In this work, I develop a mathematical formalization of the Replaced Elements Model (Wagner. Quarterly Journal of Experimental Psychology: Section B, 56(1), 7, 2003), within a general framework proposed by Ghirlanda (Journal of Mathematical Psychology, 64/65, 8-16, 2015, Journal of Mathematical Psychology, 85, 55-61, 2018), which provides a new way to apply and study the model. The result derived here has the novelty of explicitly stating how the model computes associative values without requiring either the application of complex algorithms or the use of special software. As a way of showing how to use this formalization, I apply it to the study of varied learning phenomena and several models, by either analytic means or simulations. In the process, I reproduce conclusions drawn previously for the Replaced Elements Model by other methods (Glautier. Behavior Research Methods, 39(4), 993-1000, 2007; Schultheis et al. Behavior Research Methods, 40, 435-441, 2008; Wagner. Experimental Psychology: Section B, 56(1), 7, 2003). As an interesting byproduct, I provide a general algorithm which may be applied to simulate the predictions of the replaced elements model, Rescorla-Wagner's model (Rescorla & Wagner. Classical conditioning, Current research and theory, 2, 64-69, 1972), and Pearce's configural model (Pearce. Psychological Review, 94(1), 61, 1994) among others. Concrete instances of the algorithm, coded in Python, are provided in the Appendix.

A partially ordered set (or a poset, for short) is a set endowed with a partial order relation, i.e., with a reflexive, anti-symmetric, and transitive binary relation. As mathematical objects, posets have been intensively studied in the last century, coming to play essential roles in pure mathematics, logic, and theoretical computer science. More recently, they have been increasingly employed in data analysis, multi-criteria decision-making, and social sciences, particularly for building synthetic indicators and extracting rankings from multidimensional systems of ordinal data. Posets naturally represent systems and phenomena where some elements can be compared and ordered, while others cannot be and are then incomparable. This makes them a powerful data structure to describe collections of units assessed against multidimensional variable systems, preserving the nuanced and multi-faceted nature of the underlying domains. Moreover, poset theory collects the proper mathematical tools to treat ordinal data, fully respecting their non-numerical nature, and to extract information out of order relations, providing the proper setting for the statistical analysis of multidimensional ordinal data. Currently, their use is expanding both to solve open methodological issues in ordinal data analysis and to address evaluation problems in socio-economic sciences, from multidimensional poverty, well-being, or quality-of-life assessment to the measurement of financial literacy, from the construction of knowledge spaces in mathematical psychology and education theory to the measurement of multidimensional ordinal inequality/polarization.

We present a new experimental paradigm intended to allow for the acquisition of the data needed for testing strong hypotheses regarding the nature of encoded representations and the real-time processing of those representations using the same set of trials. The design is motivated by two formal theories: general recognition theory (Ashby & Townsend. Psychological Review, 93, 154-179, 1986), which addresses internal representation, and systems factorial theory (Townsend & Nozawa. Journal of Mathematical Psychology, 39, 321-359. 1995), which addresses the foundational characteristics of real-time processing. We show in the results of two experiments, one with very simple and a second with more complex stimuli, that this paradigm is capable of producing data that can allow for inferences regarding both representation and processing from the same set of trials and that those two sets of inferences can be found to be coherent with one another, allowing for the potential for the results of behavioral experimentation to seriously constrain formal and computational modeling. In this sense, the work is coherent with an overarching theme in Mary Peterson's work, specifically as an application of two theory-driven approaches to questions in cognitive representation and processing.

Unidimensionality is a fundamental yet often overlooked prerequisite for measurement. In the context of psychological measurement, the central question is whether a set of items can be logically reduced to a single latent factor. This study advocates for the application of state-trace analysis, an underutilized method from mathematical psychology, as a decisive tool to address this question. State-trace analysis provides a simple, general, and rigorous criterion for unidimensionality: monotonicity between item pairs. Identifying items within a factor that violate this criterion is straightforward, offering a practical approach to evaluating unidimensionality. This paper demonstrates the utility of state-trace analysis through exemplary applications within the framework of the five-factor model, analyzing data from the International Personality Item Pool-NEO-120 (N = 618, 000) and the NEO Personality Inventory-Revised (N1 = 857, N2 = 500). The findings reveal that maintaining the five-factor model requires significant revisions to numerous items, highlighting the potential of state-trace analysis to enhance personality measurement beyond existing methodologies. The paper concludes by discussing strategies to promote broader adoption of this method and how future designs in personality research can be tailored to effectively incorporate state-trace analysis.

The present studies use a novel approach to characterize how memory representations are updated with repetition. These studies use the free recall paradigm, which boasts greater memory advantages for spaced repetitions (Melton. Journal of Verbal Learning and Memory, 9, 596–606. 1970; Madigan. Journal of Verbal Learning and Verbal Behavior, 8, 828–835. 1969). However, a single recall of a twice-presented item precludes inferring whether the item’s first or second presentation support its recall. The present studies leverage that, in free recall, transitions reflect stronger associations and are more likely between items studied nearby in time (Healey et al., Psychonomic Bulletin & Review, 26(3), 699–720. 2019). The critical analysis asks which transitions are more likely to a repeated item: temporal neighbors from its first presentation or from its second presentation? Transitions should be equally likely from neighbors of each presentation if the repeated item’s presentations are stored independently. Transitions from second-presentation neighbors should be more likely if retrieval of item information from the first presentation strengthens the item representation during the second presentation, or if independent traces benefit from being studied more recently. Alternatively, retrieved context theory assumes that each studied item is associated with a slowly drifting temporal context, and repetition evokes study-phase retrieval of the context state from the first presentation (Howard & Kahana. Journal of Mathematical Psychology, 46, 269–299. 2002a; Siegel & Kahana. Journal of Experimental Psychology: Learning, Memory, and Cognition, 40(3), 755-764. 2014). This context retrieval should strengthen the repeated item’s associations to items with similar temporal contexts from its first presentation. As a result, retrieved context theory predicts more transitions to a repeated item from a first-presentation neighbor. Two studies provide support for the prediction of retrieved context theory, with implications for other theories.Supplementary InformationThe online version contains supplementary material available at 10.3758/s13423-025-02673-x.

ABSTRACT In this paper I pose four questions raised by Mark Textor’s The Disappearance of Soul and the Turn Against Metaphysics. These are: (1) When did Bertrand Russell abandon the subject? (2) Is acquaintance always a polyadic relation? (3) Does Idealism follow from the thesis that all relations are internal? (4) Is the development of philosophy of psychology and philosophy of mathematics linked together, that is, did the New Logic substantially influence British analytic philosophizing about the soul, or did the New Logic develop independently of theorizing about soul?

The discriminability in polytomous KST was introduced by Stefanutti etal. (Journal of Mathematical Psychology, 2020, 94, 102306). As the interesting topic in polytomous KST, this paper discusses the discriminability around granular polytomous knowledge spaces, polytomous knowledge structures, polytomous surmising functions and polytomous skill functions. More precisely, this paper gives some equivalences between the discriminability of polytomous surmising functions (resp. polytomous skill functions) and the discriminability of granular polytomous knowledge spaces (resp. polytomous knowledge structures). Such findings open the field to a systematic generalization of the discriminability in KST to the polytomous case.

The present text is a supplement to the article “Hermann Cohen’s Philosophy of Mathematics, or What is Wrong with the Marburg Method” published in “Vo­prosy filosofii” (Vol. 2, 2023). That article examined a special form of interpreta­tion of mathematical functions formulated in Herbart’s mathematical psychology and Fechner’s psychophysics and their adjustment as transcendental dominants in Cohen’s epistemology. The purpose of this article is to provide a more rigor­ous justification for the hypothesis that Cohen’s infinitesimal is not a collective notion of natural-scientific construction, but an adaptation of precisely that form of mathematical inference that was briefly fundamental to the philosophical pro­gram of psychology. The way we propose to work with the text is to model the epistemological mechanics, and to analyze the theoretical result to which it leads. The author is not trying to present Cohen’s philosophy as a strictly psy­chological concept or as a complement to Fechner’s psychophysics. Neverthe­less, it seems to be important to achieve clear understanding of precisely at what theoretical level and time span the psychological foundations of Neo-Kantianism are indisputable and at what time span they are not. The author’s research posi­tion is that convergence with psychological theory is typical of the entire Neo-Kantian movement at its early stage of development, and the value of the failed result of Cohen is to demonstrate the fact that the dereification of substantiality must be followed by the denaturalization of the means by which it is carried out.

The summary in English The current study finds the reality of using selection from a face Consider the clubs' mathematical psychology sport in Palestine, southern governorate, Ascale has been created that includes two axes : Importance disabilities , and applied a sample of ( 1200 ) players in ( 40 ) clubs .The results revealed possibilities for using mathematical psychology in sports clubs on the other hand , the results showed that there are some disabilities in use mathematical psychology with players and clubs. The most important of these are : The refusal of the players and clubs to subject the players to psychological treatment or preparation, some players and sports clubs find it difficult use Mathematical psychology. The researcher recommended that players and sports clubs should be set up before the beginning During the sports season and friendly and official matches.

Rebuilding Readers’ Relationships with Mathematics: A Review of The Psychology of Mathematics: A Journey of Personal Mathematical Empowerment for Educators and Curious Minds

Numerical approximation of the first-passage time distribution of time-varying diffusion decision models: A mesh-free approach

Rational inattention when decisions take time

ABSTRACT In most areas, psychological phenomena tend to be explained only through textual constructions. Several authors, however, point to the need for theories that have a more formal nature, based on mathematical reasoning. In order to encourage broader access to its applications, we present the models and advantages of a mathematical psychology approach to the study of behavior. We review the limitations of verbal theorizing, then a common taxonomy in mathematical psychology follows, that classifies formal models as descriptive, process characterization, and explanatory. As well succeeded cases, we examine the mathematical psychology of decision making, of helping behavior, of memory, and of romantic relationships. Finally, we discuss the potential benefits and uses of this approach. Welcome to mathematical psychology.

RESUMO Na maior parte das áreas os fenômenos psicológicos tendem a ser explicados apenas por meio de construções textuais. Diversos autores, no entanto, apontam para a necessidade de teorias que tenham uma natureza mais formal, baseada em raciocínio matemático. A fim de incentivar acesso mais amplo às suas aplicações, apresentamos os modelos e vantagens da abordagem da psicologia matemática para o estudo do comportamento. Revisamos as limitações da teorização verbal, apresentando em seguida uma taxonomia, comum na psicologia matemática, que classifica os modelos de dados como descritivos, explicativos e de caracterização. Como casos bem sucedidos, examinamos a psicologia matemática da tomada de decisão, do comportamento de ajuda, da memória e dos relacionamentos românticos. Por fim, discutimos os benefícios e usos potenciais da abordagem. Bem-vindo(a) à psicologia matemática.

The goal of this study was to help Kindergarten pupils at Akobima MA Basic School enhance their composition writing skills. The implementation of the Egg Carton Math manipulative intervention enhanced kids' academic achievement, as indicated by a significantly higher average score (7) at the post-intervention stage compared to the low average score (3) during the pre-intervention stage. The findings also revealed that pupils were more engaged and motivated in the learning process. In order to do this, the Egg Carton Math manipulative was used as an intervention to improve pupil-to-pupil and teacher-to-pupil engagement. Other data-gathering approaches used at the pre-and post-intervention stages, such as observation and interview, verified that the problem was remedied once the intervention was implemented. As a result, the study suggests that the Egg Carton Math manipulative be utilized to help Kindergarten pupils improve their composition writing skills. REFERENCES Ambrose, R. C. (2002). Are we overemphasizing manipulatives in the primary grades to the detriment of girls? Teaching Children Mathematics, 9(1), 16-21. Clements, D. H. (2000). “Concrete” Manipulatives, Concrete Ideas. Contemporary Issues in Early Childhood, 1(1), 45–60. Elliot, S. N., Kratochwill, T. R., Cook, J. L. Travers (2000). Educational Psychology- Effective teaching and Effective Learning (third edition), McGraw-Hill, New York. Freer W., D. (2006). Keeping It Real: The Rationale for Using Manipulatives in the Middle Grades. Mathematics Teaching in the Middle School, Vol.11 (5). 238-242. Gorski, P.C. (2018). Teacher-Action Research. Critical Multicultural Pavilion. Riel, M. (2020). Understanding Action Research. Centre for Collaborative Action Research, Pepperdine University. Sarama J. Clements D.H., (2016). Physical and Virtual Manipulatives: What Is “Concrete”? , International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives, Mathematics Education in the Digital Era 7, Shahid, N., Asif, M., & Pasha, A. (2022). Effect of Internet Addiction on School Going Children. Inverge Journal of Social Sciences, 1(1), 12-47. Thompson, P., & Thompson, A. (1990). Salient aspects of experience with concrete manipulatives. In Proceedings of the 14th Annual Meeting of the International Group for the Psychology of Mathematics (pp. 46–52). Mexico City.

In mathematical psychology, the model of decision practice represents the development of moral judgment that deals with the time to decide the meaning of the various choices and selecting one of them for use. Most animal behavior research classifies such situations as two distinct phenomena. On the other hand, reward plays a big part in this kind of study since, based on the selected side and food location, such circumstances may be classified into four categories. This paper intends to investigate such types of behavior and establish a general functional equation for it. The proposed functional equation can be used to describe several psychological and learning theory models in the existing literature. By using the fixed point theory tools, we obtain the results related to the existence, uniqueness, and stability of a solution to the proposed functional equation. Finally, we give two examples to support our main results.

Procedural knowledge space theory (PKST) was recently proposed by Stefanutti (British Journal of Mathematical and Statistical Psychology, 72(2) 185-218, 2019) for the assessment of human problem-solving skills. In PKST, the problem space formally represents how a family of problems can be solved and the knowledge space represents the skills required for solving those problems. The Markov solution process model (MSPM) by Stefanutti et al. (Journal of Mathematical Psychology, 103, 102552, 2021) provides a probabilistic framework for modeling the solution process of a task, via PKST. In this article, three adaptive procedures for the assessment of problem-solving skills are proposed that are based on the MSPM. Beside execution correctness, they also consider the sequence of moves observed in the solution of a problem with the aim of increasing efficiency and accuracy of assessments. The three procedures differ from one another in the assumption underlying the solution process, named pre-planning, interim-planning, and mixed-planning. In two simulation studies, the three adaptive procedures have been compared to one another and to the continuous Markov procedure (CMP) by Doignon and Falmagne (1988a). The last one accounts for dichotomous correct/wrong answers only. Results show that all the MSP-based adaptive procedures outperform the CMP in both accuracy and efficiency. These results have been obtained in the framework of the Tower of London test but the procedures can also be applied to all psychological and neuropsychological tests that have a problem space. Thus, the adaptive procedures presented in this paper pave the way to the adaptive assessment in the area of neuropsychological tests.

Reviewed by: The Psychology of Mathematics: A Journey of Personal Mathematical Empowerment for Educators and Curious Minds by Anderson Norton Firdous Ahmad Mala Anderson Norton The Psychology of Mathematics: A Journey of Personal Mathematical Empowerment for Educators and Curious Minds Oxfordshire, UK. Routledge. 2022. 238 pages. USING AN APPROACH that empowers students by fostering their hidden constructions of mathematics structures, The Psychology of Mathematics offers an innovative introduction to the often-ignored and less-discussed psychology of mathematics. The author—an award-winning mathematician, educator, and writer—uses an engaging and accessible style, thereby making the reading experience both enriching and revealing. The book, by virtue of its style and simplicity, is accessible to a nonmathematical audience, too. In a dozen chapters, readers are exposed to the gorgeous world of mathematics. Combatting the common misnomer that mathematics is boring and hard, Norton offers exciting discussions on various mathematical themes, such as the power of symbols, the geometry of numbers, and the wonderful gift of mathematics. The book discusses a plethora of engaging and enriching discussions, such as the unreasonable effectiveness of numbers in our diurnal lives, the ineradicable interplay of language and mathematics, and the innate ability—found in babies and some animals—to immediately apprehend small numbers. Figures receive more appreciation and attention than numbers do. A figure speaks more than a thousand words. By focusing on space as a product of our own psychology, we make geometry more intuitive. Observing that mathematical symbols provide a way for recording the products of our mental actions, we are no longer required to keep them in the mind at all. Mathematics is a wonderful gift. In the author's words, "It is a gift that keeps on giving, having given us everything from numbers to Neptune." The author does not attempt to make mathematics easier; he only envisions making it dearer and more valuable to the reader. He does so, and successfully, by cutting down on jargon and by enhancing conversational communication of otherwise difficult concepts of geometry and other branches of mathematics. The motivation for writing this book is not simply to marvel at mathematics but also to promote mathematics as personally enriching and empowering. The book is an excellent exposition of the incessant wonder that mathematicians and philosophers have experienced and expressed for millennia. It draws on what Galileo is reported to have remarked in his 1623 masterpiece, The Assayer: "Philosophy is written in this grand book—I mean the universe—that stands continuously open to our gaze, but it cannot be understood unless one first learns to comprehend the language in which it is written. It is written in the language of mathematics." It is not an exaggeration to proclaim that mathematics is the language in which the universe has been written, and Psychology attempts to bring the same fact to the fore for a nonmathematical audience. [End Page 79] Firdous Ahmad Mala Government Degree College Sopore, Jammu and Kashmir Copyright © 2022 World Literature Today and the Board of Regents of the University of Oklahoma

Virtual social networking increases the individual's economic predictability

Attention control processes play an important role in many substantial psychological theories but are hard to reliably and validly measure on the subject-level. Therefore, associations between individual differences in attentional control and other variables are often inconsistent. Here we propose a novel neurocognitive psychometrics account of attentional control that integrates model parameters from the dual-stage two-phase model (Hübner et al., 2010), a mathematical model of selective attention, with neural correlates of conflict processing (i.e., latencies of the stimulus-locked lateralized readiness potential) in a multilayer structural equation model framework. We analyzed data from 150 participants who completed the Eriksen Flanker task while their EEG was recorded and used the neurocognitive psychometric approach to distinguish between two sequential stages of information-processing-target selection and response selection. Model parameters and neural correlates showed convergent validity and could be meaningfully related to each other. Together, these neurocognitive process parameters jointly explained 37 % of the variance in individual differences in higher-order cognitive abilities that were assessed with a battery of intelligence tests and working memory tasks. Individuals with greater cognitive abilities were not only better at focusing their attention on the target stimulus but also at subsequent response-selection. All in all, our results support the idea that individual differences in attentional control processes are related to individual differences in cognitive abilities. Moreover, they provide hope that the measurement crisis of individual differences in attentional control can be overcome by integrating measurement approaches from related disciplines such as mathematical psychology and cognitive neuroscience. (PsycInfo Database Record (c) 2022 APA, all rights reserved).