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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}= 

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Mathematics and “Democracy”

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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 AK47’s. FRELIMO freedom fighters attack a RENAMO camp and return 77 more AK47’s. How many AK47’s are there now in the FRELIMO camp?


Paper 2

Who is (was) and why is it important to know?

Ebrahim Mamdani

George Ellis

Ismail Mohamed

Thomas Muir



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


Muir was to superintendent general in the Cape during the late 1800’s and early 1900’s. 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-1800’s).

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)


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-1980’s. However, elements (vestiges) of the political dimensions of mathematics can be traced quite far back.


Some history

differential accessibilityalong 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.


Early Greek mathematics:

Mathematics was divided into a “computational aspect…called logistica (word related to our “logistics”) [and] arithmetica…a 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.


Recent Developments


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.


Ethnomathematics as cultural reappropiation project (Mozambique)

Ethnomathematics as an epistemic project (Brazil)

Criticalmathematicseducation (Freirean, USA)

Critical Mathematics Education—Danish mathematics and democracy

People’s Mathematics -- opposition to and action-taking against forces that inhibit and reduces the possibilities of human potential (South Africa)


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.


PISA as a quest to test the readiness of 15-year olds to identify and critique mathematical installations and deal with socio-mathematical controversies.


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?



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.

Is South Africa under a dictatorship?

Should the mathematical lens be the only one?


How does the “political” manifest itself when teachers engage in mathematical work with an issue which presumably has high political content?


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.


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 anyone’s 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 summaryshould outline the model, its assumptions, its strengths and weaknesses, and the expected results.










Pattern of teachers’ mathematical modelling work


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


Five highest scoring items

My future, my health and current gadgets


POLITICIANS and the importance of mathematics


More children graduating from schools with in mathematics and improved test scores in the subject will significantly contribute towards economic development.


“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.

In South Africa: Scholastic achievement follows economic cycle patterns rather than the other way round


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.


Høyrup’s Challenge

The current world order is either unwilling and unable to address the most pressing problems of the world—food, shelter, poverty, etc

These problems are social but they are also mathematical

Archer’s enduring educational research result

Schooling achievement outcomes are related to the socio-economic status (SES)


Bush’s 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 method…We 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?