Can You Really Subtract Something That Isn’t There?

Exploring negative numbers with a servo-powered zero pairs display

When teaching about negative numbers I usually start with a real-life context, like temperature, finance or trips to subterranean floors of a building. However, it is not long before these contexts become forced.

For underlying calculations such as -3 - (-6) , at a stretch you could say that “It was super cold one night, but the next morning the sun took the cold away”. However it is much simpler to explain that subtracting a negative is the same as adding a positive.

This type of explanation works well for learners who can remember rules by rote. However, many students need to ‘see’ why the rules work for them to stick. Or, as Jo Boaler puts it in her book “Mathematical Mindsets”

“When students visualize mathematical concepts and understand the underlying structures, they are better able to remember and apply those concepts. Rote memorization without understanding often leads to shallow learning and poor retention.”