How mathematics education can impact our “school-leaving” pupils

At the end of Grade 12, students receive their academic reports: their entire educational journey summarised on one A4 sheet of paper. It does not say ‘Captain of the Second Basketball Team’ or ‘Board 5 of the Chess Team’. It only lists the subjects a student has completed and how well, or poorly, they have fared on their educational voyage. To achieve a “school-leaving” result indicates that a student has gained sufficient knowledge, and passed their exams well enough, to leave their school days behind and plunge into the big pond that is adulthood. When little ones arrive for their first day of schooling, in my mind, they are what the philosopher John Locke would call a ‘tabula rasa’: a blank canvas upon which to paint a masterpiece. What role does mathematics play in this process? Are we painting by numbers? Are we sending spotty Jackson Pollocks out into the world to bombard and baffle the public at large? Or are we empowering students to take the brush out of our hands to paint their own works of art?

First, let us look at the possible outcomes students in South Africa are aiming to achieve in their 12 years of schooling. There are four different ways to pass matric – the bachelor pass, the diploma pass, the higher certificate pass, and a school leaving pass – and many ways to fail.

A bachelor pass means a student achieved a minimum of: 40% for a home language, 50% in four higher credit subjects and 30% in two remaining subjects. Many would consider these results to be evidence of a job well done. Schools even boast about their bachelor pass rates across the country. Achieving these results, however, by no means secures the average student a spot at a top university. Students with seven distinctions in matric often compete with academic powerhouses who finished matric with twice as many distinctions, like Christiaan and Carla Botes. They achieved 24 distinctions between them, with Christiaan raking in 14 distinctions at the end of 2022.

The minimum for a diploma pass is 40% for a home language and four other subjects, as well as 30% for one other subject. Higher certificate passers achieved 40% for their home language, 40% in two other subjects, including a second language, and 30% in three remaining subjects. This kind of pass permits a student to fail one subject, not including mathematics, home – and additional-languages or life orientation. A school-leaving pass means receiving a 40% for a home language, 40% for two other subjects and 30% for three other subjects, including a home language, permitting one failure, even if that failure is the additional language.

Despite the low bar, there are many schools around South Africa that have never managed to get all of their matrics to pass. It seems that achieving a 100% pass rate in good schools is rather tough, but achievable. For resource-challenged schools, it must be an almost insurmountable task. If you ask Mihlali Makhalima, the headmaster of Ulwazi High School in Mdantsane in the Eastern Cape of South Africa, he will tell you what extreme lengths his school had to go to for all his matrics to pass. For example, no cell phones are allowed at school at all. Matrics attend school 7 days a week, Monday to Monday, from 7 a.m. to 6 p.m., during regular school time. They do not attend church. They do not have parties. The school does not even have a matric dance. Before exams, matric students live at their modest school: six weeks of incubation before the June exams, two weeks of incubation before prelims and another six weeks before finals. During incubation periods, teachers work from early morning until midnight and parents volunteer to sleep at the school thereafter to care for the matrics and make sure they get some rest. This is no small task and requires a level of input and commitment from all the parties involved that borders on insanity. The students all pass their matric exams, and have done so for 10 years, but if such an enormous undertaking is necessary for matrics to all make it, I fear education in South Africa is in big trouble overall.

Many, if not most, schools, pupils and parents simply cannot or will not match the efforts of Ulwazi High School. Poor academic results are commonplace and many students and parents are content with their children just finishing school and getting a passing mark – in whatever form. Average and slightly above average results do not guarantee success after school either. Being a phenomenal student seems to be the only pathway to future success and happiness, right? Wrong.

Money can be made in any sphere of life. The tricky bit is finding a niche that pays for the talents one possesses, whatever they may be. This is a message that often does not reach parents and one that needs to be put on great big banners around schools. Getting students to choose the subjects they are passionate about is key: nobody is going to master a subject that they do not care about, no matter what their parents say. The reality is that medicine and engineering are not the only pathways to build wealth or to contribute to society. South Africa also needs actors, comedians, hairdressers, electricians, plumbers, carpenters, and other tradespeople to be well-trained and ready to jump into the job market. So, if academic prowess does not automatically translate into future success, what should mathematics teachers focus on in the classroom? The answer lies not in what we teach, but in who we teach. Teachers: focus on the person in front of you and help them achieve self-actualization as best you can. Many of our students are going to do jobs that currently do not even exist yet. There was no such thing as a ‘social media business consultant’ when we were discussing my future career options when I was in high school, for example. And if there was, it was certainly not talked about. Instead, I was pressured to become a doctor or chartered accountant, as that is “where the real money lies” (to quote my grandfather).

In reality, most of the professionals I know got their foot in the door through people they already knew in a particular sphere of employment. One friend of mine knew someone who worked as a maths tutor and they buddied up to start a tutoring business. Another friend worked as a merchandise salesman at music festivals because an old friend from school called when they were short-staffed: this young man eventually became the manager for the entire merchandising department of one of the largest music festival companies on the continent. Studies are important, and they completed tertiary studies along the way, but most people I know did not get their jobs by following the conventional route.

Anecdotal evidence like this is obviously not indicative of a greater trend in the nation overall, but I would like to focus on what helped my friends keep their jobs once they got a start. They were asked to stay in their positions by being reliable people who can manage their time well while also working cohesively with others. They learn from their mistakes and can take responsibility when the pawpaw hits the fan.

Working to a deadline, taking criticism well and improving your next effort, good communication skills, and being knowledgeable about technology relevant to the job in question, are invaluable skills to any employer. However, skills are only half the battle won. What kind of people are we trying to mold in our classrooms? Textbooks, curricula, and assessments are there, mostly to appease the powers-that-be that ‘education’ is taking place in classes. They are a measuring stick, more than anything else. These structures are all for naught if our students do not learn how to think for themselves, how to think critically, or how to adapt to an ever-changing world.

The mantra at the first school I worked at was that we are in the business of producing good fathers, good husbands, and good citizens. We hoped to teach young men to contribute positively to their families, their community, and our country – maybe even the world. It is worth noting that I have, so far, worked at monastic boy’s schools, hence the lack of female representation in that statement. Educators in co-ed and all-girls schools are surely also trying to produce good mothers, good wives, and good citizens.

On the topic of boys versus girls education, I think it is important to learn some lessons from a social experiment done in England in the early 2000s titled ‘Boys and Girls Live Alone’. Ten boys and ten girls (aged 11-12) were left without adult supervision in separate houses and their behaviors were observed over the course of five days. Both houses were stocked with food, games, toys, books, and paint for the children to use and play with. All the youngsters attended a cooking course prior to the experiment so that they could all cook some basic meals.

In the boys’ house, chaos reigned. No group meals were organized. The boys mostly drank sugary sodas and ate cereal. Play-time was often rough and quieter boys tried to isolate themselves from the more rambunctious boys in the bunch. Bullying and destructive behavior were the main sources of entertainment. By the end of the experiment, the house was completely trashed; covered in paint and food that had never been cooked with.

In the girls’ house, organized group meals took place more often than not. The play was more constructive and more cohesive than that of the boys: they put on a fashion show and cleaned the house afterward, for example. When arguments broke out, the girls reconciled quickly. They were not without their issues, but they were far more organized than their male counterparts. They put together a cleaning schedule so the mess was more manageable and by the end of the week, the house was left still intact, for the most part.

The inevitable lesson from the experiment, for me, was this: what we expect from our little ones, is what we will get. How people treat boys and girls was (and is) still fundamentally different. Parents are more critical of their daughters and the parents of the young ones in the experiment mentioned that they clearly hold their daughters to a higher standard than their sons. The outdated expression that ‘boys will be boys’ comes to mind. I see no reason why boys and girls cannot master the same skills. We need only visit a few Japanese schools to see that boys and girls are equally capable of being clean, well-organized, and respectful of others and their surroundings. In Japan, boys and girls as young as five clean their schools: they sweep, mop, and polish. The cleaning part of the children’s daily life at school is so impactful that many schools in Japan do not have any cleaning staff. The lesson learned here is that if we expect our children to be excellent, they will rise to the challenge. If we let our young men get away with murder during their youth, I predict they will expect the same treatment as adults. One visit to Johannesburg’s rougher parts of the city will teach you that many men have this expectation already. South Africa needs the next generation of youngsters to be better than we are right now.

Finally, how does a mathematics educator tackle this task of creating good fathers, mothers, husbands, wives, and citizens? The challenge is to create someone who can walk confidently into the grown-up world and take on the challenges that lie at his or her doorstep. The key word in this endeavor is empowerment.

Build lessons that focus on educating students about the issues they will likely have to face after school. The vital part is to teach them that these problems are solvable: that they have the power to make the world a better place by being the best versions of themselves. Remember that great minds like that of Steve Biko and phenomenal rugby talents like that of Siya Kolisi did not make waves on their own. They had to bounce their ideas off the people around them. They needed teachers to believe in them. In our classes sit the next world leaders, the next CEOs, the next Proteas and Springboks, and they are in dire need of a good mathematical education.

One of the hurdles that maths teachers must jump over, is the idea of being a maths purist. Interlinking mathematical concepts with topics in physical and life sciences, life orientation, languages, research techniques, psychology, philosophy, and even sports will be a vital part of getting children excited about learning about mathematics. Knowing that they get to use their maths skills to engage more meaningfully with the world around them is a great motivator to keep learning. Take your class outside and let each student run the 100-metre sprint while a friend times them. Use that information to generate an average, so that they can get a sense of how data is collected and how statistical measures work. Let your students walk around a cricket pitch and count their steps to get a sense of what it means to ‘walk the perimeter’ of a shape. Approaching maths from a more physical standpoint will help students get a sense of maths in their own bodies, which builds confidence and understanding – especially for younger students.

For older students, mathematics becomes more theoretical and less practical the closer they get to matric. But why not ground your teaching in practical application? When teaching Grade 10 parabolas, for example, ask students how we managed to get cars to drive at night. Is it worthwhile to put a streetlight every few meters on roads in the middle of nowhere? Probably not. Hence, how do we incorporate light into the design of the car so that it shines light only where you want it to? Eureka! We use a light fixture that will focus light from the focal point of a small bulb in one specific direction. To do this, we need parabolas. So, by using a little bit of sharp mathematics, humans are enabled to transport themselves and materials at night using motor vehicles, and so the global economy grows. If you are a maths teacher and find that you do not have a handful of these kinds of stories to get your students to understand the practical application of what they learn, perhaps it is time to rethink that lesson plan.

If nothing else, help students understand that they will likely never be asked to solve a trigonometry problem in the workplace, but that the process of solving the tough trig equation hard-wires their brains for a kind of problem-solving way of thinking. Effectively, we provide our students with a problem-solving toolkit. At the very core of our business as maths teachers, we are preparing students to leave our classrooms and be able to identify a problem, take into account as many ‘variables in the equation’ as they can see, to find all the possible ways of solving the problem and choosing the best solution for the given context. In addition, they will learn that they will likely fail to solve the problem perfectly the first time and they can always learn, adapt, and approach it from another angle. The greatest indicator of future success, in my opinion, is grit: one’s ability to overcome hardship and failure. Mathematics is a great space to develop some, if one does not have some grit in their bones already.

At best, students in our classrooms should leave being excited and curious about the world, having been asked to think about some interesting mathematics issues faced by the best humans to have wandered the planet. Students should learn about those of us who have spent our lives pondering infinity, geometry, rationality, logic, and the universe. Imagine learning about the folklore of Pythagoras, who believed that fava beans contained the spirits of the dead, and his followers who deemed numbers to be holy entities. A student’s knowledge of Pythagoras should not end at that old theorem about right-angled triangles. Bertrand Russell, Carl Friedrich Gauss, and Srinivasa Ramanujan, to name but a few of the greats, have amazing life stories and we can tell those stories to our students to give context to how humans have enjoyed playing with numbers for as long as we have had them. Part of the fun and beauty of mathematics is that it is not, in fact, really about the workplace or the adult world at large all of the time. Nobody is ever going to wonder what Qhama’s age would be if he is twice as old as he was seven years ago (as if we had access to that information and not his current age). These kinds of questions are fun for their own sake and challenge our minds to think differently. Let students explore. Let them learn about the history of mathematics and the mathematicians who helped us get to where we are today. Let them hear the stories of brilliant humans and how our numbers came about: that the number zero and negative numbers did not ‘exist’ for the longest time, and have only become relevant rather recently in human history. Let them debate about whether the Americans have it right with their imperial measurement system or if the rest of the world is on a better path using the metric system. Encourage curiosity. Indulge the seemingly ‘silly’ questions. If a student asks you why the sky is blue, lead them on an investigation to find out why, and hopefully, they can learn to find answers to similar burning questions in the future. In essence, we are trying to get students to take the brush out of our hands and paint for themselves. We are not here to hold their hand and force them to paint by numbers until the end of time. The era of schools being used to produce factory workers only is over. We are producing artists who should go out and share their craft with the world.

Some may say that I am mad, that there is no time for these approaches to teaching with such a full syllabus, or that they do not know any good stories. Our lessons are what we make of them. Telling a powerful story to set the scene for learning a particular topic takes only a few minutes, but may linger in a student’s mind for a lifetime. Looking back, I do not remember the lesson about solving cubic equations, but I do remember a teacher who was passionate about them and told me the story of how mathematicians of old used to have maths duels for the top spot in town and how cubic equations were involved in one of the funniest maths duels ever had. I can still solve cubic equations today, but that is not the point. The point is that I learned more about mathematics, about exploration, about history, and about what it means to be human from these stories than I ever learned from the exercise of solving cubic equations. Tell stories that give context to what a student is learning. This will help frame their learning in context and provide a platform for teachers to mold the next generation to beat us in all spheres of life, including in the classroom.

Lastly, here is some fuel for the tank if you feel you are nearing empty. UNESCO published some insightful numbers a few years ago that gave me hope that we are on the right track. In the year 1999, the percentage of students NOT attending school in Sub-Saharan Africa stood at roughly 41%. In the year 2019, twenty years on, that number has been slashed to 19%. We are by no means out of the woods yet, as one in five children still miss out on mainstream education. But more people being exposed to mathematics education, means more people are able not only to help themselves but also capable of solving a wider array of problems that face our modern society. If you are a teacher, keep going. We are educating the planet, one child at a time.