Krzysztof Cipora

Krzysztof Cipora
Loughborough University | Lough · Centre for Mathematical Cognition

PhD in Psychology

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64
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Publications

Publications (64)
Article
Full-text available
Mathematics anxiety (MA) is negatively associated with mathematics performance. Although some aspects, such as mathematics self-concept (M self-concept), seem to modulate this association, the underlying mechanism is still unclear. In addition, the false gender stereotype that women are worse than men in mathematics can have a detrimental effect on...
Article
Full-text available
Maths anxiety is common and refers to feelings of anxiety, fear and other negative emotions and thoughts in individuals when confronted with mathematical tasks or numerical information. Self-report measures of maths anxiety have been created, but the majority are in English and are not culturally relevant to all countries. This study aimed to trans...
Article
Full-text available
In this paper, we discuss several largely undisputed claims about mathematics anxiety (MA) and propose where MA research should focus, including theoretical clarifications on what MA is and what constitutes its opposite pole; discussion of construct validity, specifically relations between self-descriptive, neurophysiological, and cognitive measure...
Article
Full-text available
Working memory (WM) is one of the most important cognitive functions that may play a role in the relation between math anxiety (MA) and math performance. The processing efficiency theory proposes that the rumination and worrisome thoughts (induced by MA) result in less available WM resources (which are needed to solve math problems). At the same ti...
Preprint
Psychological science could greatly benefit from research synthesis, especially when it comes to overcoming limitations of too small samples tested in single studies. However, initiatives aimed at sharing large, curated trial-level data from cognitive tasks remain scarce. To address this problem, we initiated a collective effort allowing to assembl...
Preprint
Full-text available
The Spatial-Numerical Association of Response Codes (SNARC) effect (i.e., faster left/right side responses to small/large magnitude numbers, respectively) is considered as strong evidence for the link between numbers and space. The studies have shown considerable variation in this effect. Among the factors determining individual differences in the...
Preprint
Full-text available
Despite variety of cultures, our shared biology and the universality of finger counting suggests that numbers are embodied. Another lines of research show that numerical cognition might be bound to what our bodies are able to do. Differences in finger counting are apparent even within Western cultures. Relatively few indigenous cultures have been s...
Preprint
One of the most fundamental effects used to investigate number representations is the Spatial-Numerical Association of Response Codes (SNARC) effect showing that responses to small/large numbers are faster with the left/right hand, respectively. However, in recent years, it is hotly debated whether the SNARC effect is based upon cardinal representa...
Article
Full-text available
Teachers are strong role models for their pupils, especially at the beginning of education. This also holds true for math: If teachers feel anxious about math, the consequences on the mathematical education of their pupils is detrimental. Previous studies have shown that (future) elementary school teachers have higher levels of math anxiety than mo...
Preprint
Full-text available
In this paper we list ten fairly undisputed claims about Mathematics Anxiety (MA) and propose where MA research should focus on. The areas future MA research should focus on comprise (a) theoretical clarifications on what MA is, and what constitutes its opposite pole, (b) construct validity – specifically relations between self-descriptive, (neuro)...
Preprint
Full-text available
Maths anxiety is common and refers to feelings of anxiety, fear and other negative emotions and thoughts in individuals when confronted with mathematical tasks or numerical information. Self-report measures of maths anxiety have been created, but the majority are in English and are not culturally relevant to all countries. This study aimed to trans...
Preprint
Working memory (WM) is one of the most important cognitive functions that may play a role in the relation between math anxiety (MA) and math performance. The processing efficiency theory proposes that the rumination and worrisome thoughts (induced by MA) result in less available WM resources (which are needed to solve math problems). At the same ti...
Preprint
Full-text available
This is a draft of the Editorial of a Special Issue "Direct and Conceptual Replication in Numerical Cognition".
Preprint
Mathematics anxiety (MA) is negatively associated with mathematics performance. Although some aspects, such as mathematics self-concept (M-self-concept), seem to modulate this association, the underlying mechanism is still unclear. In addition, the false gender-stereotype according to which women are worse than men in mathematics, can have a detrim...
Article
Full-text available
The SNARC (Spatial-Numerical Association of Response Codes) effect (i.e., a tendency to associate small/large magnitude numbers with the left/right hand side) is prevalent across the whole lifespan. Because the ability to relate numbers to space has been viewed as a cornerstone in the development of mathematical skills, the relationship between the...
Article
Full-text available
Research on multi-digit number processing suggests that, in Arabic numerals, their place-value magnitude is automatically activated, whenever a magnitude-relevant task was employed. However, so far, it is unknown, whether place-value is also activated when the target task is magnitude-irrelevant. The current study examines this question using the p...
Article
Full-text available
The symbolic number comparison task has been widely used to investigate the cognitive representation and underlying processes of multi-digit number processing. The standard procedure to establish numerical distance and compatibility effects in such number comparison paradigms usually entails asking participants to indicate the larger of two present...
Article
Full-text available
A recent study based on the SPoARC effect (Spatial Position Association Response Codes) showed that culture heavily shapes our cognition and more specifically the way we organize our thoughts ; when Western adults are asked to keep in mind a sequence of colors, they mentally organize them from left to right, whereas right-to-left reading/writing ad...
Preprint
Full-text available
Already in toddlerhood, children begin to master the system of number word meanings. The role of grammar, and in particular grammatical number inflection, in early stage of this process has been well documented. It is not clear, however, whether the influence of the grammatical language structure also extends to more complex later stages. In the cu...
Preprint
The symbolic number comparison task has been widely used to investigate the cognitive representation and underlying processes of multi-digit number processing. The standard procedure to establish numerical distance and compatibility effects in such number comparison paradigms usually entails asking participants to indicate the larger of two present...
Preprint
Full-text available
Teachers are strong role models for their pupils, especially at the very beginning of education, and as such, pupils tend to share their teacher’s attitudes. This also holds true for math: If teachers feel anxious about math, the consequences on the mathematical education of their pupils is detrimental.Previous studies have shown that (future) elem...
Article
Full-text available
Doing basic maths seems to be a pretty common thing. 2 + 2 equals 4, both in France and in China. 7 × 8 equals 56, both in the United States of America and in Germany. Although most of us use the same symbols to write down numbers (1, 2, 3, 4, …), we use very different words for these numbers simply because we speak different languages. In this art...
Preprint
Full-text available
Numerous studies revealed effects of some linguistic properties like inversion or reading/writing direction on number processing. However, it remains more controversial, whether influences at a syntactic level, such as singular vs. plural form associated with certain numbers, can also influence magnitude and place-value processing and vice versa. I...
Preprint
In response to a recent point raised by Fischer at al. (2020), we discuss the theoretical implications of both the original Attentional SNARC (Att-SNARC) and its recent failed multi-laboratory replication. In our view, the theoretical importance of the original Att-SNARC can be summarized in two points: (1) there is a conceptual link between number...
Article
Full-text available
The numerical distance effect (it is easier to compare numbers that are further apart) and size effect (for a constant distance, it is easier to compare smaller numbers) characterize symbolic number processing. However, evidence for a relationship between these two basic phenomena and more complex mathematical skills is mixed. Previously this relat...
Article
The attentional spatial-numerical association of response codes (Att-SNARC) effect (Fischer, Castel, Dodd, & Pratt, 2003)—the finding that participants are quicker to detect left-side targets when the targets are preceded by small numbers and quicker to detect right-side targets when they are preceded by large numbers—has been used as evidence for...
Article
Full-text available
Evidence from multiple studies conducted in the past few decades converges on the conclusion that numerical properties can be associated with specific directions in space. Such spatial-numerical associations (SNAs), as a signature of elementary number processing, seem to be a likely correlate of math skills. Nevertheless, almost three decades of re...
Preprint
Full-text available
An important part of any math curriculum is solving word problems. Such problems are particularly difficult for many students. It has been shown that the difficulty of word problems arises from the characteristics of the problems themselves (e.g., arithmetic and linguistic characteristics) and the solver (e.g., mathematical and reading ability as w...
Preprint
Full-text available
The numerical distance effect (it is easier to compare numbers that are further apart) and size effect (for a constant distance, it is easier to compare smaller numbers) characterize the analogue number magnitude representation. However, evidence for a relationship between these two basic phenomena and more complex mathematical skills is mixed. Pre...
Preprint
Full-text available
Evidence from multiple studies conducted in few past decades converge to the conclusion that numerical properties can be associated with specific directions in space. Such Spatial-Numerical Associations (SNAs) as a signature of elementary number processing seem to be a likely candidate for a correlate of math skill. Nevertheless, almost three decad...
Article
Full-text available
Based on a theory of impulsive and reflective human behavior, we test the effects of transcranial direct current stimulation (tDCS) targeting either prefrontal or parietal cortex in either hemisphere. In a confirmatory registered report, cathodal tDCS is administered to conceptually reproduce tDCS modulations of implicit spatial-numerical associati...
Preprint
Full-text available
In everyday situations, numbers appear in a linguistic context: we communicate and perceive numbers within sentences. However, languages differ in how they refer to numerosities. One such difference is grammatical number: the way singular and plural grammatical forms are used when referring to certain numbers. We know that differences in grammatica...
Preprint
The aim of cognitive psychology is to obtain insights into human cognition in general. For this purpose, group-studies are typically conducted on representative samples so that the results can be generalized to the population. Using this approach, individual differences in such group-level cognitive phenomena are typically neglected and not much is...
Preprint
The SNARC (Spatial-Numerical Association of Response Codes) effect (i.e., a tendency to associate small / large magnitude numbers with left / right hand side), an instance of implicit, directional Spatial-Numerical Association (SNA), is prevalent across whole lifespan, including children and adolescents. However, there are considerable interindivid...
Article
Full-text available
The Spatial–Numerical Association of Response Codes (SNARC) effect (i.e., faster reactions to small/large numbers on the left-/right-hand side) is usually observed along with the linguistic Markedness of Response Codes (MARC) effect—that is, faster left-/right-hand responses to odd/even numbers. The SNARC effect is one of the most thoroughly invest...
Article
Full-text available
A strong link between bodily activity and number processing has been established in recent years. Although numerous observations indicate that adults use finger counting (FC) in various contexts of everyday life for different purposes, existing knowledge of FC routines and their use is still limited. In particular, it remains unknown how stable the...
Preprint
A commentary being part of the book edited by K.S. Mix and M. Battista.
Preprint
Full-text available
Undoubtedly, tight links between space and number processing exist. Usually, findings of Spatial-Numerical Associations (SNA) are interpreted causally, i.e., that spatial capabilities aid or are even a fundamental cornerstone of mathematical skill. In this book chapter, we question this seemingly ubiquitous assumption.To start with, there is no rob...
Preprint
Research on multi-digit number processing suggests that, in Arabic numerals, the magnitude of a number is automatically processed based on the place-value system. The current study examined whether this automatic processing extends to magnitude-irrelevant parity processing by using the parity congruency effect. The parity status of a decade digit i...
Article
Full-text available
Numerical categories such as parity, i.e., being odd or even, have frequently been shown to influence how particular numbers are processed. Mathematically, number parity is defined categorically. So far, cognitive, and psychological accounts have followed the mathematical definition and defined parity as a categorical psychological representation a...
Article
Full-text available
The Abbreviated Math Anxiety Scale (AMAS) is one of the most popular instruments measuring math anxiety (MA). It has been validated across several linguistic and cultural contexts. In this study, we investigated the extent of administration method invariance of the AMAS by comparing results (average scores, reliabilities, factorial structure) obtai...
Chapter
Tight cognitive links between space and number processing exist. Usually, Spatial-Numerical Associations (SNAs) are interpreted causally: spatial capabilities are a cornerstone of math skill. We question this seemingly ubiquitous assumption. After presenting SNA taxonomy, we show that only some SNAs correlate with math skill. These correlations are...
Chapter
Battista et al. rightly point out the importance of the relation between spatial and geometric reasoning. They are also working towards more fine-grained analyses considering different aspects of both spatial and mathematical reasoning, and postulate that analyses should examine particular skills, rather than these very general constructs. The auth...
Article
Full-text available
The Spatial Numerical Association of Response Codes (SNARC) effect describes a stimulus-response association of left with small magnitude and right with large magnitude. Usually, it is estimated by means of regression slopes, where the independent variable only has a limited number of levels. Inspection of the literature reveals that it is not diff...
Article
Full-text available
In the field of numerical cognition it is often highlighted that the domain-specific systems, referred to as “Approximate Number System” (ANS), or “The Number Sense” (NS)1, constitute the basis for mathematical skills (Feigenson et al., 2004; Dehaene, 2011). However, recently, Leibovich et al. (2016) stressed the role of domain-general factors, esp...
Article
Full-text available
Maths anxiety is considered to be one of the important predictors of maths achievements. Numerous studies indicate that a teacher’s maths anxiety as well as teaching methods may be one of the causes of maths anxiety in children. Data obtained from American college students indicate that students choosing majors in pre-service education are characte...
Article
Full-text available
While mathematically impaired individuals have been shown to have deficits in all kinds of basic numerical representations, among them spatial-numerical associations, little is known about individuals with exceptionally high math expertise. They might have a more abstract magnitude representation or more flexible spatial associations, so that no au...
Article
The mental number line metaphor describes how numbers are associated with space. These spatial-numerical associations (SNA) are subserved by parietal structures (mainly intraparietal sulcus [IPS] and posterior superior parietal lobule [PSPL]). Generally, it is assumed that this association is a basic cornerstone for arithmetic skills. In this revie...
Article
Full-text available
Math anxiety has an important impact on mathematical development and performance. However, although math anxiety is supposed to be a transcultural trait, assessment instruments are scarce and are validated mainly for Western cultures so far. Therefore, we aimed at examining the transcultural generality of math anxiety by a thorough investigation of...
Chapter
Full-text available
1 Informacje wprowadzające Jak wskazano w poprzednich rozdziałach niniejszej ekspertyzy, mobilność polskich naukowców uzależniona jest od szeregu czynników natury ogólnej (sytuacja ekonomiczna, sposoby zatrudnienia) jak i inicjatyw mających bezpośrednio na celu promowanie mobil-ności. Może być ona również uzależniona od specyfi ki poszczególnych dz...
Article
Full-text available
Finger counting plays an important role in mathematical cognition, especially in the acquisition of the concept of number and elementary math competence. Fingers are spontaneously used to count because of their constant availability and easiness of manipulation. Stable counting order within hand facilitates the acquisition of ordinal as well as car...
Article
Full-text available
Finger counting being present in vast majority of cultures, plays very important role in the mathematical cognition. The practice of finger counting had large impact on the development of mathematics in a form we all know. Both neuropsychological studies and recent developments in cognitive neuroscience show close relationship between numerical and...
Article
Full-text available
The SNARC (spatial-numerical association of response codes) described that larger numbers are responded faster with the right hand and smaller numbers with the left hand. It is held in the literature that arithmetically skilled and nonskilled adults differ in the SNARC. However, the respective data are descriptive, and the decisive tests are nonsig...

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Projects (3)
Project
The main aim of this study is to explore emotions and attitudes towards mathematics among elite STEM students. More specifically, we are interested in what characterizes STEM students who report high mathematics anxiety and how mathematics anxiety is related to other anxiety types as well as to motivation, attitudes, perceptions, and positive emotions towards mathematics. We will run Bayesian correlations, Exploratory Factor Analysis, and Latent Profile Analysis. Results could guide future efforts and help us understand this relatively understudied population.
Archived project
There are multiple space-number associations, directional ones like the SNARC effect or non-directional ones like interval-spaced relations between numerical and spatial distance in the number line estimation task. The goal of this project is to understand and differentiate different space-number associations and their impact on arithmetic