Periodic Reporting for period 1 - MORE-or-LESS (do Maths Outcomes Reflect Expertise Linked to Effective Strategy Selection? Event related brain potentials and eye movement studies in children and adults)
Reporting period: 2016-09-01 to 2018-08-31
Maths is often considered the “bugbear” among the school subjects, not only in relation to the achievement (or school grade), but also for the negative feelings often associated with its learning experiences. The negative halo of poorly developed mathematical knowledge affects in the first place, the protagonists of the learning (i.e. the children), but it also extends later in life reducing peoples’ employment opportunities and salaries (Geary, 2011).
There is a shared understanding that learning maths involves a complex interplay of cognitive, motivational and emotional processes (Carey, et al., 2016, Hill, et al., 2016; Mammarella, et al., 2015) implemented by an extended neural network of the brain (Szucs, Devine, Soltesz, Nobes, & Gabriel, 2014). Indeed, mathematical difficulties may be associated not only with specific mathematical learning disorders, but also with cognitive weaknesses (e.g. working memory, executive functions, etc., Caviola, et al., 2014) and emotional impairments (Ashcraft & Kirk, 2001; Devine, et al. 2017).
A substantial number of studies provide evidence that both domain-specific (i.e. aspects directly related to mathematics and numbers) and domain-general aspects have been found having an impact on mathematics performance (Krajewski & Schneider, 2009; Passolunghi & Lanfranchi, 2012). Within this framework, the flexibility and adaptability of strategic behaviour (Rittle-Johnson, Star, & Durkin, 2012; Verschaffel, Luwel, Torbeyns, & Van Dooren, 2009) is highly important as the correct execution of arithmetic problems implies a series of steps, which include adaptively switching between arithmetic strategies in order to select and apply the most efficient one (Siegler & Lemaire 1997, Siegler & Shipley 1995).
The literature presented so far refers to arithmetical proficiency extensively investigated by behavioural methods, but the more recent use of psychophysiological measures has provided some evidence relating to the neurobiological basis of arithmetical processing.
There is a shared understanding that learning maths involves a complex interplay of cognitive, motivational and emotional processes (Carey, et al., 2016, Hill, et al., 2016; Mammarella, et al., 2015) implemented by an extended neural network of the brain (Szucs, Devine, Soltesz, Nobes, & Gabriel, 2014). Indeed, mathematical difficulties may be associated not only with specific mathematical learning disorders, but also with cognitive weaknesses (e.g. working memory, executive functions, etc., Caviola, et al., 2014) and emotional impairments (Ashcraft & Kirk, 2001; Devine, et al. 2017).
A substantial number of studies provide evidence that both domain-specific (i.e. aspects directly related to mathematics and numbers) and domain-general aspects have been found having an impact on mathematics performance (Krajewski & Schneider, 2009; Passolunghi & Lanfranchi, 2012). Within this framework, the flexibility and adaptability of strategic behaviour (Rittle-Johnson, Star, & Durkin, 2012; Verschaffel, Luwel, Torbeyns, & Van Dooren, 2009) is highly important as the correct execution of arithmetic problems implies a series of steps, which include adaptively switching between arithmetic strategies in order to select and apply the most efficient one (Siegler & Lemaire 1997, Siegler & Shipley 1995).
The literature presented so far refers to arithmetical proficiency extensively investigated by behavioural methods, but the more recent use of psychophysiological measures has provided some evidence relating to the neurobiological basis of arithmetical processing.
Thus, as part of the MORE-or-LESS project, we aimed to develop a coherent series of studies in which we implemented different behavioural and psychophysiological techniques to investigate the associations of problem features, stressful situations and strategic behaviour. These measures together enable researchers to reliably assess and investigate children’s individual differences in mathematical learning and allow clinicians and teachers to become aware of their educational approaches, especially in children with maths difficulties. (i.e. not overloading their cognitive recourses). Furthermore, Dr Caviola and the research team investigated, for the first time, the physiological parameters related to characteristics of eye-movements that could disclose strategic behaviour from a more objective perspective.
The first step consisted of an extensive check of the research field: due to the high variability in the types of tasks (both for complexity and nature) an accurate review of the literature was performed. It resulted in a systematic review that highlighted how task difficulties (i.e. complex problems of time constraints) can interfere with or modulate the selection process of problem-solving strategies. Central to this framework is also the view that negative emotions, such as math anxiety or pressured situations, can negatively affect maths performance and impair strategy choice (Caviola, et al., 2017).
Building on her extensive expertise in mathematical cognition and developmental psychology, Dr Caviola contrasted two experimental paradigms for the assessment of child strategy choice, under the supervision of Prof. Jo-Anne Lefevre from Carleton University (ON). First findings based on the observation of about 320 children who performed a complex mental calculation task indicated that third-grade children were more likely to report less-efficient strategies (i.e. counting) and relied more on the right-to-left solution algorithm (i.e. written calculation) compared to fifth-grade children who more often used efficient memory-based retrieval and conceptually-based left-to-right (i.e. decomposition) strategies. Nevertheless, all strategies were reported or selected by both older and younger children and strategy use varied with problem complexity and presentation format for both age groups. These results supported the overlapping waves model of strategy development and provide detailed information about patterns of strategy choice on complex subtraction problems (Caviola, et al., 2018).
The first step consisted of an extensive check of the research field: due to the high variability in the types of tasks (both for complexity and nature) an accurate review of the literature was performed. It resulted in a systematic review that highlighted how task difficulties (i.e. complex problems of time constraints) can interfere with or modulate the selection process of problem-solving strategies. Central to this framework is also the view that negative emotions, such as math anxiety or pressured situations, can negatively affect maths performance and impair strategy choice (Caviola, et al., 2017).
Building on her extensive expertise in mathematical cognition and developmental psychology, Dr Caviola contrasted two experimental paradigms for the assessment of child strategy choice, under the supervision of Prof. Jo-Anne Lefevre from Carleton University (ON). First findings based on the observation of about 320 children who performed a complex mental calculation task indicated that third-grade children were more likely to report less-efficient strategies (i.e. counting) and relied more on the right-to-left solution algorithm (i.e. written calculation) compared to fifth-grade children who more often used efficient memory-based retrieval and conceptually-based left-to-right (i.e. decomposition) strategies. Nevertheless, all strategies were reported or selected by both older and younger children and strategy use varied with problem complexity and presentation format for both age groups. These results supported the overlapping waves model of strategy development and provide detailed information about patterns of strategy choice on complex subtraction problems (Caviola, et al., 2018).
In recent years, new ground-breaking concepts emerged suggesting that more “objective” measures seem necessary to better understand the underpinning dynamics of mathematical learning. Regarding both the strategies selection and the impairment due to intrusive thoughts (i.e. math anxiety), self-reported data (collected through questionnaires) seems to be the primary measure. On this perspective, Dr Caviola together with Dr Szücs made a substantial contribution to the field by investigating physiological parameters related to the characteristics of eye-movements that could indicate math anxiety indirectly. Eye movements were gathered from 90 participants while they solved complex addition problems in two different time-pressure conditions (high vs. low). An increase in stress due to time pressure conditions and task difficulties, during a computerized calculation task, was associated to an increase in anxiety levels: all physiological parameters resulted to be sensitive to induced stress through time pressure and task difficulty in a comparable way. A set of additional analyses investigating characteristics of strategic behaviour according to problem difficulties, suggested that only the difficulty of the problems presented had an effect on strategy selection whereas no variation was found for time pressure.
Moreover, Dr Caviola and the colleague of the Centre for Neuroscience in Education with the supervision of Dr Szücs, develop an ERP study in order to understand the effect of time pressure on solving complex problems. The analysis of what cognitive processes lead to correctly or incorrectly solved a complex problem was studied using a sequential presentation and verification task. Currently, Dr Caviola et al. are in the process of exploring the association between observed behavioural answers and psychophysiological measures in a full dataset of 60 university students. In particular, the analyses are focusing on the N400 effect, a negative event-related brain potential component believed to reflect the integration of a stimulus into a semantic context. In the domain of arithmetic, it is believed to represent the differential effort needed for the integration of congruent and incongruent results. The preliminary results showed that the amplitude of the N400 resulted to be affected by the task complexity. Moreover, both the timing and the topography of the effect seem to be in line with the data reported in the literature (Szucs & Csépe, 2005; Szucs & Soltész, 2010; Avancini et al., 2014).
Furthermore, Dr Caviola since October 2018, is working as a Lecturer at the School of Psychology of at University of Leeds. This permanent position is a direct result of a career growth fostered by the Marie Curie fellowship and will allow Dr Caviola to continue working on these papers.
Moreover, Dr Caviola and the colleague of the Centre for Neuroscience in Education with the supervision of Dr Szücs, develop an ERP study in order to understand the effect of time pressure on solving complex problems. The analysis of what cognitive processes lead to correctly or incorrectly solved a complex problem was studied using a sequential presentation and verification task. Currently, Dr Caviola et al. are in the process of exploring the association between observed behavioural answers and psychophysiological measures in a full dataset of 60 university students. In particular, the analyses are focusing on the N400 effect, a negative event-related brain potential component believed to reflect the integration of a stimulus into a semantic context. In the domain of arithmetic, it is believed to represent the differential effort needed for the integration of congruent and incongruent results. The preliminary results showed that the amplitude of the N400 resulted to be affected by the task complexity. Moreover, both the timing and the topography of the effect seem to be in line with the data reported in the literature (Szucs & Csépe, 2005; Szucs & Soltész, 2010; Avancini et al., 2014).
Furthermore, Dr Caviola since October 2018, is working as a Lecturer at the School of Psychology of at University of Leeds. This permanent position is a direct result of a career growth fostered by the Marie Curie fellowship and will allow Dr Caviola to continue working on these papers.