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?

sounds like he is on the right track. lets hope he in not foiled at primary school by the use of text books. In my experience this turns children off maths, so that they start to not actually think about what they are doing. It becomes about finishing a page and not understanding the process. By high school many have been so turned off that maths does not seem real.

As you can probably tell from my latest Twitter comment and one about a week or so ago. I think that one of our problems in Secondary Maths is what happens in Primary Schools. The article that etalbert cited and I retweeted supports this. The UK are trying to address the problem. When will we?

I’m guessing it’s going to be a while.

Congratulations that your son already gets it. As a subscriber to constructivist precepts (among others), I daresay that you’ve given him a foundation so he can make this conceptual jump. Numeracy begins at home.

Directed numbers can be tricky and I’ve blogged a strategy here http://malyn.edublogs.org/tag/directed-numbers/ .

I also created a Mothers’ Day task/homework where students earn and lose brownie points and get a total; if you take away the negatives, your total is higher – a good application of 2 negatives becoming positive. I can tell you that I made many mums happy and I’d say it helped teach/reinforce directed numbers to boot….maybe I should blog about this as well.