I know you'll like my plan, I know it's a game-changer, and that your advice would really help it work, so I'm going to shamelessly persist in trying to get your attention.
Thank you. This article touched on a topic really dear to me. I am a child of Russian Mathematics Academics but I grew up and went to a state funded grammar school in Manchester. My Farther is mathematician at the University of Manchester, he was one of the people you contacted when you tried to set up Russian style maths schools. I believe he even helped to draft a program for the school. You may recall the names: Dr Theodore Voronov, Prof.Alexandre Borovik, Prof Andrei Voronkov and Dr Hovhannes Khudaverdian.
Along side my regular department of education curriculum. I experienced the Russian tradition of Super Curricular Circles as My parents and many other Russian exPats set up a Saturday "Russian School". We had lessons in mathematics, Physics, biology, Russian and Art taught by the parents who were experts in those subjects. So I am in a unique position to compare both:
Unlike my farther, I am not particularly Mathematically gifted yet thanks to the Russian maths lessons I was able to keep up with the UK curriculum with ease. In Year 4 I was already working with Long division, multiplication tables, decimals. By the time I was in year 6 I was comfortable with algebra.
The UK system depends so much on Rote learning. Rote learning can be a useful tool but only if the idea that is drilled in is understood by the pupils. The classic example is the times table. In Russia it is still learn of by heart from a young age.
But what Russian maths taught me in comparison to UK is how to think threw problems. The best example is geometry. I started to learn geometry axioms at 12 in Russian school beginning with pythagorus . Our homework was to use the axioms to come up with basic proofs ourselves. It was tough at the time but when I figured them out for myself I learned them forever because they were my proofs.
I was staggered that at GCSE maths we were given the proofs the learn BY ROTE!! A great big sheet was handed out and we were told to learn them for the test. Bear in mind this was at a grammar school which is rated outstanding and supposedly specialises in science. How is that useful for the students.
Again, I want to emphasise that I was not mathematically gifted but I was able to achieve these things because Russian Maths pushed and challenged me in interesting ways. Solving proofs myself was engaging and fulfilling.
My father despaired when the Russian style maths schools that you were working on were blocked. They are not elitist quite the opposite: children who were taught maths from primary school age like me did not need much extra help to pass the 11plus maths. With the current UK curriculum children need rich parents with lots of tutoring to even attempt it.
P.s. In my personal biased opinion the way History is taught in England is even worse than maths. I personally have tutored GCSE and A level History for a few years and despaired at the state is is in. Jumping from topic to topic, century to century (ww1, Tudors, ect) is horrible for children. All historical context is missing. The most popular GCSE history topic is Germany 1918-1945 but how can you even teach that if a lot of the students never learned about ww1? 80% of my students did not know what Prussia was!
Madness. Worse still, I am not sure what to do about it.
Feynman's account of the process during the 60s made for depressing reading. That's what it was like *then*? Add a few more generations of atrophy, and here we are I suppose.
Speaking of building outside the state system: we had a brief and highly successful period of charter schools in New Zealand, before they were done away with as a high priority by the incoming Ardern government. Not enough control. Too elitist.
Many such cases.
As someone with near-term plans to begin a family and who’s scouring any and all materials looking for a way my coming young uns might conceivably be educated so that they’re half-ready for the challenges that await them in mid-century, this reading list is an absolute goldmine.
The wider philosophy is true to my own experience of the British education system (both sides), and also to my feeling for the amount of ripe-for-capture alpha in developing specialised ‘tools for thinking’ apt for our day and age. There’s already a mostly-unheralded reasoning deficit that’s setting in among younger generations; any system that manages to even partially implement a more metacognitive strategy with specific epistemological techniques will make a massive difference. Have written on them before and will be doing much more in the coming time.
Hope you’re recovering well after your op.
Education is such a miserable story. One of the few achievements of this Tory government was your DoE reforms, the fact that Gove got endlessly attacked in the Guardian was proof of what a good minister he was.
Dom, do you have a window into the psychology of the education egalitarians? When you look at people like Polly Toynbee, Fiona Miller and Melissa Benn (fanatical supporters of the current system), do you think there is some coherent argument in their heads or is it just self-serving corruption? It frightens me how passionate these individuals and their supporters get on this subject when any objective study of the British school system can see its failing in its current form? I remember the arguments between Richard J Evans and Niall Ferguson on History teaching and how Evans remains such a committed supporter of the current system despite the dire lack of widespread historical knowledge among the population.
On the subject of adaptive testing - I am a director of well known education not for profit. We have a single adaptive reading assessment to assess reading ability from EYFS to KS2 (soon to be upgraded to assess using speech recognition ai...) I'd be interested to see if we could repurpose that into a maths assessment as well. We don't have any speciality in maths so would need help on content, but we have the systems, have relationships with 1000s of schools for one thing or another, and know how to build assessments and measure performance. Let me know if interested.
Simon Singh runs online maths circles: https://parallel.org.uk/circles worth a look.
‘Can We Survive Technology?’ (essay by von Neumann) sheds light on the importance of politicians needing to understand science and technology. The combination of politics and science is inherently destructive in its current form because neither group has any understanding of the other. The future of education must be the replication of Plato’s Academy!!!
Apologies in advance as this comment is not directly related to your post, but this nonetheless feels the best place to put it.
I am a 20 year old second year PPEist at Oxford, and honestly, I have a feeling I am 20-30 years away from becoming you. My course is almost entirely useless, and seems to have an enormous amount of assumptions baked in which based on my own cognitive differences I simply do not share, and that seem entirely alien to me. I’ve also found it difficult to connect with many of my peers, and have yet to really find anyone who seems to share my perspectives and degrees of cognitive difference.
The more I read of your writing, the more I get the sense that, while individual views and perspectives may differ, you nonetheless approach things with an attitude and mindset that seems similar to my own in a way that I have yet to observe in others. You also have the advantage of vastly more experience both in operating the world in general, and also in the world of policy making which I seek to one day enter. With that in mind, while I recognise that this is an unorthodox request, as someone who it would seem is likely to have a unique insight into my situation and perspectives, I would enormously appreciate any help and advice you are able to offer?
Some of these books are out of print and hard to find.
You can download the pdf of "Let's Play Geometry" from here: https://archive.org/details/ZhitomirskiShervinLetsPlayGeometry
Dominic, I have an intense interest in your policy outlook for education and elsewhere. I have been discussing your latest piece with a successful ex KMS student. Recently he has been busy setting up his old school with a network of potential teachers, backers, and policy reformers. One of them includes a highly successful man who helped found and run a notable quant fund. Happy to put you in contact.
Just listened to your Podcast with this guy Dwarkesh! I am not a historical subscriber to his Podcast, yet the algorithm still hit my feed!!
You came across really well!
Clearly you should be the face of the TSP!
p.s. like the way you pulled a politician special on answering his questions about TSP!
Fascinating article, thanks for sharing.
My own dyscalculia mind has been perpetually frustrated at how maths is taught in the UK. Schooling in 70/80s was wholly inadequate for me, despite some good teachers trying their best for me, and heaven knows I definitely tried for them. Low passed my GCSE x2 and then ran away from maths.
In workplace colleagues and clients had no idea. Would get compliments on being good at figures. I just learnt to harness what I was good at (organising, tech) and applied it to figures (spreadsheets, pre-meeting prep) and worked it out.
About 2 years ago I did Functional Skills Maths whilst off work due to sporting injuries. Turns out not only could I do maths in a learning setting but I could actually enjoy it. Searching out extra resources online for additional practise.
We should make the baseline for maths the Functional Skills qualification not GCSE. By all means offer both, especially for those learners with a passion or career need for academic maths.
This is backed up by Chief Examiners and moderators. They have long pointed out by the time we currently offer Functional Skills people have to have failed GCSE at least twice. But by then their confidence is shattered and they’ve little to no interest in going again.
And that’s why I remain perpetually frustrated with DfE’s approach to maths. We have the answers, we already have the syllabus and papers, but DfE prefer to remain committed to failing students when they could be building them up, giving them skills for life, and (dare I say it...) perhaps even have students enjoy maths.
Really thought provoking post. My lad is 6 in February and in a (really great) local primary.
Need to start taking the education seriously and backfilling what seems to be a poor educational system.
Conflict for me is there’s only so much time in the day and im building a business so it’s drawing a lot of time. Building out a curriculum based on these resources is, whilst a beautiful thought, something I’ll start then stop cause life gets in the way.
Curious to get the feedback of the many smart people here on two options that come to mind:
1. Get him on Khan Academy kids - complete, then move to Khan Academy proper and make his way through the maths track.
- Actually doing myself (as pulling myself up by my bootstraps as Dom was famously quoted on and Sal Khan really is an incredible tutor.
- It’s self-paced so again avoids boredom.
- Pluuus their AI support tutor goes lives soon (if not already so).
2. For the real world, putting him in Kumon.
- But I’m getting mixed feedback on this from people I know.
- Some absolutely rave about it and a number I know have gone into become scholars. But others says it’s wrong as purely learn by rote.
- What are your thoughts on Kumon here? Is there any data/reports that outline th efficacy of the program?
In case somebody is interested, another chain of Maths Circles in the UK
and a free maths problem database (under construction at the moment)