**Chapter 3 of Mathematical Mindsets**

What is mathematics, really?And why do so many students either hate it or fear it – or both? Mathematics is different from other subjects, not because it is right or wrong, as many people would say, but because it is taught in ways that are not used by other subject teachers, and people hold beliefs about mathematics that they do not hold about other subjects.

Keith Devlin, a top mathematician, has dedicated a book to this idea (mathematics is about patterns). In his book *Mathematics: The Science of Patterns* he writes:

As the science of abstract patterns, there is scarcely any aspect of our lives that is not affected, to a greater or lesser extent, by mathematics; for abstract patterns are the very essence of thought, of communication, of society, and of life itself. (Devlin, 1997)

An example in life:

The spider web is an amazing feat of engineering that could be constructed using calculations, but the spider intuitively uses mathematics in creating and using its own algorithm.

Mathematics exists throughout nature, art, and the world, yet most school students have not heard of the golden ratio:

https://www.mathsisfun.com/numbers/golden-ratio.html

…and do not see mathematics as the study of patterns.

the questions that drive mathematics. Solve problems and making up new ones is the essence of mathematical life. If mathematics is conceived apart from mathematical life, of course it seems – dead

Reuben Hersh (1999) What is Mathematics, Really?

Over the years, school mathematics has become more and more disconnected from the mathematics that mathematicians use and the mathematics of life.

Four stages of mathematics:

- Posing a question
- Going from the real world to a mathematical model
- Performing a calculation
- Going from the model back to the real world, to see if the original question was answered