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I am currently looking for a Post-Doc and a PhD student who want to join the LaPsyDÉ lab for 4 and 3 years, respectively. Here is a short description of the theoretical background and the overall idea of the project. If you are interested, send your application via email to: knops {Dot) andre (funny a-like symbol} gmail [dot} com.

Despite recent evidence suggesting the involvement of inhibitory control functions and spatial attention to mental arithmetic (Szucs, Devine, Soltesz, Nobes, & Gabriel, 2014; Toll, Van der Ven, Kroesbergen, & Van Luit, 2011), neither inhibition nor spatial attention represent unitary constructs. To the contrary, they comprise different facets (see below). What is still missing, are (a) a detailed description of the longitudinal trajectories and inter-relation of these factors and their facets, as well as (b) their respective neuro-functional correlates. We need to understand the key processes and how they (a) interact and (b) develop over lifetime. In the following, I briefly describe three key factors that appear of utmost relevance for the current project: the approximate number sense, domain-general factors (e.g. inhibition), and spatial attention.

First, humans are equipped with a core capacity to approximately perceive and process (e.g. compare, add up) non-symbolic quantities – the approximate number system (ANS). The ANS has been shown to represent the stepping stone for the later acquisition of formal mathematical competencies in school (Dehaene, 2011). Being equipped with the ANS from birth, during childhood the ANS precision increases, peaking in adulthood (around 30 years), and decreasing again thereafter (Halberda et al., 2012). Importantly, training the ANS using non-symbolic (i.e. using dot patterns) addition and subtraction problems improves symbolic (i.e. using Arabic digits) math proficiency (Park & Brannon, 2013). It has been argued that the ANS provides humans with the ‘start-up’ tools for the acquisition of more advanced symbolic mathematical skills (Piazza, 2010). At the neural level, the ANS is supported by bilateral cortical circuits in the intraparietal sulcus (IPS, (Knops, 2016)). It remains an unresolved question, whether the relationship between ANS and numerical competencies is mediated by domain-general factors (Knops, Nuerk, & Goebel, 2017).

Inhibition is a cognitive process that serves to suppress existent or forthcoming engagement in either perceptual or response-related processes. No consensus has been reached concerning the factorial structure of inhibition. One the one hand, inhibition has been divided into two main facets, response inhibition (go/no go task, stop signal task) and distractor resistance (as in number Stroop or letter flanker tasks) (Rey-Mermet, Gade, & Oberauer, 2017). An alternative factorization (Zhang, Geng, & Lee, 2017) of inhibition differentiates between interference resolution, action withholding (as in go/no go paradigms), and action cancellation (as in stop-signal task). At the neural level, inhibition relies on a set of regions including the inferior frontal gyrus, the right median cingulate, the paracingulate gyri, and the right superior parietal gyrus (Zhang et al., 2017) (Crone & Steinbeis, 2017)

Inhibition plays a pivotal role in mental arithmetic. During numerosity perception, inhibition is important for allowing the formation of an abstract representation over and above non-numerical stimulus features (Gilmore et al., 2013). During mental arithmetic, inhibition serves in excluding non-adapted strategies (Vanbinst & De Smedt, 2016) or inconclusive response alternatives (Cho et al., 2012). However, evidence is inconclusive (Bellon, Fias, & De Smedt, 2016; Keller & Libertus, 2015).  This may in part be due to unspecific way the term inhibition has been used, equally referring to the inhibition of motor responses and irrelevant visual or auditory information. A detailed description of how different facets of inhibition contribute to the development of numerical competencies remains elusive.

Spatial attention has been argued to play an important role during mental arithmetic (Knops, Thirion, et al., 2009). Shifts of spatial attention give rise to a cognitive bias, the operational momentum (OM) effect (Knops, Viarouge, et al., 2009). For the very same outcome of an addition or subtraction problem (e.g. 6+4=10 or 14-4=10), participants’ estimates are systematically smaller for subtractions compared to additions. Preliminary results across studies suggest a non-linear development of OM during infancy and childhood: The OM effect for ordinal numerical and size sequences has been demonstrated in babies (Macchi Cassia, McCrink, de Hevia, Gariboldi, & Bulf, 2016; McCrink & Wynn, 2009) but preschool children show an inverse OM effect (Knops, Zitzmann, & McCrink, 2013). A cross-sectional study (Didino et al., in preparation) suggests that OM reaches an adult-like pattern at approximatively 9 years of age. In adult participants, OM correlates with attentional re-orienting in a Posner paradigm (Katz, Hoesterey, & Knops, under revision). In further support of the idea that attention contributes to mental arithmetic, Knops and colleagues (Knops, Thirion, et al., 2009) were able to predict whether participants engaged in addition or subtraction on the basis of neural activity pattern during attentional shifts to the right or left, respectively.

Hence, while the available evidence points towards an involvement of attentional resources in mental arithmetic (Masson, Letesson, & Pesenti, 2018; Masson & Pesenti, 2014, 2016; Masson et al., 2017; Mathieu et al., 2016), further studies are required to delineate the developmental trajectory and the exact nature of the involvement. In particular, it remains unclear which of the multiple cognitive steps involved in re-orienting (orienting towards a cued position; exogenous attraction of the appearing target at another position; overruling initial orienting in favor of the new target position (disengagement); orienting towards target (shift & engage); response selection) drives the correlation with the operational momentum effect.

The project aims at disentangling the different components that drive the association of mental arithmetic with domain-specific and domain-general functions. In particular, we are interested in the developmental trajectory of this association which gives rise to seemingly non-linear trends (e.g. OM effect in babies and adults but not in children). Yet, this may merely reflect the differential impact of different heuristics, core capacities and emergence of controlled, top-down strategies.

HypothesesThe emergence of numerical competencies is subject to different influences during development. During early years, intuitive behavior prevails. The behavior jointly reflects the characteristics of the most important neuro-cognitive core capacity – the approximate number system – and core intuitions about the physical world (e.g. object permanence).  With increasing age, children acquire more elaborated and explicit numerical competencies such as counting, for example. These often precede the understanding of the underlying concepts, such as cardinality, for example. During this period, domain-general competencies such as inhibition start to emerge and influence behavior. As introduced above, inhibition and certain attentional facets continue developing throughout childhood and reach maturity at the age of emerging adulthood only. As children “develop increasing intentional control over their behavior and cognition (Bjorklund, 2013)”, they are increasingly capable of (a) inhibiting inappropriate (or planned) motor responses and (b) resisting to distractors. This is reflected in the increasing ability to reorient attention from invalidly cued to unattended locations in a Posner paradigm, for example. From this complex interaction and based on the above findings concrete hypotheses are derived that will be pursued in this project.

We will address these in an accelerated longitudinal design (Galbraith, Bowden, & Mander, 2017) that goes beyond existent cross-sectional data. Four cohorts of children will be recruited during the project and tested once a year during three consecutive years. At start, cohorts will be split by 2 years of age, starting at the age of 12 months (cohort 1) and ranging until the age of 7 years (cohort 4). Overall, this allows following the development of numerical skills and the relation with domain-specific and domain-general factors from the age of 1 until the age of 9. A bundle of specific cognitive parameters (standardized and experimental measures) will be measured, covering arithmetic and numerical performance, attentional parameters, inhibitory functions, and the most important control variables known to influence scholar achievement (e.g. general intelligence, socio-economic status, reading skills). The project also involves the measurement of children’s brain activity via functional magentic resonance imaging (fMRI).

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