Towards an interdisciplinary approach to introduce economic modelling in Secondary Education: a proposal on the derivative and the marginal analysis
DOI:
https://doi.org/10.46661/ijeri.4701Keywords:
Economic models, marginal analysis, derivative function, virtual learning object, interdisciplinary approachAbstract
The paper describes a virtual learning object (VLO) built under an interdisciplinary perspective integrating Economía and Matemáticas aplicadas a las Ciencias Sociales, which are both subjects within the Humanidades y Ciencias Sociales area in Bachillerato. Such VLO is created out of a sequence of applications designed in the software Geogebra and organized around the mathematical concept of the derivative function and its role as an essential tool in economic modelling (mainly linked to what is usually known as marginal analysis).
The proposal aims to exemplify a set of materials and activities that could be designed and used in an integrated way by teachers of both subjects. From the viewpoint of teaching Economía, this type of approaches may facilitate the transfer of mathematical knowledge to the field of economic modelling, which is especially relevant when taking into consideration the propaedeutic purpose of Bachillerato. Concerning the teaching in Matemáticas, research on its didactics as well as the curriculum content for the Educación Secundaria Obligatoria (ESO) and Bachillerato highlight the dual goal of developing students’ modelling competency and enhancing their learning of the mathematical concepts involved.
Downloads
References
Al-Salami, M.K., Makela, C.J. & De Miranda, M.A. (2017). Assessing changes in teachers’ attitudes toward interdisciplinary STEM teaching. International Journal of Technology and Design Education, 27(1), 63-88 (2017). DOI: https://doi.org/10.1007/s10798-015-9341-0
Arango, J., Gaviria, D. & Valencia, A. (2015). Differential calculus teaching through virtual learning objects in the field of management sciences. Procedia-Social and Behavioral Sciences, 176, 412-418. DOI: https://doi.org/ 10.1016/j.sbspro.2015.01.490
Arbain, N. & Shukor, N.A. (2015). The effects of Geogebra on students achievement. Procedia-Social and Behavioral Sciences, 172, 208-214. DOI: https://doi.org/10.1016/j.sbspro.2015.01.356
Área-Moreira, M. (2009). La sociedad de la información, las tecnologías y la educación. En M. Área-Moreira (Ed.). Introducción a la tecnología educativa. Tenerife. Universidad de La Laguna.
Ariza, A., Llinares, S. & Valls, J. (2015). Students’ understanding of the function-derivative relationship when learning economic concepts. Mathematics Education Research Journal, 17(4), 615-635. DOI: https://doi.org/10.1007/s13394-015-0156-9
Arnold, I. J. M., & Straten, J. T. (2012). Motivation and math skills as determinants of first-year performance in economics. The Journal of Economic Education, 43(1), 33-47. DOI: https://doi.org/10.1080/00220485.2012.636709
Artigue, M. (2013). L’impact curriculaire des technologies sur l’éducation mathématique. Cuadernos de Investigación y Formación en Educación Matemática, 8(11), 295-305. DOI: https://doi.org/10.36397/emteia.v4i1.2236
Ballard, C. L. & Johnson, F. (2004). Basic math skills and performance in an introductory economics class. The Journal of Economic Education, 35(1), 3-23. DOI: https://doi.org/10.3200/JECE.35.1.3-23
Blomhøj, M. (2019). Towards integration of modelling in secondary mathematics teaching. En G.A. Stillman y J.P. Brown (Eds.). Lines of Inquiry in Mathematical Modelling Research in Education, pp. 37-52. Suiza: Springer. DOI: https://doi.org/10.1007/978-3-030-14931-4_3
Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? En S.J. Cho (Ed.). The Proceedings of the 12th International Congress on Mathematical Education (pp. 73-96). Springer International Publishing. DOI: https://doi.org/10.1007/978-3-319-12688-3_9
Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58.
Brady, C. (2018). Modelling and the representational imagination. ZDM - Mathematics Education, 50(1-2), 45-59. DOI: https://doi.org/10.1007/s11858-018-0926-4
Brante, G. & Brunosson, A. (2014). To double a recipe-interdisciplinary teaching and learning of mathematical content knowledge in a home economics setting. Education Inquiry, 5(2), 301-318. DOI: https://doi.org/10.3402/edui.v5.23925
Bray, A. & Tangney, B. (2017). Technology usage in mathematics education research. A systematic review of recent trends. Computers & Education, 114, 255-273. DOI: https://doi.org/10.1016/j.compedu.2017.07.004
Cabrera-Medina, J.M., Sánchez-Medina, I.I. & Rojas-Rojas, F. (2016). Uso de objetos virtuales de aprendizaje OVAS como estrategia de enseñanza-aprendizaje inclusivo y complementario a los cursos teóricos-prácticos. Una experiencia con estudiantes del curso física de ondas. Revista Educación en Ingeniería, 11(22), 4-12.
Carlson, M., Jacobs, S., Coe, E., Larsen, S. & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education, 33(5), 352-378. DOI: https://doi.org/10.2307/4149958
Carlson, M., Oehrtman, M., & Engelke, N. (2010). The precalculus concept assessment: A tool for assessing students’ reasoning abilities and understandings. Cognition and Instruction. 28(2), 113-145. DOI: https://doi.org/10.1080/07370001003676587
Casasús-Estellés, T., Ivars-Escortell, A. & López-Rodríguez, M.I. (2018). Present and future of the e-learning in economics schools and faculties. Multidisciplinary Journal for Education, Social and Technological Sciences, 5(1), 44-64.
Chevallard, Y. (2007). Passé et présent de la théorie anthropologique du didactique. En L. Ruiz-Higueras, A. Estepa y F.J. García (Eds.). Sociedad, Escuela y Matemáticas. Aportaciones de la Teoría Antropológica de la Didáctica, pp. 705-746. Jaén: Servicio de publicaciones de la Universidad de Jaén.
Duval, R. (1993). Registres de représentation sémiotique et fonctionnement cognitif de la pensée. Annales de Didactique et de Sciences Cognitives, 5, 37-65. IREM de Strasbourg, Francia.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of Mathematics. Educational Studies in Mathematics, 61, 103-131. DOI
https://doi.org/10.1007/s10649-006-0400-z
Freudenthal, H. (2002). Revisiting Mathematics Education : China Lectures. Norwell: Kluwer Academic Publishers.
Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM - International Journal on Mathematics Education, 38(2), 143-162. DOI: https://doi.org/10.1007/BF02655886
Geiger, V., Faragher, R. & Goos, M. (2010). CAS-enabled technologies as ‘agents provocateurs’ in teaching and learning mathematical modelling in secondary school classrooms. Mathematics Education Research Journal. 22(2), 48-68. DOI:
https://doi.org/10.1007/BF03217565
Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A Calculus Course as an Example. Educational Studies in Mathematics, 39, 111-129. DOI: https://doi.org/10.1023/A:1003749919816
Kaiser G. & Brand S. (2015) Modelling competencies: Past development and further perspectives. En G. Stillman, W. Blum, M. Salett Biembengut (Eds.). International Perspectives on the Teaching and Learning of Mathematical Modelling, pp. 129-149. Cham: Springer.
Katzner, D.W. (2003). Why mathematics in economics? Journal of Post Keynesian Economics, 25(4), 561-574.
Klaassen, R.G. (2018). Interdisciplinary education: a case study, European Journal of Engineering Education, 43(6), 842-859, DOI: https://doi.org/10.1080/03043797.2018.1442417
Kllogjeri, P. (2010). GeoGebra: A global platform for teaching and learning math together and using the synergy of mathematicians. En M.D. Lytras, P. Ordonez De Pablos, D. Avison, J. Sipior, Q. Jin, W. Leal Filho, L. Uden, M. Thomas, S. Cervai & D.G. Horner (Eds.). Technology Enhanced Learning. Quality of Teaching and Educational Reform. Communications in Computer and Information Science, 73. Springer, Berlín, Heidelberg.
Lesh, R., & Doerr, H. M. (2003). Models and modeling perspectives on mathematics problem solving, learning and teaching. En R. Lesh & H. M. Doerr (Eds.). Beyond Constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching, pp. 3-58. Mahawah, NJ: Lawrence Earlbaum.
Maaß, K. (2006). What are modelling competencies? ZDM - International Journal on Mathematics Education, 38(2), 113-142. DOI: https://doi.org/10.1007/BF02655885
Marín-Díaz, V., Burgos-Mellado, S. & López-Pérez, M. (2018). Formación de docentes para la inclusión digital desde el plan escuela 2.0: estudio de un caso. International Journal of Educational Research and Innovation (IJERI), 10, 274-298.
Ministerio de Educación, Cultura y Deporte de España (MECD). (2013). Marcos y pruebas de evaluación de PISA 2012: Matemáticas, Lectura y Ciencias. https://www.educacionyfp.gob.es/dctm/inee/internacional/pisa2012/marcopisa2012.pdf?documentId=0901e72b8177328d
Mkhatshwa, T.P. (2019). Students’ quantitative reasoning about an absolute extrema optimization problem in a profit maximization context. International Journal of Mathematical Education in Science and Technology, 50(8), 1105-1127. DOI: https://doi.org/10.1080/0020739X.2018.1562116
Mora-Vicarioli, F. (2012). Learning objects: The importance of its use in the virtual education. Revista Calidad en la Educación Superior, 3(1), 104-118.
Morales, L., Gutiérrez, L. & Ariza, L. (2016). Guía para el diseño de objetos virtuales de aprendizaje (OVA). Aplicación al proceso de enseñanza-aprendizaje del área bajo la curva de cálculo integral. Revista Científica General José María Córdova, 14(18), 127-147.
Niss, M. (2003). Mathematical competencies and the learning of mathematics: The Danish Kom Project. Proceedings of the 3rd Mediterranean Conference on Mathematical Education, 115-124.
Pollak, H. O. (1979). The interaction between mathematics and other school subjects. En UNESCO (Eds.). New Trends in Mathematics Teaching IV, pp. 232-248. París.
Rai, B.K., So, C.K. & Nicholas, A. (2010). A primer on mathematical modelling in Economics. Journal of Economic Surveys. 26(4), 594-615. DOI:
https://doi.org/10.1111/j.1467-6419.2010.00655.x
Real Decreto 1179/1992, de 2 de octubre, por el que se establece el currículo del Bachillerato (BOE-A-1992-23406). https://www.boe.es/buscar/doc.php?id=BOE-A-1992-23406
Real Decreto 1105/2014, de 26 de diciembre, por el que se establece el currículo básico de la Educación Secundaria Obligatoria y del Bachillerato. https://www.boe.es/boe/dias/2015/01/03/pdfs/BOE-A-2015-37.pdf
Roorda, G., Vos, P. & Goedhart, M. (2007). 5.8-The concept of the derivative in modelling and applications. En C., Haines, C., Galbraith, P., Blum, W. & S. Khan (Eds.). Mathematical Modelling. Education, Engineering and Economics-ICTMA 12, pp. 288-293. Woodhead Publishing. DOI: https://doi.org/10.1533/9780857099419.5.288
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1-36. DOI: https://doi.org/10.1007/BF00302715
Thompson, P. W. & Carlson, M. (2017). Variation, covariation and functions: Foundational ways of thinking mathematically. En Cai, J. (Ed.). Compendium for research in Mathematics Education, pp. 421-456. Reston, VA: National Council of Teachers of Mathematics.
Tur, G.I. & Shakhovnina, N.V. (2015). Applications as a way of implementation of interdisciplinary connections of mathematical and economic disciplines. Science and Education a New Dimension. Pedagogy and Psychology,37(75), 14-16.
Wiley, D.A. (2000). Connecting learning objects to instructional design theory: A definition, a metaphor, and a taxonomy. En D.A. Wiley (Ed.). The Instructional Use of Learning Objects: Online Version.
Zandieh, M. (2000). A theoretical framework for analyzing student understanding of the concept of derivative. En Research in Collegiate Mathematics Education IV, 8, pp. 103-127. Arizona: Conference Board of the Mathematical Science.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 María Gutiérrez-Portilla, Paula Gutiérrez-Portilla, Pedro Álvarez
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.