Mathematics is one way of understanding the world and universe.

Patterns are everywhere. Patterns occur in geometry (eg wallpaper/tiles patterns using various geometrical shapes/figures), in music, in human behavior (eg voting patterns )

What the mathematician does is mainly looking for a pattern or to examine abstract patterns which give rise to different branches of mathematics - numerical patterns/patterns of numbers and counting (arithmetic and number theory), patterns of shape, symmetry and regularity (geometry; the mathematics of beauty- transformation), patterns of motion and change (mathematics in motion- calculus), patterns of reasoning and communicating (logic; logical arguments/connections), patterns of chance (probability theory - making prediction etc), patterns of closeness and position (topology), and so on.

Those patterns can either real or imagined, visual or mental, static or dynamic, qualitative or quantitative,

purely theoretical or utilitarian.

Those patterns can arise from the world or phenomena around us, from the depths of space and time

( geometry of the universe; three- dimensional physical universe etc), or from the inner workings of the human mind.

Discuss the implications of maths as a science of patterns to the teaching and learning of mathematics in secondary schools.