Research Trends in Digital Technologies and Modeling in Mathematics Education

Juan Fernando Molina-Toro; Paula Andrea Rendón-Mesa; Jhony Alexander Villa-Ochoa

doi:10.29333/ejmste/108438

Full Text (PDF)

Juan Fernando Molina-Toro ¹ ^* , Paula Andrea Rendón-Mesa ², Jhony Alexander Villa-Ochoa ²

More Detail

¹ Master in Mathematics Education. Mathematics Education Area, Universidad de Antioquia, COLOMBIA² Doctor in Education. Mathematics Education Area, Universidad de Antioquia, COLOMBIA^* Corresponding Author

Abstract

This document presents a literature review that analyzes the articulation of modeling and digital technologies in the field of Mathematics Education. The review aims to find evidence of the use of digital technologies in modeling processes and how these practices can change some ways of working with students in the classroom. The results show, on the one hand, different roles that technology plays when it is articulated to a modeling process (as a resource in the process or as a means that reorganizes the process) and the uses given to diverse technological tools in the empirical studies analyzed. The findings present a new category that extends the classification of technologies and suggest the need to expand both theoretical and empirical research to get a better understanding of the impact of digital tools in modeling processes. In addition, the findings draw attention to the inclusion of mobile devices in future studies.

Keywords

mathematics education
modeling
digital technologies

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, 2019, Volume 15, Issue 8, Article No: em1736

https://doi.org/10.29333/ejmste/108438

Publication date: 11 Apr 2019

Article Views: 4340

Article Downloads: 2468

Open Access References How to cite this article

References

Alves, D. B., & de Souza Júnior, A. J. (2013). Mathematics Education in a Digital Culture. Journal of Mathematical Modelling and Application, 1(8), 32–41. Retrieved from http://gorila.furb.br/ojs/index.php/modelling/article/view/3354.
Bassanezi, R. (2002). Ensino–Aprendizagem Com Modelagem Matemática: Uma Nova Estratégia. São Paulo: Contexto.
Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15–30). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-0910-2_3.
Blum, W. (2015). Quality Teaching of Mathematical Modelling: What Do We Know, What Can We Do? In S. Cho (ed), The Proceedings of the 12th International Congress on Mathematical Education (pp. 73–96). Cham: Springer. https://doi.org/10.1007/978-3-319-12688-3_9.
Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45–58. Retrieved from http://gorila.furb.br/ojs/index.php/modelling/article/view/1620.
Blum, W., & Leiss, D. (2007). How do Students and Teachers Deal with Modelling Problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (eds) Mathematical Modelling: Education, Engineering and Economics-ICTMA 12 (pp. 222–231). Horwood: Chichester.
Blum, W., Galbraith, P., Henn, H. W., & Niss, M. (Eds)(2007). Modelling and Applications in Mathematics Education. New York: Springer. https://doi.org/10.1007/978-0-387-29822-1.
Borba, M. C., Villarreal, M. E., & Soares, D. S. (2016). Modeling using data available on the internet. In C. Hirsch & E. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 143–152). Reston: National Council of Teacher of Mathematics.
Borba, M. de C., & Villarreal, M. E. (2005). Humans-with-Media and the Reorganization of Mathematical Thinking. New York: Springer. https://doi.org/10.1007/b105001.
Brown, J. P. (2015). Visualisation Tactics for Solving Real World Tasks. In G. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences (pp. 431–442). Cham: Springer. https://doi.org/10.1007/978-3-319-18272-8_36.
Buteau, C., Muller, E., Marshall, N., Sacristán, A. I., & Mgombelo, J. (2016). Undergraduate Mathematics Students Appropriating Programming as a Tool for Modelling, Simulation, and Visualization: A Case Study. Digital Experiences in Mathematics Education, 2(2), 142–166. https://doi.org/10.1007/s40751-016-0017-5.
Campos, I. S., & Araújo, J. L. (2015). Envolvimento dos Alunos em Atividades de Modelagem Matemática: relação com o saber e possibilidades de ação. Bolema: Boletim de Educação Matemática, 29(51), 167–182. https://doi.org/10.1590/1980-4415v29n51a09.
Daher, W. M. (2015). Discursive positionings and emotions in modelling activities. International Journal of Mathematical Education in Science and Technology, 46(8), 1149–1164. https://doi.org/10.1080/0020739X.2015.1031836.
Daher, W. M., & Shahbari, J. A. (2015). Pre-service teachers’modelling processes through engagement with model eliciting activities with a technological tool. International Journal of Science and Mathematics Education, 13(1), 25–46. https://doi.org/10.1007/s10763-013-9464-2.
Dalla Vecchia, R., & Maltempi, M. V. (2012). Modelagem Matemática e Tecnologias de Informação e Comunicação: A realidade do mundo cibernético como um vetor de virtualização. Bolema: Boletim de Educação Matemática, 26(43), 963–990. https://doi.org/10.1590/S0103-636X2012000300010.
Diniz, L. N., & Borba, M. C. (2012). Leitura e Interpretação de Dados Prontos em um Ambiente de Modelagem e Tecnologias Digitais: o mosaico em movimento. Bolema: Boletim de Educação Matemática, 26(43), 935–962. https://doi.org/10.1590/S0103-636X2012000300009.
Frejd, P. (2013). Modes of modelling assessment-a literature review. Educational Studies in Mathematics, 84(3), 413–438. https://doi.org/10.1007/s10649-013-9491-5.
Frejd, P., & Ärlebäck, J. B. (2017). Initial Results of an Intervention Using a Mobile Game App to Simulate a Pandemic Outbreak. In G. Stillman, W. Blum, & G. Kaiser (eds) Mathematical Modelling and Applications (pp. 517–527). Cham: Springer. https://doi.org/10.1007/978-3-319-62968-1_43.
Galbraith, P., Goos, M., Renshaw, P., & Geiger, V. (2003). Technology Enriched Classrooms: Some Implications for Teaching Applications and Modelling. In Q.-X. Ye, W. Blum, K. Houston, & Q.-Y. Jiang (Eds.), Mathematical Modelling in Education and Culture: ICTMA 10 (pp. 111–125). Chichester: Woodhead Publishing. https://doi.org/10.1533/9780857099556.3.111.
Geiger, V. (2011). Factors Affecting Teachers’ Adoption of Innovative Practices with Technology and Mathematical Modelling. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling: ICTMA14 (pp. 305–314). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-0910-2_31.
Greefrath, G. (2011). Using technologies: New possibilities of teaching and learning modelling–Overview. In G. Kaiser, W. Blum, R. Borromeo-Ferri, & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling (pp. 301–304). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-0910-2_30.
Greefrath, G., & Vorhölter, K. (2016). Teaching and Learning Mathematical Modelling: Approaches and Developments from German Speaking Countries. Cham: Springer. https://doi.org/10.1007/978-3-319-45004-9.
Greefrath, G., Hertleif, C., & Siller, H.-S. (2018). Mathematical modelling with digital tools—A quantitative study on mathematising with dynamic geometry software. ZDM - Mathematics Education, 50(1–2), 233–244. https://doi.org/10.1007/s11858-018-0924-6.
Greefrath, G., Siller, H.-S., & Weitendorf, J. (2011). Modelling considering the influence of technology. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.)Trends in teaching and learning of mathematical modelling (pp. 315–329). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-0910-2_32.
Jesson, J., & Lacey, F. (2006). How to do (or not to do) a critical literature review. Pharmacy Education, 6(2), 139-148. https://doi.org/10.1080/15602210600616218.
Kaiser, G. (2005). Mathematical modelling in school–Examples and experiences. In H.W. Henn & G. Kaiser (Eds). Mathematikunterricht im Spannungsfeld von Evolution und Evaluation. Festband für Werner Blum (pp. 99–108). Hildesheim: Franzbecker.
Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302–310. https://doi.org/10.1007/BF02652813.
Krekic, V., & Namestovski, Z. (2009). Computer modelling in mathematics education. In 2009 7th International Symposium on Intelligent Systems and Informatics (pp. 355–360). Subotica: IEEE. https://doi.org/10.1109/SISY.2009.5291132.
Lingefjärd, T. (2012). Learning Mathematics through mathematical modelling. Journal of Mathematical Modelling and Application, 1(5), 41–49. Retrieved from http://gorila.furb.br/ojs/index.php/modelling/article/view/2896.
Lingefjärd, T., & Meier, S. (2010). Teachers as managers of the modelling process. Mathematics Education Research Journal, 22(2), 92–107. https://doi.org/10.1007/BF03217568.
Maas, K. (2007). Modelling in Class: What Do We Want the Students to Learn? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical Modelling: Education, Engineering and Economics (ICTMA 12) (pp. 63–78). Chichester: Horwood Publishing. https://doi.org/10.1533/9780857099419.2.63.
Marshall, J. A., & Carrejo, D. J. (2008). Students’ mathematical modeling of motion. Journal of Research in Science Teaching, 45(2), 153–173. https://doi.org/10.1002/tea.20210.
Molina-Toro, J. F. (2013). La modelación con tecnología en el estudio de la función seno. (Tesis de maestría no publicada). Universidad de Medellín.
Molina-Toro, J. F., & Villa-Ochoa, J. A. (2013). La modelación con tecnología en el estudio de la función seno. Revista Científica, 2, 80–84. https://doi.org/10.14483/23448350.5496.
Neves, R. G., & Teodoro, V. D. (2013). Computational modelling, interactive environments and science, technology, engineering and mathematics education [Modelação computacional, ambientes interactivos e o ensino da ciência, tecnologia, engenharia e matemática]. Revista Lusofona de Educacao, (25), 35–58. Retrieved from http://www.scielo.mec.pt/scielo.php?script=sci_abstract&pid=S1645-72502013000300004&lng=es&nrm=.
pf.
Ortega, M., & Puig, L. (2017). Using Modelling and Tablets in the Classroom to Learn Quadratic Functions. In G. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical Modelling and Applications (pp. 565–575). Cham: Springer. https://doi.org/10.1007/978-3-319-62968-1_47.
Parra-Zapata, M. M., & Villa-Ochoa, J. A. (2016). Interacciones y contribuciones. Forma de participación de estudiantes de quinto grado en ambientes de modelación matemática. Actualidades Investigativas en Educación, 16(3), 1–27. https://doi.org/10.15517/aie.v16i3.26084.
Pereira, R. S. G., & Júnior, S. (2013). Mathematical modeling and the teaching of adjustment function: a pedagogical handbook. Bolema: Boletim de Educação Matemática, 27(46), 531–546. https://doi.org/10.1590/S0103-636X2013000300013.
Pereira, R. S. G., Seki, J. T. P., Palharini, B., Neto, J. C., Silva, A. C., Damin, W., & Martins, B. O. (2017). Modelagem matemática e tecnologias digitais educacionais: possibilidades e aproximações por meio de uma revisão sistemática de literatura. Revista de Ensino de Ciências e Matemática, 8(2), 80–94. Retrieved from http://revistapos.cruzeirodosul.edu.br/index.php/rencima/article/view/1214.
Perrenet, J., & Adan, I. (2010). The academic merits of modelling in higher mathematics education: A case study. Mathematics Education Research Journal, 22(2), 121–140. https://doi.org/10.1007/BF03217570.
Perrenet, J., & Zwaneveld, B. (2012). The many faces of the mathematical modeling cycle. Journal of Mathematical Modelling and Application, 1(6), 3–21. Retrieved from http://gorila.furb.br/ojs/index.php/modelling/.
article/view/2815.
Pons, M. O., & Espinosa, L. P. (2015). Modelización de una situación real con tabletas: el experimento de la pelota. Modelling in Science Education and Learning, 8(2), 67–78. https://doi.org/10.4995/msel.2015.3519.
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.2009.05.004.
Rendón-Mesa, P. A. (2016). Articulation between mathematics and the field of action of product design engineering: contributions of mathematical modeling [Articulación entre la matemática y el campo de acción de la ingeniería de diseño de producto: aportes de la modelación matemática] (Doctoral dissertation) (not published). Universidad de Antioquia. Medellín.
Rodríguez Gallegos, R., & Quiroz Rivera, S. (2016). El rol de la experimentación en la modelación matemática. Educación Matemática, 28(3), 91–110. https://doi.org/10.24844/EM2803.04.
Sekulić, T., & Takači, Đ. (2013). Mathematical modelling, computers and GeoGebra in university and college mathematics education. In 2013 36th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO) (pp. 625–630). Opatija: IEEE.
Siller, H.-S., & Greefrath, G. (2010). Mathematical modelling in class regarding to technology. Siller, H. S., & Greefrath, G. (2010). Mathematical modelling in class regarding to technology. In V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.), Proceedings of the sixth congress of the European Society for Research in Mathematics Education (pp. 2136–2145). Lyon: INRP.
Soares, D. da S., & Borba, M. de C. (2014). The role of software Modellus in a teaching approach based on model analysis. ZDM - Mathematics Education, 46(4), 575–587. https://doi.org/10.1007/s11858-013-0568-5.
Stillman, G. (2011). Applying metacognitive knowledge and strategies in applications and modelling tasks at secondary school. In G. Kaiser, R. Borromeo Ferri, W. Blum, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling. ICTMA 14 (pp. 165–180). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-0910-2_18.
Stillman, G., & Brown, J. P. (2014). Evidence of implemented anticipation in mathematising by beginning modellers. Mathematics Education Research Journal, 26(4), 763–789. https://doi.org/10.1007/s13394-014-0119-6.
Suárez Téllez, L., & Cordero Osorio, F. (2008). Elementos teóricos para estudiar el uso de las gráficas en la modelación del cambio y de la variación en un ambiente tecnológico. Revista Electrónica de Investigación En Educación En Ciencias, 3(1), 51–58. Retrieved from http://www.scielo.org.ar/scielo.php?pid=S1850-66662008000100005&script=sci_arttext&tlng=en.
Suárez Téllez, L., & Cordero Osorio, F. (2010). Modelación-graficación, una categoría para la matemática escolar. Resultados de un estudio socioepistemológico. Revista Latinoamericana de Investigación En Matemática Educativa, 13(4-II), 319–333.
Trigueros, M. (2009). El uso de la modelación en la enseñanza de las matemáticas. Innovación Educativa, 9(46), 75–87. Retrieved from https://www.redalyc.org/html/1794/179414894008/.
Villa-Ochoa, J. A. (2007). La modelación como proceso en el aula de matemáticas, un marco de referencia y un ejemplo. Tecno Lógicas, 19, 63–85. https://doi.org/10.22430/22565337.505.
Villa-Ochoa, J. A., & Berrío, M. J. (2015). Mathematical Modelling and Culture: An Empirical Study. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical Modelling in Education Research and Practice, International Perspectives on the Teaching and Learning (pp. 241–250). Cham: Springer. https://doi.org/10.1007/978-3-319-18272-8_19.
Villa-Ochoa, J. A., Castrillón-Yepes, A., & Sánchez-Cardona, J. (2017). Types of modeling task for the mathematics class [Tipos de Tareas de Modelación para la clase de Matematica]. Espaço Plural, 18(36), 219–251.
Villa-Ochoa, J. A., González-Gómez, D., & Carmona-Mesa, J. A. (2018). Modelling and technology in the study of the instantaneous rate of change in mathematics [Modelación y tecnología en el estudio de la tasa de variación instantánea en matemáticas]. Formación Universitaria, 11(2), 25–34. https://doi.org/10.4067/S0718-50062018000200025.
Villarreal, M. E., Esteley, C. B., & Smith, S. (2018) Pre-service teachers’ experiences within modelling scenarios enriched by digital technologies. ZDM - Mathematics Education 50(1-2), 327-341. https://doi.org/10.1007/s11858-018-0925-5.

How to cite this article

APA

Molina-Toro, J. F., Rendón-Mesa, P. A., & Villa-Ochoa, J. A. (2019). Research Trends in Digital Technologies and Modeling in Mathematics Education. Eurasia Journal of Mathematics, Science and Technology Education, 15(8), em1736. https://doi.org/10.29333/ejmste/108438

Vancouver

Molina-Toro JF, Rendón-Mesa PA, Villa-Ochoa JA. Research Trends in Digital Technologies and Modeling in Mathematics Education. EURASIA J Math Sci Tech Ed. 2019;15(8):em1736. https://doi.org/10.29333/ejmste/108438

AMA

Molina-Toro JF, Rendón-Mesa PA, Villa-Ochoa JA. Research Trends in Digital Technologies and Modeling in Mathematics Education. EURASIA J Math Sci Tech Ed. 2019;15(8), em1736. https://doi.org/10.29333/ejmste/108438

Chicago

Molina-Toro, Juan Fernando, Paula Andrea Rendón-Mesa, and Jhony Alexander Villa-Ochoa. "Research Trends in Digital Technologies and Modeling in Mathematics Education". Eurasia Journal of Mathematics, Science and Technology Education 2019 15 no. 8 (2019): em1736. https://doi.org/10.29333/ejmste/108438

Harvard

Molina-Toro, J. F., Rendón-Mesa, P. A., and Villa-Ochoa, J. A. (2019). Research Trends in Digital Technologies and Modeling in Mathematics Education. Eurasia Journal of Mathematics, Science and Technology Education, 15(8), em1736. https://doi.org/10.29333/ejmste/108438

MLA

Molina-Toro, Juan Fernando et al. "Research Trends in Digital Technologies and Modeling in Mathematics Education". Eurasia Journal of Mathematics, Science and Technology Education, vol. 15, no. 8, 2019, em1736. https://doi.org/10.29333/ejmste/108438