“Exponential” as just “another word” to say “fast”? Fostering narratives about the intra-/extra- mathematical importance of mathematics through connections within, and across, curriculum subjects

While mathematics is seen as a sine qua non of curricula around the world, emphasis on appreciating the importance of connections across the topics that constitute the backbone of said curricula, within and beyond mathematics, is often limited (Yeoman et al., 2017; Nardi, 2017). In this paper, I discuss the rarely tapped-into pedagogical potential of rapprochement and synergy amongst communities of mathematics teachers towards identifying said connections and incorporating them in students’ learning experiences. The theoretical underpinnings of the analyses I present are largely commognitive (Sfard, 2008) – particularly constructs such as: literate (e.g., mathematical) and colloquial (as in everyday, public) discourses (ibid.; p.118); and, object-level learning (“growth in the number and complexity of endorsed narratives and routines” (Sfard, 2008; p. 300) about mathematical objects) and meta-level learning (“change in the metarules of the discourse” (ibid) about mathematics).
I see the incorporation of said connections in students’ learning experiences as fostering what I label (Nardi, a; b) as “fuel” (as opposed to “fossil”) narratives about mathematics – with “fossil” denoting often externally imposed reverence for a mathematical object, yet alienation from its meaning, utility and purpose; and, ”fuel” denoting meaningful and empowering engagement with a variety of mathematical, and other, “realisations” (Lavie et al., 2019) of a mathematical object. I conjecture that incorporating connections in students’ learning experiences can support at least two – interrelated – goals, one at object-level and one at meta-level. I will describe and elaborate these conjectures through evidence collected in studies I have recently been involved in (one of which involves investigating student narratives about one mathematical object, “exponential growth”, that featured prominently in public health announcements during the Covid-19 pandemic).


Elena Nardi is Professor of Mathematics Education at the University of East Anglia (Norwich, UK). She studied Mathematics in Thessaloniki (Greece) and Mathematics Education in Cambridge (MPhil) and Oxford (DPhil). Her monograph Amongst Mathematicians: Teaching and Learning Mathematics at University Level was published by Springer in 2008. Her recent projects include the British Academy funded CAPTeaM project (Challenging Ableist Perspectives in the Teaching of Mathematics). She leads the RME (Research in Mathematics Education) Group at UEA and co-leads, with Irene Biza, the MathTASK research and development programme. She is member of the ESRC Peer Review College and of the Coordinating Group of the International Network for Didactic Research in University Mathematics (INDRUM). She is co-Editor in Chief of Springer’s International Journal for Research in Undergraduate Mathematics Education and Advisory Editor of the Routledge journal Research in Mathematics Education, the official journal of BSRLM, the British Society for Research into the Learning of Mathematics. She is member of the Editorial Board of Educational Studies in Mathematics, Mathematical Thinking and Learning, Journal of Mathematics Teacher Education and Mathematics Teacher Education and Development.
URL: www.uea.ac.uk/education/people/profile/e-nardi, archive.uea.ac.uk/~m011