I discovered the real lesson learned from this elective is realising exactly what fundamental mathematics is. Previously I had thought that the fundamentals were just the four basic operations (addition. subtraction, multiplication and division) because they seem to underpin all other mathematical problems. I wasn’t completely wrong as basic ideas and principles is one element of fundamental mathematics as defined by Liping Ma (2010). She claims that the fundamentals are connectedness, multiple perspectives, basic ideas and longitudinal coherence. The more I have read about the four elements the more sense it makes. It seems obvious now that, that is what all our inputs were geared towards.

Connectedness (breadth and depth); not just making connections between the operations in order to understand one or the other better but making connections between the other three elements; connections across the curriculum e.g. maths and astronomy (science); connections to everyday life.

‘Mathematics does not consist of isolated ideas, but connected ideas.’ (Ma, 2010, p112).

Multiple perspectives; the ability to see different approaches to the same problem, knowing everyone learns differently so views things in a different light. That point is particularly important for teaching as teachers have to recognise different learning styles among the children in the class, therefore, adapting lessons to suit all. Also teaching children that there is more than one way to arrive at the right answer is a valuable lesson for problem solving later in life.

‘Being able to calculate in multiple ways means that one has transcended the formality of an algorithm and reached the essence of the numerical operations – the underlying mathematical ideas and principles’ (Ma, 2010, p112).

Basic ideas; the foundations to advanced branches of mathematics. Often revisited in maths education as a sound understanding of them supports future learning.

Longitudinal coherence; thoroughness and progression. This element basically combines the other three to create a better understanding of mathematics as a whole. A sound knowledge of all the elements will lead to progression. Knowing the basics and building on them; the ability to see where and how these can be used and or developed later on. Gives a sense of purpose to what you are learning if you know it will be useful further down the line or in everyday life.