UNIVERSITY OF EAST ANGLIA
School of Education & Lifelong Learning
Main Series UG Examination 2012-13
CHILDREN, TEACHERS AND MATHEMATICS
EDU-3B23
Time allowed: 3 hours
Attempt ALL questions from ALL sections.
Notes are not permitted in this examination
Do not turn over until you are told to do so by the Invigilator
EDU-3B23
Copyright of the University of East Anglia
Module Contact: Prof Elena Nardi
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Section 1
Inside school: Changing perceptions of mathematics through improving learners’
experience of school mathematics.
[Total – 20 marks]
1
Describe briefly the meaning of the terms Instrumental and Relational
Understanding as in the work of Richard Skemp (e.g. 1976). Include a brief
example in your description.
[4 marks]
2
Describe briefly the meaning of the terms Classroom Social Norms and
Sociomathematical Norms as in the work of Paul Cobb and colleagues (e.g.
1996). Include brief examples in your description.
[4 marks]
Below is an episode from a lesson in the Y6 class of Ms Chambers.
Ms Chambers asks the students to work on the following problem:
Is 371 a prime number?
One of the students, Neil, complains that this is a very large number and that it
would take very long to check all its possible divisors. Ms Chambers invites views
from the class on Neil’s complaint. Anna raises her hand and Ms Chambers invites
her to speak.
Anna: I don’t think this needs to take as long as Neil thinks: 371 is less than 400
and 400 is the square of 20. So, all we need to check is 1, 2, 3, 4, 5…. all the way
to 20. Check all the numbers below 20.
Another student, Barack, then asks permission to speak.
Barack: Not even all of these! All we need to check is all primes below 20 and we
are done!
A third student, Clive, waves his hand impatiently. Ms Chambers signals to him that
he can speak.
Clive: What a waste of time! 1 is a prime number. 37 is a prime number. So 371 is
a prime number! Problem solved!
‘Thank you, all’, says Ms Chambers, ‘there are quite a few ideas floating around.
Shall we take them one by one?’
3
Solve the mathematical problem in the above episode. Justify your answer.
[3 marks]
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Use the terms in questions 1 and 2, or any other that you deem appropriate, to
answer the following:
4
How would you respond to Anna?
[2 marks]
5
How would you respond to Barack?
[2 marks]
6
How would you respond to Clive?
[2 marks]
7
How would you conclude the lesson in a way that provides a satisfactory
response to the mathematical problem and appease Neil’s exasperated
comment?
[3 marks]
TURN OVER
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Section 2
Outside school: Understanding public perceptions of mathematics, particularly
representations of mathematics and mathematicians in popular culture.
[Total - 10 marks]
8
The text below is an excerpt from the play, and film, Proof written by David
Auburn (2001). Write a brief analysis of this scene, particularly with regard to
how it portrays mathematics and mathematicians.
[5 marks]
CATHERINE, a young woman with an interest and ability in mathematics, is the
daughter of ROBERT, a famous mathematician who passed away recently,
following a lengthy period of mental illness. HAL is one of his last graduate
students. HAL and CATHERINE are talking about the highly energetic and anxious
professional life of mathematicians, sometimes leading to extreme choices such
as drug use to boost creativity.
HAL: They think math’s a young man’s game. Speed keeps them racing, makes
them feel sharp. There is this fear that your creativity peaks around twenty-three
and it’s all downhill from there. Once you hit fifty it’s over, you might as well teach
high school.
CATHERINE: That’s what my father thought.
HAL: I dunno. Some people stay prolific.
CATHERINE: Not many.
HAL: No, you’re right. Really original work – it’s all young guys.
CATHERINE: Young guys.
HAL: Young people.
CATHERINE: But it is men, mostly.
HAL: There are some women.
CATHERINE: Who?
HAL: There’s a woman at Stanford. I can’t remember her name.
CATHERINE: Sophie Germain.
HAL: Yeah? I’ve probably seen her at meetings, I just don’t think I’ve met her.
CATHERINE: She was born in Paris in 1776.
HAL: So I’ve definitely never met her.
CATHERINE then recounts the story of Sophie Germain, the female mathematician
who was not allowed a formal education and had to pretend she is a man,
Antoine-August Le Blanc, in order to have her work read and published. She
concludes with reciting the note of acknowledgement that Germain received from
the leading mathematician of the times, Gauss, once her identity was revealed.
“I memorised it”, says CATHERINE.
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9
Amongst other things, the excerpt offers evidence of the ubiquitous discourse
in popular culture regarding an alleged link between mathematical ability and
madness. Discuss.
In your response use some of the terms that we employed in the module
sessions. Examples of these terms are: attitudes, beliefs, emotions,
perceptions, identity, discourse, Visibility Spectrum and T.I.R.E.D.
[3 marks]
Also in your response aim to use other examples from popular culture, either
from the ones we drew on during the module sessions or elsewhere.
[2 marks]
TURN OVER
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Section 3
Inside school: Deploying representations of mathematics and mathematicians in
popular culture to discuss public perceptions of mathematics in the classroom.
[Total - 20 marks]
10
An educator needs to work not only on providing the best possible
mathematical experiences to learners but also to discuss and dispel myths
about mathematics that are common in popular culture. In the module sessions
we discussed at least five of these myths abbreviated as Innate, Male, Introvert,
Creative and Burn out. Describe three of these briefly.
[6 marks]
11
At the Appendix to this paper you will see a still from the film Mean Girls. In this
scene Cady Heron (Lindsay Lohan, on the right of the picture) has been
selected (by the rival team) to represent her school’s Math Club in the ‘sudden
death’, final part of a state mathematical competition. According to the rules of
the competition each team selects the representative of the opposing team.
She has been selected by the rival team as ‘the girl’, the perceived weak
member of her team. Her opponent is pictured opposite her. The scene, and
this still, gives plenty of opportunity to discuss commonly held perceptions of
mathematics. Offer such a discussion. In your response use some of the terms
that we employed in the module sessions to discuss some of these
perceptions. Examples of these terms are: attitudes, beliefs, emotions,
perceptions, identity, discourse, Visibility Spectrum and T.I.R.E.D.
[7 marks]
12
How can the still, the trailer or the film itself, be used in class to trigger
discussion of these perceptions and on how these perceptions may influence
the students’ own views about mathematics?
In your proposition include your aim, activity and evaluation strategy, namely: a
description of a class activity, the objective that this activity aims to achieve and
how you would evaluate whether this objective has been met.
[7 marks]
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Section 4
Outside school: Understanding and improving representations of mathematics,
mathematicians, mathematics learners and mathematics teachers in the media and
in popular culture.
[Total - 10 marks]
13
Below is a newspaper clip that presents some devastating findings about the
teaching of school mathematics. Discuss.
[5 marks]
14
Suggest briefly how educators and researchers can work towards improving the
representation in the media and popular culture of efforts to improve students’
experience of mathematics in school.
[3 marks]
In your response use examples, either from the ones we used in the module
sessions or elsewhere.
[2 marks]
END OF PAPER
EDU-3B23
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Appendix to EDU-3B23
Mean Girls (2004)
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