Lab

# Attila Krajcsi's Lab (The Number Works)

Our lab works on numerical cognition and on methodological issues. Find more information on our website: https://www.thenumberworks.org

# Featured projects (3)

Project
Methodological works related to various areas of behavioral sciences.
Project
We investigate how preschoolers understand numbers, starting from the very beginning of understanding symbolic numbers (i.e., understanding the cardinality principle), until they start formal math education.
Project
Symbolic and non-symbolic numbers are thought to be processed by an evolutionary ancient, simple representation, the Analogue Number System (ANS), which system is thought to be the very base of number understanding. We offer an alternative account for symbolic number understanding, proposing a human specific, simple representation similar to a network of concepts or to the mental lexicon. It is a comprehensive model for symbolic number processing phenomena. See more details at http://www.thenumberworks.org/discrete_semantic_system.html

# Featured research (14)

In elementary symbolic number processing, the comparison distance effect (in a comparison task, the task is more difficult with smaller numerical distance between the values) and the priming distance effect (in a number processing task, actual number is easier to process with a numerically close previous number) are two essential phenomena. While a dominant model, the approximate number system model, assumes that the two effects rely on the same mechanism, some other models, such as the discrete semantic system model, assume that the two effects are rooted in different generators. In a correlational study, here we investigate the relation of the two effects. Critically, the reliability of the effects is considered; therefore, a possible null result cannot be attributed to the attenuation of low reliability. The results showed no strong correlation between the two effects, even though appropriate reliabilities were provided. These results confirm the models of elementary number processing that assume distinct mechanisms behind number comparison and number priming.
According to the dominant view in the literature, several numerical cognition phenomena are explained coherently and parsimoniously by the Approximate Number System (ANS) model, which supposes the existence of an evolutionarily old, simple representation behind many numerical tasks. We offer an alternative account that proposes that only nonsymbolic numbers are processed by the ANS, while symbolic numbers, which are more essential to human mathematical capabilities, are processed by the Discrete Semantic System (DSS). In the DSS, symbolic numbers are stored in a network of nodes, similar to conceptual or linguistic networks. The benefit of the DSS model and the benefit of the more general hybrid ANS–DSS framework are demonstrated using the crucial example of the distance and size effects of comparison tasks.
Learning the meaning of number words is a lengthy and error‐prone process. In this review, we highlight outstanding issues related to current accounts of children’s acquisition of symbolic number knowledge. We maintain that, despite the ability to identify and label small numerical quantities, children do not understand initially that number words refer only to sets of discrete countable items, not to other nonnumerical dimensions. We question the presence of a sudden change in children’s understanding of cardinality, and we report the limits of the give‐a‐number task. We also highlight that children are still learning the directional property of the counting list, even after acquiring the cardinality principle. Finally, we discuss the role that the Approximate Number System may have in supporting the acquisition of symbolic numbers. We call for improvements in methodological tools and refinement in theoretical understanding of how children learn natural numbers.
While knowledge on the development of understanding positive integers is rapidly growing, the development of understanding zero remains not well-understood. Here, we test several components of preschoolers’ understanding of zero: Whether they can use empty sets in numerical tasks (as measured with comparison, addition, and subtraction tasks); whether they can use empty sets soon after they understand the cardinality principle (cardinality-principle knowledge is measured with the give-N task); whether they know what the word “zero” refers to (tested in all tasks in this study); and whether they categorize zero as a number (as measured with the smallest-number and is-it-a-number tasks). The results show that preschoolers can handle empty sets in numerical tasks as soon as they can handle positive numbers and as soon as, or even earlier than, they understand the cardinality principle. Some also know that these sets are labeled as “zero.” However, preschoolers are unsure whether zero is a number. These results identify three components of knowledge about zero: operational knowledge, linguistic knowledge, and meta-knowledge. To account for these results, we propose that preschoolers may understand numbers as the properties of items or objects in a set. In this view, zero is not regarded as a number because an empty set does not include any items, and missing items cannot have any properties, therefore, they cannot have the number property either. This model can explain why zero is handled correctly in numerical tasks even though it is not regarded as a number.
The Give-a-number task is one of the most frequently used tests to measure the number knowledge of preschoolers at the time they acquire the meaning of symbolic numbers. In the task, an experimenter asks for a specific number of objects from a child. The literature utilizes several versions of this task, and usually it is assumed that the different versions are equivalent and that they do not have an effect on the measured number knowledge. In the present study, the specific potential effect of the follow-up questions posed after a trial on the measured number knowledge is investigated. Three versions of follow-up questions are compared. The results demonstrate that different versions affect the measured number knowledge of children. These results highlight that follow-up questions should be considered in studies using the Give-a-number task, and more generally, various versions of the Give-a-number task may have an essential effect on the measured number knowledge, thereby partly accounting for conflicting findings in the literature.

Department
• Department of Cognitive Psychology
• Numerical cognition and methodological issues https://www.thenumberworks.org

# Members (9)

• Research Centre for Natural Sciences
• Central European University
• RWTH Aachen University
• Royal Holloway, University of London
• Central European University
• Eötvös Loránd University
• Eötvös Loránd University
Ákos Laczkó
• Not confirmed yet

# Alumni (3)

• University of Greenwich
• University of Szeged