Decolonising mathematics, a case for their aestheticising

Building on Nathalie’s PhD work, Aestheticising Mathematics, the keynote focused on aestheticising in three areas:

• mathematics,
• mathematics education, and
• mathematics education research.

To help us understand what is meant by aestheticising, Nathalie discussed different meanings and origins of the word. For Kant, aesthetic means ‘of good taste’ or ‘universal beauty’, which we often associate with art or literature. This links to the common usage of the term, where it means ‘beautiful’, or ‘to have style’, or even ‘to be positively valued’. Nathalie then considered the etymology of the word: coming from Greek, it indicates ‘to perceive with sense’, which is, interestingly, quite different from the common meaning of the word. From this, Nathalie took a radical shift and formulated a ‘contemporary’ meaning of aestheticising as ‘sensing’ or ‘sense making’.

When addressing the notion of aestheticising mathematics, Nathalie started by giving examples of mathematics that are more akin to the Kantian definition of aesthetic as related to beauty, such as Euler’s identity, or the proof of irrationality, which are often described as beautiful or elegant. She contrasted this with the example of fractals: by asking questions such as ‘how does it make you feel?’ or ‘what do you sense?’, Nathalie argued that we can approach fractals in a more embodied way. This new way of examining mathematics would aestheticise them in the contemporary meaning of the word, through ‘sensing’ the mathematics.

This shift in thinking about mathematics is an interesting yet uncomfortable one for me, as I have always viewed mathematics as a place of logic and reason, devoid of any need for emotion. I expect others have felt the same. Moreover, it is less apparent why we need to think in this way. Indeed, it is the word ‘think’ that Nathalie drew our attention to next.

Why aestheticising mathematics?

Nathalie posited that feeling about mathematics is in stark contrast to traditional western philosophies of knowing. She argued that both Descartes and Kant proposed we know because of the human mind, which is in a hierarchical relationship with the body, which is merely to be known, and is of lesser value than the mind.

But according to Nathalie, hierarchical relationships can have serious consequences, such as political ones due to the notions of difference. She gave the example of the white abled-bodied males being seen as superior to females, non-whites, or disabled-bodied in the political and social spheres. She drew us back to the initial example of the hierarchical dichotomy of Western reason versus other ways of knowingsuch as feeling, sensing, etc. She claimed that accepting Western reason as being more valid has had a colonising effect in the world, while other ways of doing mathematics have been dismissed.

Colonising is certainly a buzzword in academia at present, especially considering the Black Lives Matter movement and attempts to decolonise curricula in education, so her points are relevant and ‘on trend’. That said, mathematics is often perceived to be a subject which is less problematic in terms of colonising due to being a sort of ‘universal language’, so Nathalie gives an interesting lens to question the need to explore the decolonisation of mathematics.

What does aestheticising mathematics and its education look like?

At the heart of aestheticising mathematics is the examination of the social-material parts of mathematics. As alluded to with the contemporary definition, the notions of feeling and sensing mathematics could be part of this. For example, Lipka et al.’s (2019) research on the use of polar coordinates among Inuit communities for navigating, ie sense making, contrasts the more commonly used Cartesian coordinates. Another example is the language used in Korean when describing fractions, with the denominator being spoken first and the numerator second, which emphasises the importance of the bottom number. Borden’s (2011) research, on how certain languages express concepts as actions (eg instead of ‘straight’ we would say ‘goes straight’, which is kinetic and not only visual) is another way of rethinking – or rather, of feeling – mathematics.

This seems like a big ask, as the mathematics taught in schools are often rigid in both content and the approaches expected, leaving little room for aestheticising. This leads into Nathalie’s second part of her talk, about aestheticising mathematics education. Nathalie acknowledged that this has already begun in some arenas, with the notions of seeing as understanding, the use of fingers for counting and manipulatives more broadly. However, thinking (or reasoning) is still seen as more important, especially when compared to the body.

Nathalie made the case for dualism, as a more continuous – and less discrete – way of thinking about the body and the mind. Due to the possible dangers with binary thinking (like hierarchical relationships, as mentioned above), we need to consider a different approach. Piaget’s work on child development, which identified that there is a growing use of the mind and a lesser use of the body as a child grows up, is one example whereby the body is seen as less valued as a child matures. Similarly, Bruner’s work on the enacted, the iconic and then the symbolic is another where abstraction is seen as more advanced than the concrete.

It seems astonishing that Nathalie questions the work of some of the most well-known and influential researchers in education, yet she doesn’t seem to expect us to throw the baby out with the bath water. Instead, she calls on us to consider new theories in learning, including dualism. She claims that more modern theories of learning, reflecting the tech-dependent society we live in, are needed today.

Her research using the app ‘Touch counts’, an app for 3- to 6-year-olds, shows how, with the use of technology, all of Bruner’s stages (enacted, iconic, and symbolic) can happen at the same time, and a lot of sensing (visual, touch, oral, movement) can take place when engaging with the mathematics in the app. Aestheticising could therefore be about considering all the senses (of which there are at least six), which could be how we aestheticise mathematics education in the future.

Yet, there is still the issue of the disjunction of mathematics itself and school mathematics. As Nathalie stated, it is like giving the students a camera to use but filling the curriculum with perspective drawings: the tools and resources afforded to us by technological advancements are not commonly used in school mathematics, or even banned in many places.

Aestheticising mathematics education research

In her final section, Nathalie started by addressing how we communicate in the mathematics education research arena. She likened this to Shapin’s (1984) description of scientific enquiry, whereby a small group are allowed to witness, and a wider literate group, or ‘public’, can read scientific papers (as is the case today with journal articles). This matter of fact-ness in scientific convention pervades into current academic research, with only a small literate group able to participate or read the work, and often, the heart and spirit of the research is not able to shine through due to the constraints of standard practices. Instead, Nathalie proposed different ways to communicate to reach a ‘new public’, which is more inclusive than the old ‘public’.

First, she argued that we can reach a new public through new and creative methods such as re-enactment, as used in research asking participants to re-enact what they noticed in videos of the 2016 Rio Olympics (Vogelstein, Brady & Hall, 2019), or rebuilding crime scenes (Fuller & Weizmann, 2021) as part of forensic investigations, called investigative aesthetics. The thought of researchers and participants recreating or cocreating as a means of data collection is appealing and could address some of the issues of the more traditional methodologies, such as the hierarchical relationship between researcher and participant, or the difficulties of understanding statistical tables by the less literate. However, one concern remains over the validity of these methods (linking back to the issue of scientific enquiry) and raises the question of what we mean by validity – ie, whether we should let go of the gold standard of the double-blind study, in order to pursue new ways of research. Indeed, in order to aestheticise education research.

Second, reaching this new public can be done through ‘mobilising knowledge’, as Nathalie put it, which, until now, has primarily been done through journal articles and books. That’s not to say we abandon publications altogether (indeed, we need to meet the expectations of funders and research institutions, who expect publications) but perhaps the focus should go beyond publications, towards using different ways of communicating and reaching wider audiences. Nathalie left it to us, the audience, to imagine what this might look like; certainly, in the digital age of Zoom and online learning, there are many new opportunities for us to ‘mobilise knowledge’. 

In summary,

You can watch the recording of the lecture below: