How SA can find safety in numbers
Teaching is a middle-class job. A teacher can earn a living at teaching but no one gets rich on a teacher's salary. Teaching is also a job that looks to the future, that helps to prepare young people for the rest of their lives.
And so one might say that the more than 900 teachers who gathered at the 19th annual national congress of the Association for Mathematics Education of South Africa represented South Africa's middle class, important players in South Africa's future.
They came to the University of the Western Cape during their school holidays, and almost all were assembled in the hall for the opening of the congress, waiting for the association's officers, university and government officials, plenary session speakers, and other dignitaries to march in.
As the opening plenary session speaker, I was among the marchers, and immediately on entering the hall was startled to hear a group of about 15 or so young children singing Gaudeamus Igitur.
"It's South Africa in 2013," I thought, "yet I am hearing a famous European university song that is hundreds of years old, one quite familiar to me."
I started singing with the children, harmonising as I always do when a part song is being sung. It comes naturally to me to do this, because my mother was a professional singer and through high school and college I spent much of my spare time singing in choirs and directing them.
When I was certified to teach maths, music — choral music — was the subject that I used to fulfil the requirement of having a second subject to teach.
A full hour was allocated for the speeches and another ceremony that took place before I was to speak. This is a long time and a speaker learns to sit stoically through boring welcomes and other rituals. But almost immediately there was a disruption in my stoicism.
The national anthem was not just being sung; it was being sung in four parts. The audience was singing like a well-trained church choir, pulsating the verses in a manner that was unlike any I had ever heard before. People of all races all singing together — this was the new South Africa. I took out my handkerchief from my pocket.
I had already been in the country for a week, at the University of the Witwatersrand and the University of Pretoria, speaking and meeting with people, discussing curriculum, teaching and learning.
But universities are special places, "ivory towers" some call them, shielded from everyday life. They tend to be liberal and they are filled with people with a common purpose of probing knowledge, learning and teaching. Race does not play as great a role.
Although I had met many currently practising teachers, they were subdued in the university environment. Now I was seeing the teachers as they are, for the first time.
At opening sessions of conferences at universities, it is almost always the case that a university official will greet those assembled. Accordingly, Brian O'Connell, the rector at UWC, stepped to the podium. He and I had chatted for 10 minutes or so at breakfast just a few hours earlier, and I expected the usual low-key welcome with a description of the university, both stated with pride.
Instead, Brian delivered an emotional call to arms, recounting the role of UWC in dismantling apartheid, pointing out the poor performance of South African students in international maths assessments, and exhorting those assembled to seize the present and work to raise the level of education for all South African students significantly.
In that moment, I wished I had prepared a different talk. My talk, about what it means to understand some maths, was analytical, not the kind of talk that rouses a crowd.
But I can be passionate, as I was on one occasion in Pretoria when I said: "What sense is there in manipulating symbols if you don't know a purpose for them, if they do not answer a question or solve a problem in which someone might be interested? If the teacher of algebra does not convince students of the utility of the subject, beyond its being on a high-stakes test, who will?"
But here, in the opening session of the congress, my talk had been prepared and could not be changed. How could I follow Brian O'Connell? Fortunately, there were a number of speakers in between us, and there was a short break while people left the stage.
As an outsider who still has never visited one maths classroom in South Africa, I cannot presume to know what is going on in them, and my views come only from what I heard.
It does seem that learning maths as symbol manipulation without meaning permeates the entire curriculum, and that the maths we use every day is not related to the maths needed for business, science, engineering, and all the other advanced areas that use maths.
How else can one explain that at grade 10 the curriculum divides into two distinct tracks, maths literacy and (pure) maths, where even a successful student in the former track cannot transfer into the latter?
How else can one explain that the (pure) maths track does not seem to include any real-world applications of maths? Taking hope of eventual success in maths away from the large numbers of students in the mathematical literacy track is not a way to increase their performance.
My impression is that the range of student performance in South Africa is about the same as the range in the United States, but the distribution is significantly different.
In the US, perhaps 15% of students are very high-performing, as a group equal to students anywhere in the world. They form the upper end of a normal distribution with a mean about equal to the countries of Europe and a larger standard deviation than most. South Africa has its high performers — often from private schools — but does not seem to have as much of a middle-performing group and has a large group of low performers, some lower than any in the US.
South Africa's low performers are generally found in the townships and rural areas, whereas the lowest performers in the US tend to be in the cities. But there are commonalities in our two countries.
In both, these places of low performance have high unemployment, fewer families with two parents, and a much lower standard of living than places with high-performing schools.
The schools are often under-equipped with books and support materials and, most seriously, understaffed and with an undereducated current staff. I heard of many places in South Africa where there are 45 or more pupils in a class, and of primary school teachers who know essentially no arithmetic.
In the US, a class size of about 25 is the norm, a class size of over 35 is uncommon, and even the poorest-prepared of teachers know some of their subject.
My particular interest is in curriculum; that is, what maths is expected to be learnt, who is expected to learn that maths, and at what ages. From what I heard, the following are great needs in South African school maths:
• Disassociation from pure rote. A large body of research dating back to before World War II has shown that "meaningful" learning produces better skill performance than rote learning. This meaning can derive from showing why the maths works; that is, discussing general properties that underlie the needed processes.
Alternatively, the meaning can derive from real-world applications familiar to the student or from concrete materials or pictures that mimic the processes.
In contrast, it seems that everything from basic facts to complex algorithms are taught in some classes with no meaning whatsoever. If a child cannot check his or her work in some way other than to repeat it, then the child does not have command of that content;
• Incorporation of applications. Maths is a language through which we attempt to describe and understand the physical, biological, economic and social world. A look at a daily newspaper demonstrates that in today's world numeracy is not separate from literacy but a part of it.
Maths permeates the descriptions of current events, editorials, advertisements, sports, business and weather. Every physical object has a geometry. We cannot get along without computers, and computers run on maths.
The ability to deal with data and statistics is needed by everyone, for everyday tasks such as where to shop and what to buy and for high-level governmental and business decisions that affect millions.
Accordingly, all over the world today's students are being asked to learn more maths than their parents or grandparents encountered in school, and this maths tends to be peppered with real data and real applications. South Africa seems behind in this regard;
• Technology. South Africa also seems behind most of the rest of the developed world in its use of calculators and computers to assist in learning and doing maths. For instance, calculators are required on 70% of the Singapore national test required of all students in grade six.
In the US, graphing calculators have been ubiquitous in high schools for almost two decades and their use is required on college entrance tests.
In Australia, parts of the new national curriculum include the use of computer algebra systems that can automatically do the manipulative skills that have been commonly taught in algebra through calculus, and the national tests assume students have this technology.
These developments make it possible for students to deal with a host of interesting situations and problems that would be difficult to approach without the technology, but they are particularly threatening in classrooms and for people whose only experiences in maths at school have been with these manipulative skills; and
• Teacher training and teacher recruiting. Even in today's computer age, in which — at least in theory — students can learn through instruction delivered electronically, the future of any country's educational system depends on the teachers it has to guide those students.
Here is where a great strength of South Africa lies — in people like those I saw and met at the congress.
I heard the horror stories of teachers sitting in teachers' lounges and not teaching, but I also spoke with many teachers who are teaching six classes a day with large numbers of young children in each class.
It is obvious that to get the most learning from our children, conditions in schools must make it enjoyable to come to school, and there must be knowledgeable teachers guiding students everywhere along the way.
In the countries that perform the best on international assessments, teachers are valued and, as a result, some of the best students enter the teaching profession. For South Africa, the creation of a large and well-educated teaching force in schools would seem perhaps to deserve the highest priority.
Zalman Usiskin is an emeritus professor at the University of Chicago and director of the university's Chicago School Mathematics Project, a position he has held for 26 years. He was an invited speaker at the Association for Mathematics Education of South Africa at its recent congress at the University of the Western Cape