# What is number sense?

What is number sense and why is it so imporant to have?
10 January 2023

## Question

Chris - Ems one for you. I gather you are going to be speaking at the Cambridge Festival later on in the year. I've done that a few times. You are gonna talk about number sense specifically and how having a bit more of that could help everybody really. So what's really the thrust of your argument for that?

Ems - Well, number sense is something that gets overlooked so easily. We mentioned before about long division, long multiplication, doing procedures, but when was the last time you're in the supermarket queue and you are trying to work out, did you have enough to cover the bill? And you went, 'oh, it's okay. I've got some squared paper, a pencil and a ruler. I'll just quickly do a bit of long division or multiplication and I'll figure the whole thing out.' Life doesn't work that way. You find yourself in a situation, you're at the petrol station, you're paying, you've gotta quickly deal with numbers and you've gotta have a feel for numbers and know you've got it right or wrong. And that's what we call number sense. So it's not just knowing the facts, it's having the confidence to play with it and recognize mistakes. So what I like to do is find out when it's gone wrong, okay? I like disasters, I like mistakes. And then see what we can learn from them. So what I've come up with is a top five IT disasters. These are projects where people have been incredibly ambitious and said, you know, we wanna go to Mars, we wanna have the biggest subs, we wanna have the fastest trains. So they're ambitious projects. These are projects that have secured funding. So they have gone through loads of different levels, as we all know when we try and get funding, not easy. So you've got an ambitious project, you've got it funded, and then it fails at the end in a very embarrassing way because of number sense. And quite often one of the things that happens is the conversion from metric and imperial.

Chris - A spacecraft that had a problem. Very expensive consequences. Well, you are nodding Matt, it's quite a classic one . Isn't there a difference between imperial and metric?

Matt - Yes, exactly. I think there was, I forget the exact details, I think it was a European spacecraft that was using a software program designed by Americans and the software program supplied an acceleration in sort of foot pound hectares or whatever stupid thing Americans use. And then the spacecraft interpreted that as a metric and crashed into Mars

Chris - <laugh> costly mistake.

Ems - \$328 Million costly mistake, <laugh>. Two years development, nine month journey. They got it there, they got it into the Martian atmosphere and that's when they lost it. I mean, how much do you feel? You're sat there, following this for months. You've got an investment, a long term project, and it burns up at that point. I just can't imagine how those guys must have felt.

Matt - I know.

Chris - Very nasty <laugh>. Would being better at maths have spotted that though? If I had a bit more numeracy, would I necessarily. I mean these are bright people and if they don't spot that, why do you think a paucity of math's ability is the problem?

Ems - I think it's what we value. At the moment, what we tend to value is, 'did you get the right answer?' Okay, have you got an answer? Move on to the next one. Our exam system favors that. Even down in primary school you get a 20 question booklet. How quickly can you get it through? They aren't encouraged to check and look back and estimate. And the mistakes that I'm looking at, you could avoid through that. You could save your 328 million just by going, 'do you know what? Those figures don't look right'. But too often we trust everybody's figures and we don't sit down and go, 'do you know what?' That sort of sucking of teeth you might get when someone's doing DIY? You know, measure twice and you know, check it carefully.

Chris - I learned that the hard way. I do a lot of mechanical type stuff and, and I had to find out the hard way. You measure twice and cut once. You are nodding as well, Tom.

Tom - I just love this idea of Ems' number sense and the idea of questioning things because I think so many people get turned off many sciences when they're at school because there's an idea that you have to memorize what's right or wrong and it's only really where you get into doing your own research and you know a topic really well that you realize that most people aren't really sure of all the things that you learned at school and that the most exciting things are mysterious and probably most of the things that are thought to be right will be wrong at some stage in the future. And that's so much more exciting than proving whether your brain can remember stuff. This idea that, you know, for example in natural history, like we have so few explanations for so many of the things that animals do. And I think that's really exciting and I think many more people will be drawn into it with this idea that they can contribute and play rather than don't get it wrong.

Chris - Yeah, it's excitement for what we don't know rather than getting right just what we think we know.

Tom - Totally.