[keithpeter]

Going back around the millennium or before when I last taught A level maths at college, we had them in over the summer before term started for a two week intensive algebra and basics course.

Seemed to help.

The original author (Tim Gowers, a Fields medallist and professor of mathematics at Cambridge) has a totally hilarious blog post about being asked to coach a teenager doing A level maths...

https://gowers.wordpress.com/2012/11/20/what-maths-a-level-d...

[zazen]

Thanks for linking that, it's a great read. I really should read more of Gowers' posts.

The phrase "memory works far better when you learn networks of facts" was a happy find - I've never been able to express that idea so concisely.

I remember discovering they'd moved "differentiation from first principles" away to a further-maths module, as if it's a peripheral, difficult little oddity for the keen kids to hear about. It was the surest, saddest sign that the powers that be had given up on genuinely educating the average A-level maths student.

[mncharity]

> memory works far better when you learn networks of facts

One challenge with teaching a more rough-quantitative Fermi-question-ish introduction to sciences, is it's more sensitive to integration and correctness of understanding. With a Trivial-Pursuit memorize and regurgitate style of "understanding", damage from misconceptions and fragmentation of knowledge is local. Whereas rough-quantitative reasoning benefits from being able to... slide around the knowledge space. Jagged misconceptions and fragmented knowledge seriously impedes the sliding. I imagine memory is similar. Nice phrase.