Durham University MMath seeking teaching experience

I am fresh out of my Master's degree from the University of Durham in Mathematics, and am seeking experience teaching mathematics. I have an A* in A-level mathematics and further mathematics, whose certificate I would be of course willing to provide a scan of upon request. My specialty, and my deepest insights, are in the more abstract / pure areas of mathematics which I have found via discussion with classmates are the biggest leap between school and university-level maths. This does not detract from my knowledge of other areas which school requires one to learn. My fianceé is currently studying a degree in child development and education, which has led me to a generally student-led teaching philosophy. My own experiences in studying maths tell me that "why?" is the most important question when learning new mathematical concepts, and my aim is to guide my student into building intuition for the subject. As an example, if I was to teach the multiplication axioms I would show the geometric intuition by cutting up rectangles. Indeed the geometric intuition behind things like the quadratic formula are well-understood and well-under-studied. I believe that teaching this would be a great benefit. Maths is neither hard to learn nor teach, it is simply impossible to teach effectively to a group.