Exploring neuro-mathematical connections in the resolution of a contextualized geometric problem
DOI:
https://doi.org/10.33830/ijdmde.v2i1.11821Keywords:
Neuro-mathematical connections, Mathematics education, Problem-solving, GeometryAbstract
This study aims to explore the neuro-mathematical connections activated by high school and university students when solving a contextualized geometric problem. The urgency of this research lies in the need to deepen our understanding of the cognitive and neurological processes involved in mathematical problem-solving, particularly in spatial reasoning tasks. The theoretical framework combines Connections Theory and the Onto-semiotic Approach, focusing on the typology of neuro-mathematical connections. The qualitative, descriptive methodology was carried out in three phases: (1) selection of volunteer participants from high school and university levels; (2) data collection through the application of a geometric problem involving the volume of two boxes, with video recordings capturing students’ problem-solving processes; and (3) analysis using the theoretical framework to identify and interpret the neuro-mathematical connections activated during the task. The results revealed a rich network of cognitive processes encompassing mathematical practices, objects, processes, and semiotic functions. Specifically, students demonstrated: recognition of mathematical terms and symbols; activation of visual perception, spatial reasoning, and motor coordination; association of concepts and formulas; execution of intermediate calculations and unit conversions; sequential problem-solving; and reflective verification of results. These findings support the claim of the Extended Theory of Connections that connections are inherently cognitive processes. This research contributes to the field of mathematics education and cognitive science by providing an in-depth analysis of how students engage with mathematical problems through neuro-mathematical pathways. Future research should expand this work by incorporating neuroimaging or eye-tracking technologies to further validate and visualize the cognitive mechanisms underlying mathematical reasoning.
References
Adu-Gyamfi, K., Bossé, M.J., & Chandler, K. (2017). Student connections between algebraic and graphical polynomial representations in the context of a polynomial relation. International Journal of Science and Mathematics Education, 15, 915–938. https://doi.org/10.1007/s10763-016-9730-1
Alsina, Á. (2020). Mathematical Connections through STEAM Activities in Early Childhood Education. Unión-Ibero-American Journal of Mathematics Education, 16 (58), 168-190. https://doi.org/10.29333/ejmste/11710
Arfken, G. B. (1985). Mathematics for physicists. Academic Press. https://doi.org/10.1016/C2013-0-10310-8
Azcárate, C., & Camacho, M. (2003). Research in didactics of analysis. Venezuelan Mathematical Association. Special issue, X(2), 115-134.
Banegas, J. A. (2023). Multimodalidad lingüística y comprensión en multimodality matemáticas and [Linguistic comprehension in mathematics]. Estudios Filosóficos, 72(210), 303-325.
Bortoli, M. D. F., & Bisognin, V. (2023). Conexões matemáticas no ensino de progressões aritméticas de ordem superior. Bolema: Boletim de Educação Matemática, 37, 250-270. http://dx.doi.org/10.1590/1980-4415v37n75a12.
Breda, A. (2021). Assessment and redesign of a unit on proportionality using the Didactic Suitability tool. Uniciencia, 35(1), 38-54. http://dx.doi.org/10.15359/ru.35-1.3
Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections [Unpublished PhD Thesis]. Faculty of Education-Simon Fraser University, Canada.
Campo-Meneses, K. G., & García-García, J. (2023). Mathematical connections identified in a lecture on exponential and logarithmic functions. Bolema: Boletim de Educação Matemática, 37, 849–871. https://doi.org/10.1590/1980-4415v37n76a22
Cantillo-Rudas, B. M., & Rodríguez-Nieto, C. A. (2024). Relaciones entre la neurociencia y la educación matemática: Un estado del arte [Relationships between neuroscience and mathematics education: A state of the art]. Caminhos da Educação Matemática em Revista, 14(1), 33-50. https://periodicos.ifs.edu.br/periodicos/caminhos_da_educacao_matematica/article/view/1626/1595
Cantillo-Rudas, B.M., Rodríguez-Nieto, C.A., Moll, V.F., & Rodríguez-Vásquez, F.M. (2024). Mathematical and neuro-mathematical connections activated by a teacher and their student in geometric problem solving: A theory-interconnectedness perspective. Eurasia Journal of Mathematics, Science and Technology Education, 20(10), em2522. https://doi.org/10.29333/ejmste/15470
Caviedes-Barrera, S., De Gamboa, G., & Badillo, E. R. (2023). Mathematical objects that configure the partial area meanings mobilized in task-solving. and International Journal of Mathematical Education in Science Technology, 54(6), 1092-1111. https://doi.org/10. 1080/0020739X.2021.1991019
De Gamboa, G., Badillo, E., & Font, V. (2023). Meaning and structure of mathematical connections in the classroom. Canadian Journal of Science, Mathematics and Technology Education, 23(2), 241-261. https://doi.org/10.1007/s42330-023-00281-2.
Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical cognition, 1(1), 83-120.
Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20(3-6), 487-506.
Dolores-Flores, C., & García-García, J. (2017). Conexiones Intramatemáticas y Extramatemáticas que se producen al Resolver Problemas de Cálculo en Contexto: un Estudio de Casos en el Nivel Superior [Intra-mathematical and extra-mathematical connections that occur when solving Calculus’ problems in context: A case study at a higher level]. Bolema: Mathematics Education Bulletin, 31(57), 158-180. https://doi.org/10.1590/1980-4415v31n57a08 .
Dolores-Flores, C., Rivera-López, M., & García-García, J. (2019). Exploring mathematical connections of pre-university students through tasks involving rates of change. International Journal of Mathematical Education in Science and Technology, 50(3), 369-389. https://doi.org/10.1080/0020739X.2018.1507050
Downton, A., y Livy, S. (2022). Perspectivas sobre el razonamiento geométrico de los estudiantes en relación con los prismas. Revista Internacional de Educación en Ciencias y Matemáticas , 20(7), 1543-1571.
Drijvers, P., Godino, J. D., Font, V. y Trouche, L. (2013). Un episodio, dos perspectivas. Estudios Educativos en Matemáticas, 82 (1), 23-49. https://doi.org/10.1007/s10649-012-9416-8
Eli, J. A., Mohr-Schroeder, M. J., & Lee, C. W. (2011). Exploring mathematical connections of prospective middle-grades teachers through card-sorting tasks. Mathematics Education Research Journal, 23(3), 297 319. https://doi.org/10. 1007/s13394-011-0017-0.
Evitts, T. (2004). Investigating the mathematical connections that preservice teachers use and develop while solving problems from reform curricula [Unpublished PhD dissertation]. Pennsylvania State University.
Font, V., & Contreras, Á. (2008). The problem of the particular and its relation to the general in mathematics education. Educational studies in mathematics, 69, 33-52.
Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82(1), 97-124. https://doi.org/10.1007/s10649-012-9411-0.
García-García, J., & Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing Calculus tasks. International Journal of Mathematical Education in Science and Technology, 49(2), 227-252. https://doi.org/10.1080 /0020739X.2017.1355994
García-García, J., & Dolores-Flores, C. (2020). Exploring pre-university students’ mathematical connections when solving Calculus application problems. International Journal of Mathematical Education in Science and Technology, 52(6), 912–936. https://doi.org/10.1080/0020739X.2020.1729429.
García-García, J., & Dolores-Flores, C. (2021). Pre-university students' mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33, 1-22. https://doi.org/10.1007/s13394-019-00286-x
Giraldo-Rojas, J. D., Zabala-Jaramillo, L. A., & Parraguez-González, M. C. (2021). Neuromatemática un estudio interdisciplinario: el caso de las emociones expresadas en la construcción del paralelepípedo. Scientia et Technica, 26(3), 378-390. https://doi.org/10.22517/23447214.24751
Girelli, L., Lucangeli, D., & Butterworth, B. (2000). The development of automaticity in accessing number magnitude. Journal of experimental child psychology, 76(2), 104-122. https://doi.org/10.1006/jecp.2000.2564
Godino, J. D. (2014). Síntesis del enfoque ontosemiótico del conocimiento y la instrucción matemática: motivación, supuestos y herramientas teóricas. Universidad de Granada, 1-60.
Godino, J. D., Batanero, C., & Font, V. (2003). Fundamentos de la enseñanza y el aprendizaje de las matemáticas para maestros [Fundamentals of teaching and learning mathematics for teachers]. Universidad de Granada.
Godino, J. D., Batanero, C., & Font, V. (2007). The onto semiotic approach to research in mathematics education. ZDM–Mathematics Education, 39(2), 127-135. https://doi.org/10.1007/s11858-006-0004-1.
Godino, J. D., Batanero, C., Burgos, M., & Wilhelmi, M. R. (2024). Understanding the onto-semiotic approach in mathematics education through the lens of the cultural historical activity theory. ZDM–Mathematics Education, 56(6), 1331-1344.
Godino, J. D., Rivas, H., Arteaga, P., Lasa, A., & Wilhelmi, M. R. (2014). Ingeniería didáctica basada en el enfoque ontológico-semiótico del conocimiento y la instrucción matemáticos. Recherches en didactique des Mathématiques, 34(2/3), 167-200.
Gutiérrez, D. I., & Neuta, K. A. (2015). Prevalencia de las habilidades perceptuales visuales, la integración viso motora, los movimientos sacádicos, la atención visual y el proceso de lecto-escritura en niños entre 6-7 años de la ciudad de Bogotá en estratos 5 y 6 [Prevalence of visual perceptual skills, visual-motor integration, saccadic movements, visual attention and the reading-writing process in children between 6-7 years of age in the city of Bogotá in strata 5 and 6] [Master’s thesis, Universidad de La Salle].
Hatisaru, V. (2022). Mathematical connections established in the teaching of functions. Teaching mathematics and its applications. An International Journal of the IMA, 42(3), 207-227. https://doi.org/ 10.1093/teamat/hrac013.
Henik, A. & Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory & cognition, 10, 389-395. https://doi.org/10.3758/BF03202431
Kidron, I., y Bikner-Ahsbahs, A. (2015). Impulso a la investigación mediante la interconexión de teorías. Enfoques de la investigación cualitativa en educación matemática: Ejemplos de metodología y métodos , 221-232.
Lakatos, I. (2015). Pruebas y refutaciones: La lógica del descubrimiento matemático [Proofs and refutations: The logic of mathematical discovery]. Prensa de la Universidad de Cambridge.
Ledezma, C., Rodríguez-Nieto, C. A., & Font, V. (2024). The role played by extra-mathematical connections in the modelling process. Avances de Investigación en Educación Matemática, 25, 81-103. https://doi.org/10.35763/aiem25.6363.
Libertus, M. E., Feigenson, L., & Halberda, J. (2013). Is approximate number precision a stable predictor of math ability?. Learning and individual differences, 25, 126-133. https://doi.org/10.1016/j.lindif.2013.02.001
Macías, J. V., & Cuellar, A. A. (2018). Prueba piloto de habilidades visomotoras y visoperceptuales en niños entre cinco y siete años en un colegio de sector rural [Pilot test of visual-motor and visual-perceptual skills in children between five and seven years old in a rural school] [PhD thesis, Universidad de La Salle].
Mastropieri, MA, y Scruggs, TE (1989). Elaboraciones reconstructivas: Estrategias que facilitan el aprendizaje de contenidos. Learning Disabilities Focus, 4 (2), 73-77. https://doi.org/10.1177/105345128902400404
Mayer, R. E., & Moreno, R. (2003). Nine ways to reduce cognitive load in multimedia learning. Educational Psychologist, 38(1), 43-52. https://doi.org/10.1207/ S15326985EP3801_6.
Mhlolo, M. K. (2012). Mathematical connections of a higher cognitive level: A tool we may use to identify these in practice. African Journal of Research in Mathematics, Science and Technology Education, 16(2), 176–191. https://doi.org/10.1080/10288457.2012.10740738
Ministerio de Educación Nacional (Ministry of National Education) [MEN]. (2006). Estándares básicos de competencias en lenguaje, Matemáticas, ciencia y ciudadanas. Bogotá, Colombia: MEN.
Mora, C. D. (2003). Estrategias para el aprendizaje y la enseñanza de las matemáticas [Strategies for learning and teaching mathematics]. Revista de Pedagogía, 24(70), 181-272.
Narváez-Rumié, O. M., Hernández Rodríguez, S. D., Caraballo Martínez, G. J., & Molano-Pirazán, M. L. (2019). Destrezas visuales y el proceso de escritura: Evaluación en escolares de primero y segundo grado [Visual skills and the writing process: Assessment in first and second graders]. Área Andina.
Osler, J. E. (2012). Trichotomy Squared A Novel Mixed Methods Test and Research Procedure Designed to Analyze, Transform, and Compare Qualitative and Quantitative Data for Education Scientists who are Administrators, Practitioners, Teachers, and Technologists. i-manager's Journal on Mathematics, 1(3), 23.
Osler, J. E., & Mason, L. R. (2016). Neuro-mathematical trichotomous mixed methods analysis: using the neuroscientific tri-Squared test statistical metric as a post hoc analytic to determine North Carolina School of Science and Mathematics Leadership Efficacy. Journal on Educational Psychology, 9(3), 44-61.
Pahmi, S., Vrapi, A., & Supriyadi, E. (2024). Implementation of virtual reality to enhance spatial abilities: a study on aspects, effects, and differences in participants’ initial ability levels. International Journal of Didactic Mathematics in Distance Education, 1(2), 54–69. https://doi.org/10.33830/ijdmde.v1i2.9108
Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connection theoretical approaches: First steps towards a conceptual framework. ZDM–Mathematics Education, 40(2), 165-178. https://doi.org/10.1007/s11858-008-0086-z
Price, M. S., & Henao Calderón, J. L. (2011). Influencia de la percepción visual en el aprendizaje. Universidad de La Salle. Fundación Universitaria del Área Andina, 9(1), 89-102. http://revistas.lasalle.edu.co/index.php/sv/article/view/221
Radford, L. (2008). Connecting theories in mathematics education: Challenges and possibilities. ZDM–Mathematics Education, 40, 317-327. https://doi.org/10.1007/s11858-008 0090-3.
Rodríguez-Nieto, C. A., & Font Moll, V. (2025). Mathematical connections promoted in multivariable calculus’ classes and in problems-solving about vectors, partial and directional derivatives, and applications. Eurasia Journal of Mathematics, Science and Technology Education, 21(4), em2619. https://doi.org/10.29333/ejmste/16187.
Rodríguez-Nieto, C. A., Cabrales, H. A., Arenas Peñaloza, J., Schnorr, C. E., & Font, V. (2024). Onto semiotic analysis of Colombian engineering students’ mathematical connections to problems solving on vectors: A contribution to the natural and exact sciences. Eurasia Journal of Mathematics, Science and Technology Education, 20(5), em2438. https://doi.org/10.29333/ejmste/14450
Rodríguez-Nieto, C. A., Font, V., Borji, V., & Rodríguez-Vásquez, F. M. (2022a). Mathematical connections from a networking theory between extended theory of mathematical connections and onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 53(9), 2364–2390. https://doi.org/10.1080/0020739X.2021.1875071
Rodríguez-Nieto, C. A., Nuñez-Gutierrez, K., Rosa, M., & Orey, D. (2022b). Conexiones etnomatemáticas y etnomodelación en la elaboración de trompos y tacos de carne. Más allá de un antojito mexicano [Ethnomathematical connections and ethnomodelling in the preparation of trompos and meat tacos. Beyond a Mexican snack]. Revemop, 4, Article e202202. revemop.e202202.
Rodríguez-Nieto, C. A., Pabón-Navarro, M. L., Cantillo-Rudas, B. M., & Moll, V. F. (2025a). The potential of ethnomathematical and mathematical connections in the pre-service mathematics teachers’ meaningful learning when problems-solving about brick-making. Infinity Journal, 14(2), 419-444. https://doi.org/10.22460/infinity.v14i2.p419-444
Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & García-García, J. (2021c). Exploring university Mexican students’ quality of intra-mathematical connections when solving tasks about derivative concept. EURASIA Journal of Mathematics, Science and Technology Education, 17(9), em2006. https://doi.org/10.29333/ejmste/11160
Rodríguez-Nieto, C., Rodríguez-Vásquez, F. M., & García-García, J. (2021a). Pre-service mathematics teachers’ mathematical connections in the context of problem-solving about the derivative. Turkish Journal of Computer and Mathematics Education, 12(1), 202-220. http://dx.doi.org/10.16949/turkbilmat.797182
Rodríguez-Nieto, C., Rodríguez-Vásquez, F. M., Font, V., & Morales-Carballo, A. (2021b). Una visión desde el networking TAC-EOS sobre el papel de las conexiones matemáticas en la comprensión de la derivada [A view from the ETC-OSA networking of theories on the role of mathematical connections in understanding the derivative]. Revemop, 3, e202115. https://doi.org/10.33532/revemop.e202115
Rosa, M., & Orey, D. (2021). An ethnomathematical perspective of STEM education in a glocalized world. Bolema: Boletim de Educação Matemática, 35, 840-876. https://doi.org/10.1590/1980-4415v35n70a14
Rousselle, L. & Noel, M.P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102, 361-395. https://doi.org/10.1016/j.cognition.2006.01.005
Rubinsten, O. & Henik, A. (2005). Automatic activation of internal magnitudes: A study of developmental dyscalculia. Neuropsychology, 19(5), 641-648. https://doi.org/10.1037/0894-4105.19.5.641
Rubinsten, O., Henik, A., Berger, A., & Shahar-Shalev, S. (2002). The development of internal representations of magnitude and their association with Arabic numerals. Journal of Experimental Child Psychology, 81(1), 74-92. https://doi.org/10.1006/jecp.2001.2645
Ruiz-Soto, I. S. (2018). Estrategia didáctica para el fortalecimiento del cálculo de perímetro, área y volumen mediante el uso de prismas de bases rectangulares bajo el enfoque de enseñanza para la comprensión (EpC) en estudiantes de cuarto de primaria del Colegio de la Compañía de María “La Enseñanza” de Medellín. Facultad de Ciencias.
Selinski, N. E., Rasmussen, C., Wawro, M., & Zandieh, M. (2014). A method for using adjacency matrices to analyze the connections students make within and between concepts: The case of linear algebra. Journal for Research in Mathematics Education, 45(5), 550-583. https://doi.org/10.5951/jresematheduc.45.5.0550.
Serna D.L.J. (2020). Aproximación a las Neuromatemáticas: el Cerebro Matemático. Editorial Tektime.
Serway, R. A. (1990). Physics for scientists and engineers. Saunders College Publishing.
Sudirman, S., & Alghadari, F. (2020). Bagaimana mengembangkan kemampuan spasial dalam pembelajaran matematika di sekolah?: Suatu tinjauan literatur. Journal of Instructional Mathematics, 1(2), 60-72. https://doi.org/10.37640/jim.v1i2.370
Tenny, S., Brannan, G. D., Brannan, J. M., & Sharts-Hopko, N. C. (2021). Qualitative Study. In I. StatPearls (Ed.), StatPearls. StatPearls Publishing. http://www.ncbi.nlm.nih.gov/pubmed/29262162
Vásquez-Ramírez, CJ (2019). Narrativa pedagógica del proceso de identificación y análisis de las estrategias para la resolución de problemas en estudiantes del grado décimo de la institución educativa Teófilo Roberto Potes de la ciudad de Buenaventura a través del aprendizaje de las figuras geométricas . Tesis. Universidad Autónoma de Manizales.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Benilda Maria Cantillo-Rudas
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
