Related but not the same: Ordinality, cardinality and 1-to-1 correspondence in finger-based numerical representations

Abstract

Finger-based numerical representations have gained increasing research interest. However, their description and assessment often refer to different numerical principles of ordinality, cardinality and 1-to-1 correspondence. Our aim was to investigate similarities and differences between these principles in finger-based numerical representations. Sixty-eight healthy adults performed ordinal finger counting, cardinal finger montring (showing the number of gestures) and finger-to-number mapping with twisted arms and fingers. We found that counting gestures and montring postures were identical for Number 10 but differed to varying degrees for other numbers. Interestingly, there was no systematic relation between finger-to-number mapping and ordinal finger counting habits. These data question the assumption of a unitary embodied finger-based numerical representation, but suggest that different finger-based representations co-exist and can be recruited flexibly depending on the numerical aspects to be conveyed.

Keywords:

• 1-to-1 Correspondence
• Cardinality
• Finger-based numerical representations
• Finger counting
• Ordinality

Mirjam Wasner, Korbinian Moeller and Hans-Christoph Nuerk are members of the “Cooperative Research Training Group” of the University of Education, Ludwigsburg, and the University of Tuebingen, which is supported by the Ministry of Science, Research and the Arts in Baden-Württemberg, Germany. They are also associated with the LEAD Graduate School [GSC1028], funded by the Excellence Initiative of the German federal and state governments. Martin Fischer was supported through DFG Grant FI 1915/2-1 on “Manumerical cognition”.

Mirjam Wasner, Korbinian Moeller and Hans-Christoph Nuerk are members of the “Cooperative Research Training Group” of the University of Education, Ludwigsburg, and the University of Tuebingen, which is supported by the Ministry of Science, Research and the Arts in Baden-Württemberg, Germany. They are also associated with the LEAD Graduate School [GSC1028], funded by the Excellence Initiative of the German federal and state governments. Martin Fischer was supported through DFG Grant FI 1915/2-1 on “Manumerical cognition”.

Notes

¹ We would like to thank an anonymous reviewer for drawing attention to this possibility.