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I am very passionate about maths, I have been a teacher at Secondary schools and I have also been a maths tutor with individuals.
If it's a case of teaching towards GCSE I would work with actual past papers, ask the student to solve them and little by little I would be picking up on their weak areas and work on them. I would be asking the student to solve problems the whole time, and the idea would be to solve the High Level GCSE.
If the student is an A-level student I would work in s similar way, by solving past papers of A level maths and then finding out the weak areas of student, and work on different problems of the sort.