Ah, to redesign school. Had you asked me that when I was younger my solution would be… get rid of it. Ah the days of youth…
How would I can School, well my attention immediately would be to reshape the curriculum as it is a terrible need of an overhaul. First up would be to freshen up the Music Education setup and actively encourage all students to learn musical instruments. This would not only help with cognitive skills but encourage creativity and encourage one to regulate themselves, plus it is incredibly fun at the same time. Not everyone will be successful but music education needs to cover listening as well, so there would a certain degree of playlisting going on in order to educate that there is a broad spectrum to music.
I would make the three sciences; Biology, Chemistry and Physics mandatory at GCSE level with a hands on approach. I would revise Maths to make it more relevant to every day including basic concepts such as budgeting, calculating taxes etc but make sure the basics numeracy skills are up to scratch. The more theoretical aspects I would split into a separate block and make it an additional course to take.
P.E. I would alter to make it focus on keeping students fit and healthy and make team sports an option, as not everyone is sporty and those who are not end up idling about. I speak from experience.
I would favour a more interactive teaching model with shorter lessons and smaller classes to allow more focus on the student and to stop kids getting bored.
And I would push for home skills like sewing and cookery lessons. We live too much in a consumer culture of instant gratification and microwave food. Get people cooking and people will get healthier and again be more creative.