The mathematics of democracy
The 2012 Helen Suzman Memorial Lecture
Jonathan D Jansen
University of the Free State
“So teach us to number our days that we may gain a heart of wisdom” Psalm 90 v 12
The mathematics of democracy
The 2012 Helen Suzman Memorial Lecture
The first and only time I met the politician Helen Suzman was in a principal’s office occupied by another great South African, the mathematics wizard TW Kambule. There was, quite literally, blood on the streets of Soweto in the lingering violence of the early 1990s and yet in this model school run by South Africa’s teacher, sat three people with the same concern: how do we create from this chaos a stellar education system that overcomes the bitterness and devastation of the present past?
Since I did not expect to see Ms Suzman, her sudden entry into the principal’s office was a joyful surprise, at first, but with the oversensitive antenna of a black consciousness adherent on high alert, I was cautious. What relaxed me was the warmth that existed between two great human beings—the principal who demonstrated how to instill a love of mathematics in generations of black learners against overwhelming odds, and the politician who fought tirelessly to instill commonsense in the minds of the white nationalists in Parliament. On reflection, that day was, symbolically, a meeting of content (mathematics) and context (society), a reminder that you cannot have quality mathematics teaching without a democratic and decent society in which to learn and live and love together.
What’s math got to do with it?
No school subject enjoyed so much attention among the post-1948 racial ideologues than mathematics. Maybe they knew something as the overused quotation of the Minister of Bantu Affairs suggested in his rhetorical question when he introduced the Bantu Education Bill in Parliament in 1954:
“What is the use of teaching the Bantu child mathematics when it cannot use it in practice? That is quite absurd. Education must train and teach people in accordance with their opportunities in life.”
Then, and now, as Verwoerd recognized, there was a direct relationship between school mathematics and occupational destinies. In fact, today no serious university admits a student into any discipline, and especially not into the scientific, medical and commercial fields, with anything less than mathematics.
But the broader value of mathematics was of course recognized in earlier civilizations. Who can forget Napoleon’s famous quip that ‘the advancement and perfection of mathematics are intimately connected with the prosperity of the state’ or Hogben’s dictum that ‘Mathematics is the mirror of civilization?’ For the biblically minded, imagine Noah’s dilemma if he did not know mathematics, given the precise dimensions provided for the Ark:
This is how you are to build it: The ark is to be three hundred cubits long, fifty cubits wide and thirty cubits high (Genesis 6:15)
Why is mathematics so fundamental to history, design, art and engineering? Because mathematics is not about numbers. It is about value—practical value, disciplinary value and cultural value (Gauri Dushi). We count and calculate, measure and anticipate, earn and spend, tithe and gamble, wonder and worry, with the aid of mathematics. We design buildings and navigate the universe using mathematics. And it is through mathematics that we learn, from a young age, those values indispensable for democracy—discovery, invention, concentration, alternative solutions, patience, perseverance, discipline, logic, order and economy. Is it possible, I sometimes wonder, that the oft-noted parsimony in the novels of Nobel Laureate, JM Coetzee, might have something to do with his initial training in mathematics? This is after all the man who once delivered a lecture to the Philosophical Society on “Poetry and the language of mathematics.”
I think back to the great mathematics teachers that I encountered in my life. More than any other discipline, this is where I learnt organization, argument and the sheer joy of resolution.
The board is neatly prepared. The word problem is translated into a simple equation, and that is the first miracle—how on earth did she distil from words three or four variables lined-up in an equation?
The challenge set: “If Y equals 3 and Z equals 9, prove that X lies in the range 7 to 12?” Then she takes you through five steps which require that you follow, carefully, the logical progression from step 1 to step 5. What seemed to be so complex, in words, is now digestable in mathematical symbols.
And then, with the pride of the gladiator having slain the beast in full public view of the Coliseum, the magic words appear after the solution: Quod Erat Demonstradum, as the teacher draws a deft line under those three Latin words. Pure, simple magic. The class, like the inhabitants of the Coliseum, stand in awe.
“Now class,” follows the teacher, “your homework is to solve the 13 similar problems on page 39 using these methods. You are free to use your own methods (a good math teacher would say) BUT … show me your reasoning” (ask audience for these last four words).
The state of mathematics in South Africa
Mathematics has become the standard measure of the health of nations with respect to education and development. Virtually every national and international test of achievement includes or singles out numeracy or mathematics. And in every one of those cross-national tests, South Africa is a bottom-dweller among nations, either dead last—as in the recent World Economic Forum rankings (62nd out of 62 nations)—or near the bottom.
There can be no question that the neglect of academic education for black schoolchildren over decades, if not centuries, is one of the reasons for this state of affairs. But why has nothing moved in the last two decades? Why does it appear we have gone backwards in math and science achievements at school level? Why is it that a small number of schools account for the largest percentage of mathematics passes in the country, and the majority remain stuck with a diluted form of mathematics?
The answer of course lies in the three parts: the legacy of racist decisions (what we inherited); the exercise of poor decisions (what we stuffed up; OBE being the most obvious); and the absence of any decisions (what we failed to do; such as the timely delivery of learning materials).
We did not deal with the simple reality that our teachers in the poorest schools do not know enough mathematics, do not know enough about mathematics teaching, and do not teach mathematics (or any other subject for that matter) in stable learning environments.
But there were other problems. We tried to be smart with complex curricula when what was needed was to build slowly and systematically the foundations of teaching and learning mathematics in the primary schools. We still reduce education to forced feeding sessions just before the exams—especially in math and science—when what was needed was the optimal use of regular classroom time. And then the greatest scam of all, we gave up, and found another way of dealing with the mathematics challenge; we created another kind of math.
I am sure originally there were good reasons for the policy position that every child must do some form of mathematics, whether it is the standard grade mathematics of a previous area or the mathematical literacy of today. And if you water-boarded me, I might confess that for a small minority of students basic numerical proficiency is better than no mathematics at all. I might even concede under pain of torture that in certain fields, such as drama, higher order mathematics might not be that crucial to success in such a career.
But certainly not the kind of low-level thinking that has come to constitute mathematical literacy today, epitomized perhaps by this ridiculous question in the November 2012 examination:
Mathematical Literacy, Paper I Picture B (as on maths paper)
1.1.7 State whether the following event is CERTAIN, MOST LIKELY or IMPOSSIBLE:
Christmas Day is on 25 December in South Africa. (2)
The problem remains: why do we have such a huge majority of matriculants in mathematical literacy compared to mathematics? And why the sharp migration from math to math lit? Why this racial and class inequality where the middle class children in well-resourced schools do mathematics and poor mainly black children in neglected schools do the literacy version?
That answer is simple.
We compensate for poor mathematics teaching by moving students, en masse, towards the lower or less strenuous form of mathematics (standard grade or mathematical literacy) in order to improve the results in both forms of math.
I do not for one moment believe that more than the majority of our Grade 12 students are unable or incompetent to do mathematics; that is simply not possible. But in a system where the foundations of numeracy are extremely shaky in the early grades, and never corrected in the middle to higher grades, of course learners will approach the senior grades (10, 11 and 12) with an intense dislike for mathematics (constant failure breeds dread of the subject and breaks down personal confidence) and, forced to do some kind of mathematics, choose the easier option.
Of course, principals of schools under huge pressure to up their school results, and district and provincial heads desperate to improve their national standings in the now widely publicized results, become part of this plot to put a good face on exam results. There will of course be no push back from the national ministers (basic and higher education) because their own reputations in the presidency and in public depend on better results in matric.
And so what you have here is this tight network of mutually reinforcing decisions which binds all levels of the system into a complicity of low expectations for academic education in general and mathematics education in particular.
The only loser in this shameful game is the learner who then shows up at university realizing that her or his dream of becoming an engineer or accountant or doctor has been shattered in this game of shoring up adult reputations at the expense of the child.
This might offend blind loyalists of the current regime, but let me be clear: the consequences of this government’s thinking about mathematics are not dissimilar to that of Verwoerd’s government: why teach the black child mathematics? Rather, teach him or her mathematical literacy, and condemn them to the kinds of jobs they are fit to occupy. Neither Verwoerd nor Motshekga (and her predecessors) believe that the black child can or should do mathematics, for the students captured and stuck in this dramatic migration from mathematics to mathematical literacy are overwhelmingly black.
Show me your reasoning
What then is the context in which mathematics has been downgraded in the choices that adults and children make every day in the nation’s schools? It is a context that despises smart people. The most recent example of this is the president’s comments about “clever blacks” in his apparently off-the-cuff remarks to traditional leaders in Parliament where the Traditional Courts Bill was under discussion. The president took aim at blacks who “become too clever” and “become the most eloquent in criticizing themselves about their own traditions and everything.” And everything, yes.
That African is used here in an ethno-genetic sense and culture as something racially insular, is red meat for another day. What should concern us, also, is the anti-intellectualism that continuously expresses itself in the public utterings of the powerful. The Minister of Higher Education wants a law that prohibits criticism of the president; I can only assume he is joking. The powerful organizations in the country insist on “group think” rather than individual expression on everything from the choice of president ahead of Mangaung to the criticism of racists like Jimmy Manyi.
“Show me your reasoning,” in the words of a mathematics teacher, is both a call for an individual defense of the path taking to solve a problem, as it is an elevation of the mind in making judgments about right and wrong approaches to the math solution.
The problem with “clever blacks” is that its discursive roots lie in the colonial reference to the “cheeky native.” You know too much; you come across as too smart; you speak too sharply; you can think for yourself. For those with short memories, an almost identical passage to the President’s rant against “clever blacks” is found in a 1936 statement by the Committee on Native Education that “There is still strong opposition to their education because 1) it makes him “cheeky” 2) It makes him turn against his culture and his people”.
All of those meanings are embedded in the derisory reference to clever blacks. Note that nobody ever speaks about clever whites; it is inappropriate of course, they are supposed to be clever as a matter of race. That is the president’s point: there is “the white man’s way” and there is the African way. These clever blacks are selling out to the former, rejecting the quiet subservience that yields to the authority of the African big man, just like in that romantic past where women knew their place and thinking people subdued their minds and passions to chiefly authority.
Which brings me to the chaos in the land at the moment; from Marikana to De Doorns, the country is burning. The people have learnt through gainful experience that to protest is to destroy—burn, attack, insult, vilify, undermine—and to dance, that oddly bizarre South African response to events both tragic and triumphant.
Where is the table of reason in this crisis? Where are the long debates and the application of the mind to what is, no doubt, a complex economy that absorbs pools of unskilled or low-skilled labour from more than one country to enrich a few? Where were the anticipatory actions by politicians and farmers alike to address the historical problem of low wages among the poorest of citizens? Where is the analysis that links the violence of De Doorns to this epicenter of the xenophobia that struck the region not too long ago? Where are the financial calculations that test the proposition that raising wages in a fragile global and domestic economy invariably leads to job losses on implementation?
No, this is not a country that resorts to reasoning in a crisis; we resort to rage. We use our muscles not our minds. We are inflamed by images we do not like, rather than words we fail to ponder. We lack the capacity to anticipate the consequences of destructive action, for that would require logical processes of thought for which we do not have the mental preparation.
It does not help, by the way, that behind the flames of the wine farm protests lies a long-held political threat to make the province ungovernable.
But there is a much deeper problem here that I wish to warn about. More and more young people are flooding the ranks of the semi-literate, unemployable masses whose only job might be in the dark underground caverns of the mines or toiling in the unbearable heat of the pesticide-covered vineyards of the cape. In those smothering conditions a dangerous lesson is being learnt: you can raise your wages (and life chances) dramatically by protesting violently.
There is, for these youngsters, an alternative to schooling to get ahead. Violence, pure and simple. And then we make the fatal error of rewarding violence with higher wages. In the minds of the protestor, this is the route to follow the next time round.
In other words, the violence we witness almost weekly—from miners to truckers to workers on wine farms—is, in essence, a failure of education. These young and middle-aged people dancing and looting in the Cape, and brandishing weapons during protests in the North West, are the people that we failed with more and better education. We failed to keep them in school, and while in school we failed to teach them the values that come with good mathematics education—reasoning, logic, and the long-term benefits calculated to come from finishing school and getting a post-school qualification.
I hate to be a prophet of doom, but let me say this. If we do not stop the free fall in education within the next 10 to 15 years, this democracy will implode and all chances of creating an economically productive and humanely compassionate society will be lost.
It is not only the growing numbers of semi-literate youth that should concern us; it is the fact that the values base of a good education has begun to give way below us. Boys stabbing and sometimes killing each other; rapes by school principals; pregnant school girls; drugs in schools; cell phone cameras recording all kinds of school playground atrocities—check out the headlines day after day. This is only the beginning.
There is one picture that I cannot remove from my mind. It shows up repeatedly on the front pages of the news. Last week it was there again, this time in Meadowlands. Lying flat on their faces with hands tied behind their backs are nine human bodies with heavily armed policemen looking over them. The alleged criminals are young, they are men and they are black. There was the usual “tip-off” about a cash-in-transit robbery. This picture plays itself out in my mind over and over again.
What if those young men stayed in school? What if they stayed in school and did mathematics? What if through the teaching of mathematics they learnt not only numbers but values such as perseverance and the dignity of work?
I hold the firm belief that every South African child, taught well, can succeed in mathematics. Some of you would have read my column about a young woman called “Thembi” who was raped by a family member at the age of 9 and witnessed her father beat her beloved mother to death the next year. Despite a traumatic life and impoverished schooling, she was taken up in a good high school in Bloemfontein in Grade 10. This year she is in matric, taking both mathematics papers and scoring 90% and 94% in the two tough math examinations. The same person, a different mathematics classroom.
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It is a matter of justice, therefore, that we cannot punish the children of the poor for weak and inconsistent teaching in the subject. It is a question of equal opportunity when the mainly white and black middle-class students take mathematics and the children of the poor are stuck with mathematical literacy. It is and should be a concern of democracy that without access to the best in mathematics education, we fail to strengthen the foundations of a still fragile society given the values that are lost in poor math teaching.
Maybe there was a reason that Suzman the politician met Kambule the mathematician in a Soweto school that day. Helen Suzman might even have anticipated that connection between mathematics and society in one of her most famous statements, a testament to challenge us all:
“I stand for simple justice, equal opportunity and human rights. The indispensable elements in a democratic society—and well worth fighting for.”
 In some translations, that is, about 450 feet long, 75 feet wide and 45 feet high or about 135 meters long, 23 meters wide and 14 meters high
 Recorded by JC Kannemeyer (2012), JM Coetzee, A life in writing, Jonathan Ball Publishers, p. 88 (translation from Afrikaans by Michiel Heyns)
 For an excellent discussion on mathematics and reasoning see Joan L Richards (2012), Connecting mathematics with reason, In mathematics and democracy, The Mathematical Association of