My Journal

Maths Grinds
17 Oct 2020

Numerical Intuition

Posted By

Confused, Hands, Up, Unsure, Perplexed, Young


We all have a Number Sense but what you may not fully appreciate is that this Number Sense is drilled into us from Primary school. We are not born with much of a Number Sense nor do we naturally develop it untaught. The only Number Sense that is pre-wired is the sense of how much 1, 2, 3 and more than 3 is. In fact the 3 is probably pushing it although I believe one indigenous South American tribe can “sense” up to 4. Here by sense I mean that we can look at 4 of a thing and know that there is 4 of it and not say 3 or 2 of it.


Thanks to education we have a very good, in fact, amazing Number Sense. We know and can quickly tell (via counting) how much there is of something and if it is more or less of it than of something else. We can even do this without counting. This is not natural, the fact that it seems natural is a testament to our modern education. However, I do worry.


Serval weeks ago I was buying something that was on sale, its price was €2.85 and I was buying 3 of them. When the total came to some number over €10 I knew something was obviously wrong. My brain quickly used the fact that 3 times 3 is 9 (something drilled into all of us) and my brain knew that this was an overestimate (again I recall spending much time in school on rounding and estimating). When I asked if the total was right the checkout worker looked confused although I couldn’t tell if she was confused at me for asking or that the machine was totaling up incorrectly.


Some weeks before that I had a similar encounter when I was buying a jacked on sale. It was priced at €60 with a sale of 20% off, nice! I took it to the checkout and I was told the price would be €50. Now I quickly worked out that a tenth of 60 is 6 so my discount should have been 12 (i.e. double a tenth to get a fifth which is 20%). And I was only getting €10 off. Again, I had to query it. He seemed a bit confused and the manager came over to fix it. The jacket was set to the wrong price on the system. But was I the first to mention the error? How many people were overcharged? Did no one spot this?


Today something similar happened. I was buying 3 cronuts. Now when it came time to pay I was told the total was €8, fine, worth every cent! I then added a last minute item, I asked “Could I have a latte with that?”. So, the coffee was added and the bill came to €12! The first thought that jumped into my head was that 8 plus 4 is 12 so the coffee is 4. So I asked (in perhaps a put-out tone), “Is the coffee €4?”. The reply was one of near disgust, the mere suggestion that a coffee could be that much. However, when I pushed if that was the right total she just could not see the problem. She couldn’t see that my total going from 8 to 12 meant I was being charged €4 for coffee.


At this point two other workers came over to help, the three of them were working the till to figure out what the issue was, only one of them could see something was numerically wrong! It was clear the other two were confused by me challenging the total and the possibility that the machine totaled up wrongly!


In the end the error was caused by human inputting (I think), that is, I was being billed for 2 cronuts + 1 coffee and cronut rather than 3 cronuts + 1 coffee. The store offers two specials, 3-cronut-special or coffee-cronut special. It was cheaper for me to go for 3-cronut-special and a coffee (what I originally ordered) rather than 2 cronuts and a coffee-cronut special.


These recent retail misadventures have made me realize that we may be losing our Number Sense and that is a real shame. I suspect as we move more into the digital world of calculators, spreadsheets, phones and so on that the need for a Number Sense will vanish until at one point the majority of us may not notice we are being over-charged. Or maybe we are already there?

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