… with a little help from my friends
I’ve been teaching maths for a fair few years now and I am definitely in that dangerous stage of thinking I know it all and have seen it all before. Things have certainly changed since I first picked up a piece of chalk and faced the enemy taught my first class – chalk itself is now never seen in a classroom; emails probably existed when I started teaching, but were unknown in school; and paper, pen and textbook still ruled supreme – but two plus two is still four, and dividing by zero was forbidden then as it remains so now.
A few days in to a new term a colleague asked a simple question:
Bounds – what is lower bound of 100 rounded to one significant figure?
Over the initial shock of the alarm clock once again rousing me from my slumber, but not yet numbed from a term’s tiredness, I had the time and energy to ponder this question, not one I’d considered before in all my years in the classroom. My initial thought was 50, with the upper bound being 150 and I sketched out for my colleague a simple number line, numbered 0, 100, 200 etc – numbers with one significant figure – and drew in my upper bound at 150, and then my lower bound of 50.
He gave me a warm smile, recognising I had stumbled into his trap, and passed me ladder out of his trap by asking me to consider 64. What would that round to one significant figure?
And then it dawned on me, the lower bound must be 95. Anything between 95 and 100 would round, to one significant figure, to 100, but anything below 95 wouldn’t round to 100. The bounds need not be symmetrical. I’d never thought about that before, but I am grateful to my colleague (and friend’s) gentle questioning to prompt me to do so.
Another friend (and colleague) decided to do what so many students would do – ask ChatGPT (something that was available only in the most fanciful of Science Fiction when I first started teaching.) And this was its answer:
We all agreed that ChatGPT was wrong in this instance. As 2025 dawns its encouraging to note that, at least sometimes, real intelligence still beats artificial intelligence (even if it did take me a little while to get there!)