From Symbolic Form to Epistemic Artifact: Praxeological Analysis of Mathematics in Historical Images for Interdisciplinary Art Education

DOI: https://doi.org/10.5209/aris.109116
Keywords: Art education, History of mathematics, Mathematics and art, Anthropological Theory of the Didactic, Visual semiotics

Abstract

Today, visual arts and mathematics are taught as isolated territories. This disconnection has fragmented learning, obscuring the profound dialogue between number and form. This article bridges both disciplines. To achieve this, it analyzes historical images not merely as aesthetic objects, but as conceptual tools that process and transmit mathematical thought. Through the Anthropological Theory of the Didactic (ATD), we propose an adaptation of the praxeological model applied to historical images, enabling the "reading" of the geometry and arithmetic concealed within art. To verify its utility, we examine the works of six masters—ranging from the precision of Da Vinci, Pacioli, and Dürer to the modernity of Oliver Byrne and M. C. Escher—deconstructing the praxis (tasks and techniques) and logos (technologies and theories) inherent in each masterpiece. Results confirm that these images operate as genuinely autonomous didactic media, capable of structuring, justifying, and legitimizing geometric, arithmetic, and topological knowledge through visual language. We conclude that integrating this perspective into the art classroom and STEAM projects not only enriches the curriculum but also restores the image's power as a tool for discovering the world. Ultimately, this approach rescues mathematics from mechanical repetition, transforming it into a shared visual experience.

Author Biographies

Ismael Cabero-Fayos, Jaume I University

ACADEMIC BACKGROUND

He holds a PhD in Science (Cum Laude) from Jaume I University of Castellón (2019), a Master’s degree in Computational Mathematics from Jaume I University of Castellón, and a Bachelor’s degree in Mathematics from the University of Valencia. He has been accredited as an Associate Professor.

TEACHING EXPERIENCE

He is currently a lecturer in the Bachelor’s Degree in Primary Education at Jaume I University. He has also worked as a lecturer at UNIR (International University of La Rioja) and at the University of Valencia from 2015 to 2020, where he taught Mathematics Education across all levels (Early Childhood, Primary, Secondary, and Upper Secondary). He has also trained teachers in the field of new technologies and worked as a Secondary Education teacher for 20 years.

RESEARCH PROFILE

He is a permanent lecturer (Profesor Permanente Laboral) with one six-year research period (CNEAI) recognized. He has more than sixteen articles indexed in JCR or Scopus, eight of them focused on teacher education. He is co-author of a book on education published by Octaedro (Q1 in SPI), and has coordinated five symposia supporting new educational and communication trends at International Education Conferences, from which four additional books have been published, three of them also ranked Q1 in SPI. He has authored eight Q1 SPI book chapters with Dykinson publishing house. He has presented at more than fourteen additional education conferences, serves as a reviewer for several educational journals, and is a member of the editorial board of one journal and the scientific committee of three journals, one conference, and one academic workshop. He has also been involved in teacher training in the field of new technologies.

He has participated in several research projects, including an ongoing MINECO project, and is the Principal Investigator of another ongoing project at Jaume I University.

 

Mercedes Ventura-Campos, Jaume I University

She holds a degree in Psychology and Psychopedagogy, as well as a PhD in Work and Organizational Psychology from the Universitat Jaume I (UJI), where she currently serves as an Assistant Professor in the Department of Pedagogy and Didactics of Social Sciences, Language, and Literature (Specializing in Educational Didactics and School Organization). Since 2004, she has been part of the WANT Psychosocial Prevention team, focusing her research on teacher technostress, positive psychology, educational leadership, and neuroeducation.
She is the co-director of the Master's Program in Applied Positive Psychology and training programs in positive education, neuroeducation, and healthy, resilient organizations. Her research trajectory integrates psychology, organizational behavior, and education, with a focus on developing evidence-based models of leadership, socio-emotional well-being, neurodidactic strategies for learning across educational fields, and the creation of healthy educational organizations.
She has published 42 scientific contributions in high-impact journals, book chapters, and monographs, and has participated in 82 national and international conferences. She has been involved in 15 competitive projects (as Principal Investigator in one) and 9 knowledge transfer projects. She is part of the Neuroedu innovation group, participating in 16 projects (as Principal Investigator in three), and has contributed to the design of materials on neurodidactics, leadership, positive psychology, and socio-emotional learning.

Noelia Ventura-Campos, Jaume I University

Noelia holds a degree in Mathematics from the University of Valencia, a Master's in Computational Mathematics, and a PhD in Mathematics from the Universitat Jaume I, where she received the Extraordinary Doctoral Award in Sciences. She is currently a tenured professor in the field of Mathematics Education at the same university, where she carries out her teaching and research activities.
Since 2005, she has been part of the Neuropsychology and Functional Neuroimaging Group (NNF), focusing her work on the statistical analysis of MRI images to study the brain. She has participated in various research projects, notably those on the neural bases of learning and changes in functional connectivity. This work has resulted in publications in international scientific journals.
Since 2015, she has also been a member of the research group in Mathematics and Experimental Sciences Education, where she investigates arithmetic-algebraic problem-solving, STEAM, educational robotics, and computational thinking.
Her career combines education and neuroscience, promoting the study of the impact of learning on the brain, brain plasticity, and neural networks applied to mathematics education. Her current focus is on Mathematical Neuroeducation, a field in which she was recognized in 2025 with the Young Researcher Award from the UJI.

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Published
2026-07-01
How to Cite
Cabero-Fayos, I., Ventura-Campos, M., & Ventura-Campos, N. (2026). From Symbolic Form to Epistemic Artifact: Praxeological Analysis of Mathematics in Historical Images for Interdisciplinary Art Education. Arte, Individuo Y Sociedad, 38(3), 661-675. https://doi.org/10.5209/aris.109116
Issue
Vol. 38 No. 3 (2026)
Section
Articles

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