Zero is a threshold concept ...
In computing zero (0) is a number, meaningful, significant and applicable in all number systems. So you may think that it applies in binary, it does. It also applies in octal, decimal and hexadecimal.
Now, already I guess some of you reading this are thinking … well of course we all know that zero applies in maths. I agree, of course it does. The threshold concept is developing the notion that we must count from 0, not 1.
I have seen programming loops, subnet calculations and memory addresses all fail because some hapless student has forgotten to count from 0. Why, because since we were toddlers, we would be encouraged to start from 1 when being presented with our fingers.
Counting from one to ten is sensible; it fits our biological imperative; it does not require explaining and can be based entirely on experience.
Yet that immediate process makes the first time teaching of zero challenging in schools. I cannot recall when this done, as zero is both nothing and a numeric threshold.
Consider this line of pretend code:
for catapult = -10 to 5
For many this presents an immediate conundrum, as they would assume that the loop in question runs for 15 iterations. Whereas when you include the 0’th position, it is actually repeating itself 16 times.
So, please teachers, parents and generally interested souls. Pray tell, how would you broach the positional value of 0 as a relevant number. Should we teach children to count from 1 to 10 or from 0 to 9?
One solution is logical, the other practical. The reality is, the sooner our children grasp this relatively simple notion. The sooner we can encourage potential engineers, scientists, computer geeks and the suchlike to flourish.