Project description

Mathematics is essential to society, yet student proficiency is declining in Europe. Math anxiety affects 30% of students and 10% of teachers—especially females—negatively impacting math performance and career choices. Our project supports Higher Education Institutions (HEIs) by integrating targeted resources into teacher-training programs. This will enhance math education and help prevent math anxiety—an often overlooked but critical issue in teacher training.

Internationally recognized European experts on math anxiety and education will provide HEIs with multilingual, free-to-use, and user-friendly resources, including (1) instruments to measure math anxiety, (2) cognitive-behavioural interventions to help future teachers address their own math anxiety, (3) a psychoeducation program to address math anxiety in classrooms, and (4) a Massive Open Online Course (MOOC) published at the Copernicus College as a structured learning resource for HEIs to integrate into curricula.

The project aims to fill a critical gap in teacher training curricula by raising awareness of math anxiety and provide practical interventions. Strengthening HEI teacher-training programs will ensure that new educators can recognize and address math anxiety early. Embedding these resources into HEI programs will boost educators’ confidence, foster a positive learning environment, and, in turn, improve math competence across Europe.

The project is carried out by an international consortium of the following universities: Jagiellonian University in Krakow (Poland; leading institution), University of Padova (Italy), Thomas More University in Antwerp (Belgium), and KU Leuven (Belgium).

Project description

Mathematical skills play a vital role in achieving individual well-being and professional development, while also contributing significantly to societal advancement (OECD, 2016). Research has revealed that numeracy and math achievements emerge from configurations of both domain-specific and domain-general cognitive processes. Particularly, numerous studies have focused on the involvement of the memory system in mathematical cognition, revealing that working memory capacity (Peng et al., 2016, J. Educ. Psychol.) and the performance of arithmetic fact retrieval constitute robust predictors of math skills (Geary, 2011, Dev. Behav. Pediatr.). Notably, a reduced ability to memorize and retrieve basic arithmetic facts is among the diagnostic criteria for dyscalculia (DSM-5-TR, 2022, APA). Surprisingly, the contribution of more fine-grained long-term memory processes associated with verbatim (the exact information) and gist (the information’s meaning), as distinguished by the Fuzzy-Trace Theory (Reyna & Brainerd, 2023, Nat. Rev. Psychol.) to mathematical cognition has received little attention (Obidziński, Bażela, Hohol, 2025), even though the theory has already been applied in the context of early numeracy (Brust-Renck & Reyna, 2023, Risk Anal.). What is more, although credible, previous research on memory systems—namely, working memory and facts retrieval—and mathematical cognition has mostly stemmed from different theoretical frameworks, which has made it difficult to draw more general conclusions. Last but not least, previous research on the cognitive determinants and correlates of poor math skills has focused primarily on deficits, leaving compensatory mechanisms largely overlooked.

The project aims to fill these research gaps by applying the Fuzzy-Trace Theory and multinomial processing tree modeling as a unified approach to investigate the relationships between different dimensions of gist and verbatim memory and mathematical skills, with particular emphasis on possible, so far overlooked, fine-grained memory deficits and compensatory mechanisms in dyscalculia. The project will be divided into three phases. In the first two phases, we aim to conduct a series of behavioral experiments to investigate the relationships between different dimensions of numerical memory and mathematical skills in two groups: typically developing young adults (first phase) and young adults with developmental dyscalculia and matched controls (second phase).

Dimensions of numerical memory to be investigated will include verbatim and gist long-term memory for symbolic and non-symbolic numerical material, working memory in the context of verbatim and gist representation of numerical information, and arithmetic facts retrieval. All of them will be measured with entirely novel or substantially revised tasks grounded in the Fuzzy-Trace Theory. Math skills will include non-symbolic and symbolic numerical magnitude processing, arithmetic fluency, math reasoning, and spatial processing and will be assessed using well-recognized paradigms. In the final phase, we will address an additional research question regarding the possibility of classifying participants into those with dyscalculia and those without it through data mining, based on patterns found in the studies conducted during the second phase. Additionally, in the third phase we will prepare and publish a dataset containing all the collected data and submit an opinion paper summarizing all the project’s advances and the new research questions and avenues it inspires.

As the Fuzzy-Trace Theory, though widely applied in research on memory and reasoning (Brainerd, Bialer, Chang, 2022, JEP:LMC), has been somewhat overlooked by the majority of mathematical cognition researchers, the project aims to establish bridges between representatives of these vital research traditions. Importantly, it has the potential to shed new light on the cognitive mechanisms underlying individual differences in mathematical skills, with particular emphasis on the lower end of their continuum. Finally, the project results could serve as a foundation for future interventions aimed at helping individuals with dyscalculia.

Project description

Mathematics constitutes a core part of competencies that are important both in professional development and of the daily life of individuals and societies at large (Butterworth, 1999). Because of practical and theoretical reasons, one should not wonder why today’s efforts of many psychologists and cognitive scientists aim to discover and describe mechanisms of mathematical cognition shared by all human beings and these shaping individual differences in mathematical skills.

For several decades most research efforts focused on numerical processing. The cognitive foundation of the latter is traditionally called “the number sense.” Although its original meaning referred to the understanding of the change in a small collection of items after adding or removing an object, nowadays it extends to various number-related phenomena (Dehaene, 2011), especially approximation of non-symbolic numerosities, handled by the so-called approximate number system (ANS), and subitizing (i.e., the capacity for quick and effortless, but precise, assessment of the number of elements of small sets), handled by the object tracking system (OTS).

However, numerical cognition is much more inclusive since it also comprises operating with symbolic numbers (single and multi-digit numbers, fractions, etc.), namely, comparing them, counting, and conducting operations. These capacities are thought to be built upon domain-specific pre-linguistic mechanisms, such as ANS and OTS, but they also involve linguistic processing and domain-general cognitive resources (Hohol, Cipora, Willmes, & Nuerk, 2017). Spatial-numerical associations (SNAs; Cipora, Schroeder et al., 2018) constitute one of the most-explored aspects of numerical cognition, at least since observation that in a speeded bimanual decision task (e.g., deciding whether the number is even or odd), left-to-right readers respond faster to small magnitude numbers with their left hand and to large magnitude numbers with their right hand. This behavioral pattern, called the SNARC effect (see Dehaene, 2011), reflects a direction of the hypothetical “mental number line.” Importantly, SNAs are observed not only in elementary numerical processing since handling arithmetic operations is also associated with “mental movements” along the number line.

Even taking the diversity outlined above into account, numerical cognition should be distinguished from more advanced mathematical skills, e.g., solving algebraic equations or proving mathematical theorems, that require extensive knowledge acquired through long-term training. Many researchers claim that elementary numerical cognition constitutes scaffolding for arithmetic and the latter, in turn, for more advanced mathematical skills. The core idea is that full-fledged mathematical cognition cannot develop properly if elementary mental representations of numbers, both non-symbolic and symbolic, are not well-constructed (Dehaene, 2011; Lakoff & Núñez, 2000). On the other hand, while the performance in some tasks tackling elementary numerical representations correlates positively with mathematical achievements, other tasks reveal no correlation or mixed evidence (see Cipora, Schroeder et al., 2018). What is more, different tasks, and even their different modes, could correlate with full-fledged mathematical achievements in different ways. Schneider et al.’s (2017) meta-analysis shows a stronger association between mathematical achievements and performance in symbolic numerical tasks. However, note that in most previous research, the above association has been studied only in individuals characterized by typical–for a given age group–mathematical skills or in populations with mathematical learning deficits (e.g., developmental dyscalculia).

Very little is known about the presumed scaffolding of full-fledged mathematical cognition on the more basic numerical processing in mathematical experts. This is important since experts pass along prolonged training and purposeful practice that transform their cognitive mechanisms and build new ones. An in-depth study of expertise can contribute to understanding better performance in some tasks and control the influence of other variables (Sella & Cohen Kadosh, 2018). Unfortunately, professional mathematicians, with rather a few exceptions of behavioral (e.g., Cipora, Hohol et al., 2016; Hohol, Willmes et al., 2020; Sella et al., 2016; Meier et al., 2021) and neuroimaging (Amalric & Dehaene, 2016, 2019; Amalric et al., 2018; Popescu, Sader et al., 2019) studies still constitute an understudied group. These studies established a good starting point, but their conclusions are limited since they tested relatively small samples of professional mathematicians, usually only in single tasks or small task batteries, tapping into narrow aspects of numerical processing. Furthermore, many aspects of elementary numerical processing and SNAs, theoretically considered as the scaffolding of mathematics, have never been investigated in experts.

Despite several decades of strenuous research efforts, exploring how elementary numerical processing and SNAs relate to mathematical expertise still remains one of the essential purposes of the differential psychology of mathematics. The proposed project aims to investigate these aspects of numerical cognition by comparing two qualitatively different groups: professional mathematicians (doctoral students of mathematics and post-docs) and controls (carefully matched not only in terms of age, gender, and academic level but also in domain-general cognitive capacities) in a large set of tasks. This will be done mostly in behavioral terms, but neuroscientific measures will also be applied. The specific goals of the project include:

(1) testing hallmark numerical processing phenomena considered as scaffolding for the development of more advanced mathematical skills in the extensive battery of behavioral tasks, supported by using other methodologies (grip force sensors, oculography); these phenomena include non-symbolic and symbolic instances of analog numerical magnitude processing and various SNAs, which have never been studied in mathematicians or have been tested only on small samples and single tasks;

(2) investigating the individual prevalence of behavioral effects considered as hallmarks of elementary numerical processing and SNAs by using bootstrapping methods; 

(3) studying the structure and connectivity of the mathematician’s brain on a larger scale than before, and investigating its functional characteristics in multi-digit number processing for the first time.

Project description

The aim of this project is to propose a new, unified account of self-understanding that can help explain its role in our well-being and mental health. To achieve this goal, it is necessary to integrate topics from at least three branches of philosophy: the philosophy of mind, epistemology, and the philosophy of psychiatry. However, it would be exceedingly difficult to answer the question of what self-understanding is and what function it serves "in general." Therefore, a key methodological approach will be to examine what self-understanding is and what function it serves in psychotherapy—a process aimed at restoring mental health and balance—and to draw conclusions from this for the broader role of self-understanding.

The first part of the research will focus on the nature of self-understanding. Key philosophical and psychotherapeutic concepts will be analyzed, culminating in the outline of a new conception of self-understanding. In this account, self-understanding will be characterized as a type of "objective" understanding, meaning an understanding of a given subject matter obtained through having certain information about it and grasping the relationships between that information. In the case of self-understanding, the subject matter is "myself," and the information I possess pertains to my mental states, sensory experiences, behaviors, and life events. Furthermore, self-understanding will be characterized as comprising four dimensions: richness (how much information do I have about myself?), accuracy (are these pieces of information true?), coherence (do these pieces of information form a consistent whole?), and flexibility (am I able to revise my self-understanding when I acquire new information about myself?).

The second part of the research will examine the acquisition of self-understanding in the therapeutic process. Specifically, it will explore possible tensions between the accuracy or richness of self-understanding and its practical usefulness, as well as the challenges to achieving self-understanding, such as the misuse of authority by the therapist.

In the final part, the theory of self-understanding developed thus far will be tested and refined through its application to three more specific issues: the role of self-understanding (or the lack thereof) in specific mental illnesses and their treatment, the role of self-understanding in resolving ambiguities between "myself" and "my illness" (e.g., when a person is unsure whether to attribute a behavior to themselves or to the illness they suffer from), and the role of self-understanding in emerging therapeutic methods such as AI-assisted therapy and psychotherapy augmented by psychedelic substances.

Project description

The main goal of the project is to develop an extensive theory of legal imagination. The project is interdisciplinary in nature, combining perspectives from law, philosophy, and cognitive sciences.

• Step One: The initial step will attempt to demonstrate that legal imagination can be understood as a process of mental simulation. This will allow concepts from psychology and neurobiology to be applied to better understand how lawyers utilize imagination
• Step Two: The functions of legal imagination will then be analyzed. It is hypothesized that there are three such functions:
  •     Heuristic: Imagination helps solve legal problems by granting access to unconscious knowledge.
  •     Didactic: Imagination aids in developing intuitions.
  • Hermeneutic: Imagination is crucial for interpreting legal texts.
• Step Three: The final phase of research will examine the implications—both theoretical and practical—of recognizing the central role of imagination in legal cognition. This is expected to provide insights into legal problem-solving, statutory interpretation, and legal education.

The project aspires to restore imagination to its rightful place at the heart of legal thinking. It aims to help lawyers understand that imagination is not their adversary but an ally, one that can be harnessed to think more effectively about legal issues. Harvard law professor Thomas Reid Powell is said to have remarked: “If you think you can think about a thing which is inextricably connected with another thing, without thinking about the other thing, then you have a legal mind.” The ambition of this project is to prove Powell wrong.

Project description

The objective of the proposed project is to develop an integrative account of cognitive artifacts on various time scales, from proximal “here and now,” through developmental, up to historical, and evolutionary one. 

From the 1990s, defenders of embodied, embedded, extended, and distributed cognition (in short, “wide cognition”), have focused on arguing that artifacts, being external representations, could be indeed cognitive. As a result, many philosophers and cognitive scientists agree today that there are “things that make us smart,” to refer to the title of Norman’s (1993) book. We aid ourselves by relying on many external resources. We interact with external memory aids like timetables and calendars to remember our duties; we use maps to navigate in the environment, mathematical symbols to calculate, and diagrams to make inferences. Sometimes we do this individually, sometimes collectively. It is also well recognized that the use of external representations could facilitate the performance of human beings not only in the “here and now”, but it could also lead to building relatively persistent cognitive niches, wherein cognition is transformed in more prolonged periods. 

However, the contribution of artifacts to the transformation of cognition is typically restricted to a single time scale—or at best, various time scales are considered but investigated separately. This is an important gap in the light of the growing consensus within the philosophy of cognitive science that integration is a theoretical virtue which is driving a deeper understanding of phenomena and research progress. Thus, the proposed project aims to apply recent advancements of the new mechanicism to deliver an integrative account for artifact-based cognition. Achieving this main goal requires further developing a mechanistic continuous intertemporal integration model, extending the notion of a representational-computational mechanism to include external representations and precise analysis of spatial and temporal dimensions (i.e., component parts and operations) of “wide” cognitive systems comprising human beings and artifacts. Against this background, some classical themes of cognitive artifacts, as their taxonomy, will also be revisited with particular emphasis on the dynamical aspect of using artifacts. Special attention will be paid to processing mathematics-related cognitive artifacts such as diagrams and symbolic notations.

Project description

It can be assumed that the shape of contemporary legal systems was influenced by five key inventions—or “turning points”—that made law what it is today: institutionalization (the creation of institutions empowered to interpret, apply, and enforce law), textualization (giving law a written form), abstraction (the creation of general and abstract legal norms), universalization (the establishment of laws binding upon all), and normativization (recognizing law as the ultimate source of its binding authority). It is critically important to understand where these "inventions" came from and how they influenced the historical development of law.

By analyzing the mental mechanisms that enabled the flourishing of legal systems—and by recognizing the limitations imposed by the structure of the human mind on the possible paths of their development—one can gain fascinating insights into the nature of law. It is possible to speculate that there may be no fixed essence of law; rather, law might be better characterized as a "field of forces." It emerges from dynamic processes driven, on the one hand, by cultural innovations and, on the other, shaped by cognitive and motivational constraints deeply rooted in our evolutionary past.

Reconstructing the natural history of law may also provide a perspective on its future. Understanding the limitations inherent to the mental mechanisms responsible for the emergence of law allows us to consider which pathways of legal development are possible (or even highly likely) and which are impossible (or exceedingly improbable). This is particularly significant in the context of rapid technological advancement, which forces legal scholars to ask questions such as: Is a unified, global legal system possible? Should intelligent machines ever be granted the status of autonomous legal entities