“‘Fingerprints’ from Analogue Counting to Touch-Base Interfaces” – Laura Jimenez Rojas
An apparent oxymoron was brought to the TiM seminar: tangible mathematics. Nathalie Sinclair introduced an interesting connection between embodied cognition in mathematics and digital technologies. Currently, she is working on the development of a multimodal app that helps young learners to expand the faculty of number sense.
Sinclair alluded to the concept of multiplication as the point of departure to think of the multimodal app. She expressed that the thought that underlies multiplication may resemble that of adding, although it is not the same. It is a different kind of growth that can be thought of as “propagation”.
However, the notion of multiplication has been very much reduced to adding. This may be related to the traditional teaching strategies, for instance, multiplication tables charts. Here the process of thinking is limited to the use of memory and written symbols.
She referred to the idea of “one-handed mathematics” as the core problem of the naturalized approach to this science. Whether with a pencil or a computer mouse, “doing maths” has been understood as a process exclusive to the mind.
However, there is an anthropomorphic mathematical history that has been forgotten. In 1930 the mathematician Tobias Dantzig already said that:
“except that our children still learn to count on their fingers and that we ourselves sometimes resort to it as a gesture of emphasis, finger counting is a lost art among modern civilized people. The advent of writing, simplified numeration, and universal schooling have rendered the art obsolete and superfluous. Under the circumstances, it is only natural for us to underestimate the role that finger counting has played in the history of reckoning.” (Dantzig 2005, 10).
Although for Sinclair, it is not about the analogue art of finger counting, she raises attention to the concepts of “experience” and “gesture”. One the one hand, the speculative empiricism of Alfred North Whitehead allows an understanding of knowledge as being a relational process. This kind of process is based on the idea that the object I seek to know is not determined yet, and this is due to a circular relation in which the two parts bring each other up.
On the other hand, Gilles Châtelet introduces the “matter” of mathematics. Brian Rotman asserts: “Refusing the Aristotelean division between movable matter and immovable mathematics, Châtelet insists throughout that mathematics cannot be divorced from ‘sensible matter’, from the movement and material agency of unconscious as well as conscious bodies. Mathematics is an ‘embodied rumination’, inseparable from the contemplative, a-logical and intuitive operations of thought.” (Rotman 2015, n.d.).
The framework that Sinclair draws upon Whitehead and Châtelet allows her to propose a very interesting app. Fingers come to dance on the iPad touch-screen. The screen is divided into two spaces, representing the factors that will perform the multiplication. The combinations are infinite as the affordances of the technology are based on a sense of propagation, change and transformation.
For Sinclair, experience and gesture in mathematical thinking are about the “feeling of multiplication”. She presents a new possibility to re-inscribe mathematics in the body, in a way in which the body shifts from being a passive collector of cognition into an experience of embodiment in the digital age, because as Sinclair affirmed: “concepts are material”.
- Dantzig, Tobias. 2005. Number: The Language of Science. Ed. Joseph Mazur. New York: Pi Press.
- Rotman, Brian. “Mathematical Movement: Gesture”. Brian Rotman (blog). 6 Feb. 2015. Accessed December 20, 2018. https://brianrotman.wordpress.com/articles/mathematical-movement-gesture/
- Finger Symbols (From manual published in 1520) in Dantzig, Tobias. 2005. Number: The Language of Science. Ed. Joseph Mazur. New York: Pi Press.