February 2024
Sarah Wolff (Denison University)
Almost exactly a year ago, I flew to Kimberley, South Africa as a U.S. Fulbright Scholar. I spent about six months working at a local university in the mornings and a STEM nonprofit in the afternoons. This was a remarkable, challenging, and deeply thought-provoking experience, affecting how I view mathematics education both broadly and within my own classroom. I hope to share some of that here, but let me begin with some context.
Image source: https://southafrica-info.com/infographics
The Northern Cape province of South Africa is an area that has historically lacked educational opportunities and access. Kimberley, the capital of the Northern Cape, was once the second largest city in South Africa but is now most known for ‘the Big Hole,’ an abandoned De Beers diamond mine in the city center. The lack of education, opportunity, and jobs in this area has led to significant generational poverty, homelessness, and alcohol and drug abuse. More recent challenges in Kimberley include water and electricity shortages — the city regularly shuts its water off every evening starting at 8pm and occasionally for days at a time. All of South Africa has been experiencing loadshedding in which the electricity is switched off for several hours multiple times each day.
Sol Plaatje University (SPU), one of the youngest universities in South Africa, was founded in Kimberley in 2013 and provides a beacon of opportunity not previously found in the Northern Cape. The only university in the Northern Cape province and one of only two universities created post-Apartheid, SPU has expanded access to education for those from disadvantaged communities. Young people in Kimberley now see college as a possibility; the majority of students at SPU hail from the Northern Cape. At Sol Plaatje University, among other responsibilities, I taught Discrete Mathematics for the second year Data Science students.
The Maths and Science Leadership Academy (MSLA) is a nonprofit STEM education program in Kimberley that was founded in 2006. They identify learners in grades 9-12 who have potential, the desire to succeed academically and who are in need, providing ongoing STEM support through after-school science, math, and digital literacy classes. They also hold Saturday and holiday academies, providing additional classes as well as career guidance and university application support. MSLA opens early, closes late, works weekends and holidays, and is run by a total of four people. And their dedication shows: for the last 13 years, every Grade 12 MSLA student has passed the National Senior Certificate Exams, most at a Bachelor’s pass level, which is the achievement level needed to be admitted to university. At MSLA, I was the primary maths instructor for the entire Grade 11 class — about 90 students — and subbed for the Grade 9’s, Grade 10’s, and Grade 12’s as needed.
Me with the Grade 11s – some of the most inspiring students I’ll ever meet
A Spiraled Curriculum
One of the most notable differences in STEM education in South Africa is curricular design. In the US, high school subjects are typically taught in yearly blocks — a year of algebra, a year of geometry, a year of chemistry, a year of physics, etc. In South Africa, much of the same content is covered but the topics are spiraled, i.e., taught in small blocks that build on each other each year. For example, in Grade 10 they learn to solve a system of two linear equations in two unknowns. In Grade 11, they learn to solve a system of two equations in two unknowns where one is linear and one is quadratic.
MSLA Grade 11 Workschedule
Teaching topics for only a couple of weeks at a time can feel like constant whiplash. This was further exacerbated by the fact that I was teaching students from over 10 different schools. While each school was supposed to be teaching the prescribed curriculum for the prescribed amount of time, students were, understandably, often coming to MSLA at different places in the curriculum. You try teaching students to write circle geometry proofs in only two weeks! Especially if the first week is reminding them of the two weeks of geometry that they learned a year ago and can’t remember. Many of my classes inevitably began with “I know half of you are currently still learning about topic x but we’re going to be talking about completely different topic y today… and let’s start by reviewing what you did last year when you learned topic y”.
As jarring as it often felt in practice, the idea behind spiraling the curriculum is brilliant. Returning to topics over time is an important reinforcement strategy. They might not have enjoyed it, but I watched students reinforcing and strengthening constantly as they worked to recall last year’s material and extend it further. Further, when done well, interleaving material “improves mathematics learning not only by improving discrimination between different kinds of problems, but also by strengthening the association between each kind of problem and its corresponding strategy.” [1]. I saw this in my students as they frequently tried to identify a problem type and then recall a strategy for that type.
Though our courses here in the U.S. are not typically spiraled, the content inevitably builds on prior material. Interleaving is a strategy that we can introduce to help our students learn more deeply. It could be as simple as reviewing/recalling/testing material from the first few weeks of class before extending it in later weeks or as involved as adding a review day or two to recall and connect material from prior courses. On a curricular level, we do something at Denison that I love: we teach computational linear algebra in our multivariable calculus class. That way, once students start linear algebra they are reinforcing, strengthening, and extending skills from a prior class rather than jumping into an entirely new-feeling topic.
Assessment
In South Africa, assessment dominates the education landscape. At the end of each school year students take subject examinations which determine whether or not they can move on to the next year. These exams are most important in Grade 12 as they almost entirely determine whether a student can go on to study at university and what subjects the student can study.
Once in university, exams still dominate the learning experience. When designing my course at SPU I was encouraged to have the entire grade determined by examinations. As someone used to writing and grading weekly problem sets, this completely changed how I approached and designed my classes. I could write an entire article on that alone, but I was most surprised by my change in mindset when writing a test.
The overarching goal of a test is to assess whether the students have learned the material. But I imagine that many of us also have a desired distribution in the back of our minds — guided by school and departmental norms. I am used to designing a test that will sort the students into neat little piles and achieve the average percentage that is typical at my institution. And often, if that average isn’t what I’m looking for, I’ll curve the grades up or create some activity that allows students to get a few points back.
The practice of curving an exam simply isn’t done in South Africa because marks are standardized. Image teaching a coordinated course…except the coordination is nationwide. Each instructor at the university level sends each semester test and final exam, along with rubrics, to another instructor —a moderator —- to have the exam approved before it is administered. For the final exams, once they are finished grading, the instructor sends a percentage of the marked exams to the moderator to be checked. If the course is an ‘exit-module,’ i.e., if the students are in their final year of studies, the moderator must be external to the institution.
As mentioned, test scores completely determine whether a student progresses in their degree: a score of 50% or higher is considered a ‘pass’ and at SPU a score of 70% or higher is a ‘distinction’. Those are the only two bars and so the average percentage doesn’t matter. The only metric that matters is how many students pass the class; indeed, instructor performance evaluations are tied to pass rates. Just imagine the look of confusion when I asked a colleague what a typical test average should be!
When writing a test, I was no longer thinking about differentiating my students and writing ‘cute problems’ to separate the A’s from the C’s. Instead, I was thinking about the core course goals and topics and writing questions that would assess those course goals and topics. The questions were more straightforward because they should be: I needed the exam to demonstrate that a student met a standard. That was it. That was the goal. And shouldn’t that always be the goal? In many ways it felt more like mastery-based grading. My job was to help them all achieve the course standards rather than to impose a filter, and I loved it.
Of course, this was still very difficult to do without any homework or weekly practice outside of class that could be graded. And there were a lot of other outside factors that made teaching extremely complicated and difficult. But using a standards-based framework when writing exams is a mindset shift that I want to keep as I design my future courses.
Language
One of the first things you’ll notice in the classroom in South Africa is a higher level of formality. Titles are important, greetings are important, and a student would never dare say the word ‘you’ to a teacher. For example, a student might say to me “Good morning ma’am, and how is ma’am today? I had a question about the material that ma’am covered yesterday…”
As someone who is always overthinking myself socially, this level of formality made me constantly worried that I was coming off as a rude American. Common thoughts: “Oh no! I asked a question and forgot to first say ‘Good morning how are you?’ Wait, can I say ‘you’ to this person?”
Added to this level of formality are many small wording differences. About halfway through my time in Kimberley, as I drove my car on the left-hand side of the road, turned on my flicker (turn indicator) while approaching the robot (traffic light) and turned into the garage (gas station) to put petrol (gas) into my car, I realized that I was finally starting to get used to some of the language differences between South African English and American English. Most of these differences were fun! But in an academic setting, these differences can be obfuscating. Layered with unspoken norms, they can lead to pitfalls pretty quickly.
As a few examples, I asked multiple times for sample syllabi as I was trying to plan my course, but what I should have asked for were learner guides. While writing my learner guide, I needed to decide whether I was giving class tests or semester tests, which both have very specific meanings. I also needed to include a signature sheet in the learner guide for each student to submit. At the end of the semester, the registrar computed the CASS mark — total grade so far in the class — and I needed to send an email approval before students could be told if they were allowed to sit for the final exam.
At my first exam, a student asked me where the register was. Huh? Apparently, every exam must have a register (roster) for students to sign to prove that they were present. Also, the students must write each exam on specific exam paper that I provide. None of my colleagues had thought to tell me about these practices, understandably, because it is absolutely standard country-wide at all education levels. This happened much more frequently than I would have expected – hidden norms obfuscated by slightly different language that led to missteps.
Luckily, none of the mistakes I made led to irreparable damage. However, the experience has made me think much more deeply about norms and expectations within my classroom and school. I’ve been teaching at the university level for over 10 years and I am very comfortable asking questions and getting help…still, I made frequent mistakes and missteps and felt lost all the time! Think about our first-year, first-generation, and international students attempting to navigate a brand-new environment with hidden norms and expectations. A question we should all be asking ourselves: is our language clarifying or obfuscating?
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Uprooting myself and moving away from my family (and cats!) to spend half a year teaching on a different continent was challenging, sometimes frightening, and often lonely. But it was also exhilarating and extremely transformative both personally and professionally. If you ever have the opportunity to live and work elsewhere, do it! It will be difficult but you won’t regret it.
Huge thanks to the Fulbright program and Denison University for this incredible opportunity!
Citations
[1] https://pubmed.ncbi.nlm.nih.gov/24578089/