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Exploring the numerical mind by eye-tracking: Brain, cognition and action

Applicant Hartmann Matthias
Number 167995
Funding scheme Ambizione
Research institution
Abt. Kognitive und Restorative Neurologie Universitätsklinik für Neurologie Inselspital
Institut für Psychologie Universität Bern
Institution of higher education University of Berne - BE
Main discipline Psychology
Start/End 01.01.2017 - 31.12.2019
Approved amount 453'798.00
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Keywords (5)

numerical cognition; cognitive neuroscience; embodied cognition; cognitive psychology; mental number line

Lay Summary (German)

Zahlen sind omnipräsent in unserer Umgebung. In diesem Projekt wird mit neurowissenschaftlichen Methoden untersucht, auf welchen kognitiven und neuronalen Mechanismen das Zahlenverständnis beruht.
Lay summary

Ziele des Forschungsprojekts

Zahlenverarbeitung gehört zu unserem Alltag, und Defizite führen zu beachtlichen Einschränkungen im schulischen und beruflichen Erfolg. Die Frage wie genau wir Zahlen verstehen, repräsentieren und damit mentale Operationen durchführen können ist nach wie vor unklar. Im Gehirn werden Zahlen von den selben neuronalen Netzwerken verarbeitet wie räumliche Relationen und andere Grössen/Mengeninformationen. Zudem zeigt sich auf der Verhaltensebene, dass Zahlen eine starke räumliche Assoziation haben (z.B. kleine Zahlen links und grosse Zahlen rechts – je nach kultureller Erfahrung). Das Ziel dieses Projektes ist es die Zahlenverarbeitung besser zu verstehen, in dem ein umfassender Ansatz verwendet wird, bei dem sowohl die neuronale Verarbeitung, die kognitive Repräsentation von Zahlen, sowie der Bezug zu Motorik und Handlungen betrachtet wird. Konkret wird die Rolle verschiedener Gehirnareale für die grundlegende Zahlenverarbeitung untersucht, die Rolle der räumlichen Assoziationen fürs Rechnen, und auch wie unsere Wahrnehmung und Aufmerksamkeitssteuerung durch die Zahlenverarbeitung beeinflusst wird.

Wissenschaftlicher und sozialer Kontext

Die Verarbeitung von Zahlen ist eine kognitive Schlüsselkompetenz, welche insbesondere für den schulischen und beruflichen Erfolg entscheidend ist. Das Projekt fördert das Verständnis der Denkprozesse, welcher der Zahlenverarbeitung zugrunde liegen. Die gewonnenen Erkenntnisse können im klinischen und pädagogischen Bereichen nützlich sein.

Direct link to Lay Summary Last update: 10.11.2016

Responsible applicant and co-applicants



Sharing a mental number line across individuals? The role of body position and empathy in joint numerical cognition
Hartmann Matthias, Fischer Martin H., Mast Fred W. (2019), Sharing a mental number line across individuals? The role of body position and empathy in joint numerical cognition, in Quarterly Journal of Experimental Psychology, 72, 1732-1740.
Unbounded number line estimation as a measure of numerical estimation
Reinert Regina Miriam, Hartmann Matthias, Huber Stefan, Moeller Korbinian (2019), Unbounded number line estimation as a measure of numerical estimation, in PLOS ONE, 14(3), e0213102-e0213102.
Further to the right: Viewing distance modulates attentional asymmetries (‘pseudoneglect’) during visual exploration
Hartmann Matthias, Sommer Nils R., Diana Lorenzo, Müri René M., Eberhard-Moscicka Aleksandra K. (2019), Further to the right: Viewing distance modulates attentional asymmetries (‘pseudoneglect’) during visual exploration, in Brain and Cognition, 129, 40-48.
Tracking the continuous dynamics of numerical processing: A brief review and editorial
Faulkenberry Thomas J., Witte Matthias, Hartmann Matthias (2018), Tracking the continuous dynamics of numerical processing: A brief review and editorial, in Journal of Numerical Cognition, 4(2), 271-285.
Anodal High-definition Transcranial Direct Current Stimulation over the Posterior Parietal Cortex Modulates Approximate Mental Arithmetic.
Hartmann Matthias, Singer Sarah, Savic Bane, Müri Rene M., Mast Fred W., Anodal High-definition Transcranial Direct Current Stimulation over the Posterior Parietal Cortex Modulates Approximate Mental Arithmetic., in Journal of Cognitive Neuroscience.


Group / person Country
Types of collaboration
NeuroCognitive Plasticity / Leibniz-Institut für Wissensmedien Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Potsdam Embodied Cognition Group/University of Potsdam Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Exchange of personnel

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Swiss Psychological Society Conference (SPS-SGP) Individual talk Summing up: What eye movements tell us about spatial-numerical associations in mental arithmetic 09.09.2019 Bern, Switzerland Hartmann Matthias;
European Conference on Eye Movements Poster Power-large and precision-small: Decoding affordance effects during visual search by eye movements analysis 18.08.2019 Alicante, Spain Hartmann Matthias;
European Workshop of Cognitive Neuropsychology Talk given at a conference Does tDCS over the parietal cortex improve approximate mental arithmetic? 28.01.2019 Bressanone, Italy Hartmann Matthias; Singer Sarah;


Numbers are omnipresent in everyday life, and processing numbers is a key cognitive competence that is crucial for success at school and at work. Numerical cognition has long been considered as a prototypically abstract domain of cognition that is decoupled from sensory and motor processes. However, recent research revealed that the representation of numbers is tightly linked to space and bodily actions: Numbers are cognitively represented spatially along a “mental number line”, with small numbers on the left and larger numbers on the right side, depending on cultural and finger counting habits. Crucially, body and eye movements along the “mental number line” systematically interact with ongoing numerical processes. The projects proposed here address several fundamental issues in numerical cognition that have remained unclear from previous research, using sophisticated eye tracking paradigms. Eye-trackers measure the position of the eye gaze, and consequently the focus of spatial attention, with a high spatial and temporal resolution in an unobtrusive manner. Eye tracking enables on-line access to the mind, allowing a more fine-grained analysis of cognitive processes than previous studies in this domain that mainly focused on response times alone. Project I will use the added value of eye-tracking in order to clarify the causal contribution of different brain areas (e.g., the left and right posterior parietal cortex) during the four basic arithmetic operations (addition, subtraction, multiplication, and division) by means of non-invasive transcranial magnetic brain stimulation. The exact neuronal mechanisms involved for different numerical tasks has remained controversial, and the knowledge from this project will be relevant for a better understanding of numerical disabilities and their potential cognitive rehabilitation in patients suffering from brain damage.Project II will investigate cognitive biases in numerical cognition, particularly the extent to which the shared mechanisms between numbers and space play a role in mental arithmetic. It has been hypothesized that addition is conceptualized as rightward, and subtraction as leftward movement along the mental number line. To test this hypothesis, participants’ arithmetic performance will be assessed while they make physical eye movements that are congruent or incongruent with the hypothesized mental movement along the number line. A particular aim of Project II is to find out whether eye movements play a functional role for mental arithmetic. This project taps into the more general question of whether sensorimotor systems contribute to comprehension processes, which is a central assumption of the “embodied cognition” approach, and currently one of the most debated issues in psychology and neuroscience.Performing mental arithmetic is only one aspect of the numerical mind. It is assumed that the cognitive mechanisms allowing for symbolic number manipulation (as during mental arithmetic) are based on a more general “number sense” that is inherent to animals and newborn humans, allowing to process magnitude-related information used for action (estimate spatial distances, object size, time to reach etc). Project III uses the added value of eye-tracking to explore the integration of object and grasp size in the context of action. In a change-detection paradigm, participants explore small and large objects and respond to changes either with a precision grip (associated with grasping small objects) or a power grip (associated with grasping large objects). It will be assessed whether participants’ visual attention is systematically biased towards objects that are congruent with the observers’ grip size, and further characteristics of action-perception interactions will be explored. The results from the studies proposed here will significantly advance the understanding of neuronal and cognitive mechanisms of the numerical mind, and more generally how sensory and motor processes are involved in cognition, thus contributing to important ongoing debates in psychology, neuroscience and philosophy.