Mathematical and neuro-mathematical connections activated by a teacher and his student in the geometric problems-solving: A view of networking of theories
Full Text (PDF)
Benilda María Cantillo-Rudas 1 , Camilo Andrés Rodríguez-Nieto 2 , Vicenç Font Moll 3 , Flor Monserrat Rodríguez-Vásquez 4 *
More Detail
1 Universidad de Panamá, Panamá, PANAMÁ2 Universidad de la Costa, Barranquilla, COLOMBIA3 Universitat de Barcelona, Barcelona, SPAIN4 Universidad Autónoma de Guerrero, Chilpancingo, MEXICO* Corresponding Author
Abstract
The research goal is twofold: to articulate neuro-mathematics with the extended theory of mathematical connections that uses onto-semiotic approach tools and to explore the connections established by a teacher and his student when solving a problem about the volume of two boxes, one of toothpaste and the other of tomato. This research was developed in two stages: the theories were articulated assuming concordances and complementarities, highlighting the notion of connection, and a context of reflection was considered carried out in three phases where the participants were selected, participant observation was carried out in the classroom during solving a problem and then analyzing the data with the new tool to explore mathematical and neuro-mathematical connections. The findings present the mathematical connections established by the teacher and the student of meaning, feature, procedural, different representations (alternate, equivalent, and from a horizontal mathematization view), and part-whole, as well as neuro-mathematical connections of: recognition of terms and symbols; visual perception, spatial skills and motor coordination; association of mathematical concepts and formulas; intermediate calculations and unit conversion; solve operations step by step and understand the process; verification and conclusion, activated in the brain areas linked to each mathematical practice sequentially.
License
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Article Type: Research Article
EURASIA J Math Sci Tech Ed, Volume 20, Issue 10, October 2024, Article No: em2522
https://doi.org/10.29333/ejmste/15470
Publication date: 15 Oct 2024
Article Views: 350
Article Downloads: 412
Open Access References How to cite this articleReferences
- Alfaro-Carvajal, C., Flores-Martínez, P., & Valverde-Soto, G. (2019). La demostración matemática: Significado, tipos, funciones atribuidas y relevancia en el conocimiento profesional de los profesores de matemáticas [Mathematical demonstration: Meaning, types, assigned functions and relevance in the professional knowledge of mathematics teachers]. Uniciencia, 33(2), 55-75. https://doi.org/10.15359/ru.33-2.5
- Alvarenga, K., Domingos, A., & Cabrera Zuñiga, D. (2022). Neurociencias cognitivas en la formación de profesores de matemática [Cognitive neurosciences in the training of mathematics teachers]. UNIÓN- Revista IberoAmericana de Educación Matemática, 18(65), 1-21. https://www.revistaunion.org/index.php/UNION/article/view/460
- Arenas-Peñaloza, J. A., & Rodríguez-Vásquez, F. M. (2022). Understanding ratio through the Pirie-Kieren model. Acta Scientiae, 24(4), 24-56. https://doi.org/10.17648/acta.scientiae.6826
- Arfken, G. B. (1985). Mathematics for physicists. Academic Press.
- Arsalidou, M., Pawliw-Levac, M., Sadeghi, M., & Mascual-Leone, J. (2018). Brain areas associated with numbers and calculations in children: Meta-analyses of fMRI studies. Developmental Cognitive Neuroscience, 30, 239-250. https://doi.org/10.1016/j.dcn.2017.08.002
- Azcárate, C., & Camacho, M. (2003). La investigación en didácticas del análisis [Research in didactics of analysis]. Asociación Matemática Venezolana. Edición especial, X(2), 115-134.
- Banegas, J. A. (2023). Multimodalidad lingüística y comprensión en matemáticas [Linguistic multimodality and comprehension in mathematics]. Estudios Filosóficos, 72(210).
- Béjar, M. (2014). Una mirada sobre la educación, neuroeducación [A look at education, neuroeducation]. Padres y Maestros, Madrid: Universidad Pontificia Comillas, 35, 49-52. https://doi.org/10.14422/pym.v0i355.2622
- Bikner-Ahsbahs, A. (2022). Adaptive teaching of covariational reasoning: Networking “the way of being” on two layers. The Journal of Mathematical Behavior, 67, Article 100967. https://doi.org/10.1016/j.jmathb.2022.100967
- Bikner-Ahsbahs, A., & Prediger, S. (2010). Networking theories–An approach for exploiting the diversity of theoretical approaches. In B. Sriraman, & L. English (Eds.), Theories of mathematics education (pp. 589-592). Springer. https://doi.org/10.1007/978-3-642-00742-2_46
- Blum, W. (2002). ICMI study 14: Applications and modelling in mathematics education–Discussion document. Educational Studies in Mathematics, 51(1), 149-171. https://doi.org/10.1023/A:1022435827400
- Bortoli, M. D. F., & Bisognin, V. (2023). Conexões matemáticas no ensino de progressões aritméticas de ordem superior [Mathematical connections in teaching higher-order arithmetic progressions]. Bolema: Boletim de Educação Matemática, 37, 250-270. https://doi.org/10.1590/1980-4415v37n75a12
- Buckley, P. B., & Gillman, C. B. (1974). Comparisons of digits and dot patterns. Journal of Experimental Psychology, 103(6), 1131-1136. https://doi.org/10.1037/h0037361
- Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections [Unpublished PhD thesis]. Simon Fraser University.
- Calzadilla-Pérez, O. O. (2023). Mapeo cienciométrico de las neurociencias de la educación: Miradas para la formación de docents [Scientometric mapping of educational neurosciences: Perspectives for teacher training]. Estudios Pedagógicos (Valdivia), 49(1), 281-303. https://doi.org/10.4067/S0718-07052023000100281
- Campo-Meneses, K. G., & García-García, J. (2023). Conexiones matemáticas identificadas en una clase sobre las funciones exponencial y logarítmica [Mathematical connections identified in a class 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.
- Caviedes-Barrera, S., De Gamboa, G., & Badillo, E. R. (2023). Mathematical objects that configure the partial area meanings mobilized in task-solving. International Journal of Mathematical Education in Science and Technology, 54(6), 1092-1111. https://doi.org/10. 1080/0020739X.2021.1991019
- Chein, W. (2012). The brain’s learning and control architecture. Current Directions in Psychological Science, 21, 78-84. https://doi.org/10.1177/0963721411434977
- Cohen Kadosh, R., Cohen Kadosh, K., Schuhmann, T., Kaas, A., Goebel, R., Henik, A., & Sack, A. T. (2007). Virtual dyscalculia induced by parietal-lobe TMS impairs automatic magnitude processing. Current Biology, 17, 689-693. https://doi.org/10.1016/j.cub.2007.02.056
- Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education. Routledge. https://doi.org/10.4324/9781315456539
- Cohen, R., & Walsh, V. (2009). Non-abstract numerical representations in the IPS: Further support, challenges, and clarifications. Behavioral and Brain Sciences, 32, 356-373. https://doi.org/10.1017/S0140525X09990987
- Cohen, R., Soskic, S., Luculano, T., Kanai, R., & Walsh, V. (2010). Modulating neuronal activity produces specific and long-lasting changes in numerical competence. Current Biology, 20(22), 2016-2020. https://doi.org/10.1016/j.cub.2010.10.007
- Coronado, J. P. (1998). Las matemáticas en el arte, la música y la literatura [Mathematics in art, music and literature]. Tendencias Pedagógicas, (50), 235-244.
- 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
- De la Serna, J. (2020). Aproximación a las neuromatemáticas: El cerebro matemático [Approaching neuromathematics: The mathematical brain]. Editorial Tektime.
- Dehaene, S. (1996). The organization of brain activations in number comparison: Event-related potentials and the additive-factors method. Journal of Cognitive Neuroscience, 8(1), 47-68. https://doi.org/10.1162/jocn.1996.8.1.47
- Dehaene, S., & Changeux, J. P. (1993). Development of elementary numerical abilities: A neuronal model. Journal of Cognitive Neuroscience, 5(4), 390-407. https://doi.org/10.1162/jocn.1993.5.4.390
- 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. https://doi.org/10.1080/02643290244000239
- Departament d’Ensenyament. (2017). Competències bàsiques de l’àmbit matemàtic [Basic skills in the mathematical field]. http://ensenyament.gencat.cat/web/.content/home/departament/publicacions/colleccions/competencies-basiques/eso/eso-matematic.pdf
- 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
- 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. (2007). Una perspectiva ontosemiótica sobre cuatro instrumentos de conocimiento que comparten un aire de familia: Particular/general, representación, metáfora y context [An ontosemiotic perspective on four instruments of knowledge that share a family resemblance: Particular/general, representation, metaphor and context]. Educación Matemática, 19(2), 95-128. https://doi.org/10.24844/EM1902.04
- 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
- Font, V., Trigueros, M., Badillo, E., & Rubio, N. (2016). Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educational Studies in Mathematics, 91(1), 107-122. https://doi.org/10.1007/s10649-015-9639-6
- Freudenthal, H. (1991). Revisiting mathematics education. Kluwer Academic Publisher.
- García-García, J. G. (2019). Escenarios de exploración de conexiones matemáticas [Mathematical connection exploration scenarios]. Números: Revista de Didáctica de las Matemáticas, 4(100), 129-133.
- 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. (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
- Gebuis, T., Cohen Kadosh, R., De Haan, E., & Henik, A. (2009). Automatic quantity processing in 5-year olds and adults. Cognitive Processing, 10, 133-142. https://doi.org/10.1007/s10339-008-0219-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 [Neuromathematics an interdisciplinary study: The case of emotions expressed in the construction of the parallelepiped]. 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., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos [Institutional and personal meaning of mathematical objects]. Recherches en Didactique des Mathématiques, 14(3), 325-355.
- 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-The International Journal on Mathematics Education, 39(1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
- Godino, J. D., Batanero, C., & Font, V. (2019). The onto-semiotic approach: Implications for the prescriptive character of didactics. For the Learning of Mathematics, 39(1), 37-42.
- Guerrero, R. (2021). El cerebro infantil y adolescente: Claves y secretos de la neuroeducación [The child and adolescent brain: Keys and secrets of neuroeducation]. Libros Cúpula.
- 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].
- Hackett, G. (1985). Role of mathematics self-efficacy in the choice of math-related majors of college women and men: A path analysis. Journal of Counseling Psychology, 32, 47-56. https://doi.org/10.1037/0022-0167.32.1.47
- 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
- Hawes, Z., & Ansari, D. (2020). What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior. Psychonomic Bulletin & Review, 27, 465-482. https://doi.org/10.3758/s13423-019-01694-7
- 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
- Hummes, V., Breda, A., & Font, V. (2022). El desarrollo de la reflexión sobre la práctica en la formación de profesores de matemáticas: Una mirada desde el lesson study y los criterios de idoneidad didáctica [The development of reflection on practice in mathematics teacher training: A look from lesson study and criteria of didactic suitability]. In J. G. Lugo-Armenta, L. R. Pino-Fan, M. Pochulu, & W. F. Castro (Eds.), Enfoque onto-semiótico del conocimiento y la instrucción matemáticos: Investigaciones y desarrollos en América Latina. Editorial Universidad de Los Lagos.
- Kenedi, A. K., Helsa, Y., Ariani, Y., Zainil, M., & Hendri, S. (2019). Mathematical connection of elementary school students to solve mathematical problems. Journal on Mathematics Education, 10(1), 69-80. https://doi.org/10.22342/jme.10.1.5416.69-80
- 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., Font, V., & Sala, G. (2023). Analysing the mathematical activity in a modelling process from the cognitive and onto-semiotic perspectives. Mathematics Education Research Journal, 35(4), 715-741. https://doi.org/10.1007/s13394-022-00411-3
- Ledezma, C., Rodríguez-Nieto, C. A., & Font, V. (2024). The role played by extra-mathematical connections in the modelling process. AIEM–Avances de Investigación en Educación Matemática, 25, 81-103. https://doi.org/10.35763/aiem25.6363
- Ledezma, C., Sol, T., Sala-Sebastià, G., & Font, V. (2022). Knowledge and beliefs on mathematical modelling inferred in the argumentation of a prospective teacher when reflecting on the incorporation of this process in his lessons. Mathematics, 10(18), Article 3339. https://doi.org/10.3390/math10183339
- Lee, K., & Fong, N. (2011). Neuroscience and the teaching of mathematics. National Institute of Education, Singapore.
- Leikin, R. (2018). How can cognitive neuroscience contribute to mathematics education? Bridging the two research areas. In Proceedings of the 13th International Congress on Mathematical Education (pp. 363-383). Springer. https://doi.org/10.1007/978-3-319-72170-5_21
- Lent, R. W., Lopez, F. G., & Bieschke, K. J. (1993). Predicting mathematics-related choice and success behaviors: Test of an expanded social cognitive model. Journal of Vocational Behavior, 42, 223-236. https://doi.org/10.1006/jvbe.1993.1016
- 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
- Lyons, I. M., & Beilock, S. L. (2013). Ordinality and the nature of symbolic numbers. Journal of Neuroscience, 33(43), 17052-17061. https://doi.org/10.1523/JNEUROSCI.1775-13.2013
- 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].
- 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
- MEN. (2006). Estándares básicos de competencias en lenguaje, matemáticas, ciencia y ciudadanas [Basic standards for language, mathematics, science and citizenship skills]. Ministry of National Education.
- Mendoza-Arenas, R., Delgado-Baltazar, M., Ruiz-Salazar, J., & Álvarez-Huertas, F. (2022). Neurociencias y enseñanza de la matemática en las universidades: Antología de la situación didáctica [Neuroscience and the teaching of mathematics in universities: Anthology of the didactic situation]. Mount Scopus Journal, 2(4), 33-51. https://doi.org/10.31219/osf.io/wp4e7
- Menon, V. (2016). Memory and cognitive control circuits in mathematical cognition and learning. In M. Cappelletti, & W. Fias (Eds.), Progress in brain research (pp. 159-186). Elsevier. https://doi.org/10.1016/bs.pbr.2016.04.026
- 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
- MOE. (2006). Mathematics syllabuses–Lower secondary. Ministry of Education.
- 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.
- Mora, F. (2007). Neurocultura: Una cultura basada en el cerebro [Neuroculture: A culture based on the brain]. Alianza Editorial.
- Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215(5109), 1519-1520. https://doi.org/10.1038/2151519a0
- 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.
- NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
- Obersteiner, A., Dresler, T., Bieck, S. M., & Moeller, K. (2019). Understanding fractions: Integrating results from mathematics education, cognitive psychology, and neuroscience. In A. Norton, & M. W. Alibali (Eds.), Constructing number. Research in mathematics education (pp. 135-162). Springer. https://doi.org/10.1007/978-3-030-00491-0_7
- Olkun, S. (2022). How do we learn mathematics? A framework for a theoretical and practical model. International Electronic Journal of Elementary Education, 14(3), 295-302. https://doi.org/10.26822/iejee.2022.245
- 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), Article 23. https://doi.org/10.26634/jmat.1.3.1948
- 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. https://doi.org/10.26634/jpsy.9.3.3772
- Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44(3), 547-555. https://doi.org/10.1016/j.neuron.2004.10.014
- Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connection theoretical approaches: First steps towards a conceptual framework. ZDM–The International Journal on Mathematics Education, 40(2), 165-178. https://doi.org/10.1007/s11858-008-0086-z
- Price, M. S. M., & Henao, J. (2011). Influencia de la percepción visual en el aprendizaje [Influence of visual perception on learning]. Ciencia y Tecnología Para la Salud Visual y Ocular, 9(1), 93-101.
- Radford, L. (2008). Connecting theories in mathematics education: Challenges and possibilities. ZDM–The International Journal on Mathematics Education, 40, 317-327. https://doi.org/10.1007/s11858-008-0090-3
- Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83(2, Pt.1), 274-278. https://doi.org/10.1037/h0028573
- Rivera-Rivera, E. (2019). El neuroaprendizaje en la enseñanza de las matemáticas: La nueva propuesta educativa [Neurolearning in mathematics teaching: The new educational proposal]. Revista Entorno, 67, 157-168. https://doi.org/10.5377/entorno.v0i67.7498
- Rodríguez-Nieto, C. A., & Alsina, Á. (2022). Networking between ethnomathematics, STEAM education, and the globalized approach to analyze mathematical connections in daily practices. Eurasia Journal of Mathematics Science and Technology Education, 18(3), Article em2085. https://doi.org/10.29333/ejmste/11710
- 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), Article em2438. https://doi.org/10.29333/ejmste/14450
- Rodríguez-Nieto, C. A., Escobar-Ramírez, Y. C., Font, V., & Aroca, A. (2023). Ethnomathematical and mathematical connections activated by a teacher in mathematical problems posing and solving. Acta Scientiae, 25(1), 86-121. https://doi.org/10.17648/acta.scientiae.7356
- Rodríguez-Nieto, C. A., Font, V., & Rodríguez-Vásquez, F. M. (2022a). Literature review on networking, of theories developed in mathematics education context. Eurasia Journal of Mathematics, Science and Technology Education, 18(11), Article em2179. https://doi.org/10.29333/ejmste/12513
- Rodríguez-Nieto, C. A., Font, V., Borji, V., & Rodríguez-Vásquez, F. M. (2022b). 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. (2022). 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. https://doi.org/10.33532/revemop.e202202
- Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & Font, V. (2022c). A new view about connections. The mathematical connections established by a teacher when teaching the derivative. International Journal of Mathematical Education in Science and Technology, 53(6), 1231-1256. https://doi.org/10.1080/0020739X.2020.1799254
- Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & Font, V. (2023a). Combined use of the extended theory of connections and the onto-semiotic approach to analyze mathematical connections by relating the graphs of f and f’. Educational Studies in Mathematics, 114, 63-88. https://doi.org/10.1007/s10649-023-10246-9
- Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & García-García, J. (2021c). 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. https://doi.org/10.16949/turkbilmat.797182
- Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., Font, V. & Morales-Carballo, A. (2021a). A view from the TAC-EOS network on the role of mathematical connections in understanding the derivative. Revemop, 3, Article e202115.
- Rodríguez-Nieto, C., Rodríguez-Vásquez, F. M., & García-García, J. (2021b). 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), Article em2006. https://doi.org/10.29333/ejmste/11160
- 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
- Sagula, J. E. (2023). Pensamiento estadístico y probabilístico, un puente entre neurociencias e inteligencia artificial [Statistic and probabilistic thinking, a bridge between neuroscience and artificial intelligence]. e-CUCBA, (20), 61-71. https://doi.org/10.32870/ecucba.vi20.297
- Santens, S., Roggeman, C., Fias, W., & Verguts, T. (2010). Number processing pathways in human parietal cortex. Cerebral Cortex, 20(1), 77-88. https://doi.org/10.1093/cercor/bhp080
- Sawamura, H., Shima, K., & Tanji, J. (2002). Numerical representation for action in the parietal cortex of the monkey. Nature, 415(6874), 918-922. https://doi.org/10.1038/415918a
- 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
- Serway, R. A. (1990). Physics for scientists and engineers. Saunders College Publishing.
- Tuttle, C., & Davidesco, I. (2023). Integrating authentic neuroscience research into the high school biology curriculum. The American Biology Teacher, 85(7), 373-378. https://doi.org/10.1525/abt.2023.85.7.373
- Vargas-Vargas, R. A. V. (2013). Matemáticas y neurociencias: Una aproximación al desarrollo del pensamiento matemático desde una perspectiva biológica. Unión–Revista Iberoamericana de Educación Matemática, 9(36), 37-46.
- Verschaffel, L., Lehtinen, E., & Van Dooren, W. (2016). Neuroscientific studies of mathematical thinking and learning: A critical look from a mathematics education viewpoint. ZDM Mathematics Education, 48, 385-391. https://doi.org/10.1007/s11858-016-0781-0
How to cite this article
APA
Cantillo-Rudas, B. M., Rodríguez-Nieto, C. A., Font Moll, V., & Rodríguez-Vásquez, F. M. (2024). Mathematical and neuro-mathematical connections activated by a teacher and his student in the geometric problems-solving: A view of networking of theories. Eurasia Journal of Mathematics, Science and Technology Education, 20(10), em2522. https://doi.org/10.29333/ejmste/15470
Vancouver
Cantillo-Rudas BM, Rodríguez-Nieto CA, Font Moll V, Rodríguez-Vásquez FM. Mathematical and neuro-mathematical connections activated by a teacher and his student in the geometric problems-solving: A view of networking of theories. EURASIA J Math Sci Tech Ed. 2024;20(10):em2522. https://doi.org/10.29333/ejmste/15470
AMA
Cantillo-Rudas BM, Rodríguez-Nieto CA, Font Moll V, Rodríguez-Vásquez FM. Mathematical and neuro-mathematical connections activated by a teacher and his student in the geometric problems-solving: A view of networking of theories. EURASIA J Math Sci Tech Ed. 2024;20(10), em2522. https://doi.org/10.29333/ejmste/15470
Chicago
Cantillo-Rudas, Benilda María, Camilo Andrés Rodríguez-Nieto, Vicenç Font Moll, and Flor Monserrat Rodríguez-Vásquez. "Mathematical and neuro-mathematical connections activated by a teacher and his student in the geometric problems-solving: A view of networking of theories". Eurasia Journal of Mathematics, Science and Technology Education 2024 20 no. 10 (2024): em2522. https://doi.org/10.29333/ejmste/15470
Harvard
Cantillo-Rudas, B. M., Rodríguez-Nieto, C. A., Font Moll, V., and Rodríguez-Vásquez, F. M. (2024). Mathematical and neuro-mathematical connections activated by a teacher and his student in the geometric problems-solving: A view of networking of theories. Eurasia Journal of Mathematics, Science and Technology Education, 20(10), em2522. https://doi.org/10.29333/ejmste/15470
MLA
Cantillo-Rudas, Benilda María et al. "Mathematical and neuro-mathematical connections activated by a teacher and his student in the geometric problems-solving: A view of networking of theories". Eurasia Journal of Mathematics, Science and Technology Education, vol. 20, no. 10, 2024, em2522. https://doi.org/10.29333/ejmste/15470