Teachers and pedagogy

							Key findings from the focus groups
We held 27 focus groups. 15 of these were with Year 11 school students and 12 with
undergraduates (mostly third years, but three were mixed second/third years, one
was with mixed third/fourth and one was with first years). The 15 focus groups with
Year 11 students were spread evenly across three schools – Franklin, a rural South
West comprehensive with a mainly white middle-class intake but a number of rural
poor, Shelley, a London comprehensive with a diverse intake in terms of social class
and ethnicity and Saint Joan’s, a comprehensive in a large town in the South West
with a mainly white intake but a mix of middle-class and working-class students. In
each school we did one all female focus group and one all male focus group and
three that were mixed. The school focus groups mostly had 5 or 6 people in, but one
had 4 and another had 7. The 12 focus groups with undergraduates were divided
into students pursuing maths degrees and those who were studying social sciences
or humanities subjects (these were mostly social science students but included a few
doing English). Of the six focus groups with maths students, three were held in two
different Russell Group universities with high RAE funding, and three were held in
two different post-1992 universities with no RAE funding. There was the same split
in the focus groups with social science and humanities students with half being held
in two different Russell Group universities and half in a single post-1992 university.
The undergraduate focus groups generally had between 3 and 6 participants
although one had only 2 people and 1 had only 1 (it really is very difficult to get
undergraduates to turn up to focus groups when you’re offering them only juice and
biscuits!). These latter are not really ‘focus groups’ as such but we have analysed
them here because we used the schedule for the focus groups to do them.
You can find the focus group schedule elsewhere on the website. We used this
schedule flexibly which meant that we sometimes didn’t cover everything with every
group and certainly didn’t cover everything to the same extent or in the same order
with each group, we tried to follow-up on what was important to them as well as on
what was important to us. Time was particularly constrained in Saint Joan’s where
the focus groups had to fit into a 50 minute lesson, after allowing for changeover
time this gave less scope for following up different threads than in the other schools
where we had an hour lesson slot and with the undergraduates where we were often
able to go a little over an hour when people were willing. You can find the analytic
framework for the focus groups elsewhere on the website. In the team, each of us
took responsibility for looking at two areas across the focus groups. Debbie looked at
teachers and pedagogy and at school/university maths, Heather looked at reasons for
choosing and/or liking maths and at what is maths? and Marie-Pierre looked at images of
mathematicians and at responses to particular texts. When we analysed we kept the data
with the focus group (we developed a two way grid to do this with the focus groups
going vertically and the themes horizontally) since each group had its own feel to it
and we saw the groups as spaces in which participants were engaged in speaking
identities into being and in negotiating and contesting meanings and we wanted our
analysis of mathematics and popular culture to be embedded within these processes.
Finally this is a working document. Although the project is over we are all still
thinking about what the participants said to us, about how to make sense of it and
about how to connect the focus group data with the survey, texts and interviews.
Teachers and pedagogy
Our schedule for the focus groups did not include any specific questions about
teachers or teaching/pedagogy. However, as can be seen below, this was a topic that
exercised many of the focus groups, particularly in the schools. Our participants had
many strong views of what constituted good and bad teaching and, along with more
widely dispersed images on maths and mathematicians, their views and experiences
of teachers and pedagogies were deployed in the choices they made and were
making.

Year 11 focus groups
There was a strong theme that came out from the pupil focus groups that was about
their perceptions and experience of their teachers. School students were particularly
exercised when they felt that their teachers were unable to control the class. They felt
that it affected their ability to learn and that in disrupted classrooms they didn’t get
through much of the syllabus.

FG04: talking about disruption in class:

Annie: Yeah. I don't think the teachers have the right way of controlling the kids that
don’t like it coz we had a kid taken out of our class because the teacher couldn’t
control him. But he wasn’t actually that bad, they sometimes take things out of
proportion so like someone talks, ‘get outside now’. They need to control that. I
know the kids that got taken out of our class. I think he likes it because everyone
laughs when he does something funny. She encourages that, she tells him off and
then everyone laughs and so.
Debbie: He becomes the class clown.
Annie: Yeah, they need to stop that and deal with it in a different way because it’s
not working and it’s not getting any better. So that’s one thing with maths at this
school that they need to start looking at I think.
Susie: And once with us, our class was getting quite loud and our teacher like
couldn’t tell us off so she just went out the lesson and didn’t come back till the end.
And we just had the whiteboard on and the games and that’s all we did the whole
lesson.
Phoebe: Coz she couldn’t control it.

They stressed the importance of good explanation and the problems caused them
when explanation was inadequate and/or not understood and some recognition of
the difficulties of explaining. In relation to explanation and understanding, they
stressed the importance of doing (rather than copying) maths and talked about
teachers having to cater to different learning styles.

FG01; FG03; FG12: emphasis on ‘explaining’:

Madonna: If you’ve got it explained well, you know what to do and you wouldn’t
mind doing it.
John: And then when you, sometimes when you do ask for the bit of extra explaining
it doesn’t come to you for a while. As in like the teacher’s already got to go to, what,
three or four other people and then by the time they get to you you're meant to have
finished.

Firefly: Yes because it’s different to like English and, it’s more like a foreign language
because it really is quite stressful when you’re trying to explain some stuff, I imagine

Amelia: She explains it like really well and like when you can’t understand she
doesn’t go ‘oh I have said this 4 times’ or something. She will come over and help
you do it yourself and have a one on one with you.

In relation to explanation and understanding, they stressed the importance of doing
(rather than copying) maths and talked about teachers having to cater to different
learning styles. Some talked about group work and learning socially.

FG04; FG09: the role of ‘doing’ maths:

Annie: I think our teacher’s going in the right direction because she uses the
whiteboards a lot and she’ll occasionally play a game that will get us all interested.
But she does a lot of, she writes on the board and you copy it down and I know I do
not learn like that, I just copy it down and I don’t take any of it in. So they need to try
and accommodate for everyone’s style of learning a bit more because everyone learns
in a different way. But they only really go to the straight copy on the board because
some kids do learn that way but they need to broaden that.

Bubba: Sometimes when we’re in the class, she has this big whiteboard and we can
play games so make it more interactive and still you can be doing maths and be
interactive, because you still have to do things like times-ing and stuff, and so it
makes it more fun and plus people are learning at the same time

Another key point made, connected to learning styles, was that it was important for
the pupils and teachers to ‘fit’, to be suited to each other.

FG05: learning styles:

Bobby: I think it kind of depends on the way you learn and the way the teachers
teach.
Leslie: Yeah, yeah.
Bobby: Coz if you learn one way and the teacher’s teaching a different way it’s going
to be hard for you. Whereas a different teacher it could be suited more for you.

Some students expressed a strong desire for the maths they do at school to be
connected to ‘real life’ (see also, what is maths, below).
FG04: maths and ‘real life’:
Phoebe: I think they should explain, when you learn something new they should
explain why you should know this for every day life coz that makes kids want to
learn more because then they know like ‘I need to know this so I am going to make
myself concentrate and learn it.’
Having teachers they saw as ‘bad’ led to students expressing significant anxiety
about what the effect might be on their exam results.
FG05: exam anxiety:
Louise: Like, they [teachers] don’t really ever go over exam questions – and they
word things really weird and you get really confused.
Bobby: Mmm
Louise: And then you lose a mark.
Bobby: Yeah, we go, like, straight down the line, but, like, in maths they, like, some
of the question they, like, try to throw you off the mark so you don’t know what
you’re doing.
Louise: They kind of give you, they say right this is algebra and that’s how you do it
– and then it’s worded different into an exam so then you are like ‘well actually I
don’t know what that means’ but really you do.
There was a strongly expressed need to be listened to and heard and this is linked to
anxiety and ‘explaining’, and perhaps to the desire for understanding so commonly
found in maths. Being listened to was opposed to being shouted at and being afraid
to ask for fear of feeling stupid.

FG15; FG07: the need to be heard:

Wilbert: I think if the teacher also has a bad attitude and if they’re generally like
grumpy all the time, do you know what I mean, if they’re snappy and stuff like that.
I think really we are going to go in there with the wrong state of mind, and that is not
very, and they come across to us as a not very nice person really. So we’re not going
to want to go.
Cameron: The teacher always says ‘don’t worry you’ll get it.’ and she’s like ‘Do you
need to go through it again?’ and she’s really nice about it and our other teacher was
like ‘why don’t you understand? it’s not hard’.
Amajeutia: Or ‘You’re not listening.

Heather: Yeah. So what makes you scared to ask your teacher? That’s quite
interesting.
Ariel: It’s coz it’s like the easiest question but when I don’t understand it, it’s like I’m
stupid or something. < And I’m scared to ask coz they’ll be like ‘dur’ coz I don’t
understand it, so (inaudible).
Heather: Right. So, how do you cope with that?
Ariel: Get frustrated! Yeah

There are questions to be asked about how much of this is specific to maths?
Throughout the focus groups, students made comparisons between subjects – though
this is clearer in the undergraduate focus groups (see below).

Undergraduate focus groups
It was interesting to note that the students in the groups of maths undergraduate
groups spoke little about their teachers (especially their school teachers) but there
was a strong presence of teachers in the talk of the social science/humanities
undergraduates. In these latter groups, the talk of maths teachers was often in the
form of ‘horror stories’ about terrible maths teachers who could, perhaps, be held
responsible for the students’ decision not to continue with maths. This may be partly
an artefact of the situation, in that they knew that they were in a focus group
specifically of students who had dropped maths.

FG26: bad teachers:

Erik: Our maths teacher was like an automaton, he just sat there and he’d bark at
people if they spoke. He was generally quite monotone. And one of our science
teachers when we did sex ed, he was just so nervous he’d start flapping and going
bright red. So that was quite animated.
Jeff: Our maths teacher at middle school used to chuck our maths book at us. You
hand them in for homework, he gives them back at the beginning of the next class.
He’s throwing them at our heads, make sure we’re awake.
Erik: We used to get smacked on the head with ours, actually.
<
Louise: Our teacher would go around the class, and he’d be handing the books back,
and he’d give it to you, and if you were talking whilst he was handing the books, or
trying to tell you what you got, he’d hit you on the head with it. ‘Take you maths
book, look at it, you need to learn from your mistakes, all those mistakes in your
book.’
Debbie: So kind of humiliating, trying to. Did they successfully? Did you feel
humiliated?
Louise: Not really, I just thought, ‚Okay, right.‛ I didn’t really value maths enough
to be upset if I got something wrong, I’d be like ‚Okay.‛ I think it’s sort of, by the
end of year 11, we just saw maths as a doss subject. Okay, we’ll try and pass the
exam but we don’t really care about what class is like, we’d just play noughts and
crosses in our books and games, and get on with the questions at the same time.
<
Jeff: Unless you’re either really driven to learn or you’re in one of the higher sets
where people, sort of, okay at it so there’s not much disruption – it can get very
difficult,
Louise: Although having said that, in the top classes, I found that I was in the top
classes but sort of at the bottom of the class if you know what I mean. And when you
get to that stage, the teachers only really give a crap about the top five students and I
never got any help. My dad had to teach me at home because the teacher would
ignore me.

However, there were also undergraduates who had good experiences of school
maths but had chosen not to go on with it.

FG27: good teachers:

Clare: And I had a young woman and she was young and she used to talk to us
about football and rugby and we used to think she was so nice.
Beth: Yeah
Clare: Because she was younger and you know, and I think her maths lesson went so
much better than the other teacher I used to have. She was just chatting, getting the
message across but in like a really good way
School maths/university maths
We asked the participants how they felt about maths, whether they were still doing it
as school or university students or had given it up and were now studying social
sciences or humanities.
Maths students in the Russell Group universities often stressed the difficulty of the
transition from school maths to university maths and, in particular, the difficulty in
proving results rather than just reproducing them.

FG22; FG24: proof in university maths:

Bridget: It’s a different emphasis I think. Like university maths there’s an emphasis
on proving stuff. School maths there’s an emphasis on methods of how to work stuff
out.
Babs: Like school maths was just working through questions and there’s not really
that much, like I think that’s one of the differences between uni maths and school
maths is school maths is like simple stages. You do a question and it would be like
just one bit of, whereas with the university question it will be, you have lots and lots
of stages which aren’t obvious and aren’t pointed out to you, so you have to really
think it through yourself. I think with something like coursework it’s introducing
you to that kind of side of things a bit more. You have to really think about it and
think for yourself a bit more

Pseudonym : I think I actually find it kind of liberating the fact that we just started
doing proof, and just proof, as opposed to sort of learning to integrate really
complicated things for no apparent reason. And that was a big difference. I think
people don’t realise somehow you’re going to have to prove things, really. You can
get through, I think, most of even A level, without necessarily doing anything a
consequence.
Moses: Yeah, knowing why things are true but it’s like, teacher’s stated it’s true so
you just assume it’s true.

Many of our participants compared themselves (often unfavourably) to others. In
making these comparisons they (nearly) always see themselves as worse at maths
than others.

FG01; FG05; FG14: school students compare themselves to siblings and/or classmates

John: One of them’s in year 9 at the moment and I’ll see her doing her homework and
I’ll look at a problem, say I’ll remember I had to do in year 9 and I’ll just say ‘oh
Vicky, I did that, it took me about half an hour’ and she’s done it in five minutes and
I'm just like (growling noise)

Louise: My sister is younger and she does them. She has like a big book. And she is
probably better at maths than I am
Raoul: I am probably stupid, so I don’t really care *laughs+. I’m probably the smartest
kid in my family as well, and I’m pretty stupid so.
Leslie: The thing is, I think I’ll give up on maths in the end. The last thing because,
my sisters are like well cleverer than me and they both gave up maths in the second
year of 6th form. So I thought, oh my god, never going to be able to do this

Jenny: No, I’m just, prime example, Jane, she’s brilliant at maths but it all comes
naturally to her, she doesn’t really have to work at it to get it. < Whereas other
people, I know I have to work at it, I’m not good at maths but I, if I work, I can get
there


FG22: maths undergraduates comparing themselves unfavourably with others:

Zara: Because I’m still studying and when I come to a problem, can’t do it for a long
time and they can just see things straight away and see the links between things
straight away so I think they would be more mathematical than me

This may be related to the hierarchical nature of maths itself and also to cultures of
maths in which hierarchies are often established. One notable point was that many,
particularly the undergraduates, believed that people have a ‘maths ceiling’ beyond
which they can’t achieve. This can come at the end of primary school, around GCSE
time, during or at the end of a first degree, or even beyond. It can be used to explain
why some individuals or whole classes do not achieve more.

FG23: maths ceilings:

Sky (sociology student): Yeah I found it alright at GCSE I didn't find it too difficult, I
mean there were bits that I struggled with. The times I didn't like it were the times
when I felt it was pointless. A lot of it seemed like you were never going to actually
apply it to anything useful. But, no, um < And it could be quite satisfying because
unlike things like sociology if you get maths homework you work your way through
it and you do it and then it is finished, it’s like exercises, and there is a satisfaction to
that. < but when I go onto AS Level, I think people a sort of glass ceiling with maths,
and I sort of met mine with AS and suddenly I couldn't do it anymore and then I felt
like my mind didn't work in that way anymore.

Being good and liking maths may be embarrassing, especially since it is often defined
as being geeky. However, some like it nonetheless or come to like it.

FG02; FG18: liking maths:

Magdalene: [I like maths but] It’s really random and I’m really normal. Yeah.

Dave (maths undergraduate): I didn’t *like maths+ when I was younger. Now I’ve got
a degree in it, I don’t know, it’s nice because it’s something that’s quite difficult and
you feel like when you’re working you get something out of it but it’s also, there is a
lot of work behind it and it doesn’t always carry the status of other subjects. I think
you can feel a bit of a, plonker

As in the example of Davie, above, maths is often seen as requiring hard work and
this may be seen as a ‘good thing’ but it may also be seen as problematic – especially
among the school students, worried about the balance between maths and other
subjects.

FG5; FG07: maths is hard work:

Leslie: I reckon you need to give up some free time as well for Maths because unlike
other subjects, you just learn them in class and other people learn them in class, and
not many people go home and have tutors for science or, like, art or something, it’s
just a thing you learn. Well for maths you have to understand it and people work at
different levels, especially maths coz like, you have a different level of understanding
and most people do have maths tutors that I’ve spoken to. After school time.
Bobby: Yeah. Most people that I’ve spoken to, if they’ve got a tutor it’s a maths tutor.
I don’t know anyone else with any other tutors

Baros: I like maths but it means hard work and also you need to do maths you need
it for your future as well. < It’s one of the important subjects and I like it but it’s
kind of hard

Maths undergraduates also talked about how much work they had to put in to being
good at maths and some of the social science undergraduates also commented on
this.

FG19; FG22: maths is hard work:

Laura (social science undergraduate): Like my brother’s girlfriend, she pursued her
life as maths, maths, maths, and she’s really clever. *Laughter+ And she’s very hard
working. I don’t think I could do that.

Bridget (maths undergraduate): People just don’t realise that you’ve got to spend
hours and hours thinking about it and eventually it comes and that’s why it’s great.

For some of the social sciences/humanities undergraduates there was an
embarrassment around not being able to do maths, that relates to a desire for
‘basic’/’everyday’ maths.

FG21: maths as embarrassing:

Sam: It’s a lot, like even very basic questions about the algebra and stuff, and I just
don’t get it. It doesn’t work.
Ivana: Embarrassing because people expect you to know. Because you do maths at
school and if you don’t know how to work out 10%. I mean, to someone who gets it,
it’s basic, right. It’s something you get or you don’t get to me. I always I work in
Virgin and we’re always having sales all the time, and I have to teach people how to
work out the sums like. They even don’t know how to work out 10%. What I always
thought, 10% of something, you just divide by this, times by this, move the decimal
place.
Alex: That confuses me so much.
Ivana: And I understand it, but these kids will be like, ‘Oh, times that by two.’ And
they’ll have a real problem. Not me, I mean I wasn’t in the higher group at maths,
but I kind of cheating, because I never, ever learned my times table. Even now, I have
to go through it kind of in my head. Or a calculator or something, because you’re
expected to know or learn.
Particularly for the school students, there was a blurring between liking (or not
liking) maths and liking (or not liking) their teachers

FG06: blurring between liking maths and liking teachers:

Luigi : Yeah I used to hate maths but now I quite enjoy it, I quite enjoy doing the
subject, I find it is quite interesting.
Heather: So what changed your views?
Luigi: A teacher I just got kind of influenced more, because of the way that teacher
teaches, it made me more confident in maths.

For some students, the satisfaction of maths came from the fact that it was either
right or wrong, while for others this was what they did not like about it.

FG07; FG09; FG19: right and wrong answers:

Pisces: Yeah I enjoy maths because, basically because there’s always one answer it’s
not like in English where you have to be creative. You just, you can just plough your
way through it and then get down to do it in the end.
Heather: Right.
Eggbert: The same I enjoy maths because I find it quite satisfying when you get an
answer it’s like after long calculations then you get the right answer.

Jane: Quite hard. I find it quite difficult but then when you understand it and when
you get it right it’s really satisfying, like when you get the actual answer and you
realise that you actually really kind of realise that you know what you’re doing.

Laura: I liked it because it was in, there was a set way of doing it – there was only
one way and there’s one correct answer. And I found it very easy to remember. So I
guess you’ve learnt I was alright at it, I liked it. I liked it because it was in, there was
a set way of doing it – there was only one way and there’s one correct answer. And I
found it very easy to remember. So I guess you’ve learnt I was alright at it, I liked it.
<
Samantha: Also, I think, maths was considered as very boring. Like, coz, although,
you know, like I said it’s really creative, because it kind of inspires your mind – well
a lot of people thought of that as too much hard work. And it was like, it was just,
they just saw it as boring, you know. ‘Oh right, I just thought it was boring,’
obviously because I didn’t understand but I think that’s one of the reasons, because
to me, stuff like art – I did art as a GCSE and that was creative to me. But maths,
where there was only one way to do one equation, and if you didn’t understand it,
you don’t know what you’re doing. It just seemed uncomfortable.

The most common reason given for liking maths, was that one found it easy and
clear, though other influences, such as parental attitudes also came into the frame. If
you were good at it, you were likely to like it and if you weren’t you wouldn’t!

FG5; FG15: other reasons:
Raoul Just don’t like it, I don’t know why, I don’t enjoy doing it. Probably because I
am not good at it or something like that.

Cameron: It’s nice like when you work something out and you are just like ‘oh I get it
now’ and it all just kind of clicks. < On the other hand someone can grow up and
think ‘I like doing that, I enjoy it.’ I don’t know? So if your parents like it then you
will be kind of more surrounded by it

For some of the school students and, particularly for the social science/humanities
undergraduates, and even for some of the maths undergraduates who came to maths
as mature students, there were some strong, often painful feelings associated with
learning the subject

FG19: maths and pain:

Saba: I hated it. I straight up hated it, because it used to do my head in. Like, to a
point, up until year 9, we had, we didn’t actually learn anything off the teacher.
There was worksheets that we had to do up until year 9 and then they introduced
textbooks, and that was in year 10. And it was just like, algebra just got on my nerves
really. And maybe that’s what (turned me off), I don’t like to think too much. Maybe,
I don’t know. I was in the higher group and then, I kept begging my teachers to let
me go down because I never understood a word that he said. But he never let me
change groups. So I thought I didn’t have enough to be in that group, then to learn
more, if you get what I’m saying. I couldn’t, I didn’t even know the basics in that
group about algebra – I knew it, but I just didn’t think I knew it well enough. I just,
the whole experience, I didn’t like it.

The question of ‘relevance’ and ‘irrelevance’ came up time and again. It seemed that
what was seen as maths (see what is maths below), particularly at school level and
by social science/humanities undergraduates was number and ‘basic maths’.

Relationship to research questions
Teachers and experiences of school and university maths were not part of our
original research questions. However, their strong appearance in the data has made
us reflect on:
      The relationship between ‘school maths’ and ‘popular maths’ as resources or
       building a relationship with the subject.
      The relationship between maths teachers and images of people doing maths
       in the media in processes of identification.
      The similarities and distinctions in the discourses about maths and
       mathematicians re/produced in school maths and popular maths.
Reasons for choosing and/or liking maths
Enjoyment
The participants who spoke about enjoying maths drew on the following reasons:
understanding it/being able to do it; liking the certainty and/or universality of maths;
liking finding your own way/working things out/thinking; desire for control. Most of
those who spoke about enjoying maths did so ambiguously, for example: they would
like maths when they could do it and dislike it when they couldn’t; they would enjoy
some aspects of maths and not enjoy others. Unsurprisingly, mathematical pleasure
features in the talk of all the maths undergraduates but very few of the humanities
undergraduates. Many of the Year 11 students and the humanities undergraduates,
who do not enjoy maths, do talk enthusiastically of the pleasures of doing sudokus.

FG10: talking about liking maths:
Maya: I like the way the teacher teaches us how to do it coz it makes it easier to
understand and do.
<
Sarah: I like that there’s only one answer so it can only be right or wrong.
<
Candi: I’ve always quite liked maths and I’ve always been told I’m quite good at it
but I just, it’s like I know how to do things, and I understand them, but I can’t
necessarily tell someone else.
<
Jane: I find it quite difficult but then when you understand it and when you get it
right it’s really satisfying, like when you get the actual answer and you realise that
you actually really kind of realise that you know what you’re doing. < *I like it+ as
long as you just know what you’re doing.
<
Chloe: I really like maths. I think it’s really clever, it’s really an academic subject
really and I like the way that you have to actually find your own individual way
about figuring things out. People can explain but you always have to find your own
way which makes it easier for you < *academic because+ you have to think about
everything before you actually do it and it’s trial and error in everything you actually
do, so you’re constantly thinking.
<
Maria: I think maths is good but it depends on the teacher that you have coz like
some teachers that we’ve had before couldn’t explain it right so you can’t understand
but with the teacher that we have now he goes through it and (inaudible) it’s helping.

There is a complex relationship between liking maths and facility at it. For some
people these are interchangeable. In groups where it is discussed, there is an
acknowledgement that people can be good at maths but not enjoy it but the opposite
is seen as more problematic. As indicated in the key findings from the survey, this is
interesting area to explore and the possibility of understanding difficulty as
challenge might be important.

FG23: relating enjoyment from and facility at maths:
Robert: I tend to you agree with you that if you didn’t like it *maths+, it would drive
you nuts. < But then I’ve got a friend who’s in the same year as me and he really,
really loved maths and he did okay in his first year. And he really screwed up his
second year exams < but he was really sad because he really loved it and couldn’t
do it. Which I think is really odd.
Moses: I think sort of maybe you can enjoy it up to a certain point. Up to sort of
where you’re being challenged. But some people will just sort of, not like being
challenged and so they’ll, sort of, won’t enjoy it at all or anything, kind of.

Instrumental motivations
Many people discuss ‘instrumental’ for studying maths. These relate to: its role as a
critical filter giving access to opportunities with further and higher education and the
labour market; its role in securing financially lucrative employment; its role in high
stakes assessment (maths, English and science often held together as the ‘holy trinity’
of curriculum assessments). Participants also talked about needing maths for
everyday life, for example, for helping in family (in response to the gremlins adverts)
(but see later discussion of everyday vs. esoteric maths). Some groups supported the
importance of maths, while others (including both Year 11 students and humanities
undergraduates) were cynical about the status given to maths.

FG05: instrumental motivations for doing maths:

Bobby: I don’t see why it’s relevant for like most of the courses.
Raoul: It’s an excuse to make you do maths [laughter]. In a disguise.
<
Marie: Yeah because people are losing interest in maths and if you need like a C or
something in maths – for a course you want to do then you’re going to work for it,
aren’t you?
<
Bobby: I think a lot of people would just find – something else to do [chorus of
‘yeah’+. Because they just wouldn’t see the point of putting in the effort if they could
get on the course.
<
Leslie: But then again, seeing them adverts, you might not want your children to ask
you like that and you not know what it is.
Bobby: Yeah. But it would never happen in real life. I’ve never asked my Mum what
is this.
Leslie: Yeah. But surely one day you might. You never know what would happen.

Relationships: teachers and families
Teachers and teaching and classroom cultures came up very strongly in all but five of
the focus groups as a factor influencing whether people like maths. This is expected
given the close relationship, noted earlier, between enjoying maths and
understanding it and having facility at it, and the role of the teacher in making these
possible. The five focus groups where talk of teachers and teaching were absent were
all ones of maths undergraduates. However, in two of these groups (both in post-
1992 universities) taking a supportive/teaching role in relation to maths was part of
what they liked. Much of the material relevant here has been covered in detail in the
earlier section on teachers and pedagogy.
In a few cases, participants spoke of being brought up to like maths either in the
sense that they had been or that they had not but felt that this was important. Most of
the Chinese, African and Indian participants related this to a family culture tied to
their ethnicity; most found this positive but one spoke of it in terms of pressure. Five
others spoke of particular individual/s being influential, three talked about their
father and one about their father and their mother; one talked about being distanced
from their father because of his interest in maths.

FG04; FG24: Families and maths

Phoebe: Yeah, I personally, I enjoy maths because my dad brought me up to like do
maths because he was good at maths and he sort of like brought me up to do maths
and learn maths in everything we do. I mean when I was younger like going out
shopping or something. And that’s the way I’ve just learned it and so now I’m quite
good at it.

Aisha: Because often people stereotype like Chinese and Indian people as being like
really good at maths. They just assume that kind of thing. But it’s not – it does come,
like a certain amount of heritage I think. I think that like being from an Indian
culture, I think that does – in fact, all my family are mathematicians.
Debbie: Oh really?
Aisha: Like yeah. So I think it does encourage certain respect for the subject. More
than you do get in general in England. But I don’t necessarily think it’s a good
stereotype because I don’t like stereotypes.

Natural ability vs hard work.
There is a complex relationship between natural ability and hard work, with most
people supporting both the idea that you can get better at maths through hard work
and the idea that some people are naturally more able to do maths than others. Much
of the discussion of this occurs in the context of the clip from Good Will Hunting (and
other media examples) in terms of understanding Will’s motivations and of whether
people like this really exist (many peers and family members are mentioned in this
context). However, these discourses are tied not only to ones that circulate through
popular culture but also through school maths.

Stereotypes
There is quite a lot of discussion about the potential role of the popular culture
images in influencing people’s choices and feelings around maths. The discussions of
the gremlins adverts are relevant here (see later section).

FG07; FG03: popular culture influences:
Ariel had seen Stand and Deliver in her maths lesson: I thought it was good. Yeah, it
like encouraged more people in our class to think about maths and how they wanted
to pass their exams and it wasn’t just something that you sit around and do nothing.
<
Heather: Why did you want to do more afterwards?
Because all of the students were happy afterwards and you just saw them enjoying
themselves and they didn’t have to worry about anything.

Barbara: I love the idea of maths, like there’s some aspects of it but I don’t seem to
get on with it very well. I mean if I, it’s like watching a film with computer cracking
codes and things and it’s kind of like when you’re doing maths it’s kind of, I don’t
imagine this by the way but it could be like in a film.

Some representations appear to assume a particular importance for some people as
part of developing a positive relationship with maths. Thus popular culture is a
resource that people use, along with other resources, in making themselves.

FG17; FG18: the importance of particular representations:

Dave: Except for one [mathematician in film who is not a geek], the one that always
got me thinking about it when I was younger was Jurassic Park and it had Ian
Malcolm in that and he was like a cool mathematician and you’d never had a cool
mathematician before. < And he’s there and he comes up with all these crazy
theories about chaos and stuff and how everything is going to happen and it does, it
comes up but I mean the guy himself he’s done a lot of other stuff and he’s kind of a
cool character and he gets away with it. He’s still a geek but he’s nowhere near as
bad as everybody else and he kind of, he gives a different image to it but he’s like
one out of the million ones that are just geeky old mathematicians.

Mr 37: I love Deal or No Deal. There’s, it’s, I suppose it’s the programme I engage with
most mathematically. I mean it used to be Countdown in the early days, the numbers
game but now it’s Deal or No Deal and it’s about chance and probability. I suppose it’s
the gambler in me as well that likes it as well. But I’ve always been very fascinated
by randomness and probability. < There was one show that had a bookmaker on
and he was, he was the only person I’ve actually heard make some sort of sensible
statements about what’s going on because I think if there’s something like 11
numbers left, there’s a 50/50 chance of keeping the top two. He said. < And the other
nice thing is when you second guess what the banker is going to offer, to try to work
out what the algorithm is that he uses to guide him. So that’s all, I’ve really enjoyed
watching that show. *That’s interesting coz I know when we show it to some of the
school children they say things like, ‘’that’s not maths’. And then one of them might
think it’s got a little bit of probability in but it’s interesting when you know some
maths, you’re looking at it in a different way.+ It’s not presented in a mathematical
way, that’s the, my bugbear about it really. It’s presented, as really some sort of
psychic game and correct decisions are proven by the outcomes. You made a bad
decision because the prize wasn’t in the box. You know and so much, it’s very
counter intuitive, especially if you try and argue that that was the right decision,
even though it didn’t turn out right.

As discussed later, there is much awareness of and negotiation around geek
stereotypes. In many groups, participants consider whether a desire to avoid being
associated with this image would affect people’s decisions about whether to study
maths and whether the media has a role here. In the context of the Good Will Hunting
clip there are discussions of why people might want to avoid being seen as clever.
Identity work is being carried out within these discussions as people position
themselves and others. Particularly among the humanities students, there is talk of
not being a maths person and binary oppositions are strongly mobilised here.
However, this is perhaps because we are asking them why they are not doing maths
and so are putting something positive in their replies. The idea of being a maths
person relates to ideas of ‘natural ability’ and to the way some participants talk about
Will Hunting embodying and standing up for maths in the clip.

FG03; FG04: geeks and popular culture

Aby: It’s not to the extreme where people won’t, people that do enjoy maths will
deny that they enjoy maths kind of thing coz, you know, like we’ve all said that we
enjoy maths but.‛ Later, Magdalene: ‚I think like the dad [in gremlins ad] who
would be helping his daughter with her homework, I think he felt like a bit
embarrassed because he probably didn’t pay attention at school because of like the
stereotypical view of it.

Annie: Mathematicians in the media and stuff you never hear about them you just
don’t hear about them and I think that needs to be addressed as well because I think
kids get the wrong image from it and things like that.
<
Annie: If you look in films and TV series like Saved by the bell and stuff you don’t see
geeky girls.
Phoebe: That is true but there is very many, there’s quite a lot of geeky girls. But
they, in lessons they just do their work, they don’t speak to, they don’t socialise.

Relationship to research questions
      Choice in relation to maths is one of our research questions, so the role of
       popular culture in the mix of factors is important.
      Ideas of gender, class and ethnicity play out here, particularly in relation to
       the role of families and in whose bodies can be read as naturally able.
Images of mathematicians
Gender/class/ethnicity
Mathematicians are overwhelmingly constructed as white, heterosexual, middle-
class men, although such associations are often implicit (for example when students
refer to mathematicians wearing a tie). Students tend to cling to the clichés, though at
the same time they are also aware these are clichés, maybe due to the lack of
alternative constructions of mathematicians available to them By default they refer to
these clichés, unless they have somebody they know which do not fit these clichés
(often a relative or a teacher; for example, Nicole, Year 11, has a fantasy about her
female maths teacher taking over the world ‘with maths’).

FG15: on the awareness of clichés:

Wilbert: Well you always see it on telly as well and it’s hard to get it out of, I don’t
know. If you have always seen it on the telly you haven’t seen anything else of what
that person or what that thing is then you’re going to think that when you think of it.

There was a strong association between doing or being good at maths, masculinity,
and higher forms of intelligence, as well as between higher forms of intelligence and
middle/upper-classness. Men were sometimes seen as doing better at maths, and
women as doing better at English/humanities, with maths being seen as a higher
form of intelligence and these differences often being essentialised. In one particular
focus group of maths undergraduates, participants tended to sub-divide maths
specialisms between the ones which were ‘female’ and the ones which were ‘male’.

FG11; FG03: on the implicit association between maths and gender:

Researcher: What are they wearing these mathematicians?
Jesus: Suits.
Chantz: Shirt and tie.
Ashley: Gotta be a shirt hasn’t it?

Action Man: That’s my kind of image, a character like Einstein. < Steven Hawking is
an incredibly clever, isn’t he?

It was difficult to get students to talk in an explicit way of the influence of social class
and ethnicity on being good at maths. There is also sometimes a strong denial of the
influence of ethnicity, and to a less extent of gender and social class. Although they
are rarely explicit about social class, they do refer to it in their own ways (for
example using terms seen as more politically correct; referring to one of the adverts
we showed to the focus group participants, some mentioned the ‘chav dad’ or the
‘council estate dad’ for example; others talked about ‘posh’ people).
In some cases, students operate a hierarchy on the scale of ‘poshness’, between their
maths teacher and ‘mathematicians’, the later being seen as posher and with higher
forms of intelligence (though also geekier, as discussed below); this is part of a
construction of mathematicians as an elite, both in relation to intellectual and
economic capital. In the schools attracting students from a working-class background
(Shelley and Saint Joan’s), this led to binary oppositions between ‘us’ and ‘them’.

FG10: on the association between maths, middle-classness and ‘higher’ forms of
intelligence:

Maya: Yeah, I think they’re quite middle-class. It depends actually, in the, not in this
school.
Candi: Because I reckon, you know, to kind of gain that, very kind of level, that level
of intelligence you’d have to go to university. I imagine it coming quite easily to
them being brought up in a kind of good family.

Embodiment
Students have very precise ideas of what mathematicians look like, although, again,
they challenge these clichés. In one of the focus groups with Year 11 students, this
was reflected in a discussion about differences in hair length between
mathematicians and scientists (the former having short hair, the latter long hair). This
embodiment is so strong that in some cases students believe that you say from
somebody whether s/he is a mathematician or not, just from the way s/he looks. The
strong embodiment of mathematics is seen as nearly unavoidable. In one case, one
undergraduate sociology student referred to her friend she called the ‘maths geek’
who had a Pi symbol tattooed on his wrist. This is linked to the way so many
participants saw mathematicians as likely to have some form of mental health issues.

FG10: on the embodiment of mathematics:

Heather: OK, the next question is to imagine a mathematician and I want you to tell
me what comes into your head when I say that.
[laughter then all talking together] Jane: Nerdy. Maya: Scrawny.
Candi: Old man with wild, white, hair.
Some: Yeah.
Maya: That sounds like a scientist.
Candi: Yeah, that’s science.
Researcher: That’s interesting, isn’t it?
[all talk together, someone says that mathematicians have really short hair]
Jane: Glasses.
Heather: So you have these differences, so mathematicians have shorter hair than
scientists?
All: Yeah.
Maria: Scientists have crazy hair.
Heather: Like the Einstein pictures.
Maya: High top hair. [laughter]
Heather: And you were saying something about quite lanky? [all giggle]
Maria: Quite small with glasses.
Maya: Scrawny.
?: Skinny, yeah.
As noted above, references to the body are often implicitly references to the body of
an old white man.

Personality/nerd/geek/lifestyle
Mathematicians are overwhelmingly seen as being ‘nerdy’ or ‘geeky’, even in many
cases by maths undergraduates (who sometimes attempted to redefine those terms in
a positive light), in opposition to being ‘cool’. As a consequence, students being good
at maths had to do a lot of ‘identity work’ to negotiate it and avoid being labelled as
‘not cool’.
Some think mathematicians can have ‘normal’ lives, some not. However, the sole fact
that students need to state that mathematicians can have ‘normal’ lives suggests this
is far from being obvious. However, many believe that their lifestyle is dominated by
mathematics, as they are obsessed with mathematics (a common comment is that
when they don’t work, they do sudokus).
As for their body, students have a very precise idea of mathematicians’ personality,
and see them as nervous, hyperactive and socially awkward.

FG05: on mathematicians’ lifestyle as reflecting their obsession with maths:

Leslie: Working endlessly at a desk trying to work out a formula or something. I
dunno.
Heather: So they kind of never do anything else?
Bobby: Probably not.
Leslie: Yeah.
Heather: Right. Coz my next question was going to be what else do these people do,
do they have families and friends. What do they do in their spare time? But they
don’t have any spare time?
Bobby: No.
Louise: Yeah, their spare time is doing extra maths questions.
Bobby: Dedicated to what they do.

Relationships
Following on from the last section, mathematicians are seen as leading lonely life.
Their relationships are permeated by maths and they only relate with people who
share their interests (for example, some of the humanities students described the
maths students as a different ‘tribe’). However, some think that they have ‘normal’
relationships/lives, mostly in the context of maths teachers who perhaps are not
perceived as ‘proper’ mathematicians.

FG11; FG10: on mathematicians and their families:

Debbie: Do they have families?
Chantz: No because they don't get out at all they’re just sitting at home thinking
about maths. [laughter]
Ashley: They do have families but they’re quite well off do you know what I mean
they are not the sort of families like the rest of us working with budgets.

Heather: Do they have families, do they have?
Maya: Yeah, big families.
Jane: And all their kids are like that. [all laugh) [Shelley]

Genius
Mathematicians were overwhelmingly constructed as geniuses. The figure of the
mathematical genius is constructed in opposition to those using maths, e.g. civil
engineer.
Many adhere to the idea that there is something called the ‘mathematical mind’.
There is a recurrent contradiction between natural ability and being able to get better
at mathematics through effort, and a recurrent opposition between being a hard
worker and being naturally able (this is also discussed in the section on reasons for
choosing and/or liking maths).
FG03: on maths geniuses:
Barbara: Well. There are real people who are.
Abe: Absolute geniuses that.
Barbara: Well it’s like that guy who got the thing [Fields medal].
<
Action Man: But you don’t imagine people who build bridges, like civil engineers,
you don’t imagine them to be geniuses but they still do maths.
Barbara: They’re genius in their field.
Firefly: Yeah, there’s different types of maths, there’s like genius maths, which is
working out these equations and winning big prizes.

Relationship to research questions
       People have very strong images of mathematicians which although they often
        don’t link these directly to popular culture clearly draw on some of the same
        tropes common there of geekiness, madness and social awkardness (see the
        powerpoint presentation from the Gender and Education and Gender Work
        and Organisation conference for further development of these ideas).
       Ideas of gender, class and ethnicity play out strongly in these images, and
        usually implicitly.
Responses to particular representations
We showed the participants 4 clips (descriptions are contained in focus group
schedule) and also examples of sudokus. Much of what participants said about these
clips overlaps with other areas e.g. the comments on Stand and Deliver relate to
teacher and teaching so here we have recorded only brief bullet points on how the
texts were ‘read’.
Texts other than those we showed them came up in the focus groups and these are
listed in the texts page of this website.

Stand and deliver
      Most of the discussion focuses on the teacher and his pedagogy, the apple
       and the knife; the contextualisation of maths is seen as positive.
      Some didn’t like the teacher’s look and style (sinister, weird, a bully) and
       some commented on him not looking like a/their regular teacher.
      Many liked the fact that he controlled the class.
      Only one person picked up on the teachers’ sexual comment.
      Several groups discussed the stereotypes in the film and the fact that you can
       guess who the students good at maths are in the group from their look or
       their answers.

FG26; FG17: on guessing which students good at maths from looks/answers:

Erik: It was often sort of perfect school uniform. Like the little girl at the back who,
that got her apple, she had really immaculate school uniform and big glasses. And
you could spot the other mathematicians apart from the teacher as well, with the
really big glasses. < Acne scars as well, hasn’t he.

Alice: I think it just shows who has got mathematician’s mind you know like in
whole class, you know some people, some students look at an apple and say that’s an
apple and some of them (inaudible) and the girls say ah, you know, there’s 25%
missing you know. This is how mathematician < This is how maths brain works.

Good Will Hunting
      Many students misunderstood what the clip was about.
      This clip led to numerous discussions about Will Hunting not fitting the
       stereotype of the mathematician (especially in terms of social class and age)
       and about natural mathematical abilities.
      Some mentioned how important it is that media representations break the
       usual stereotypes of mathematicians.
      There were numerous discussions about whether the story was realistic; the
       idea that some people have a ‘mathematical mind’ was used to explain Will
       being a janitor and being good at maths.
      Some saw him as friendly and some saw him as rude, aggressive (range from
       naughty school boy to working class hero).

FG04; FG05: on not fitting the stereotype:
Annie: I’m surprised. But I liked it because he’s quite a big name and obviously you
can tell he’s good at maths by the things that he’s just scribbled on the board and he’s
a good looking guy so it goes against the image. And also he’s been punched in the
lip or something.
Debbie: He’s been in a fight.
Annie: So it makes you think: ‘oh right, a bit you know, he gets in fights and things.’
<
Phoebe: Yeah it shows that people who are smart at maths don’t have to be the geeky
type. They can be the Matt Damon type. So it puts the point across that you don’t
have to be all geeky to be good at maths.
Bobby: I think, I think it’s coz obviously people wouldn’t usually associate just a
cleaner with a mathematician.
Louise: Yeah. People, like, because if they had actually done in well they wouldn’t be
a cleaner would they?
Bobby: Yeah, but he obviously is.

Gremlins
      Overall, the students quite liked the second clip which featured a woman and
       showed maths as an achievement, but were less keen in the second clip
       showing a father unable to help his daughter with her maths schoolwork and
       feeling shameful and embarrassed as it was seen as not motivational and/or
       patronising.
      However, some related to the first ‘bad dad’ advert and to the father’s sense
       of shame.
      There were some disagreements about the idea suggested in the second
       advert that you need maths to do most jobs.
      These two clips were often read from a class and gender perspective,
       although using different wording (e.g. speaking of the ‘chav dad’ instead of
       the working-class dad).

FG09: on the second clip being patronising:

L. Ron: I think this Gremlins advert, if I wasn’t very good at maths, I think that
would make me feel worse if I saw that. If I can’t help my children. It’s not very
motivational; I just think it would be really depressing.
Godwin: It’s really patronizing.
Right. Why is it patronizing?
Godwin: They treat you like a child. ‘Oh you have these little gremlins - if you are
not good at’.

FG20: On the ‘chav dad’ in the second clip:

Elisha: And the Gremlins advert showed a dad more like a rough kind of, you know,
really Cockney, you know, ‘Get your mum to help’ [said with assumed Cockney
accent], kind of thing. Oh you’ve had a poor, it’s kind of life, oh, he’s obviously had a
poor education that’s why he doesn’t know how to do maths. < that’s like a Chav
dad. You know, a council estate dad that you know his English for instance.
Deal or No Deal
       There was lots of discussion about the mathematical or non mathematical
        nature of the game. Of those who related it to maths, some talked about the
        probability involved for the contestant, some mentioned that calculating the
        banker’s offer involved maths and some suggested it is mathematical because
        it involves numbers.
       Of those who thought it wasn’t mathematical, most saw it as just luck, but
        were resentful as the contestant wins by doing nothing.
       Some people watched hoping to see people win, others to see people lose.
       One maths undergraduate watched this from a mathematical perspective.

FG04; FG17: on watching Deal or No Deal

Matsui: Well, I just don’t like any of it. It’s lame. I don’t like the guy, I don’t like the
phonecalls, I just don’t like the concept of the game. I prefer say game shows where
people might actually do something to earn what they’re paid for like Who Wants to
be a Millionaire?
Debbie: Yeah, where they’ve got to answer the questions.
Matsui: Coz that’s sort of a reward then.

Mr 37: I love Deal or No Deal. There’s, it’s, I suppose it’s the programme I engage with
most mathematically. I mean it used to be Countdown in the early days, the numbers
game but now it’s Deal or No Deal and it’s about chance and probability. I suppose it’s
the gambler in me as well that likes it as well. But I’ve always been very fascinated
by randomness and probability. < And the other nice thing is when you second
guess what the banker is going to offer, to try to work out what the algorithm is that
he uses to guide him. So that’s all, I’ve really enjoyed watching that show. (see
reasons for choosing and /or liking maths for a longer version of this quote)

Sudokus
       There were some intense discussions, usually full of contradictions between
        and within people’s talk, about whether sudokus involved maths. Opinions
        often shifted very quickly due to peer pressure and in response to rational
        arguments from others (there is more detail on this in the what is maths
        section).
       Some saw it as part of school maths as parents and teachers want them to do
        it as they see it as good for their mathematical skills.
       Many did sudokus, although they often only admitted to doing it when there
        was no alternative (on public transport or out of boredom).
       Feelings of pleasure and frustration were both expressed.
       For some, this was an occupation associated with older people.

FG10: on whether sudokus are maths (and the influence of the group dynamic):
Candi: I think it’s more of a logical thing, you have to think about where you’re
(inaudible) and that’s generally quite a nice part of maths, I wouldn’t say it was
necessarily just definitely maths coz there’s loads of other things involved but I think
that as long as the technique and stuff that you use are the same it’s going to be the
same kind of subject.
Right, so it’s the technique that makes it maths rather than the numbers?
Candi: Yes.
Maria: Now I’m confused, it probably is I’m probably telling you the wrong like.
There isn’t a right or wrong like some mathematicians even say it is and some say it’s
not, so.
Maria: Dunno.
Jane: I don’t know, it’s very, I don’t know. *she sighs, all laugh]
Maria: It’s just confusing to even think like it’s maths or not.
Jane: More confusing than the games, it’s a game, yeah it’s a game.

Relationship to research questions
      ‘Reading’ texts is a complex, contested and contextualised process and the
       meaning of ‘texts’ cannot be decided outside of these ‘readings’.
      People’s own positioning in relation to maths are central to their readings of
       these texts.
      Our data are suggestive of the potential within popular cultural texts for
       opening up productive discussions about people’s ideas about maths and
       mathematicians and their own relationship with the subject.
What is maths?
Maths is numbers
There is a strong understanding among all but the maths undergraduates of maths as
numbers or doing something with them. This numbers/calculation definition of
maths is sometimes supplemented by other curriculum items such as pie charts and
algebra. There is a strong opposition between numbers and words/letters; for
example, no groups, where this comes up, can read cryptic crosswords as
mathematical. This stereotype maths is reproduced easily by all groups and is tied to
the discourses available in school maths and in pop culture maths. As with the
mathematician stereotype discussed earlier, participant talk is complex and
frequently shows a critical awareness about the problems with seeing maths as
numbers. Maths as calculation is one way of dealing with this, but generally there is
a lack of developed alternative understandings of maths to. There is often discussion
of the power of the connection between maths and numbers.

FG19: discussing sudoku:

Laura: But when people see it, they see it’s numbers, they’re like, ‘Because it’s
numbers.’ And you associate maths with numbers.

Saba would do sudokus if they used letters instead of numbers: ‚if it worked the
same way, if you had to do, you know, I would do that. < It would be maths, but I’d
choose to ignore the fact that it’s maths and just look at the letters. < As soon as I see
numbers, I don’t see anything.‛

Alternative ideas of maths
Often individuals within groups or whole focus groups put forward alternatives to
the idea of maths as number/calculation/school maths. These most often mobilise
ideas of maths as logic and ways of thinking; less often they mobilise ideas of maths
as problem solving and as about pattern. The discussions on what is maths are often
animated and involve a number of discursive shifts.

FG06: discussion of sudokus:

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. < 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.

Participants draw on a range of resources to support these ‘alternatives’ – maths
GCSE coursework (in one Year 11 and one maths undergraduate group); things
people have said (‘someone told me maths is <’ including teachers, parents and
friends); popular culture – particularly sudoku, gambling and sport (there are several
cases of people changing their views as a result of the focus group discussions on
sudokus); university maths (particularly the emphasis on proof). A question for
analysis would be to look in more detail at: Who can support an alternative
understanding of maths? And, how can they do this?
Many of the Year 11 students who have a positive relationship to maths (enjoying it,
wanting to carry on with it, feeling good at it) talk about it as more than numbers,
however, some do not, and some of those who have a less positive relationship with
maths do. The interview data should help with unpicking these differences.
The maths undergraduates each mobilise alternative versions of maths, perhaps
related to the mathematical cultures at their universities and the discourses available:
      Gillespie: FG16: maths as empathetic, strong notion about maths being about
       thoughts, understanding, everyday life; FG17: notion of maths related to art
       and ideas and as maths being more abstract and different from these.
      Charlton-Moore: FG18: problem solving as maths.
      Wollstonecraft: FG22: notion of maths as logical/analytical and not number
       work.
      Meitner: FG23/FG24: both groups joke about mathematicians being bad at
       mental arithmetic and support maths as logical and analytic skills, linked to
       problem solving and maths as everything, which is perhaps an attempt to
       colonise reality by mathematics (c.f. Ole Skovsmose’s discussion of the
       formatting power of maths).
As with the Year 11 students, there are many discursive shifts within their
discussions.

FG23: discussing what is maths:

Hannah: Well apparently like, mathematicians are even amazing in mental
arithmetic are absolutely atrocious. And people are always asking me to split the bill,
you know, when you go somewhere? I get out my phone, use my calculator. You
know, you don’t do that sort of thing anymore.
<
Pseudonym: But to me, Sudoku is nearer maths than doing your seven hundred and
fifty first integration programme, integration problem for A level. If you’re working
something out, rather than just doing it.
Esther: So you just think it’s problems, basically?
[Multiple voices]
Moses: It’s like you’re analysing of what possible cases are.
Robert: It depends whether you do it by sort of analysing every possibility, in which
case it’s just,
Moses: Yes but you eliminate possibilities, that’s the point.
Robert: But it can take some creativity for the hard ones.
Moses: Yes.
Robert: The easy ones, like numbers, yeah.
Esther: But then would you say something like, any kind of problem solving, such as
logistics or working out how you’re going to get your lorries and food to the
distribution depots on time, is that maths?
Robert: I think so. I think any kind of vague equation problem solving is maths, but
that’s just me.
Moses: If you say logic is maths, then almost everything is maths, in a way.
Pseudonym: Every sort of human process.
Robert: I’d say like someone like work out, somewhere like Tesco. Working out what
lorries needs to go where, taking different products to different stores and stuff, I’m
saying that definitely sort of – not saying it is maths, but it involves a lot of maths
and working out how to maximise the lorry load and minimise the journey travelled
and stuff like that.
Hannah: Which is kind of the opposite to what everyone thinks of maths. Everyone
thinks of maths as really hard computation, which kind of isn’t maths.

The humanities undergraduates do not as clearly reject maths as numbers, though
they do talk about alternatives. As with the Year 11 students, they usually talk in
terms of some puzzles and some applications of logic being mathematical rather than
all of these.

Disciplinary relationships
There are lots of subject contrasts made indicating the power of the construction of
knowledge into disciplines to set out what it is possible to say and to think (and to
be). Subjects can be used both to indicate similarities and distinctions. Science and
music are most often mobilised in terms of similarities and English (and ‘creative’
subjects generally) and science are most often mobilised in terms of differences. The
way that the same subjects are used to speak about similarities and differences
indicates something of the complexities of what is going on in the discussions.
Science is seen both as similar to maths in that it uses maths and as less abstract and
pure and as more practical; comparisons are also made between the people who do
different subjects which range from physical characteristics such as mathematicians
having shorter hair than scientists (FG10) to psychological characteristics such as
mathematicians not finding their ideas in the real world while physicists do, so living
‚purely in mind‛ (FG17).
There are many oppositional constructions which position maths against subjects
which are less black and white and less hierarchical and which involve words and
involve creativity. Mathematics undergraduates are most likely to cut across these
binary inscriptions. The most striking binary inscriptions come from humanities
undergraduates who posit oppositions in which their own subjects, and their own
selves, are set.

FG25: binaries maths vs. humanities:

Mary: I felt like my brain didn’t really work in that way < I mean I felt like I am a bit
more sort of waffly and a bit more sort of floaty and artsy.
<
Ellie: I think that there is kind of like the intelligence where you would make up an
argument and you rationalise like different arguments. And then there is kind of
intelligence where you would solve a problem and there is a distinct answer.

Everyday vs. esoteric maths
In nearly all the focus groups there is a distinction set up between basic/everyday
maths and complex/esoteric maths. When this distinction is introduced it is
recognised and picked up by others in the group, suggesting that it has strong
currency. What is put into each type of maths varies but calculation, timestables and
percentages most often occur in basic maths, and trigonometry and Pythagoras most
often in esoteric. This opposition is tied to notions of utility with much of maths
being classified as useless; this opposition is tied to ab/normality through various
processes of othering including the naming of esoteric maths as ‘gay’. There is much
anger among GCSE students and some among humanities undergraduates at having
to study esoteric/useless maths, though also a minority who put forward counter
positions that relate the mathematical to the everyday. These two types of maths are
sometimes associated with two sorts of people who do maths, the obsessive
mathematician and the normal mathematician.

Examples: FG11; FG15: maths and the everyday:
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.

Cameron: 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.

Relationship to research questions
      What can be seen as maths in popular culture depends on your
       understanding of maths which connects to your relationship to the subject –
       texts have many possible readings, individual participants are not consistent
       – the discursive field is very mixed
      Popular culture is a resource, though a less strong one than school maths, in
       developing understandings of what maths is; emotion is visible within maths
       in popular culture and less visible but very present in school maths
      The division between basic/everyday maths and complex/esoteric maths is
       classed and relates to the academic/vocational divide (c.f. Paul Dowling’s
       research on maths text books and social class); the accessibility of sudoku is
       often mobilised to argue that it can’t be maths
      The binary oppositions around maths and other subjects are gendered (c.f.
       Heather Mendick’s research on gender and choice of maths)
Some questions to end on
So popular, widespread discourses of maths (and mathematicians) permeated the
expression of all our participants, without necessarily having direct reference to
mass/popular media. This raises a number of questions that we are asking of our
data, and, particularly of our interview data: what are the collective fantasies of
maths and mathematicians that circulate through the popular and that hover like a
shadow around people’s talk about maths? What do such fantasies do in terms of
understandings? What do they defend against? And how are they dispersed through
popular culture and in the ‘little cultural worlds’ of particular schools and
universities or particular disciplines?




Notes:
We use a code to identify the focus groups, as follows:
FG01-FG05: Franklin School;
FG06-FG10: Shelley School;
FG11-FG15: Saint Joan’s School;
FG16-FG18: Post-1992 university mathematics undergraduates;
FG19-FG21: Post-1992 university social science undergraduates;
FG22-FG24: Russell Group university mathematics undergraduates;
FG25-FG27: Russell Group social science and humanities undergraduates.


All participants chose their own pseudonyms, mostly these go with gender but some
don’t or are ambiguous. It might help to know that the following are male: Leslie,
Ivana, Barbara, Margaret, Pseudonym, Matsui, Firefly, Ashley, Pisces; the following
are female: Erik, Jeff, Alex, Sam, Cameron. Care should be taken not to read ethnicity
or social class from any of the chosen pseudonyms.