Fundamental concepts in mathematical reasoning

This section is going to be a little different to the others in the book.   Throughout most of the book, we’re going to pose you a series of problems, and we’re confident that by working through those problems you’ll develop strong methodologies that can be generalised to support mathematical reasoning and investigation in other areas.  That’s the whole point of the book, after all!

In this section, we’re going to be a fair bit more explicit about teaching methods.  This is really just to give you additional support and help bring you up to speed quickly with some of the essential skills surrounding solving mathematical problems.  Some of it, like order of operations and describing relationships with variables, is mostly just reminding you of mathematical conventions to ensure that we’re interpreting the numbers in the same way.

We’ll look at things like the order of operations, the properties of addition and multiplication and how to work with fractions.  But the reason we’re looking at all of these really boils down to helping you develop the ability to use perhaps the single most powerful problem-solving methods we have: algebra.

Learning outcome

By the end of the section, you should be able to express proposed solutions to mathematical problems using algebra.