Dept of Mathematics Education seminar: 15 November 2023

40 mins Presentation + 20 mins Q&A: Dr Serena Rossi

Mathematics anxiety and arithmetic performance: methodological considerations, the role of individual characteristics and domain-general cognitive factors

(Loughborough) [s.rossi@lboro.ac.uk]

Abstract

Many people have negative attitudes and emotions towards mathematics, also known as “mathematics anxiety” (MA) (e.g., Dowker et al., 2016; Mammarella et al., 2019; Cipora et al., 2022). MA has a negative impact on individuals; it is linked to avoidance behaviours towards the subject with the consequent avoidance of taking additional mathematical courses during the school years, missing opportunities, as well as poor arithmetic performance (Ashcraft & Ridley, 2005, Daker, 2021). Indeed, numerous studies have consistently confirmed a negative relationship between MA and arithmetic performance (e.g., Barroso et al., 2021; Caviola et al., 2022). Several factors appear to modulate this relationship. These include environmental components, such as social and contextual factors, and individual characteristics, such as cognitive, affective, and motivational features (Chang & Beilock, 2016).

In this talk, I will present some studies in which I investigated the relationship between MA and arithmetic performance, addressing methodological considerations, and taking into account the role of individual characteristics and domain-general cognitive factors.

40 mins Presentation + 20 mins Q&A: Dr Ulises Xolocotzin

Constructing algebraic intuitions in the elementary grades: Conceptual change in functional thinking and its relation to arithmetic knowledge and domain-general cognitive skills

(Mathematics Education Department, Cinvestav, México) [ulises.xolocotzin@cinvestav.mx]

Abstract

Substantial evidence shows that with adequate materials and instruction, elementary students can engage in sophisticated algebraic practices, including noticing, expressing, and justifying generalizations. However, the learning processes involved in these developments still need clarification. How can children construct concepts such as generalization, covariation, and variable, without precedent in the arithmetic domain? How is this construction related to children’s cognitive resources and previous mathematical knowledge? We present a mixed-methods study with 105 elementary students (Grades 2, 4, and 6) without early algebra instruction who answered a functional thinking test and a battery that assessed arithmetic, IQ, and executive function. We used a conceptual change framework to characterize the intuitive strategies that students used to solve functional tasks and assessed how conceptual change processes related to arithmetic knowledge and domain-general skills. The qualitative results suggest substantial individual differences in children’s conceptual change processes. The quantitative results suggest that domain-general skills predict the sophistication of students’ conceptual changes over and above arithmetic knowledge. These results will help to refine existing theoretical accounts of hoxw algebraic thinking develops.

40 mins Presentation + 20 mins Q&A: Dr Natalia Dubinkina

Basic mental arithmetic in adults: The role of order working memory processes (Loughborough) [N.Dubinkina@lboro.ac.uk]

Abstract

Much of the research on mental arithmetic was inspired by its associations with working memory (WM; e.g., Hitch & McAuley, 1991). WM capacity is predictive of arithmetic skills and math learning difficulties (e.g., Mammarella et al., 2015). However, it remains controversial whether basic arithmetic processes in adults rely on WM resources. It was traditionally proposed that these problems are solved by long-term memory retrieval, and therefore completed faster than counting routines (Campbell, 1995). Nevertheless, recent studies suggest that some highly automated (“compact”) counting procedures are involved in performing simple arithmetic tasks. Even though these may be difficult to consciously reflect on, it is possible to reveal them, for example, by chronometric analysis (e.g., Uittenhove et al, 2016). It is unknown whether these “compact” procedures operate by scanning a spatial representation (i.e., a mental number line) or rely on a verbal count sequence (Barouillet & Thevenot, 2013). Our results suggest that order working memory processes are involved in basic mental arithmetic, and they particularly point at a role of spatial order memory (which potentially reflects reliance on a spatial representation of the number sequence).