The approximate number system in the laboratory and in daily life Bert Reynvoet KU Leuven, Belgium

Approximate number system (ANS) A system supporting the extraction of number from visual scenes without relying on symbols or language in an appoximate way Number: discrete quantity information No symbols or language: also infants and animals Approximate: performance influenced by ratio ~= Weber’s law

Approximate number system (ANS) Infants and preference looking studies (Libertus & Brannon, 2010)

Approximate number system (ANS) Older children/adults and comparison tasks

ANS: individual differences In different cohorts In the same cohort

How much number in the ANS

How much number in the ANS MORE LEFT OR MORE RIGHT? NUMBER NUMBER SIZE DENSITY SIZE DENSITY NUMBER

Controlling other visual/continuous information

Controlling other visual/continuous information

Comparing visual control! Smets, Sasanguie, Szücs & Reynvoet (2015) Comparison task 26 participants Ratios: 1.2, 1.4, 1.5 3 visual controls: G&R, Dehaene, Congruent

Comparing visual control! Smets, Sasanguie, Szücs & Reynvoet (2015) Dehaene and Congruent condition correlate (.57) No correlation of G&R With other conditions (.30) (congruent) visual Information enhances performance

Comparing visual control and presentation style! Smets, Moors & Reynvoet (2016) Same results with sequential presentation? Psychophysics: no detailed visual analysis in sequential presentation No differences between visual control conditions in estimation task (Smets et al., 2015) Comparison task 40 participants Ratios: 1.2, 1.4, 1.5 4 conditions: simultaneous/sequential versus Dehaene/Gebuis & Reynvoet

Comparing visual control and presentation style! Smets, Moors & Reynvoet (2016) Interaction presentation style and visual control, but higher performance in simultaneous condition with both control types

Comparing visual control and presentation style! Smets, Moors & Reynvoet (2016)

Comparing visual control and presentation style! Smets, Moors & Reynvoet (2016) Area extended/convex hull was not perfectly controlled: it correlated in both batches of stimuli with number, whereas it is supposed to be constant (zero correlation) in one of the batches

Comparing visual control and presentation style! Smets, Moors & Reynvoet (2016)

Comparing visual control Smets et al., 2015, 2016 Conclusions Weak (or no) correlation between performance in different visual control conditions: .30 is not reliable! Clayton et al. (2015); DeWind & Brannon (2016) Participants use visual cues: the influence of visual cues may depend on how stimuli are generated DeWind & Brannon (2016)

Comparing visual control Dewind & Brannon, 2016

Comparing visual control Smets et al., 2015, 2016 Conclusions Weak (or no) correlation between performance in different visual control conditions Clayton et al. (2015); DeWind & Brannon (2016) Participants use visual cues: the influence of visual cues may depend on how stimuli are generated (DeWind & Brannon, 2016) Participants are very fast to detect correlations Perhaps a correlation is the standard expectation?

Peoples expectations on the relation between number and visual cues: ERP Gebuis & Reynvoet, 2015

Peoples expectations on the relation between number and visual cues Gebuis & Reynvoet, 2015

Peoples expectations on the relation between number and visual cues Gebuis & Reynvoet, 2015

Peoples expectations on the relation between number and visual cues Gebuis & Reynvoet, 2015 Conclusions Participants expect that number and visual cues change in concert The interaction between number and visual cues was found after the processing of visual cues Where do these expectations come from? Daily life: number and visual cues are related Number of people on the bus, number of oranges in a bag, number of cars on a parking

Number in daily life Nijs & Reynvoet, in preparation In the lab: artifical stimuli “controlling” for the effects of visual cues In daily life: real-life stimuli where number and visual cues correlate, most of the times… Still, we can correctly decide that 5 mosquitos are more than 2 lions. Can we do that without any costs?

Nijs & Reynvoet, in preparation Number in daily life Nijs & Reynvoet, in preparation Comparison task 30 participants Independent vars: ratio (1:2; 2:3), congruency, subitizing range (in; out) 2 conditions: dot arrays and real-life stimuli (fruits)

Number in daily life Nijs & Reynvoet, in preparation

Nijs & Reynvoet, in preparation Number in daily life Nijs & Reynvoet, in preparation subitizing trials Non-subitizing trials

Nijs & Reynvoet, in preparation Number in daily life Nijs & Reynvoet, in preparation subitizing trials Non-subitizing trials

Nijs & Reynvoet, in preparation Number in daily life Nijs & Reynvoet, in preparation Conclusions Also number judgements in daily life are more difficult when number and visual cues anti-correlate.

How much number in the ANS MORE LEFT OR MORE RIGHT? NUMBER NUMBER SIZE DENSITY SIZE DENSITY Nonlinear transformations NUMBER

How much number in the ANS Work in progress

Educational implications ANS performance is related to math achievement Underlying mechanisms of ANS performance? Integration of visual cues and/into number Inhibition of visual cues What should we target in intervention studies? General form of inhibition (stroop tasks?) Domain specific mechanisms: learning to decorrelate of continuous and discrete quantity

Educational implications Number conservation requires inhibitory control (Houdé and colleagues)

Thank you for listening! Contact info: Prof. Dr. Bert Reynvoet Faculty of Psychology and Education Sciences @ KU Leuven Kulak E. Sabbelaan 53, 8500 Kortrijk BELGIUM Bert.Reynvoet@kuleuven-kulak.be www.numcoglableuven.be