Our academic calendar in South Africa runs the same as a calendar year – January to December – which means this time of the year youngsters have the duality of exam stress and excitement about their long summer holiday. It is also the time of year where I often get late-night panic texts from colleagues and friends with school-going children asking for emergency help before exams.
If I could change one thing about our schooling system, it is that we should spend more time on basic concepts. In the majority of these late-night phone calls, I need to explain something else first before – miraculously – the poor exam preparer then suddenly joins the dots quite quickly. It is wonderful to see what that does for their self-esteem, but think about the hours of unnecessary suffering in math class!
Last week Sunday the call lasted all of five minutes – four of those were spent apologizing for phoning me so late on a Sunday night… The four minutes were peppered with ‘she just doesn’t understand’, ‘just give her some rules and shortcuts that will get her to pass’ and ‘math is just so difficult’. The ‘difficult’ in question was about linear and exponential growth and luckily Miss I-can-do-math-but-I-don’t-believe-in-myself got the crux of the matter when she finally got handed the phone: I don’t even understand what that means!
Me: Think bunnies.
Her: Like Fatal Attraction?
Me: You’ve seen Fatal Attraction? (In my defence, she is only 15.)
Her: Aunty H, focus!
Me: Oops, okay. Think bunnies having bunnies. You have two bunnies, tomorrow you have 4 bunnies, the next day you have 8 bunnies, then you have 16 bunnies.
Her: I am writing math, not farming.
Me (beaming): Absolutely, but is so lovely that you already recognize that math plays a role in everything in this world! The bunnies are exponential growth. If you went to the pet shop every day and bought two bunnies – so today you have 2 bunnies, tomorrow you have 4 bunnies, the day after you have 6 bunnies – that would be linear growth.
Her: That’s it?
Me: Yes, but think big, because it is the big that confuses people. Our minds automatically tell us that the bigger the number, the more complex the calculation, but it remains bunnies.
I then proceeded to tell her the (very) abridged legend about chess: The king wanted a game that relied on skill, not on chance and he offered whoever could invent this game any reward he or she wanted. The inventor asked for a single grain of rice on the first square, two grains on the second, four on the third, etc. – so exponential growth. The king was unable to pay the inventor because, by the time they got halfway, the kingdom was out of rice.
This sounds impossible, but with 64 squares on a chessboard, the last square would have 18 446 744 073 709 551 616 grains of rice. The last square would have 504 147 146 043 tons of rice. (Statista states on their website that total rice consumption in 2020/2021 was 504 309 metric tons.)
Exponential growth is extensively used in farming, but we also use it in determining population growth, compound interest, pandemics, etc. Regardless of the size of the number, just think bunnies.
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