The perspectives in the blog have been gathered from recent research into the topic of decoloniality and mathematics education. The focus of these articles is not exclusively on higher education, so not everything mentioned in them will be directly relevant to, for example, university lecturers. As such, the purpose of this blog is to narrow that scope to tertiary education and to present to maths lecturers some practical—rather than conceptual—methods of beginning to approach decoloniality within their pedagogy.

One of the first things to say to university mathematics lecturers who are interested in engaging with decoloniality is that, by and large, decoloniality does not (or at least should not) set itself against scientific or mathematical thought. Scientific discovery is not inherently the enemy of decoloniality; decolonial scholars recognize the usefulness of algebra, geometry, trigonometry, calculus, other maths fields, and other STEM[1] disciplines, in tackling many practical and pertinent issues. This means that my decolonial critique of mathematics and its pedagogies, outside of mathematical social science courses (e.g. history of math, economics, etc.), is not concerned with arguing against the internal positivism[2] of algebra or geometry.

Rather, what concerns me as a decolonial scholar are two things: 1) the position mathematics holds within a historically Eurocentric narrative of human development, and 2) the role mathematics plays in maintaining and legitimizing structures of coloniality[3] within local and global societies. These concerns are more aptly addressed in pedagogy and practical application than with a wholesale dismissal of mathematics and European mathematicians, and below I will briefly mention three things lecturers can do to move towards a decolonial position. These thing are relatively non-activist (i.e. they do not demand any specific action to take place) but instead encourage critical and considered thought in lecturers about their role as a mathematics pedagogues and the role of maths more broadly.

**1. Understand and portray mathematics as a historically global phenomenon**

Even though many (if not most) mathematics lecturers do not heavily engage with histories of mathematical concepts and disciplines within their pedagogy, it is nevertheless important to be cognizant of these histories when teaching on a variety of topics. Near-constant references to ancient Greek mathematicians in our maths pedagogy, although these mathematicians incontrovertibly played a major role in the rigorous development of global mathematical thought, obscure the important and transformative work of Chinese, Islamic, and other non-Greek cultures on this body of thought.

Euclid, for example, is rightfully remembered as a revolutionary mathematician who wrote perhaps the most influential textbook on maths in the Western world. A call to decolonize mathematics should not be (nor be portrayed as) a call to ‘ban’ Euclid, nor to forbid teaching about him, nor to diminish his accomplishments. However, without the later contributions of medieval Islamic mathematicians during the Islamic Golden Age (building upon Greek and Indian scholarship), the transmission of mathematics to Europe would have looked vastly different.

In instances where it is relevant or important to do so, lecturers need to demonstrate their cognizance of the global history of mathematics, and at all times they need to fully understand the context of the ideas they teach.

**2. Recognize that mathematics is political**

When I say that mathematics is ‘political’, it means that mathematics (as a discipline) plays an integral role in how power is distributed within (and even between) societies and how group decisions are made. This is best understood not as something mathematics is able to do on its own but instead as an interdisciplinary deployment of various disciplines in order to organize social power or group decision making.

A basic example would be the unavoidable influence of algorithms in daily life, a confluence of mathematics and computer science alongside other disciplines depending on the intended use of the algorithm (e.g. economics, politics). The development and impact of these algorithms is not neutral, and mathematicians can find themselves developing algorithms that reinforce or reproduce inequalities within societies. Insofar as facial recognition software relies on mathematical algorithms, maths can find itself caught up in having to explain how and why facial recognition software is often particularly inaccurate on women of colour[4]. When these algorithms are used in law enforcement, housing, or employment sectors, such an inaccuracy can have material consequences on these women. Further, these consequences end up reproducing coloniality by instituting (inadvertently or otherwise) a tool of power that challenges the inherent humanity of people on a racial and gendered basis, potentially denying them access to shelter or work, or predisposing them to be a victim of mistaken identity in a law enforcement context.

Thus, the political position of mathematicians, and maths lecturers educating the next generation of mathematicians, needs to be one that fundamentally disagrees with any use of mathematics that reproduces coloniality, like racially biased algorithms. Further, such a position needs to act in defiance of the tendency of Western institutions to maintain coloniality.

**3. Consider ‘what,’ ‘why,’ and ‘for whom’**

This is a more personal or independent consideration for lecturers, because the answers to these questions will vary wildly due to a variety of factors, some of which are out of the control of the lecturer. However, broadly speaking, it is important for lecturers to understand that the skills needed to be a skilled mathematician are not identical to those needed to teach mathematics, and the overlap may not even be as great as one thinks. If one is committed (either by desire or circumstance) to being a maths lecturer, then an inherent part of that role should be consider:

- what exactly you are teaching (topics, methods, etc.),
- who comprises a particular group of students (to train future mathematicians, to teach students who need elective credit, etc.),
- why they need to know what you are teaching, and
- why your manner of teaching will help this particular group of students.

Personally, I am no mathematician, but I have sort of awestruck fondness for topology, particularly topological visualizations. As a composer and curious scholar, though, I want to know how we can see within a mathematical mind like Leonhard Euler’s a collision of hard maths and the creative arts, with topology on the one hand and, very much posthumously, neo-Riemannian music theory on the other.

A long-term goal is for learning outcomes of maths courses to be highly attuned to the needs of the students enrolled on them. Creatively speaking, I would gain more as a student from thinking about a ‘topology of music’ or a topological music theory than from a course that required me to bank topological facts for retrieval on a future exam, although there is a case to be made for the latter scenario.

Hopefully, these three points will encourage mathematics lecturers (and perhaps their students) to engage more critically with the discipline, to think about how maths naturally feeds into the sphere of politics via other disciplines, and to reconsider the position of students and their needs within the design of maths courses and programmes. Beyond this, I hope it’s clearer what the aims of decoloniality really are and how interested parties in the field of mathematics can get involved in the process.

**Further reading**

Felipe Santos Fernandes, Victor Giraldo & Diego Matos. (2022). ‘The Decolonial Stance in Mathematics Education: pointing out actions for the construction of a political agenda.’ *The Mathematics Enthusiast, 19*(1).

Gert Schubring. (2021). ‘On processes of coloniality and decoloniality of knowledge: notions for analysing the international history of mathematics teaching.’ *ZDM – Mathematics Education, 53*. DOI: 10.1007/s11858-021-01261-2.

[1] Science, technology, engineering and mathematics

[2] By this, I mean that it is not useful, from a decolonial perspective, to argue that there is something to ‘decolonize’ within, for example, an understanding of Pythagorean triples, except perhaps a clearer historical understanding of the many mathematical cultures besides the Greeks who encountered the phenomenon and theorized about it. Such an understanding would not undermine the maths itself, of course.

[3] ‘Coloniality’ can be understood as the European/Eurocentric structures of power, control and hegemony that have arisen out of a Eurocentric conception of ‘modernity’, structures which established themselves globally as part of the European colonial project.

[4] See Klare et al. (2012). ‘Face Recognition Performance: Role of Demographic Information.’