Among Sir Anthony Seldon’s many achievements in education, the Sunday Times/Wellington College Festival stands out as bringing together people with something important to say from the whole spectrum of opinion and professional practice.

This year’s Festival takes place on the Thursday and Friday of this week. Participants include the present and at least one former secretary of state, the founder of Labour’s strategies, the headmaster and a housemaster from Eton, the Socialist Education Association, Tom Sherrington, Head of King Edward VI grammar school, Chelmsford, Sir Ken Robinson, Neville Gwynne, Al Murray and a good number of teachers. The event is great value at £99 for a two-day pass (£20 for newly-qualified teachers and students) and two thousand people are expected to attend each day.

I’ll be talking about how evidence from current brain research can help us to understand language and its development, illustrated by work carried out over the internet with a parent and her two daughters from Falkirk. Over six months, and starting virtually, though not quite, from scratch, we’ve moved from basic sentence formation, gender and pronunciation to reading Le Petit Prince in French, unpacking and explaining every detail so that the girls fully understand it. It’s not as daunting as it sounds – roughly a third of words in French are shared, or nearly shared, with English, so much learning is an adjustment to what they already know.

The girls’ response has been a delight: The biggest change is that we feel we can do it.  That we are capable of understanding.  It’s like a whole world is being decoded for us… we are light years ahead of where we previously were… and it’s nice to be made to feel intelligent, to be praised. I’m starting to believe…   and they and their mother will be joining us during the session via the internet.

I found another window on the mind and its workings in the library at Cambridge University Department of Education last week. This library and its ultra-professional, helpful staff provide public access to journals that would otherwise be inaccessible to non-academics. After a visit to check out an item on visual stress and reading that had been featured on Radio 4 – my take on it is here.

Among the typical British articles on theoretical aspects of inclusion and equality, I found one from Dr Sahar Bokosmaty, of the University of Wollongong, Australia, on the teaching of geometry.  For me, geometry at secondary school was purgatory of migraines, late nights and time wasted trying to solve problems by what Dr Bokosmaty describes as “means to end” methods – i.e. using whatever means I had at my disposal, which usually meant a protractor. If measuring two angles with this device showed that they were equal, I did not understand how this could not constitute proof.  Result, misery, and the only consolation in the longer term is that the experience helped me to understand how other people feel when they can’t do something that is important to them.

Dr Bokosmaty’s approach is to give children many worked examples of problem solving, so that they come to see and understand what the tools of Euclidian geometry are, and how to apply them. The results meet the most exacting requirements of modern statistics – including the supposed holy grail of randomisation – and show that building up children’s knowledge of the operations and techniques they need to use is the foundation of problem solving. The applications run across education.

The success I’ve had with  the most difficult reading problems – described by our political opponent  Sue Palmer as “miraculous” – is based on this principle. If children find blending sounds difficult, I use lots of worked examples of the same combination before moving them gently to doing it for themselves once they’ve understood what they need to do. Teaching a ten year old his tables and arithmetic facts led to an impromptu comment yesterday that his favourite subject was maths. It had become his favourite subject because he had learned how to do it, and so achieved satisfaction.

Knowledge frees the mind to think.