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- how to use different frames of reference, probably in the context of an introduction to galilean relativity

- how to approach problem-solving (https://arxiv.org/ftp/physics/papers/0508/0508131.pdf is a great read as a starting point)

- how to connect the mathematics they've studied to their A-Level Physics curriculum (some of the mathematical concepts they meet in maths but aren't explicitly linked to the physics A-Level are vector and scalar products, differential equations, and matrix algebra)

I am, however, interested to discuss with others which parts of university required the biggest conceptual leaps, especially when those leaps can be more gently introduced earlier. Again, the idea is very much not to just teach first year content, but more to provide a gentle introduction to tools (for example changing reference frame) which are both vital and intitially difficult to grasp.

This is a UK-based school, and the students will all be studying A-Level Physics, Mathematics, and Further Mathematics. Syllabuses are easily available online but in my brief attempt to convert to American qualifications it looks like they will have seen

**much**more maths than someone taking AP statistics and AP calculus, and about the same amount of Physics as someone taking AP physics 1 and 2, but as much as someone taking AP physics C.

Thanks!