Looking for mathematics Heather Mendick and Marie-Pierre Moreau Institute for Policy Studies in Education, London Metropolitan University Debbie Epstein School of Social Sciences, Cardiff University firstname.lastname@example.org
Mathematical Images and Identities: education, entertainment, social justice Funded by the Economic and Social Research Council: RES-000-23-1454 What discourses are there about mathematics and mathematicians within contemporary popular cultural representations? How are these discourses deployed by learners in constructing their relationships with mathematics? How are these discourses and processes gendered, classed and raced?
Data collection 2 groups of participants: • Year 10 – Year 11 pupils • Year 2 – Year 3 undergraduates 4 phases of data collection and analysis: • Survey • Texts • Focus groups • Individual interviews
Generating data on… What is maths? Thinking about images of maths and mathematicians in popular culture, pick 2 you remember clearly and fill in the information about each in the boxes below: Name and where you saw it: Describe the main things that you remember about it: What were your opinions and feelings about it?
Absence of mathematics Left blank… Example 1: 163/648 = 25% Example 2: 318/648 = 49% Examples 1 and 2: 157/648 = 24%
4 entries each Get Rid of Your Maths Gremlins adverts Monopoly Radio quizzes Sport (cricket, tennis, football, darts, snooker)
TV advert It was for a learning programme for adults. They used a gremlin in it. Thought it was an OK advert. Felt that it wouldn't really encourage adults. TV – advert. A parent not being able to help their child with maths homework - an advert encouraging elders to take courses. Positive - encouraging advert. TV at home Get rid of your maths goblins (get help with maths) Could be usefull T.V. an advert for maths About how to understand it better I didn't really care
3 entries each Newspaper items (financial and about maths) Rainman Stand and Deliver Stephen Hawkings on Simpsons/Richard and Judy The Da Vinci Code(book)
Steven Hawking on Richard & Judy. Him talking about his simplified books for normal people. Interesting Simpsons Steven Hawking was on simpsons. It was quite funny. The Simpsons Stephen Hawking was on it. I think it was just another joke on the programme.
2 entries each Back to the Future Catch Me if You Can Einstein My Wife and Kids The Da Vinci Code (film) The Weakest Link Who Wants to be a Millionaire?
1 entry each The Apprentice … Beauty and the Geek … The Brain Game … Chess … Come Together (Aerosmith) … Dambusters … Digital Fortress … Don't Know Much About History (Sam Cook) … Dr Kawashima's brain training … Dr Who … Eggheads … Enigma … Friends … Futurama … Google … Grange Hill … Unpredictable (Jamie Foxx)… Johnny Ball stage show … Jurassic Park … Kiddy.com … Knights of the Old Republic … Logic Puzzles … The Lottery … Mambo Number 5 (Lou Bega) … Matilda … Mean Girls … Mission Impossible 1 … Mission Impossible 3 … Newsround … Number Criss Cross … Pi … The Price is Right … Primes on the radio … Puzzle Pirates … Runescape … Russ Noble … The Simpsons … Solitaire … Test the Nation … Tetris … Tweenies …Wikipedia … Yellow Submarine (The Beatles)
Focus groups: exploring what is maths? Open approach: Tell us something about how you feel about maths? Use of video excerpts: Stand and Deliver, Good Will Hunting, Bad Dad/Bubblegum Gremlins adverts, Deal or No Deal Sudokus: Are they maths? What about if they used letters or colours instead of numbers? What makes something maths for you? Can you think of any other examples of maths in popular culture? 15 groups of Year 11 pupils: 3 different schools, asked for diverse groups: 3 mixed, 1 all female and 1 all male focus group in each school with 4-7 people in each
What is maths? Themes from the analysis Maths as numbers, as doing stuff with numbers, as broader than this but limited by school maths Maths as a way of thinking involving some combination of logic, puzzles, patterns and problem solving Maths as compared to other subjects: science, music, computing, English (and other ‘creative’ subjects), languages Everyday vs. esoteric maths
Maths as numbers or a way of thinking Heather: Is it maths, sudoku?When you look at it do you think it’s maths or don’t you? Pink: Yeah. Sky: It’s got numbers, yeah. Heather: What about everyone else do people think it’s maths? Luigi: Yeah, like kind of sequencing, you’ve got to try and get it. I think you have got to have lots of patience to play sudoku because like sometimes it won’t be the right number and so you have to kind of keep doing it and just, you know, keep your calm and be patient. Kate: It’s all logic. Heather: So tell me about the logic thing, is that what makes it maths? Luigi: Like in each cube the logic is you’ve got the numbers 1 to 9 in each, like sub square, you know it’s got to be 1 to 9 in each row, and so I think that’s the logic part of it. Heather: Because if, for example, it wasn't numbers here it was like letters like ABCD would it still be maths?
Bob: Haven't they got something [like that] already?It would still be the same because you think in the same way as you would do with numbers. It’s substitution coz you’re using letters (inaudible). Sky: I don't know I think if it started off as letters it would be different but if it was numbers and then they decided to do one with words then. Luigi: I think if it was letters it would still be maths because there’s still that logic there because you have still got to get from A to whatever in each sub square and then A in each row and so still the logic is maths. … Luigi: I think numbers play a role because I think when you see numbers I think instantly it will be maths, your first like instinct is that it’s maths. … Bob: I’m not sure it’s a good question [what makes something maths?] it’s not necessarily numbers or shapes that make something maths it’s the way you have to work it out that allows it to be maths. You have to think in a similar way as you do in maths, or you think differently to subjects such as like science. (Shelley school, mixed focus group)
Maths as numbers or a way of thinking Johnny: It’s, no because, you don’t have to add up or divide or, equations. Jenny: Yeah you’re not working, well you are working something out, but. Johnny: I don’t think it’s maths. Nathan: But it’s problem solving and that’s maths. Johnny: Yeah but there’s like a formula for moving a little thing round a block … We did four pieces of coursework on it so … Sliding puzzles. … Johnny: There’s no formula, no way of doing it, it’s just a random thing. Nathan: Have you tried to make a formula? Johnny: There isn’t a formula, otherwise people wouldn’t be so (brilliant). Artemus: What’s the formula? N plus. (laughter) …
Johnny: It’s just not maths, to me it’s basically if you can see you can play it. Heather: But Naomi you definitely said straight off I don’t do it because I don’t do maths, so you definitely think it is maths. Naomi: It’s basically logic and, I can’t remember who, but someone told me that maths is logic but put into equations … So if that’s like logic then it’s basically you’ve got, some aspect of it is to do with maths but maybe not all of it is based around that actual subject of maths. If you know what I mean. Heather: So you’re talking about things which aren’t numbers, you’re talking about problem solving, you’re talking about logic. What about you, do you think it’s maths, or not? Katie: Yes. Heather: Yeah, you do, and that’s because of what? Katie: Numbers.
Heather: Numbers right. So if it didn’t have numbers, if it was like colours, instead of like one to nine, if it was like red, yellow, blue, green and stuff, or like letters maybe, A, B, C, D? Katie: That wouldn’t be maths right. … Johnny: See I don’t agree with that. Naomi: Yeah, but like, saying ‘oh yeah right I’m 13’ is that’s maths as well? … Artemus: Yeah like 13 years after they were born. Johnny: Yeah, I can see where you’re coming from there but that’s … that’s why I say that’s not maths because you couldn’t just change the numbers for something,because people associate numbers with maths, like she just did there. Naomi: She just straightaway, automatically thinks that 13 years is maths but like say that was like what you say, A, B, C, people would say it’s not maths. Nathan: But it is maths though because like you said we did the sliding puzzle, that wasn’t numbers. (St Joan’s School, mixed focus group)
Maths and other subjects: science Mathematicians have shorter hair than scientists (Shelley, all female); Einstein:“This is like really weird but I kind of think of Einstein even though he’s a scientist not a mathematician.” (St Joan’s, all female) “They have the same sort of personality, the same character and everything, but like scientists are always trying to figure out a world order and mathematicians are always trying to figure out something I suppose.” (St Joan’s, mixed) “I think maths is science. Because all those tests on there [Brainiac] are done through knowledge of maths somehow. If they’re blowing up, using two chemicals to blow up a caravan, which is what they do most of the time, they’ve got to get the amount of chemicals right.”(Franklin, all male) “It’s [maths] not physical, like chemistry, you can’t see it.” (Shelley, all male) “[Maths is] shapes but not graphs. I see graphs as science for some reason.” (St Joan’s, mixed)
Everyday vs. esoteric maths Ashley: I’ll start. I think a lot of it personally is a waste of time and a lot of it is, there’s no way that regardless of what job or what career you choose to go into after school there’s no way that you’re going to use half the stuff we learn in school. Gabs: Certainly no trigonometry you would never use that in normal life. Ashley: I know for a fact that my dad works with cars and my mum’s a hairdresser and they’ve never used any of that. My mum’s never come in and said ‘oh I had to do some algebra today’. Things like, you can see how they can be relevant, things like algebra when working with like how you make x, you can see how they’d be relevant. But like you said with trigonometry and stuff like that a lot of it is just pointless. And it’s hard as well, we shouldn't have to put that much effort and work into something if it’s that useless to us. (St Joan’s, mixed)
“You know when people say like ‘oh you’re never going to use maths in your life’. I always think, you know that advert about like, what is it, oh it’s for taxes or something and it says ‘oh I don’t do taxes’ and it shows all the things in the pub and there’s inflation and stuff and then they say well we don’t do taxes. And it reminds me of that. Coz like it’s being really naïve I think if you say your life doesn’t involve maths because it’s all around you all the time.” (St Joan’s, mixed) Johnny: Not sure optional subject, but I think. Nathan: Two top sets. Jenny: Yeah. Johnny: Yeah. A gay set (laughter) and a normal top set that want to learn. … Johnny: I don’t know, like we said about the people, mathematicians, they’ve got no life, nothing … I’d class them as gay. So that’s what I think. (St Joan’s, mixed)
Individual interviews Imagine the world a hundred years into the future… • What do you think the world is like? • Do people learn and do maths? • Would you like to live there? Why/Why not? Imagine a world where mathematicians appear on TV regularly… • What do you think this world is like? • What are the mathematicians like? • What do they do on TV? • Would you like to live there? Why/Why not?
Some thoughts… What is maths? is a long-contested question … Is there a potential role for popular culture as a Trojan horse for troubling absolute, objective, people-free conceptualisations of maths within the curriculum? c.f. Sarah Greenwald and Peter Appelbaum Is there a role for popular culture as a resource in developing different relationships with maths?
Barbara: Yeah, I think also because I, I’m sure this [sudoku] is good like into, good at introducing people to maths because I worked at a pub once and my chef, who is kind of you know like, stereotypical chef probably, so you wouldn’t expect him to be like, into maths, that’s just being, um, ah, what’s the word again? Prejudiced, yeah. Heather:Yeah. Barbara:But he was like really into sudoku. So I think if you like that then it kind of opens you up to other Abe:Things. Barbara:Yeah, like paths to other aspects of maths. (Franklin, all male)
Dominic: Before I came to like this meeting I just thought that maths was a like thing that has divide, times and plus and minus and all that stuff and that’s what I would say. Heather: And now you’ve changed your mind? Dominic: Yeah, it’s made a little bit of difference to what I understand. … Dominic: The question ‘what is maths’ I don’t think it will ever be answered because it just goes on and there are so many different things and I think you have to spend like at least I don’t know, more than a life time thinking about what maths is, I don’t think it’s possible to put it into like simple logic. (Shelley, mixed)