Dept of Mathematics Education seminar: 20 November 2024

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40 mins Presentation + 20 mins Q&A: Dr Mateusz Hohol

Does Elementary Numerical Cognition Scaffold Advanced Mathematics? Insights from Studies on Mathematical Experts.

(Jagiellonian University, Cracow, Poland) [Mateusz.hohol@uj.edu.pl]

Abstract

Mathematics is a core component of the competencies essential for professional development and daily life, both for individuals and societies. Today, many psychologists and cognitive neuroscientists seek to understand the mechanisms of mathematical cognition shared by all humans, as well as the individual differences in mathematical skills. A widespread view suggests that elementary numerical cognition, associated with frontoparietal networks, provides the scaffolding for arithmetic, which is considered the foundation of more advanced mathematical skills. The core idea is that fully developed mathematical abilities can only emerge if the elementary representation of numbers is well-established.

However, most previous research supporting this view has focused on the association between general mathematical achievement and performance on tasks involving elementary numerical processing in groups with average mathematical skills or populations with math learning difficulties. Research on numerical cognition in experts is much rarer, yet it offers a unique opportunity to test whether core numerical processing truly scaffolds advanced mathematics.

In my talk, I will present the current state of research on numerical cognition (and its neural basis) in professional mathematicians and prodigious calculators. I will focus on what differentiates these two groups from the general population. Next, I will explore what distinguishes professional mathematicians from individuals with extraordinary, but very narrow, numerical abilities. This analysis will underscore the value of studying experts to address the fundamental question: “Where does mathematics come from?”

40 mins Presentation + 20 mins Q&A: Dr Sabrina Burr

The Development of Fraction Knowledge & Misconceptions

(The University of Sheffield) [s.burr@sheffield.ac.uk]

Abstract

Global declines in mathematics performance, including in the UK, are pervasive. Amongst the skills that pupils must acquire, an understanding of fractions is essential. Fraction knowledge is a key predictor of advanced mathematics skills and integral in both science-based and less maths-intensive careers. Unfortunately, fractions are notoriously difficult for pupils to master. As pupils work to expand their understanding of number, misconceptions can arise because they erroneously apply natural number reasons to rational number problems. In this talk, I will present findings from research investigating the development of fraction knowledge, taking into consideration the relations among whole number and fraction skills, performance across subconcepts of fraction knowledge, the development and transformation of misconceptions, and the use of computer tutors in fraction learning.