Tier 2 shortage list applications

Hi,
I currently don’t live in the UK but I want to apply for the Tier 2 visa based on the shortage occupation list. I am a maths teacher.
My question is how or where do I find the right school with authorisation to employ tier 2 visa applicants?
Also, how or where will I find the vacancies from such schools? It’s like a mine field. I’ve seen the list from Home Office of the approved employers but it is soooo long and voluminous.
Any links or anything will be helpful.

Thank you in advance.

Same list, filter your search results for schools.

https://www.gov.uk/government/publicati ... rs-workers

For vacancies, school websites.