Negative Numbers

An interesting discussion with my 6 year old son over dinner this evening got me thinking. He loves doing mental arithmetic at the dinner table and we were doing sums like 6+3 = and 9 – 4 = when I threw in 1 – 2 =. His immediate response was “What is the number before zero?” After I told him it was -1 I then asked him 2 – 5 = which he immediately got correct. This was followed by -2 – 5 = and other similar questions.

The logic of the number line continuing was obvious for him but this is often not the case for many students. Many of my current Yr 9 class struggle with any form of non-calculator arithmetic (and yes I am forcing them!) becoming particularly muddled when negative numbers are included. It appears to me that most have remembered just one rule (when you have two negative signs it becomes a plus) with very little understanding. Of course this rote learning will never be an adequate substitute for true understanding – so why does my 6 year old comprehend naturally something so many have a great deal of difficulty with? Perhaps it is their (negative?) exposure to Mathematics in the classroom over many years? If Mathematics was only ever “rules” to be learnt rather than understood? An over-reliance on the use of calculators? Any thoughts?

So I just changed my lesson for Period 5 tomorrow. My objective now is to see how much the kids in my class really understand about negative numbers and arithmetic operations with directed numbers and to identify any misconceptions. Previous ways I have tried include – number lines – walking backwards and forwards modeling the number line and actions – walking up and down stairs to model operations. Does anyone have any better ideas?