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RESEARCH PAPER
Onto-semiotic analysis of Colombian engineering students’ mathematical connections to problems-solving on vectors: A contribution to the natural and exact sciences
1
Universidad de la Costa (CUC), Barranquilla, COLOMBIA
2
Universidad de La Salle, Bogotá, COLOMBIA
3
University of Barcelona, Barcelona, SPAIN
Online publication date: 2024-04-08
Publication date: 2024-05-01
EURASIA J. Math., Sci Tech. Ed 2024;20(5):em2438
KEYWORDS
ABSTRACT
The mathematical connections Colombian engineering students activated when they solved
vector problems were explored. The study was based on the extended theory of connections and
the onto-semiotic approach. We followed a qualitative methodology that consisted of three
stages: (1) selection of engineering students as participants; (2) application of a questionnaire with
15 tasks on vectors to the participating students; and (3) analysis of these data based on the
theoretical articulation. The results show that students perform arithmetic operations with vectors,
find the scalar and vector product, the norm of a vector, the angle between vectors, and unit
vector based on mathematical connections (procedural, meaning, different representations, and
implication), detail from an onto-semiotic point of view. However, some students have difficulty
finding the angle between vectors because they misuse the norm. Furthermore, the new
metaphorical connection based on mnemonics activated by the “law of the ear” is reported. The
connections activated by engineering students to solve problems about vectors may have been
influenced by the explanations provided by their calculus teacher, who promotes connections for
the teaching and learning mathematical concepts.
REFERENCES (76)
1.
Artigue, M., & Bosch, M. (2014). Reflection on networking through the praxeological lens. In A. Bikner-Ahsbahs, & S. Prediger (Eds.), Networking of theories as a research practice in mathematics education (pp. 249-265). Springer. https://doi.org/10.1007/978-3-....
2.
Balbuena, S. E., & Buayan, M. C. (2015). Mnemonics and gaming: Scaffolding learning of integers. Asia Pacific Journal of Education, Arts, and Sciences, 2(1), 14-18.
3.
Barniol, P., & Zavala, G. (2016). A tutorial worksheet to help students develop the ability to interpret the dot product as a projection. EURASIA Journal of Mathematics, Science and Technology Education, 12(9), 2387-2398. https://doi.org/10.12973/euras....
4.
Berry, J., & Nyman, M. (2003). Promoting students’ graphical understanding of the calculus. The Journal of Mathematical Behavior, 22(4), 479-495. https://doi.org/10. 1016/j.jmathb.2003.09.006.
5.
Bor, D., & Owen, A. (2007). A common prefrontal-parietal network for mnemonic and mathematical recoding strategies within working memory. Cerebral Cortex, 17(4), 778-786. https://doi.org/10.1093/cercor....
6.
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101. https://doi.org/10.1191/147808....
7.
Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections [Unpublished PhD thesis]. Simon Fraser University.
8.
Campo-Meneses, K. G., Font, V., García-García, J., & Sánchez, A. (2021). Mathematical connections activated in high school students’ practice solving tasks on the exponential and logarithmic functions. EURASIA Journal of Mathematics, Science and Technology Education, 17(9), em1998. https://doi.org/10.29333/ejmst....
9.
Campo-Meneses, K., & García-García, J. (2020). Explorando las conexiones matemáticas asociadas a la función exponencial y logarítmica en estudiantes universitarios colombianos [Exploring the mathematical connections associated with the exponential and logarithmic function in Colombian university students]. Revista Educación Matemática [Mathematics Education Journal], 32(3), 209-240. https://doi.org/10.24844/em320....
10.
Cárcamo, A., Barquero, B., Badillo, E., & Fuentealba, C. (2023). Errores en subespacios vectoriales: Un estudio exploratorio con estudiantes de primer año de ingeniería [Errors on vector subspaces: An exploratory study with first year engineering students]. Formación Universitaria [University Education], 16(2), 13-24. https://doi.org/10.4067/S0718-....
11.
Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education. Routledge. https://doi.org/10.4324/978020....
12.
De Gamboa, G., Badillo, E., Ribeiro, M., Montes, M., & Sánchez-Matamoros, G. (2020). The role of teachers’ knowledge in the use of learning opportunities triggered by mathematical connections. In S. Zehetmeier, D. Potari, & M. Ribeiro (Eds.), Professional development and knowledge of mathematics teachers (pp. 24-43). Routledge. https://doi.org/10.4324/978100....
13.
Díaz-Urdaneta, S., & Prieto-González, J. (2015). Sobre los signos de las razones trigonométricas con GeoGebra, una manera de trascender las reglas nemotécnicas [About the signs of trigonometric ratios with GeoGebra, a way to transcend mnemonic rules]. In R. Flores (Ed.), Acta Latinoamericana de matemática educativa [Latin American educational mathematics act] (pp. 1647-1655). Comité Latinoamericano de Matemática Educativa [Latin American Committee on Educational Mathematics].
14.
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-mathematics and extra-mathematics connections that occur when solving calculus problems in a context: A case study in higher level education]. Bolema, 31(57), 158-180. https://doi.org/10.1590/1980-4....
15.
Drijvers, P., Godino, J. D., Font, V., & Trouche, L. (2013). One episode, two lenses. Educational Studies in Mathematics, 82(1), 23-49. https://doi.org/10.1007/s10649....
16.
Drushlyak, M. G., Semenikhina, O. V., Proshkin, V., & Sapozhnykov, S. V. (2021). Training pre-service mathematics teacher to use mnemonic techniques. Journal of Physics: Conference Series, 1840, 012006. https://doi:10.1088/1742-6596/....
17.
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....
18.
Evitts, T. (2004). Investigating the mathematical connections that preservice teachers use and develop while solving problems from reform curricula [Unpublished doctoral dissertation]. Pennsylvania State University.
19.
Fiallo, J. (2010). Estudio del proceso de demostración en el aprendizaje de las razones trigonométricas en un ambiente de geometría dinámica [Study of the demonstration process in learning trigonometric ratios in a dynamic geometry environment]. University of Valencia.
20.
Flores, C., Cuellar, M., González, O., Ramírez, M., Cruz, V., & Aguirre, V. (2017). Problemas de entendimiento conceptual con las operaciones entre vectores [Conceptual understanding problems with operations between vectors]. Latin-American Journal of Physics Education, 11(4), 1-5.
21.
Flores-García, S., González-Quezada, M., & Herrera-Chew, A. (2007). Dificultades de entendimiento en el uso de vectores en cursos introductorios de mecánica [Understanding difficulties in the use of vectors in introductory mechanics courses]. Revista Méxicana de Física [Mexican Journal of Physics], 53(2), 178-185.
22.
Font, V. (2007). Una perspectiva ontosemiótica sobre cuatro instrumentos de conocimiento que comparten un aire de familia: Particular/general, representación, metáfora y context [An onto-semiotic perspective on four instruments of knowledge that share a family resemblance: Particular/general, representation, metaphor, and context]. Educación Matemática [Mathematics Education], 19(2), 95-128.
23.
Font, V., & Contreras, A. (2008). The problem of the particular and its relation to the general in mathematics education. Educational Studies in Mathematics, 69, 33-52. https://doi.org/10.1007/s10649....
24.
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....
25.
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....
26.
Frías, A., & Castro, E. (2007). Influencia del número de conexiones en la representación simbólica de problemas aritméticos de dos pasos [Influence of the number of connections on the symbolic representation of two-step arithmetic problems]. PNA, 2(1), 29-41. https://doi.org/10.30827/pna.v....
27.
Galindo-Illanes, M. K., Breda, A., Chamorro Manríquez, D. D., & Alvarado Martínez, H. A. (2022). Analysis of a teaching-learning process of the derivative with the use of ICT oriented to engineering students in Chile. EURASIA Journal of Mathematics, Science and Technology Education, 18(7), em2130. https://doi.org/10.29333/ejmst....
28.
García-García, J. (2019). Escenarios de exploración de conexiones matemáticas [Mathematical connections exploration scenarios]. Revista Números [Magazine Numbers], 10, 129-133.
29.
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.
30.
García-García, J., & Dolores-Flores, C. (2021a). Preuniversity students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33(1), 1-22. https://doi.org/10.1007/s13394....
31.
García-García, J., & Dolores-Flores, C. (2021b). 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/10.1080/002073....
32.
Godino, J. D. (2022). Emergencia, estado actual y perspectivas del enfoque ontosemiótico en educación matemática [Emergence, current state and perspectives of the ontosemiotic approach in mathematics education]. Revista Venezolana De Investigación En Educación Matemática [Venezuelan Journal of Research in Mathematics Education], 2(2), e202201. https://doi.org/10.54541/revie....
33.
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 [Research in Didactics of Mathematics], 14(3), 325-355.
34.
Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM, 39(1-2), 127-135. https://doi.org/10.1007/s11858....
35.
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.
36.
Gutierrez, E., & Martín, J. (2015). Dificultades en el aprendizaje de vectores, en los estudiantes que cursan materias del ciclo introductorio de la F.C.E.F. y N. de la U.N.C. [Difficulties in learning vectors, in students who study subjects in the introductory cycle of the F.C.E.F. and N. from the U.N.C.]. Revista de Enseñanza de la Física [Journal of Physics Teaching], 27(2), 89-96. https://doi.org/10.1080/002073....
37.
Hoffmann, M. (2018). Matemáticas. Fórmulas, reglas y mnemetécnicas [Mathematics. Formulas, rules and mnemonics]. Marcombo S. A.
38.
Keller, A. (2016). The mathematical chapter of the Āryabhaṭīya: A compilation of mnemonic rules? Archives Internationales d’Histoire des Sciences [International Archives of History of Science], 75, 75-100.
39.
Khatin-Zadeh, O., Farsani, D., & Breda, A. (2023). How can transforming representation of mathematical entities help us employ more cognitive resources? Frontiers in Psychology, 14, 1091678. https://doi.org/10.3389/fpsyg.....
40.
Kidron, I., & Bikner-Ahsbahs, A. (2015). Advancing research by means of the networking of theories. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative methods in mathematics education–Examples of methodology and methods (pp. 221-232). Springer. https://doi.org/10.1007/978-94....
41.
Ledezma, C., Font, V. & Sala, G. (2022). Analyzing the mathematical activity in a modelling process from the cognitive and onto-semiotic perspectives. Mathematics Education Research Journal, 35, 715-741. https://doi.org/10.1007/s13394....
43.
Maccini, P., Mulcahy, C., & Wilson, M. (2007). A follow-up of mathematics interventions for secondary students with learning disabilities. Learning Disabilities Research and Practice, 22(1), 58-74. https://doi.org/10.1111/j.1540....
44.
Makau, P. M., Muola, J. M., & Amukowa, W. (2019). Appropriateness of mnemonic techniques on mathematics and social studies learning outcomes in public primary school in Machakos sub-County, Kenya. International Journal of Academic Research in Business and Social Sciences, 9(9), 990-999. https://doi.org/10.6007/IJARBS....
45.
Manalo, E., Bunnell, J. K., & Stillman, J. A. (2000). The use of process mnemonics in teaching students with mathematics learning disabilities. Learning Disability Quarterly, 23(2), 137-156. https://doi.org/10.2307/151114....
46.
Márquez-García, A. (2013). Conocimiento profesional de un grupo de profesores sobre la división de fracciones [Professional knowledge of a group of teachers on the division of fractions] [Master’s thesis, Universidad de Granada].
47.
Mastropieri, M. A., & Scruggs, T. E. (1989). Reconstructive elaborations: Strategies that facilitate content learning. Learning Disabilities Focus, 4(2), 73-77. https://doi.org/10.1177/105345....
48.
Mendoza-Higuera, E., Cordero, F., Solís, M., & Gómez, k. (2018). El uso del conocimiento matemático en las comunidades de ingenieros. Del objeto a la funcionalidad matemática [The use of mathematical knowledge in engineering communities. From object to mathematical functionality]. Bolema, 32(62), 1219-1243. https://doi.org/10.1590/1980-4....
49.
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/10.1080/102884....
51.
Nelson, P., Burns, M., Kanive, R., & Ysseldyke, J. (2013). Comparison of a math fact rehearsal and a mnemonic strategy approach for improving math fact fluency. Journal of School Psychology, 51(6), 659-667. https://doi.org/10.1016/j.jsp.....
52.
Ni, L. B., & Hassan, N. A. B. (2019). The use of mnemonic and mathematical mnemonic method in improving historical understanding. International Journal of Educational and Pedagogical Sciences, 13(2), 93-97.
53.
Possani, E., Trigueros, M., Preciado, J. G., & Lozano, M. D. (2010). Use of models in the teaching of linear algebra. Linear Algebra and its Applications, 432(8), 2125-2140. https://doi.org/10.1016/j.laa.....
54.
Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connection theoretical approaches: First steps towards a conceptual framework. ZDM, 40(2), 165-178. https://doi.org/10.1007/s11858....
55.
Radford, L. (2008). Connecting theories in mathematics education: Challenges and possibilities. ZDM, 40, 317-327. https://doi.org/10.1007/s11858....
56.
Reyes, D., Montiel, G., & Cantoral, R. (2014). ‘Cuando una crece, la otra decrece’...¿ proporcionalidad inversa o directa? [‘When one grows, the other decreases’... inverse or direct proportionality?]. Premisa, 62, 3-15.
57.
Rodríguez-Gallegos, R., (2017). Repensando la enseñanza de las matemáticas para futuros ingenieros: Actualidades y desafíos [Rethinking mathematics teaching for future engineers: News and challenges]. IE Revista de Investigación Educativa de la REDIECH [IE Educational Research Magazine of the REDIECH], 8(15),69-85. https://doi.org/10.33010/ie_ri....
58.
Rodríguez-Nieto, C. A. (2021). Conexiones etnomatemáticas entre conceptos geométricos en la elaboración de las tortillas de Chilpancingo, México [Ethnomathematical connections between geometric concepts in the preparation of tortillas from Chilpancingo, Mexico]. Revista de investigación desarrollo e innovación [Journal of Research, Development and Innovation], 11(2), 273-296. https://doi.org/10.19053/20278....
59.
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), 1-22. https://doi.org/10.29333/ejmst....
60.
Rodríguez-Nieto, C. A., & Escobar-Ramírez, Y. C. (2022). Conexiones etnomatemáticas en la elaboración del sancocho de guandú y su comercialización en Sibarco, Colombia [Ethnomathematic Connections in the Preparation of Sancocho de Guandú and its Marketing in Sibarco, Colombia]. Bolema: Boletim de Educação Matemática, 36, 971-1002. https://doi.org/10.1590/1980-4....
61.
Rodríguez-Nieto, C. A., Font, V., & Rodríguez-Vásquez, F. M. (2022c). Literature review on networking, of theories developed in mathematics education context. EURASIA Journal of Mathematics, Science and Technology Education, 18(11), em2179. https://doi.org/10.29333/ejmst....
62.
Rodriguez-Nieto, C. A., Font, V., Borji, V., & Rodriguez-Vasquez, 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.
63.
Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M. & Font, V. (2023). 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....
64.
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(e202115), 1-32.
65.
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), em2006. https://doi.org/10.29333/ejmst....
66.
Rodríguez-Vásquez, F., & Arenas-Peñaloza, J. (2021). Categories to assess the understanding of university students about a mathematical concept. Acta Scientiae [Journal of Science], 23(1), 102-135. https://doi.org/10.17648/acta.....
67.
Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & Font, V. (2022a). 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/10.1080/002073....
68.
Salgado, H., & Trigueros, M. (2014). Una experiencia de enseñanza de los valores, vectores y espacios propios basada en la teoría APOE [A teaching experience of eigenvalues, eigenvectors, and eigenspaces based on APOS theory]. Revista Educación Matemática [Mathematics Education Journal], 26(3), 75-107.
69.
Sánchez, A., Font, V., & Breda, A. (2022). Significance of creativity and its development in mathematics classes for preservice teachers who are not trained to develop students’ creativity. Mathematics Education Research Journal, 34(4), 863-885. https://doi.org/10.1007/s13394....
70.
Seckel, M. J., Breda, A., Sánchez, A., & Font, V. (2019). Criterios asumidos por profesores cuando argumentan sobre la creatividad matemática [Criteria assumed by teachers when discussing mathematical creativity]. Educação e Pesquisa [Education and Research], 45, 1926. https://doi.org/10.1590/S1678-....
71.
Stewart, J. (1999). Cálculo de una variable, trascendentes tempranas [Calculus of a variable, early transcendents]. Cengage Learning.
72.
Tairab, H., AlArabi, K., Rabbani, L., & Hamad, S. (2020). Examining grade 11 science students’ difficulties in learning about vector operations. Physics Education, 55(5), 055029. https://doi.org/10.1088/1361-6....
73.
Test, D. W., & Ellis, M. F. (2005). The effects of LAP fractions on addition and subtraction of fractions with students with mild disabilities. Education and Treatment of Children, 28(1), 11-24.
74.
Thanheiser, E., Melhuish, K., Sugimoto, A., Rosencrans, B., & Heaton, R. (2021). Networking frameworks: A method for analyzing the complexities of classroom cultures focusing on justifying. Educational Studies in Mathematics, 107, 285-314. https://doi.org/10.1007/s10649....
76.
Vargas, J., & Urzúa, T. (2018). Metaorganización de variables químicas en resolución de mezclas en disoluciones [Meta-organization of chemical variables in resolution of mixes in dissolutions]. Revista Chilena de Educación Científica [Chilean Magazine of Scientific Education], 17(1), 37-43.
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