A Focus on Pedagogy
Abstract
Mathematics at university level can be challenging as students are introduced to statements, proofs, and approaches they have not seen such as those in abstract mathematics. How students take on such topics greatly moulds their abilities in other topics and on their learning journey as a whole. Valuing learning while they’re being exposed to new theories and dimensions of mathematics helps them be resilient when it come to the difficult abstract parts, and seeing those difficulties as opportunities for improvement. There is a clear belief in the education literature on the growth mindset that student abilities in grasping mathematical concepts can be developed. There is a variety of positive behavioural and academic outcomes associated with that belief which can be developed by interventions in teaching, assessment, and learning strategies. However, what do those interventions look like? Based on Systems 1 and 2, as outlined in Daniel Kahneman’s celebrated book ‘Thinking, Fast and Slow’, this paper explores how, and to what extent, the mathematical mindset of undergraduate students may be shaped as a result of the layering of slow and fast cognitive processes. When are the two systems used to learn new mathematical concepts, and when using what they already know in the process? And how does the use of these systems influence problem solving, students’ thoughts and their ability to progress? The paper aims to use these questions to develop the rationale behind teaching strategies that should be used to reflect those findings, and discusses some limitations and difficulties that may arise while using such strategies.
Dr Layal Hakim is a senior lecturer and Stage 1 coordinator in the Department of Mathematics at the University of Exeter. She undertook a Bachelor of Science (Hons) in Mathematics from the Department of Mathematics Sciences at Brunel University London, where she also completed a PhD exploring applied mathematics field of Integral Equations in Fracture Mechanics. After her postdoctoral research at Imperial College, Layal joined the University of Exeter in April 2018. Through her work on multiple education committees at the University of Exeter—including Project Experience and Project Enhance, which spearheaded the institution’s response to the Covid-19 pandemic—Layal facilitates institution-wide excellence in teaching practice by influencing education strategy, curriculum design, and colleague development. Layal has also led and/or contributed to five separate projects in the University of Exeter’s prestigious Education Incubator. Her diverse work is unified by the common theme of seeking innovative ways to create an inclusive and enjoyable learning journey for HE students. Outputs from previous projects include e-assessments for Stage 1 students, a mobile application framework, and the establishment of the Autism Champions group.
Professor Peter Ashwin is a Professor of Mathematics specializing in dynamical systems theory and computational modelling. He has been at Exeter since 2000, having previously held teaching and research positions at Surrey, Warwick, Nice (France) and Marburg (Germany). He is currently co-Director of Education for Mathematics at Exeter, and also the Director of the MAGIC mathematics PhD taught course centre, a consortium of UK universities that deliver and assess PhD-level taught courses using video-conferencing technology. Peter has served a Head of Department and Director of Research, and recently as co-director of Education at the University of Exeter. He is on the Council of the London Mathematical Society, is a Fellow of the Institute of Mathematics and holds a Senior Fellowship of the Higher Education Academy.
11:00 am - 1:00 pm
Friday 22nd April, 2022