Ask HN: Insights to share about math tutoring, as a student or a teacher?

I read somewhere in Kasparov's book "How life imitates chess", something along the lines of "there are many things which you cannot be taught but that you can teach yourself". I think this is particularly relevant to people that struggle at school. I'd draw one corollary from this as applied to OPs question: as soon as you can turn the student into a teacher, tasked with working out how to teach themselves. It is a meta concern which exponentiates the value of a tutor.

There are a lot of basic questions:

- How motivated is the student to learn the math? (Meaning "motivated to really work at it", not "it'd be cool to be good at this...".)

- How well prepared are they (in mathematics) for the material you're charged with teaching?

- Is the priority to ace the final exam, or to prepare them to go on in math?

- How (correctly) confident is the student in their ability to do well in math?

- How much time do both you and the student have, to devote to this?

I have tutored 3 students in Math for a term or more in the UK, here's my thoughts:

- Student motivation is crucial. Your first duty is not to be a cardboard tutor, to be interesting, different, to stir something. Without this nothing later really matters (to me it is equivalent to pursuing a relationship where there is attraction, but not laughter, fun and relaxation - it's a base ingredient)

- Tutors who uncover and help students see misconceptions and knowledge gaps do demand more mental focus, but are much more helpful; these (e.g. visiting last weeks homework mistakes) are incredibly useful mid session too to break up sessions and to illustrate progress.

- You really face a choice depending on the students motivation. I have tutored 3 maths students, 2 of which were on path to fail at their age 16 qualifications, who I did my utmost to stir interest in with relation to video gaming, science and literature respectively, and, by way of being more relatable than their teachers, helped them pass; and one who (long before ChatGPT) I recognised immediately that they were incredibly talented academically and talented at listening, but it did not show in grades because of a lack of confidence and their social beliefs about themself. After a few sessions, I introduced them to machine learning libraries (at the time sci-kit learn/nltk) far beyond anything on their syllabus and showed them beautiful ways to use maths later on to do incredibly interesting things like nearest neighbour search for conversation sentences in Friends episodes. I barely mentioned the maths until after the fact in these stirring few sessions... but once I did they knew they learned eagerly...

They latched on with such energy that their work was compared to that of someone 4 years their senior, and they (from a below average UK London school) got a place in Oxbridge (I cannot express how proud I was of them).

I think it goes to show self-belief and social-beliefs are so important to focus on. As a tutor you -can- make a difference, you -are- the fresh and more relatable start compared to a teacher. And a last important fact is be ready to use metaphors.

To really excel as a tutor I think you should attach math with wonder to something they like. For a fan on the new Matrix movie, it could be the mysterious RSA and P - NP problem. You are a revealer, a magician. Where possible hold some information in apprehension, for the next session. Make it a journey. The teacher must address every student, your work is for them. You are showing them a door to a new way of learning the world, and that door is made of a new material, that they will naturally want to learn about so they can walk through it!