Mathematics and

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Mathematics and Democracy
Paper 1
Should the activities below be used in
school-going mathematics? 1 White people,
Indians, Coloureds, Africans are examples
of non intersecting sets. Thus White people?
Africans ? Africans? Indians ? 2 A
ship travels from Cape Town to Southampton at x
knots. The total distance the ship traveled is y
miles. How many days did it take to sail from
Cape Town to Southampton? 3 In a FRELIMO camp
there are 187 AK47s. FRELIMO freedom fighters
attack a RENAMO camp and return 77 more AK47s.
How many AK47s are there now in the FRELIMO
camp?
2
Paper 2
Who is (was) and why is it important to
know? Ebrahim Mamdani George Ellis Ismail
Mohamed Thomas Muir .
3
What is the point of mentioning these illustrious
mathematicians?
Firstly, they were all African mathematicians and
made substantial contributions to their academic
fields.
Secondly, accept for Mamdani, whose pedigree is
well known in South Africa through his brother
who is a political scientist, the other two made
in their particular ways contributions towards
the democracy we are now enjoying.
Ellis exposed the existence of a third force
operating to destabilize the road to democracy.
Currently involved in Basic Income Grant campaign
Mohamed (and practically his entire family) was
incarcerated, under house arrest, sacked as a
professor of mathematics at UWC for his quest for
social justice for the poor and the downtrodden.
Corollary Within the mathematics research
community in South Africa there were those who
excelled in mathematics research but also engaged
vigorously in the pursuit of justice for all
4
Muir was to superintendent general in the Cape
during the late 1800s and early 1900s. His
grave is in the cemetery in Maitland. As a
mathematician he contributed substantially to the
theory of determinants. Mathematical terms such
as Wronskian in the field was coined by him.
He also reported the following We have spent 1
on the education of the children of British
subjects and 1p on the education of natives
Two more statements to thicken the plot The
Bantu people must be taught to add so that when
they lay tables they can put the correct number
of knives, forks and spoons on the table.
(Superintendent General of Education, Free State
in mid-1800s).
Children must be taught that 2 times 2 is 4 and
not about this thing called anti-racist
mathematics. (Thatcher at British Conservative
Party Conference)
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Mathematics and democracy fall more broadly in
the domain of mathematics and politics and this
is used interchangeably within this presentation
with concentrating broadly on mathematics and
politics.
Linking mathematics, particularly school-going
mathematics, and democracy is a recent phenomenon
which started in the mid-1980s. However,
elements (vestiges) of the political dimensions
of mathematics can be traced quite far back.
6
Some history differential accessibility along
essentially class lines- golden eras of
Babylonian, Verdic (Indian), Chinese, Mayan,
Egyptian and Greek mathematics
ruling class access to quantitative mathematics
and engaged in the mathematics knowledge-making
process
ruled class engaged in qualitative mathematics
which as Alan Bishop argues is the origin of all
mathematics--all mathematics can be traced to
basic human activities such as ac-counting
(Bishop calls this counting--San people in
Botswana), organizing information, measuring and
rule-based game-playing.
Little is known about the Babylonian, Verdic,
Chinese and Egyptian mathematics other than that
mathematics was the preserve of the priestly
class and was practiced in the interest of the
ruling class.
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Early Greek mathematics
Mathematics was divided into a computational
aspectcalled logistica (word related to our
logistics) and arithmeticaa study of the
abstract mathematical properties.
This early partitioning of mathematics into
practical and academic components was also a
social stratification mechanism.
Arithmetica was the concern of philosophers and
gentleman of leisure and logistica the concern
of merchants and slaves.
during this period a criterion used to exclude
men from holding political office for ten years
was their engagement in the utilitarian
mathematics of the merchants and the slaves.
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The abacist-algorist debate
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Recent Developments
Ellis Where appropriate mathematics should be
used to expose social injustice and lead to
action to those issues which reduces human
possibility. Action must be taken.
10
Ethnomathematics as cultural reappropiation
project (Mozambique)
Ethnomathematics as an epistemic project (Brazil)
Criticalmathematicseducation (Freirean, USA)
Critical Mathematics EducationDanish mathematics
and democracy
Peoples Mathematics -- opposition to and
action-taking against forces that inhibit and
reduces the possibilities of human potential
(South Africa)
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Curricular incorporations (intended curriculum
level)
Major motivation for incorporation of the
political in mathematical education is that
competence is needed to make sound judgments
about the mathematical installations which
prescribe and predict societal affairs. Should
find its expression in a new subject called
Mathematical Literacy
South Africa To be a participating citizen in a
developing democracy, it is essential that the
adolescent and adult have acquired a critical
stance with regard to mathematical arguments
presented in the media and other platforms. The
concerned citizen needs to be aware that
statistics can often be used to support opposing
arguments, for example, for or against the use of
an ecologically sensitive stretch of land for
mining purposes. In the information age, the
power of numbers and mathematical ways of
thinking often shape policy. Unless citizens
appreciate this, they will not be in a position
to use their vote appropriately.
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PISA as a quest to test the readiness of 15-year
olds to identify and critique mathematical
installations and deal with socio-mathematical
controversies.
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Cooking instructions Place lid on pot and bring
to the boil (it should take approximately 15
minutes to get to boiling point.) Reduce the heat
and gently simmer for 30 minutes per 500 g.
How long must this piece of meat be cooked?
14
School Mathematical way Common Sense way Commentary
1674/500 3,348 3,35 X 0,5 hours 1,675 hours 5 (for 500 g) ? ½ hour 5 (for 500 g) ? ½ hour 5 (for 500 g) ? ½ hour (Total time) ? 1½ hour 6-45 (Start time) 7-15 (end of 1st ½ hour) 7-45 (end of 2nd ½ hour) 8-15 (end of 3rd ½ hour) 8-25 (additional 10 minutes to compensate)
The test of correctness is the taste not the
mathematics!
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Definition A dictatorship is a coalition such
that no other coalition in the voting set can be
a winning coalition according to the agreed
voting weight.
Parties Number of votes Number of seats
ANC 10877302 271
DA 1929816 48
IFP 1088645 27
UDM 355702 8
ID 269678 7
NNP 257815 6
ACDP 250249 6
FF 139458 3
UCDP 117758 2
PAC 113500 2
MF 55267 1
AZAPO 41771 1
Is South Africa under a dictatorship?
Should the mathematical lens be the only one?
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How does the political manifest itself when
teachers engage in mathematical work with an
issue which presumably has high political content?
A NEW SALARY SYSTEM FOR TEACHERS? The SGB of
Xolana Yizo Zwetemba High School decided to that
their school will have a fair and reasonable
salary system for the teaching staff of their
school. They hire your team as consultants to
develop a salary system for the teaching staff
that reflects the following circumstances and
principles. Principles All teaching staff should
get an increase any year that money is available.
Teaching staff should get a substantial benefit
from promotion. If one is promoted in the minimum
possible time, the benefit should be roughly
equal to the seven years of normal
(non-promotion) increases. Teaching staff who get
promoted on time (after seven or eight years in a
rank) and have careers of 25 years or more should
make roughly twice as much at retirement as a new
teaching staff member at REQV16.Teaching staff
members in the same (new) rank with more
experience should be paid more than others with
less experience. But the effect of an additional
year of experience should diminish over time. In
other words, if two staff members stay in the
same rank, their salaries should tend to get
closer over time. The project Design a new salary
system. You must also design a transition
process, that will move all salaries towards your
system without cutting anyones salary, for
existing staff members The existing staff
salaries, ranks and years of service are given in
table 1.The Chairperson of the SGB has asked for
a detailed salary system plan that can be used
for implementation, as well as a short executive
summary in clear language, which she can present
to the SGB and the teaching staff. The summary
should outline the model, its assumptions, its
strengths and weaknesses, and the expected
results.
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FORMULA-SEEKING

2
1
TECHNICAL
SOCIAL
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4
SITUATION-ANALYSIS
Pattern of teachers mathematical modelling
work
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How interested are learners in the political?
Relevance of School Mathematics Education
(ROSME) What are the contextual situations would
children in grades 8 to 10 prefer to deal with in
Mathematics? Children from LSE backgrounds in
Western Cape and Free State
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N Mean
M4. Mathematics that will help me to do mathematics at universities and technikons 1382 3.596237
Td2. Mathematics involved the sending of messages by SMS, cellphones and e-mails 1380 3.282609
T6. Mathematics involved in secret codes such as pin numbers used for withdrawing money for an ATM 1398 3.262518
M3. Numbers 1348 3.239614
G2. Working out financial plans for profit-making 1370 3.235766
Five highest scoring items
My future, my health and current gadgets
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Ls3. Mathematics to determine the number of fish in a lake, river or a certain section of the sea 1383 2.355748
A3. Mathematics involved in working out the best arrangement for planting seeds 1370 2.314599
T3. Mathematics linked to decorations such as the house decorations made by Ndebele women 1368 2.27193
g4. Mathematics of a lottery and gambling 1376 2.242733
A1. Mathematics involved for deciding the number of cattle to graze in a field of a certain size 1396 2.184097
Five lowest least-preferred items
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POLITICIANS and the importance of mathematics
Argument More children graduating from schools
with in mathematics and improved test scores in
the subject will significantly contribute towards
economic development.
But
links between education and economic growth are
far less direct than our politicians suppose.
Unfortunately, beliefs about these links dominate
current policy. (p 14-15) (Wolf, Alison (2002).
Does Education Matter? Myths about Education and
Economic Growth. London Penguin Books.)
The link Education ? Economic development is
weaker than The link Economic development ?
Education.
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In South Africa Scholastic achievement follows
economic cycle patterns rather than the other way
round
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Challenges for the Political in school-going
mathematical education
phenomenal domain as schools and schooling which
were actually created to deny the poor and
marginalized access to social, cultural and
economic capital
speaking on-behalf of the poor and marginalized
without attending to the real needs and desires
of such communities and a concomitant
non-alliance with structures and formations which
actively engage in struggles for the betterment
of the human possibility.
prototypical emergence environment, as far as its
proponents are concerned, is that of essentially
democratic stability and tolerance where there is
assurance that the dominant structures will be
virtually left untouched no matter what the
issues are that are being illuminated
belief that classroom democratic and critiquing
behaviours transfer unproblematically to
situations outside of school.
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Høyrups Challenge
The current world order is either unwilling and
unable to address the most pressing problems of
the worldfood, shelter, poverty, etc
These problems are social but they are also
mathematical
Archers enduring educational research result
Schooling achievement outcomes are related to the
socio-economic status (SES)
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Bushs Threat
Unlike medicine, agriculture and industrial
production, the field of education operates
largely on the basis of ideology and professional
consensus. As such it is subject to fads and is
incapable of cumulative progress that follows
from the application of the scientific methodWe
will change education to make it an
evidence-based field. No Child Left Behind puts
special emphasis on determining what educational
programs and practices have been proven effective
through rigorous scientific research. Federal
funding is targeted to support these programs and
teaching methods that work to improve student
learning and achievement
Is it possible to develop a schooling system and
school-going mathematical education which will
graduate learners with a high level of awareness
to address the most pressing problems of the
world?