Students Experiences of Undergraduate Mathematics

1
Students Experiences of Undergraduate
Mathematics

• Margaret Brown
• Kings College London

2
Presentation outline

• Report from 3-year project on undergraduate maths
  students, in particular
• Characterisations of different types of student
• Some characteristics of female students
• Implications for mathematics departments
• Additional evidence from a PhD study

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Students Experiences of Undergraduate
Mathematics (SEUM)

• Core Research Questions
• Why and how do students experience their
  undergraduate programmes differently?
• What helps students be successful - academically
  and attitudinally?
• One cohort of students in two Russell Group
  English universities followed for three years
  (2000 2003).
• Quantitative and qualitative data
• Exam results, annual surveys,
• Interviews, lecture and tutorial observations.

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In general, we found

• Pleasure enjoyment of mathematics declines over
  the course,
• exceptions academically successful
• Efficient studying success at school without
  hard work, leads to lack of coping at university,
  
• unless new styles of working are developed
• Self-image loss of confidence in progress leads
  to depression for some.

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Characterisations of students into ideal types
in terms ofsuccess, pleasure and belonging

• Hangers in
• Embracers
• Pragmatists
• Instrumentalists

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Hangers in students in the tail

• Who are these students?
• What do we know about these students?
• What can be done to help them?
• In our research project, this cohort subset
  define as failed 2 or more modules in January of
  their 2nd year
• (this is first set of exams that count for
  their degree).

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Who are these tail students?

• 32 (21 of cohort from one university)
• M26, F6 (overall 33 female)
• on average, lower entry score (22/30 c.f. 26/30)
• 13/28 (46) had A in A-level mathematics and
  17/28 (61) had further maths pass (only 1 grade
  A)
• comparing with top 28 students 24/28 (86) had A
  in maths and 19/28 (68) had further maths pass
  (10 grade As)
• comparing with whole cohort 102/163 (63) had A
  in maths and 75/163 (46) had further maths pass

8
By semester 1, first year

• 15 (50) of the 30 at risk students had average
  exam scorelt50,
• compared with 28 (23) of other students.

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Success, pleasure and belonging

• Raj
• Ive not had the satisfaction of getting it and
  I miss that cos Im falling so far behindReally
  have to start work. I was probably the worst
  start but to be honest I couldnt realise what
  it was going to be like cos people at my school
  dont go to university nobody could tell me.
• Rob
• I just sort of, you know getting myself in a rut
  of not doing enough work and then doing badly and
  getting rubbish marks, I was thinking I shouldnt
  really be here, but I dunno, I just sort of, my
  mum, I said to my mum

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By semester 2 first year

• 23 (78) of these at risk students had average
  exam scorelt50,
• compared with 27 (21) of other students.
• The tail students are beginning to be more
  difficult to track becoming reluctant to come to
  chat/interview or to reply to emails.

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Success, pleasure and belonging

• Dave
• I used to go to tutorials in my first year but
  Dr X asked me for my homework but I never did it
  so I stopped going because I knew hed keep
  asking for it and I couldnt do it.

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Liz boring lecturers killed any chance I had
with the maths

• Her bad exam experience
• knocks your confidence and like youre
  dreading it in a way you never knew existed, I
  kinda hated myself
• Maths is
• boring, abstract and totally meaningless
• kind of da da da da da da.
• Lecturers
• talk to the board and throw stuff to the
  students
• Feelings about maths
• dislikes maths with a passion I didnt know
  possible.
• want to get through the degree for me
• I would like to be able to apply mathematics
• to do her own work.

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Hangers in tended to be

• Mildly depressed
• Lacking in solutions
• Hanging around with other failing students
• Watching videos, drinking, but not great social
  life
• Sometimes deriving self-esteem from outside jobs

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At the end of the three years

• 8 repeated second year,
• 1 had a year out,
• 1 had transferred,
• 2 had withdrawn,
• 3 failed their finals
• all the failures of the cohort,
• 2 gained ordinary degree,
• 8 gained a third class degree,
• 6 gained a 22 class degree.

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Distribution of rankings
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Embracers

• Expressed passion and commitment to mathematics
• Participated in the course

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OliverThe more Ive worked on things the more
Ive enjoyed itall the maths is really, really
interesting

• Life mature (now 25) unicyclist trying to
  become a better person, which is really important
  to me got into this meditation and yoga stuff
• Mathematics really sort of passionate about the
  subject quite a bit in common with the
  lecturers thinking about it rather than just
  trying to pass the exam
• Other students of Charlie not bothered by maths
  any more both very influenced by each other
  theres one module hes gonna teach me and Im
  gonna teach him the other three
• Destination Teacher Training I really enjoy
  explaining stuff to people and I actually think
  Im quite good at it

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ChloeI love being a student. Theres no real
pressure and its just so nice.

• Life parents important to her now sharing with
  a friend so she has company all the time it was
  lonely in Halls
• Other students participates in extra-curricula
  mathematics residentials Ive been ever year, I
  love it integratesfirst years into the maths
  society opened up since she came to university
  tries to work things out for herself some
  lecturers are quite rude if you dont know what
  theyre talking about
• Mathematics she identifies with mathematicians
  special quality - a way of thinking outside
  what is practically possible
• Destination four year course I dont want to
  leave and her father says most people have
  degrees these days

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FlorenceI certainly think that the majority of
the content of my degree will never be useful for
anything and it will just get sort of forgotten
within six months, which is fine.

• Life emotional roller-coaster of relationships
  but I think Im happier now
• Other students lives with three successful male
  maths students (two of whom are ex-boyfriends)
  dreads lecturers who try to get participation
  does 95 of work on her own
• Mathematics the only part of university thats
  remained fairly constant Real Analysis
  fantastic pulled maths together
• Destination latest boyfriends town where shes
  reconciled to chartered accountancy training or
  something like that

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Pragmatists

• What matters is completing the course with self
  esteem intact, and gaining a degree
• Often chose mathematics as best subject, do
  well at it with not much work
• Found at all levels of academic success

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RobertIm just passive and as you say
regurgitating everything Ive been taught

• Life previously disheartened, failed to drop out
  because as his mother noted he couldnt think
  what else to do lazy obviously, in school, the
  teachers manage everything for you.
• Other students/department I dont really speak
  to anyone else in my year supervisors designed
  his final year project did better than he had
  expected in some second year exams
• Mathematics prefers physics or real problems
  maths is just the working of things, its never
  going to be that interesting to trawl through to
  the very last detail Im making sure I
  understand everything as well as memorising and
  my grades have improved so, thats, I dont know
• Destination possibly applying to stay on to do
  an MSc to help me get a job

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Instrumentalists

• Well-organised pragmatists
• Forward planning
• Taking control of their lives

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Charlie it was everything I expected and some
more

• Choice mathematics degree shows I could think
  and learn and had a logical mind and would be
  employable
• Life going well on so many fronts very, very
  good for me
• Mathematics not a particular passion
• Other students without Oliver believes neither
  would have done better than medium 2.1 I think
  working on your own is just loveless and lonely,
  youve gotta have the right course mates
• Destination risk analyst with City of London
  firm

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Ian I thought with a first class maths degree
Id be able to do whatever I wanted to do and its
not working out like that

• known hed do maths since primary school
  applied to Cambridge
• Ive never in any doubt that I was going to get
  a first overall, so it could have been harder
• final year pursuit of an actuarial career has
  not been successful they said that I hadnt
  mentioned enough team working activities in my
  interview.
• if other things fall through then I think a PhD
  might be interesting and maybe I could go on to
  be a lecturer from that I think academic ability
  is to a greater extent what you need when you do
  a PhD.
• I might apply to Cambridge again, cos I think I
  know everything I needed to get through their
  exams.

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Female Students

• Invisible
• Special
• Systemizers or empathizer?

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Invisible

• observations
• a womans answer that was not heard by the man
  who was giving the lecture
• a man described by other students as the best
  student in the year but best result achieved by
  a woman who remained silent when hearing the
  conversation.
• Lindsey one of my friends, Martha, shes top
  girl its nice to have other people around me
  that are as good

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Serafina, the witch

• It was a kind of magic she could work to make
  herself unseen. True invisibility was impossible,
  of course this was mental magic, a kind of
  fiercely held modesty that could make the spell
  worker not invisible but simply unnoticed.
  Holding it with the right degree of intensity,
  she could pass through a crowded room, or walk
  beside a solitary traveller, without being seen.
  (Pullman 1998)

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Special everyones called me strange ever
since I was like a little kid Ive always liked
doing maths

• I can remember in year four at primary school we
  used to do times table tests and theyd time
  you and I was always the first to finish.
  (Lindsey)
• Maths is my favourite. Its always been my
  favourite. The maths teacher at middle school
  was the first one that kind of really said to
  meyou should do it. You know? You could do it. I
  remember him. I liked him. (Tessa)
• Yes (I have always liked maths). Always. Even
  when I was in the infants. I used to finish my
  maths books first. I used to like to learn my
  times tables at school. I got a little badge.
  (Jessie)

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Systemizers or Empathisers

• Hypothesis about differences between the male and
  female brains, drawing on studies of autism e.g.
  In The Essential Difference (Baron-Cohen, 2003)
• Our data (e.g. Lindsey, Tessa) suggested that
  female (and male) mathematics students could be
  good at both (Egt S, but E/gtS)

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Janusz

• I feel more in control of maths than law...Im
  enjoying it much more...I just think its the
  structure of it, the way you get a theorem and
  prove it systematically...Im a bit of a
  perfectionist...
• ...maths isnt, for me its not the be all and
  end all, Ive always needed to have a social
  life...

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So....

• Women students can be different they come close
  to knowledge quietly and in control,
• A learning persona does not have to be an
  imitation of the masculine model.
• These women students invisibility is
  intentional.
• Their self-identification as special is not
  masculine. It is protective.
• Some are finding ways to participate positively.

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Conclusions and implications

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At advantage factors? (But not universal)

• Graduate or aspiring home background.
• Supportive course-mates
• Some participation in mathematics
  department/extra-curricular activities
• Experienced some aspect of pleasure doing maths
  and valued understanding.
• Ability to focus and to sort things when they go
  wrong be hard working and determined systematic
  work habits less inclination to self-delusion.

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Family background of successful students

• First year questionnaires returned from 35/43
• 29/35 had graduate parents
• Of remaining 6/35
• all older siblings had attended university (3/6)
• professional parents (2/6)
• extended family graduate Michaels uncle went to
  university and came out topIm gonna beat that
  in some way (1/6)

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Spatial aspects

• One university had a study area within the maths
  department
• Comfy chairs, lecturers around, coffee bar,
• The other had limited social space
• I come in for my lectures and go home
• But it did organise a successful voluntary
  weekend at a cheap university centre
• Several successful students shared accommodation
  with other successful students

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Discussion point how to target help to tail
students who

• cannot retrieve the situation when they start to
  do badly,
• well-intentioned, but unable to follow through.
• blame themselves for their lack of success,
• they do not say that undergrad maths too
  difficult, just say cannot study enough.
• withdraw from contact with other students
  staff
• Im sorry but Im just holding on and if I talk
  about it I might just fall apart.

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Improving the undergraduate experience

• What could be done?
• More tracking?
• More homeworks?
• More tutorials after first year?
• More help\with study skills?
• Mentors?
• Encouragement for group working?
• Group projects?