Mathematical and neuro-mathematical connections activated by a teacher and his student in the geometric problems-solving: A view of networking of theories
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Benilda María Cantillo-Rudas 1 , Camilo Andrés Rodríguez-Nieto 2 , Vicenç Font Moll 3 , Flor Monserrat Rodríguez-Vásquez 4 *
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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.
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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
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Article Downloads: 321
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- 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