Month: June 2025

School mathematics in South Africa is often seen as a sign of the health of the education system more generally. Under the racial laws of apartheid, until 1994, African people were severely restricted from learning maths. Tracking the changes in maths performance is a measure of how far the country has travelled in overcoming past injustices. Maths is also an essential foundation for meeting the challenges of the future, like artificial intelligence, climate change, energy and sustainable development.

Here, education researcher Vijay Reddy takes stock of South Africa’s mathematical capabilities. She reports on South African maths performance at grades 5 (primary school) and 9 (secondary school) in the Trends in International Mathematics and Science Study (TIMSS) and examines the gender gaps in mathematics achievement

What was unusual about the latest TIMSS study?

The study is conducted every four years. South Africa has participated in it at the secondary phase since 1995 and at the primary phase since 2015. The period between the 2019 and 2023 cycles was characterised by the onset of the COVID-19 pandemic, social distancing and school closures.

The Department of Basic Education estimated that an average of 152 school contact days were lost in 2020 and 2021. South Africa was among the countries with the highest school closures, along with Colombia, Costa Rica and Brazil. At the other end, European countries lost fewer than 50 days.

Some academics measured the extent of learning losses for 2020 and 2021 school closures, but there were no models to estimate subsequent learning losses. We can get some clues of the effects on learning over four years, by comparing patterns within South Africa against the other countries.

How did South African learners (and others) perform in the maths study?

The South African grade 9 mathematics achievement improved by 8 points from 389 in TIMSS 2019 to 397 in 2023. From the trends to TIMSS 2019, we had predicted a mathematics score of 403 in 2023.

For the 33 countries that participated in both the 2019 and 2023 secondary school TIMSS cycles, the average achievement decreased by 9 points from 491 in 2019 to 482 to 2023. Only three countries showed significant increases (United Arab Emirates, Romania and Sweden). There were no significant changes in 16 countries (including South Africa). There were significant decreases in 14 countries.

Based on these numbers, it would seem, on the face of it at least, that South Africa weathered the COVID-19 losses better than half the other countries.

However, the primary school result patterns were different. For South African children, there was a significant drop in mathematics achievement by 12 points, from 374 in 2019 to 362 in 2023. As expected, the highest decreases were in the poorer, no-fee schools.

Of the 51 countries that participated in both TIMSS 2019 and 2023, the average mathematics achievement score over the two cycles was similar. There were no significant achievement changes in 22 countries, a significant increase in 15 countries, and a significant decrease in 14 countries (including South Africa).

So, it seems that South African primary school learners suffered adverse learning effects over the two cycles.

The increase in achievement in secondary school and decrease in primary school was unexpected. These reasons for the results may be that secondary school learners experienced more school support compared with primary schools, or were more mature and resilient, enabling them to recover from the learning losses experienced during COVID-19. Learners in primary schools, especially poorer schools, may have been more affected by the loss of school contact time and had less support to fully recover during this time.

This pattern may also be due to poor reading and language skills as well as lack of familiarity with this type of test.

Does gender make a difference?

There is an extant literature indicating that globally boys are more likely to outperform girls in maths performance.

But in South African primary schools, girls outscore boys in both mathematics and reading. Girls significantly outscored boys by an average of 29 points for mathematics (TIMSS) and by 49 points for reading in the 2021 Progress in International Reading Study, PIRLS.

These patterns need further exploration. Of the 58 countries participating in TIMSS at primary schools, boys significantly outscored girls in 40 countries, and there were no achievement differences in 17 countries. South Africa was the only country where the girls significantly outscored boys. In Kenya, Zimbabwe, Zambia and Mozambique, the Southern and Eastern Africa Consortium for Monitoring Educational Quality (SEACMEQ) reading scores are similar for girls and boys, while the boys outscore girls in mathematics. In Botswana, girls outscore boys in reading and mathematics, but the gender difference is much smaller.

In secondary schools, girls continue to outscore boys, but the gap drops to 8 points. Of the 42 TIMSS countries, boys significantly outscored girls in maths in 21 countries; there were no significant difference in 17 countries; and girls significantly outscored boys in only four countries (South Africa, Palestine, Oman, Bahrain).

In summary, the South African primary school achievement trend relative to secondary school is unexpected and requires further investigation. It seems that as South African learners get older, they acquire better skills in how to learn, read and take tests to achieve better results. Results from lower grades should be used cautiously to predict subsequent educational outcomes.

Unusually, in primary schools, there is a big gender difference for mathematics achievement favouring girls. The gender difference persists to grade 9, but the extent of the difference decreases. As learners, especially boys, progress through their education system they seem to make up their learning shortcomings and catch up.

The national mathematics picture would look much better if boys and girls performed at the same level from primary school, suggesting the importance of interventions in primary schools, especially focusing on boys.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Vijay Reddy*

Imaginary numbers push the boundaries of calculus and other branches of math. Hill Street Studios/DigitalVision via Getty Images

To a nonmathematician, having the letter “i” represent a number that does not quite exist and is “imaginary” can be hard to wrap your head around. If you open your mind to this way of thinking, however, a whole new world becomes possible.

I’m a mathematician who studies analysis: an area of math that deals with complex numbers. Unlike the more familiar real numbers – positive and negative integers, fractions, square roots, cube roots and even numbers such as pi – complex numbers have an imaginary component. This means they are made of both real numbers and the imaginary number i: the square root of negative 1.

Remember, a square root of a number represents a number whose square is the original number. A positive number times itself is a positive number. A negative number times itself is a positive number. The imaginary number i depicts a number that somehow when multiplied by itself is negative.

Conversations about imaginary numbers with a nonmathematician often lead to objections like, “But those numbers don’t really exist, do they?” If you are one of these skeptics, you’re not alone. Even mathematical giants found complex numbers difficult to swallow. For one, calling -√1 “imaginary” isn’t doing it any favors in helping people understand that it’s not fantastical. Mathematician Girolamo Cardano, in his 1545 book dealing with complex numbers, “Ars Magna,” dismissed them as “subtle as they are useless.” Even Leonhard Euler, one of the greatest mathematicians, supposedly computed √(-2) √(-3) as √6. The correct answer is -√6.

In high school, you may have encountered the quadratic formula, which gives solutions to equations where the unknown variable is squared. Maybe your high school teacher didn’t want to deal with the issue of what happens when (b2 – 4ac) – the expression under the square root in the quadratic formula – is negative. They might have brushed this under the rug as something to deal with in college.

The quadratic formula can be applied in more cases when the expression under the radical is allowed to be negative. Jamie Twells/Wikimedia Commons

However, if you are willing to believe in the existence of square roots of negative numbers, you will get solutions to a whole new set of quadratic equations. In fact, a whole amazing and useful world of mathematics comes into view: the world of complex analysis.

Complex numbers simplify other areas of math

What do you get for your leap of faith in complex numbers?

For one, trigonometry becomes a lot easier. Instead of memorizing several complicated trig formulas, you need only one equation to rule them all: Euler’s 1740 formula. With decent algebra skills, you can manipulate Euler’s formula to see that most of the standard trigonometric formulas used to measure a triangle’s length or angle become a snap.

Euler’s formula relies on imaginary numbers. Raina Okonogi-Neth

Calculus becomes easier, too. As mathematicians Roger Cotes, René Descartes – who coined the term “imaginary number” – and others have observed, complex numbers make seemingly impossible integrals easy to solve and measure the area under complex curves.

Complex numbers also play a role in understanding all the possible geometric figures you can construct with a ruler and compass. As noted by mathematicians Jean-Robert Argand and Carl Friedrich Gauss, you can use complex numbers to manipulate geometric figures such as pentagons and octagons.

Complex analysis in the real world

Complex analysis has many applications to the real world.

Mathematician Rafael Bombelli’s idea of performing algebraic operations such as addition, subtraction, multiplication and division on complex numbers makes it possible to use them in calculus.

Fourier series allow periodic functions (blue) to be approximated by sums of sine and cosine functions (red). This process relies on complex analysis. Jim Belk/Wikimedia Commons

From here, much of what scientists use in physics to study signals – or data transmission – becomes more manageable and understandable. For example, complex analysis is used to manipulate wavelets, or small oscillations in data. These are critical to removing the noise in a garbled signal from a satellite, as well as compressing images for more efficient data storage.

Complex analysis allows engineers to transform a complicated problem into an easier one. Thus, it is also an important tool in many applied physics topics, such as studying the electrical and fluid properties of complicated structures.

Once they became more comfortable with complex numbers, famous mathematicians like Karl Weierstrass, Augustin-Louis Cauchy and Bernhard Riemann and others were able to develop complex analysis, building a useful tool that not only simplifies mathematics and advances science, but also makes them more understandable.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to William Ross*