Abstract
At the height of the internal fight against apartheid, People’s Education for People’s Power became one of the key action-fighting plans. People’s Mathematics for People’s Power was one of the products of the strategies. The significance of mathematics emanated from its role as a gatekeeper. In this paper focus is directed towards the place of People’s Mathematics for People’s Power and its place in the new South African mathematics Curriculum. In particular attention is given to one aspect of the People’ way of life botho (African Humanism) that enable blacks to sustain togetherness among the people, through serious economic hardships, leading to the people’s regaining of political strength. Questions are raised with regard to the extent to which the framework of the new curriculum for South Africa provides room for the previously disenfranchised and whether they will be enabled to gain access to economic and Political Power, mainly through engaging the strength of botho.

Introduction

The South African slogan, ‘People’s Mathematics for People’s Power’, arose as part of ‘People’s Education for People’s Power’. One of the principles underlying the concept of People’s Education, according to Taylor et al. [1991], is the need to democratise knowledge. Taylor et al. went on to point out that the essential aspects of such democratization are that:

• Education must be accessible to all the people of South Africa, and
• Education must be relevant to the economic, social and political activities of its participants. (p.21)

Mathematics was largely seen as one of the major stumbling blocks between mediocrity and excellence. Mathematics was presented as a body of knowledge that consisted of truths that could not be challenged. What is following next is an outline of the views of People’s Mathematics. The rest of the paper will focus on the degree to which the new South African Government Mathematics Curriculum has taken on board People’s Mathematics. The analysis of People’s Power, for the purpose of this paper, is discussed under Economic and Political Power as well as power derived from embracing People’s cultural philosophy – botho/ubuntu [Botho and Ubuntu are synonymous words, Botho used largely by the Sotho speaking group (Bapedi, Basotho and Batswana), while Ubuntu is largely used by the Nguni (Xhosa, Zulu, Ndebele; Swazi) group]. In this paper I will use botho for my own convenience.

Botho is an aspect of the African people’s culture. It has to do with concepts such as: "Motho ke motho ka batho" literally translated as: a person is a person through people; which can be further translated to mean that it is through support from other people that a person is able to achieve set goals, a statement that may be related to the collectivism, i.e.; better outcomes are achieved through working as collective. It can also be argued that it is within this background that the concept of stockfels* originated. [* Stockfels are people’s social schemes, which involve regular contribution of fixed amount of money to one member of a scheme at a time.] Through stockfels, members of the stockfel are for example, among other benefits, able to pay goods at cash price and thus save on hire purchase costs.

People’s Mathematics

Rote learning constituted one of the main approaches to mathematics teaching during the apartheid era. Adler [1991] pointed out that with only 12% of black secondary school teachers having a degree, mathematics teaching by and large was tackled bravely by teachers barely one step ahead of their students. As a result, Adler continues, authoritarianism and rote-learning methods predominate. Such approaches nurtured the view that mathematics was an unalterable body of truths, that all what the learners had to do was to memorize formulae and theorems and reproduce them whenever asked for in tests and examinations. To a large extent the questions in tests and examinations remain a meaningless set of questions that have not much bearing on students’ lives, or that of the people in the environments in which they find themselves. According to Julie [1991], "the view of mathematics as a human construction to address, describe and solve problems facing society at particular moment is suppressed and obscured", and the question that is still remaining to be answered is "Whose interest is this suppression serving?" Is this a universal phenomenon or is this typically South African? One fact that stands out is that South Africa has its own peculiar problems that have drawn the attention of the international community. As of now, not much has happened in the opinion of a number of South Africans that have previously been disenfranchised in a number of ways. Very little relief has thus far been realized by the few that managed to go through their mathematics studies. Mathematics continues to be used as a gatekeeper, but those who manage to pass through these gates do not seem to make an impact in terms of ploughing back into communities from which they arose.

Slammert [1991] argues that:

Adler [1991] also gives the background towards the establishment of the concept People’s Mathematics for People’s Power, which according to her, was also informed by earlier developments that focussed on mathematics education for democracy in South Africa. The view expressed in the foreword of Julie [1989], that which Frankenstein [1991] reiterates, is that People’s Mathematics arose as part of People’s Education, a counter - hegemonic movement to remedy the crises in education in South Africa brought to world attention by the school boycotts since the 1976 Soweto schools riots. In teaching People’s Mathematics it is expected that some of the outcomes will be the ability of students to be able to integrate knowledge from different mathematical topics; it is also expected that students will be able to perceive mathematics as a human construct, not confined to a particular species of people based on race.

The process of enabling students to integrate knowledge from different mathematics topics is a necessary step towards demystifying mathematics. People’s Mathematics takes critical account of how mathematics was and continues to be taught. As a constituent part of People Education, People’s Mathematics highlights issues that tend to reinforce mathematics education as a gatekeeper. Among contributions by Slammert [1991] we have:

Drill work is still largely considered as the best way of teaching mathematics; the investigative approach is considered as time consuming and delaying the process of completing the syllabus. The pressure of covering the syllabus is sometimes so much on teachers that they at times do not mind or are not aware that they ‘cover’ the syllabus so well that students ultimately are not able to ‘see’ the syllabus at all. Still there is very little room for student teachers at colleges of education to engage critically in the inclusion of some of the topics in school mathematics. What People’s Mathematics aspires to achieve is to ‘uncover’ the syllabus so that students can be able to see among other issues, links between various aspects of the syllabus as well as links between these aspects of mathematics and their own lives and future plans.

Adler [1991] talks about her experience from dealing with students from ‘white’ South African schools. She describes this group of students as a reflection of a presentation of mathematics as ‘... a body of knowledge that must be absorbed: questions, problems have only one answer and the object of study is to get each answer right. This technicist approach to scientific knowledge, produces students who are expert in memorising and applying rules, but who struggle to step out of this narrow frame to make meaning of their ‘knowledge’’. Fasheh [1990] on the other hand correlates most of the graduates of the formal education system within the Palestinian community with:

In the light of the above it is evident that People’s Mathematics faces serious challenges, in the sense that the current mathematics passing rate is deteriorating at an alarming rate. This is happening while the new curriculum, which, as will be shown later, has embraced a great deal of the People’s Mathematics philosophy, is being introduced. Unless drastic improvement at grade 12 level occurs between now and the implementation of the new curriculum happens at grade 12, most parents will be clamoring for the "good old days" approaches of mathematics teaching - which was mainly based upon the same uncritical rote learning that is now responsible, ultimately, for the current crisis. Or is apartheid education solely responsible for these outcomes? What has to be remembered in trying to answer this question is to borrow from the same text of Fasheh the message that, ‘... the ideological environment serves to mark "the boundaries of permissible discourse, discourage the clarification of social alternatives, and makes it difficult for the dispossessed to locate the source of their uneasiness, let alone remedy it"’.

Going Beyond the Dry Facts – The Calculations!

People’s Mathematics has to do with going beyond just dry mathematical manipulation of figures. Consider a table presented by Mathonsi (1988, p.23).
 

Comparison of Government Expenditure per Pupil

What People’s Mathematics demands is that students should look beyond the information provided - the story behind the figures. Students should pose questions beyond the teachers’. These are questions such as why was there such a disparity? How come that the government of the day allowed such state of affairs to happen? What are the implications in terms of the level/quality of education of children of different race groups? What impact could such a difference have when such students went to the university? What should be done by the government? What must we do as mathematics students?
 
 
 

  

A pie graph for the above would present the following picture:
 
 

 

How do the two representations affect your perception of the information provided? Is yet there yet another graphical approach that you could think of? How can you present the cumulative effect of the figures presented? And what story does such a picture present to you? Comparing graphs A to G what would normally guide the choice of any one of the given graphs?

Through such questions students may begin to relate mathematics to their daily lives and begin to look at newspaper graph with greater interest. What is of particular significance is the kind of questions that students are encouraged to pose. The essence of People’s Mathematics is realized through the creation of the conducive environment for students to be able to ask critical questions. This demands a great deal of time and patience.

It is appropriate to state at this stage that People’s Mathematics is actually an interactive approach. It is not only the teachers that have the privilege of asking probing questions. The students as well have a right to pose questions to other students as well as to the teacher, to inquire further about the mathematics that is being taught. Students have to find out what mathematics exactly has to be learned, how this mathematics should be learned and the reasons why the particular mathematics or mathematical activity has to be done. In responding to questions students have the freedom to answer in a manner that they feel appropriate, as a means of expressing the understanding rather than only attempting to remember what the teacher said or what the text book states. This form of interaction provides the teacher with a better conception of how students perceive mathematics and the world around them. The realization of this People’s Mathematics goal of having students enjoying the freedom of interacting with one another will take some time to be achieved. As pointed by Taylor et al. [1991], it is a long process, which needs to be worked out through before any definite answers concerning People’s Mathematics can be arrived at. By definition, People’s Education should be formulated through democratic discussions amongst as wide a spectrum as possible.

People’s Mathematics is, as also correctly viewed by Frankenstein [1991], one of the groupings in the recent international efforts to organize critical mathematics education. Working against methodologies that indirectly nurture oppression was one of the critical areas of operation of the Mathematics Commission of the NECC. People’s mathematics, has to do with bringing the critical perception of mathematics and its teaching together. Focus in the teaching of People’s Mathematics is not only on skills, but also mainly on application. Various authors such as Taylor et al. [1991] present examples of this. In this article attention is drawn to facts such as mathematics as a response to particular problems and that all cultures borrow from all cultures to suite their own needs. The tendency, as Breen [1991] outlines, is to move towards mathematical modeling and mathematics in the real world. In contextualising reality Breen does however caution that greater effectiveness will be realized if it is the students who take greater responsibility in problematising their own reality.

People’s Mathematics, as has been said of People’s Education, takes a dynamic outlook. It has to be relevant to the current students’/society’s needs as well as their future directions, i.e. foregrounds. As a result, it offers choice, freedom to decide and responsibility over the choices made. Through its critical nature, these choices are informed by developments within and around the communities. People’s Mathematics embraces democracy, thus fosters liberation of people from all sorts of oppression from a mathematical perspective.

People’s Mathematics also stresses that mathematics is a human creation and that people over the years have been able to create mathematics to suit their needs of the time. This makes a close link of People’s Mathematics with Ethnomathematics. This link of People’s Mathematics with the people’s mathematical daily lives renders it accessible, thus eliminating the gate keeping nature that characterizes the alternative mathematics.

Through the learning of mathematics there is a great potential that we as a nation can get to know South Africa better so that we can benefit from its multiplicity of resources. Mathematics provides a foundation to access different study fields for the purpose of exploiting these resources. However, as has been alluded to earlier, mathematics has been, and still has a potential of being, used as a gatekeeper. The nation is still at risk of being kept out or being disempowered through the negative approach to mathematics teaching as well as lack of resources to address the subject accordingly. Volmink [1990], addresses some of these issues as follows:
 

BOTHO

Before looking into the extent to which the new curriculum has incorporated People’s Mathematics and the extent to which the philosophy of botho was encompassed in the curriculum, it is necessary to look further into the botho concept.

Our freedom in South Africa has come with it a greater revelation of disparities between blacks and whites. The botho aspect of People’s Mathematics call for a ‘collective human response to an oppressive situation’, which in this case is general poor outcomes from schools (as exemplified by matric results), poverty and crime - some of the by-products of the apartheid regime in the land of plenty. The collective human (motho ke motho ka batho) exercise must ‘reclaim people’s lives, their sense of self-worth, and their ways of thinking from hegemonic structures, and facilitate their ability to articulate what they do and think about in order to provide a foundation for autonomous action’. (Fasheh [1990]). Working as a collective, working towards upliftment of fellow human beings, and working towards equitable distribution of our national resources is necessary if we have to reclaim our lives from the shackles of the past. Working through mathematics education is one of the main routes to success as mathematics has in the past, more than any other subject does, served as a gatekeeper towards the ‘green pastures’ for which we were not meant, according to Verwoerd.

Adler [1991] in her analysis of Breen’s [1991] work makes reference to Humanistic mathematics. There are clear similarities between this approach of mathematics and a botho perspective. Reference is made to combating elitism, racism and sexism. Under botho this is addressed under the concept of cooperative action (operating as a collective, in solidarity - addressed earlier under ‘motho ke motho ka batho’). Adler goes further to say that:

Reading through a ‘Dialogue’ between Ascher and D’Ambrosio, [Ascher and D’Ambrosio [1994]], one identifies clear links between Ethnomathematics and Botho. In response to one question on educational aspects of ethnomathematics, this was D’Ambrosios’ response:

Outcomes Based Education [OBE] Curriculum and People’s Mathematics

Outcomes Based Education and Training [OBE] is the new South African system of education that has replaced the apartheid education system. This system is being phased in, in stages as a result of training implications. There is a need to outline the context in which some of the terms are used in OBE:

Specific Outcomes:
 

Botho within the OBE

While it may be argued that botho contributed towards allowing the foreigners to invade the African soil, in some circles it could also be argued that it is the same botho that sustained the people during the dark years of oppression. Attention is now being given to the extent to which the unifying South African main world view, or philosophy of life, botho is embraced within OBE. Ndungane, the Anglican archbishop of Cape Town in his introductory article on botho in the Mail and Guardian [February 20 to 26 1998], implores that:

In some respects, the disempowering, lack of collectivism, regimentation and compartmentalization approach that is being applied in mathematics teaching has much to do with the absence of botho in our teaching approach. The empowering effect of mathematics is lost as a result of lack of the essence of togetherness. People’s Power comes from organised people. Botho does neither feature directly in the mathematics curriculum framework nor in other learning areas such as Human and Social Sciences. This is regrettable if one consider the extent to which people’s culture has been interfered with by the western ‘civilisation’, particularly through apartheid policies. The fact that botho may be incorporated under Specific Outcomes such as, "Demonstrate understanding of the historical development of mathematics in various social and cultural contexts" or "Critically analyse how mathematical relationships are used in social, political and economic relations" is not enough. Botho is a unifying concept within South African people culture and thus deserves prominence in the curriculum in no uncertain terms.

People’s Mathematics and Cultural Affirmation in the OBE?

For the large section of our mathematics teaching community, using artifacts of European origin still remains the only way for providing teaching aids. The beautiful pebbles of the South African oceans and rivers never find a way into the class rooms in the teaching of counting, colors, sizes, mass, etc. Can culture be used as a tool of oppression and at the same time be used as a tool of liberation? Through religion Africans have to a large extent been advised to look down upon their own cultural values and beliefs. This state of affairs has led to a loss of sense of direction, lack of self-esteem, values etc. Those Africans who embraced Christian faith did however remain embedded within the African culture- thanks to apartheid. During this period majority of the blacks never found an opportunity of linking up the education they received with their own culture.

One of the mathematics specific outcomes in DoE [1997c] is "Analyse natural forms, cultural products and processes as representations of shapes, space, and time". Acknowledgment is also made in the OBE document that those mathematical forms, relationships and processes embedded in the natural world and in the cultural representations are often unrecognised or suppressed. Learners should be able to unravel, critically analyse and make sense of these forms, relationships and processes. Among the range statements (that is statements that indicate the scope, depth, level of complexity and parameters of achievement on a particular specific outcome) we have:
 

• Observe nature, cultural products and processes;
• Explain use and value of cultural products and processes;
•  Analyse different cultural products and processes at different epochs;
• Represent artifacts in various mathematical forms - 2D and 3D;
• Critically analyse the misuse of nature and cultural products and processes.

Given the OBE framework such as outlined above on aspects of culture, what more would we like to have as mathematics teachers to ensure that people’s cultures are taken on board in our daily teaching? The geometric techniques used in the design and the building of thatched roof houses by some of the people in the country were never considered in the teaching of Pythagorean theorem and other areas of geometry. In some cases some of the very good builders never had an opportunity to attend any formal mathematics class. All their trade they got from their predecessors. Inclusion in a formal way of these aspects of cultural artifacts or products, as referred to in OBE, should contribute towards restoration of self pride among communities whose culture were hitherto looked down upon. Hopefully this can also bring the sense that education is not only for those who have gone through the formal schooling.

This background information is essential for our contemporary mathematics students to note that there is and there has always been some degree of mathematics among the people even those who never had an opportunity to learn mathematics in formal mathematics classes. The OBE specific outcome, "Demonstrate an understanding of the historical development of mathematics in various social and cultural contexts" presents a framework within which the teaching of mathematics can then be linked with various communities’ developments. Some of the range statements related to this specific outcome are:

• Show knowledge of counting styles in different cultures;
• Demonstrate knowledge of ways of pre-colonial counting in Africa;
• Critically analyse mathematics as a predominantly European activity;
• Analyse mathematics ideas from own culture.

That the framework for addressing the educational imbalances exists is one thing, but the actual critical analyses of these imbalances and correcting them is another. The level of contamination of people’s thinking as a result of many years of domination has to be taken up seriously in the implementation of the OBE. The extent to which people have tended to look down upon themselves is an issue that demands special attention.

Focus also has to be directed to the compatibility of the mathematical methods that were applied then and environmental conservation. In outlining the Rationale in the mathematics curriculum, Mathematics Literacy, Mathematics and the mathematical Sciences as domains of knowledge are viewed as significant cultural achievements of humanity. Thus our students have to appreciate that they can also create mathematics as their predecessors have done in the past and that their creation has to be compatible with our current environmental needs. Indeed, as Volmink [1990] outlines:
 

On the other hand, the Learning Outcomes for Teacher Education in DoE [1997a], under Areas of Learning - Life Orientation, does make provision for students to question issues that in the past would only be accepted as facts that need no questioning. This provision is covered in the statement: ‘The learner will demonstrate the ability to: Exercise a critical and informed understanding and the nature of discrimination and barriers of learning.’(p.87). On the same page it is also stated that learners will demonstrate the ability to ‘Show knowledge and appreciation of, and respect for, the beliefs, practices and cultures of the communities of South Africa.’ While this provides room for botho consideration, one interesting aspect under these ‘Life orientations’ is that students will not blindly fall into the botho culture, but will do so with some degree of critical outlook.

People’s Mathematics and Economic Power in the OBE?

Economics is the science of the production and the distribution of wealth. Production and distribution are both mathematical terms. The extent to which our school mathematics teaching addresses the empowering nature of economics as well as the disempowering nature of lack of wealth is an issue that warrants some explanation. What does it mean to say that a country is economically strong? What links does this have with People’s Mathematics?

The fact of the matter is that disparities are still so vast that the situation tends to threaten the newly born democracy. The prevailing violence is widely attributed to these vast economic disparities. In fact, according to Phinda Madi, as reported in the "Sunday Independent Business" of the 11th January 1998, " There is now serious risk of a new kind of economic apartheid where the recently unbundled organizations feel that they have now earned the right to be left alone." For the disenfranchised, it is necessary to look closely at the mathematics that is being offered in the curriculum currently and that which should be in the new curriculum, to ensure that the content and implementation contribute towards their well being economically. On the other hand if we all want to be the united "rainbow nation", it is the responsibility of those who are better off also, to ensure that necessary steps are taken to facilitate the mathematics learning that contributes towards the better life of all South Africans.

Conditions under which mathematics is being studied is an area of concern that demands action linked to People’s Mathematics for People’s Power. Julie [1991 (p.38)], made reference to the NECC acceptance of the resolution : ... teaching practice, which helps people to be creative; to develop a critical mind; to analyze . He went on to refer to the ‘ ...replacement of rote learning methodology of Bantu Education with a methodology that develop an inquiring and critical mind...’ and that reflective thinking and inquiry method were nothing new. That may have been true to the audience that was being addressed. Unfortunately for the large section of our current teaching force such concepts are still very new. Creativity still remains a rare commodity. Whilst provision of resources over the years was not equitable, the maintenance of the meager resources also left much to be desired. This tendency has not improved in most of the areas since attainment of freedom. Some of the schools are not habitable at all, not because there are no facilities but simply because of lack of some degree of creativity and minimal improvisation. The concept of collectives as an aspect of the people’s education becomes an issue of great relevance in this regard. The struggle for resources needs to take a different format. Understanding of the range statement " Demonstrate importance of social service charges, pensions, etc." may seem common for those who grew up in democracies. For a number of young and old South Africans, inclusion of such statement in the curriculum framework is essential. Over the years the understanding and the observation was that such taxes were mainly used to benefit one section of the population, the privileged whites.

One of the mandates of the People’s Mathematics Commission was to contribute towards the development of new educational materials. Very few materials for schools are available at this stage. The development of these materials has to be accompanied by a rigorous exercise of providing teachers support programmes into the effective utilization of the new materials. The range statement "Compare the financing of education under apartheid and after 1994" is very relevant. Comparing the expenditure per child for the 1975 and 1976 and 1979 and 1980 expenditure per child, a number of questions arise. What is the cumulative total of the disadvantage that built up to 1994? How does this affect the post 1994 budget for the previously disenfranchised, and why so? Critical mathematics education calls for response to such questions. The legacy of the past has created a problem to the current generation. A full understanding of the past is essential so that thorough critical approach to the solutions to our current educational problems can be resolved. Engagement of students now is essential to ensure that these problems are addressed now and not postponed.

In 1975 expenditure per child was over R500-00 more on white a white child than on an African child. In 1979 the difference was more than R1000. What is the value of a rand now as compared to the rand then? How does this provide a white child with an advantage in life? What are the critical areas where funding should be focussed in terms of addressing the backlog? How should this reallocation of funding impact on unemployment? Critical analysis is of the essence, and this has to be done in the context of the RDP demands, the ‘culture of entitlement’, the prevailing culture of teaching and learning. Have we grown wasteful over the years? What impact has the culture of ‘lack of ownership’ made on our respect for community property?

People’s Mathematics and Political Power in the 0BE?

Power has to do with the ability to act; to influence; to exercise authority or authority to exert force. We need to understand how People’s Mathematics relates to political power. Do we have a full understanding of political power? How does this relate to mathematics teaching and learning? Can we clearly outline the role of teachers, students and parents in this context? In South Africa clear definition is still necessary for people to find their feet in the fields. The power to discuss community concerns, to make recommendations with regard to steps to be taken on the basis of our mathematical understanding of issues still needs some development. Recommendations have to be considered meaningfully before people can claim to have some power over their lives. How does mathematics relate to political freedom and empowerment? How is this captured in the new curriculum? How do we achieve in our learning and teaching?

Despite the fact that South African people have attained political power there are still signs that indicate that this power has not sunk to the level of some members of the community. How mathematics is taught in the classroom now and in the future can have some impact in the way people perceive themselves in life - either as independent or as dependents. The extent to which people are and will be able to make choices in areas related to the choice of mathematics as a subject; or its contents as a field of study; or how it should be taught or studied, will determine the extent of the people’s freedom and power.

It is important to look carefully at the South African new curriculum proposal and compare it with ideas raised during the days of attempting to bring about or laying the foundations for the alternative mathematics curriculum, the People’s Mathematics. In one of the papers presented towards this ideal, Taylor et al. [1991] argued that:

The nature of the problems given to students has bearing on performance of students as well as how teachers perceive mathematics teaching. Looking at the 1986 Mini Mathematics Olympiad question papers [MASA .:1988],one finds questions such as:
 

Taylor et al. [1991], points out that the ways in which curriculum materials give meaning to mathematical ideas is crucial to the shaping of pupils’ conceptions of mathematics and the world around them. Very little during 1998 can therefore be expected from the implementation of the new curriculum at grade 1 level. 1998 marked the beginning of the implementation of OBE. Teachers at grade 1 level have only begun to familiarize themselves with OBE. The new shaping that we hope to achieve through the new curriculum can only be felt, in terms of matric outcomes, much later. However, the contents of this framework do not stop teachers from implementing some of the ideas right away. Engaging with political organizational systems and socio-economic relations is already taking place. The question could be the extent to which this engagement is taking place or how the processes link up with mathematics teaching and learning.

The product of working as collectives in and outside maths classes must have a bearing on how teachers and students develop trust in working as a group. It is within group dynamics that people’s power is generated. One area where collectives can be effective is on professional subject associations or organisations. Over the years people were discouraged to participate on the basis of colour. An effort is essential by all that have some understanding of the baggage that the majority of black South African teachers are still carrying. This baggage unfortunately continues to be transferred to younger generations. Participation by staff members from colleges of teacher education has over the years remained very limited. What this means is that very little is known by teacher trainees, and subsequently the vicious circle is being perpetuated.

The extent to which botho has been incorporated in the mathematics curriculum will remain subject to individual judgment. It should however be noted that according to the introductory statement to the policy document [DoE.1997c]:

References