Dept of Mathematics Education seminar: 18 January 2023

40 mins Presentation + 20 mins Q&A: Dr Silke Wortha

Cognitive, emotional, and motivational correlates of fraction processing

(Loughborough University) [S.M.Wortha@lboro.ac.uk]

Abstract

Understanding and mastering fractions is a critical requirement for individuals cognitive and numerical development. Yet they impose significant challenges for learners when compared to whole numbers. Especially their bipartite structure, reflecting the relative relation of numerator and denominator and their different properties compared to natural numbers, make fractions a particularly challenging learning content for children as well as adults.

Since fraction understanding is a complex mechanism that involves many different and not fully understood processes it is important to evaluate (i) different ways/ methods on how fraction magnitude understanding can be improved and (ii) the role of emotional and (iii) motivational mechanisms that could facilitate or impede fraction understanding. To address this, I will present four studies that employ different methods, use different experimental approaches, and test different age groups (i.e., children/ adolescents and adults).

(i) How to improve fraction magnitude understanding:

The first study investigated changes in neuro-functional correlates of fraction magnitude processing following an intensive 5-day number line estimation training in 48 adult participants. More specifically, I was interested in pre-post comparisons of brain activation (measured using functional magnetic resonance imaging, fMRI) associated with three target tasks (e.g., symbolic fraction magnitude comparison task, line proportion comparison task, and fraction-line proportion matching task) and additional transfer effects. This study showed that number line estimation training facilitated processing of overall fraction magnitude as indicated by the presence of a neural distance effect after training in the intraparietal Sulcus (IPS), a brain region which is specific for number processing.

The second study used a different methodological approach to foster fraction understanding in children and adults. This study aimed to evaluate whether it is possible to improve fraction understanding via transcranial direct current stimulation (tDCS) of the IPS and/or the dorsolateral prefrontal cortex (DLPFC; a brain region known to be associated with working memory). tDCS is a non-invasive technique in which a low direct current is applied, and it is known for its reputed neuromodulatory effects. I will present preliminary results of 21 children and 21 adult participants to reveal possible developmental differences in fraction processing. 

(ii) The role of (negative) emotions: In this fMRI study the role of (negative) emotions and emotion regulation for difficult tasks (i.e., symbolic fraction and proportion magnitude comparison) compared to easier tasks (i.e., decimal and pie charts magnitude comparison) in 25 adult participants was explored to get first insights of the influence of emotion regulation on rational number processing. Brain activation following the presentation of a numerical cue that signalized either a difficult or an easy upcoming rational magnitude comparison task was examined. Results showed that activation of a well-known emotion processing network including areas for emotion regulation was observed when anticipating a difficult upcoming task compared to an easy task. This suggests that a negative emotional response to difficult math tasks might be a common reaction not specific to math anxious individuals. However, whether or not this initial negative response impairs math performance, however, might depend on the ability to regulate those emotions effectively.  

(iii) The role of motivation: In this study, different motivation profiles across secondary school students were examined to evaluate the role of intrinsic and extrinsic motivation for proficiency and performance with fractions. For this, 256 7^th graders played a computerized learning game over 5 consecutive weeks. Additionally, mathematics and German (as first language) school grades, as well as the Situational Motivation Scale were assessed. Finally, motivation profiles were examined via latent profile analysis to identify possible distinct motivational subpopulations within the school students. This study revealed that motivation might be a relevant factor for improved fraction understanding but that not all children profit from it.

40 mins Presentation + 20 mins Q&A: Prof. Andrew Manches

From gesture research to educational impact

(University of Edinburgh) [A.Manches@ed.ac.uk]

Have you ever asked yourself why you move your hands when you are explaining ideas, even on the phone and no-one can see you?  When we explain ideas, particularly in domains like mathematics, we often gesture, and research is revealing how these gestures offer a unique window into the way children think, learn, and communicate their conceptual understanding. Gestures also present a valuable opportunity for practitioners – both in how they encourage children’s gestures and gesture themselves. Gestures may even help us understand and exploit the potential of technologies that can capture and exploit body-based interaction. In this talk, Professor Andrew Manches will share work from across several UKRI and other funded projects to illustrate this emerging research field and why the work offers insight into the potential, and challenges, of scaling impact of learning research through commercialisation.