Charting a course to make maths truly universal

Mathematics has the potential to be a great equalizer. Compared with other scientific and technical fields, it requires few expensive physical resources. Sometimes, a whiteboard and a marker are all that’s needed.

However, maths is one of the least diverse of the STEM disciplines of science, technology, engineering and mathematics. For instance, the Survey of Earned Doctorates conducted by the US National Science Foundation) showed that, of all 1,915 doctorates awarded in mathematics and statistics in the United States in 2021, none went to people identifying as American Indian or Alaska Native. Just 28 (1.5%) were awarded to Black or African American mathematicians or statisticians, and 33 (1.7%) to researchers who identify as belonging to more than one race.

Maths is built on a modern history of elevating the achievements of one group of people: white men. “Theorems or techniques have names associated to them and most of the time, those names are of nineteenth-century French or German men,” such as Georg Cantor, Henri Poincaré and Carl Friedrich Gauss, all of whom were white, says John Parker, head of the mathematical sciences department at Durham University, UK. This means that the accomplishments of people of other genders and races have often been pushed aside, preventing maths from being a level playing field. It has also squelched wider access to rich mathematical ideas developed by people of different backgrounds — such as Chike Obi, James Ezeilo and Adegoke Olubummo, a trio credited by the website Mathematicians of the African Diaspora with having pioneered modern maths research in Nigeria. Another example is Mary Golda Ross, a Cherokee mathematician and engineer who was a founding member of ‘Skunk Works’, a secretive division of the US aerospace manufacturer Lockheed. There, she developed early designs for space travel and satellites, among other things.

In 2022, the maths department at Durham launched a decolonization effort that was one of many initiatives aimed at making higher-education maths curricula more inclusive. Mathematicians involved in that and similar initiatives elsewhere explain how they are ushering in a new era of teaching and training for the next generation of mathematicians.

Linking culture to curriculum

Some mathematicians seeking to reform maths curricula taught in North American institutions are doing so by incorporating Indigenous cultural and community concepts. This makes courses relevant to a wider range of students, and boosts their engagement by linking content back to people and cultures.

Edward Doolittle, a mathematician at First Nations University of Canada in Regina, contrasts Indigenous mathematics with the mainstream, global way of teaching maths, in which instructors essentially present the same content regardless of where they’re teaching.

Doolittle, who’s also a Mohawk person from Six Nations in southern Ontario, says that calculus courses are structured so similarly that he could teach the subject “anywhere the students speak English”, and even take over teaching a course midstream.

Decolonizing science toolkit

By contrast, he says that Indigenous mathematics involves getting inside a culture and examining the mathematical thinking in it. He draws a further distinction between Indigenous mathematics and the practice of what he calls “indigenizing mathematics”, which, he says, involves searching for cultural examples to use in courses taught in the global version of mathematics.

Indigenizing mathematics tweaks the curriculum when it isn’t feasible to fully immerse students in ideas from an Indigenous culture, Doolittle says. “It’s very hard, if not impossible, to break out of” the global mathematics system, he notes. By indigenizing mathematics, instructors can stay within the parameters of what they’re required to cover while broadening the cultural scope of their curriculum.

Using that approach, “we have respected the knowledge of Indigenous people and are furthering our ties with Indigenous people” while still teaching students core topics, he says. For example, when teaching statistics courses, Doolittle has discussed a simplified version of the Peach Stone Game, which is based on making wagers and is played in his community. “You can analyse this in terms of a binomial probability distribution,” or the chances of two outcomes over time, he says.

“I would like to encourage many of my colleagues to engage in indigenization efforts, and hopefully to turn up interesting examples from their local area,” Doolittle says.

However, he cautions that “it’s not a matter of opening the book and grabbing an example”. Instead, he says, a thoughtful and carefully planned process “is required to do this authentically and ethically”.

For instance, it’s usually inappropriate “to share knowledge of ceremony, without really strong permissions and ethical approvals in place” from collaborator or elder members of the Indigenous community from which the example is drawn. By telling his students about something similar to the ceremonial Peach Stone Game but not identical, Doolittle avoids sharing information that isn’t meant to be made public.

One guideline to follow is that “if an example is written in a book somewhere, then we can use it”. But, Doolittle says, always double-check with another source that it’s both an accurate and an appropriate example.

Kamuela Yong, an applied mathematician at the University of Hawai‘i–West O‘ahu, stresses the importance of networking, especially if mathematicians don’t belong to the communities from which they hope to draw examples. In 2012, Yong became the first Native Hawaiian to earn a doctorate in applied mathematics, when he obtained his degree from the University of Iowa in Iowa City.

In 2019, when Yong began strategizing about indigenizing his pre-calculus course, he wanted to integrate examples from Polynesian ocean-navigation techniques. However, he and his immediate relatives “are not sea people”, he says. “My ancestors voyaged here — someone down the line was on a canoe, but not my parents or my cousins.”

So, engaging with various resources has been a key component of his curriculum overhaul and his accompanying online pre- calculus textbook, which will eventually be freely available. To begin revamping his curriculum, he identified a few strong examples through online searches.

The Polynesian Voyaging Society, a non-profit research and educational organization based in Honolulu, Hawaii, was a crucial source of information. Part of that organization’s mission is to share “the art and science of traditional Polynesian voyaging”. Yet as Yong started writing the book, he realized that his own experience didn’t give him the knowledge and connections he needed. Without further context, “it didn’t feel right” to interweave voyaging examples in his curriculum.

So, Yong engrossed himself in building connections with voyaging communities. He volunteered with various groups and talked to voyaging experts about his project. Their reception of his work was “overwhelmingly supportive”, he says.

Once he received that buy-in from people in the Polynesian voyaging community, he felt that he could responsibly include those examples in his courses. Working closely with community members can help mathematicians to avoid crucial mistakes. Yong received constructive feedback that made his examples more realistic. For example, there are certain routes from Fiji to Tonga that aren’t travelled, owing to strong ocean currents.

When instructors replace abstract examples that students often find irrelevant with ones “that you can see and experience”, the curriculum entices students to learn, Yong says. Although students might be especially interested in maths examples derived from their own cultural backgrounds, they also benefit from engaging examples that are rooted in other communities.

More students might now be able to reap those benefits, says Yong, because interest in indigenizing university mathematics is growing. In 2020, he co-founded the Indigenous Mathematicians organization. He and the other leaders of the organization plan to pull together related resources on the group’s website. It’s paramount that mathematicians approach indigenizing or decolonizing maths respectfully — but that doesn’t mean it will necessarily happen quickly, Yong notes. “Yes, we want to indigenize it, but we’re going to let it happen a little bit more organically.”

Yong urges other mathematicians to make human connections if they want to introduce maths examples from communities that they don’t belong to. Otherwise, “it’s appropriation all over again”, he notes.

‘The next Einstein will be African’

In Africa, too, a unique model of maths higher education is aiming to capitalize on human connections and local cultural context. At the African Institute for Mathematical Sciences (AIMS), which receives public and private funding, decolonizing maths teaching and training means encouraging students from across the continent, and especially women, to learn from leading lecturers, both and African and from elsewhere — and then to put their talents to work for the betterment of African communities.

The institute is a system of five centres of excellence in Cameroon, Ghana, Senegal, South Africa and Rwanda that are designed to deliver the next generation of leading mathematical thinkers on the continent. AIMS’s five centres award fully funded master’s degrees and doctorates, preparing students for jobs in academia and in industry. AIMS is built around the motto “We believe the next Einstein will be African”.

“We always have a Pan-African cohort in each centre,” says Sampson Adotey, senior manager of outreach for AIMS in Cape Town, South Africa. Adotey, who is Black, was born and raised in Africa. Each centre hosts, on average, people from 15 African countries, studying and living together in a 24-hour learning environment, he says. “Students from the same country do not stay together — we mix them up.” Students are encouraged to leave their countries’ geopolitical differences at the door, Adotey says, an approach that fosters unity in the student body.

But it is AIMS’s focus on supporting female mathematicians that led Angela Tabiri to describe its programme as “life-transforming.” Tabiri, an African mathematician at AIMS in Accra, Ghana, whose research focuses on quantum algebra, first came to AIMS Ghana to pursue her master’s degree in 2013. In 2019, she earned her doctorate in mathematics from the University of Glasgow, UK.

Tabiri had always planned to move back to Ghana to be near her family. But once she returned in 2019, her early-career struggles echoed those of many other African mathematicians. Despite her passion for sharing her maths talents at home, and having interviews at universities, the right job didn’t come up. “The system is a bit slow here,” Tabiri says.

Other African mathematicians who’ve trained abroad often find that such job-market pressures stop them from returning. Low salaries are one big driver of that talent loss, Adotey notes. African mathematicians often find that job opportunities in their home countries pay a pittance compared with elsewhere.

But Tabiri’s AIMS connections created a pathway for her to pursue maths research in Ghana. On one of her return visits, AIMS’s president encouraged her to apply for a postdoctoral fellowship, which she held for two years before becoming a research associate.

“It was great for me to have passed through AIMS and be back again to teach,” Tabiri says. When students see “a woman of their same colour” who trained at AIMS, earned a doctorate and returned to work there, it’s encouraging, she notes. “It makes them believe they can also get a PhD.” Out of more than 2,400 AIMS alumni, one-third are women.

AIMS also offers a ‘mini-MBA’ programme and a cooperative master’s degree programme. The latter pairs students with industry partners, such as banks and other financial services companies, software companies, development organizations or international research centres, for internships that last from three to six months. These learning experiences prepare them to work in industries such as big data and IT security. And Adotey says that several industry partners have hired alumni as employees.

It was more than chance that enabled Tabiri to return to AIMS Ghana. To create the future Africa that AIMS hopes for — one in which maths expertise is a catalyst for economic prosperity — the organization is using a hybrid approach to recruiting talent.

Faculty members at the centres are hired from African countries, often through partnerships with local universities. AIMS also hosts visiting lecturers from outside Africa who teach courses that range from a few weeks to two months in length. Bringing in outside researchers exposes students to top talent while they continue to expand their roots in Africa’s mathematical communities.

Now, Tabiri is cultivating Ghana’s future mathematical talent in another way. She’s the academic manager of AIMS’s Girls in Mathematical Sciences, a free nine-month programme for secondary-school students.

The scheme was founded because too few women were applying to AIMS. It equips girls with free books, a laptop and Internet access. “Some of them haven’t even seen computers,” Tabiri says. Through virtual masterclasses, academic and industry mathematicians discuss “research in a way the students can engage with”.

Each girl is paired with a mentor, and students visit AIMS Ghana during school breaks, with free meals and lodging, to attend mini courses on finance and physics. In the first cohort of students, 35 girls attended from 11 of Ghana’s 16 regions, Tabiri notes. They graduated from the programme in November 2021. “For those who have applied to university, 21 of them are doing STEM courses.”

Tabiri is confident that, in a decade from now, “these girls will be leading in research and innovation in the mathematical sciences”.

Facing misconceptions

The next generation also leads the way in the decolonization efforts at Durham’s maths department — but these haven’t been without bumps in the road. Sometimes, the efforts have led to confusion or political backlash. Just using “that word ‘decolonization’ may mean a lot of opposition that you should be ready for”, says Emmanuel Ogundimu, co-director of Durham’s biostatistics unit, who leads the decolonization initiative. But he thinks that, with patience, this work can create meaningful change.

Durham’s maths decolonization work is part of a wider movement in the United Kingdom to “decolonize the curriculum across all universities and across all subjects”, says Parker, who is white British. He says that departments were asked by the university to think about what they could do.

The Black Lives Matter movement, which accelerated following the murder in 2020 of George Floyd by a police officer in the United States, moved “the whole agenda into the forefront in this system”, says Ogundimu, who hails from Nigeria and is of Black African descent. Ogundimu and Ric Crossman, a statistician at Durham, selected three undergraduate interns to work on the decolonization project, from a pool of students who applied. Those interns – Harini Pradeep, who is of South Asian descent, and Claire De-Korte and Leah Parry, who are both white – are an integral part of the project.

Decolonizing science toolkit

From the onset, the interns “knew there would be misconceptions” in the outside world about what they’re working to accomplish, Ogundimu notes. Sometimes it’s even challenging for mathematicians and other researchers to imagine how to decolonize a quantitative subject such as maths, because they’re not used to identifying how their curriculum might be affected by colonialist or racist mindsets. Some might initially even view this work as detracting from the rigour of their instruction by focusing on what might seem to be strictly social issues. But mathematicians who have thought deeply about decolonization say that it is essential to creating an academic environment that is welcoming and conducive to the success of maths students and scholars of all backgrounds.

First, the Durham interns asked other UK maths departments about their institutions’ decolonization processes. This has revealed that other departments are also struggling to define what the process means for them — is it about rooting racism out of the curriculum, adding more-inclusive examples, diversifying who is teaching and learning maths, or all of the above?

This year, the students plan to poll other students at Durham about their understanding of decolonization and how it should be accomplished in the maths department, Ogundimu notes. Finally, they are developing a decolonization handbook for faculty members, which will “guide them through the principles of what decolonization is and how that could translate into what we want to achieve overall”.

The handbook will focus on three things: “what students are being taught, how it’s being taught and who is doing the teaching,” Ogundimu says. “What happens in other cultures? How does this impact how mathematics is communicated in general?” he asks. These curriculum changes demonstrate to students that white Westerners aren’t the only people doing mathematics.

“These ideas go a long way for getting people engaged,” Ogundimu says. “Who says that an example in statistics cannot come from some data set from ancient Egypt?” he asks.

Last year, the department faced scrutiny after some media outlets criticized its decolonization webpage, which was written mainly by Crossman, who is white. One publication even described decolonization attempts as “sinister”. The efforts were misrepresented in the media, Ogundimu says.

“Nobody says, ‘Middle-aged white men shouldn’t be cited.’ That is not the thing.” Instead, he asks, if these are the only people you have referenced in courses, then what can you do differently to include other people?

The negative coverage shows “just how easy it is to misunderstand this message”, Crossman says. And it’s “very clear evidence that the message needs to be broadcast more, not less. Because perhaps some people aren’t necessarily engaging in good faith with what we’re saying. But there’s an awful lot of other people who clearly just don’t quite understand yet where we’re coming from,” he notes.

“It’s always easy to not do the right thing because you’re too busy,” Parker says. But he encourages non-minoritized, white mathematicians such as him to empathize with “people who don’t hear people from their nation or culture mentioned”.

Durham’s senior mathematicians felt that their curriculum-reform process had to be led by the students, because otherwise “we’re in the awful situation of deciding for ourselves what’s best for them”, Crossman says. That, Parker adds, would be at odds with the concept of decolonization, because colonization “was some group of people thinking they knew best for some other group of people”.