Didactic Strategy for University Precalculus: An Implementation of Technological Environments and Problem Solving

Alexander Arévalo, Milton Fabian Castaño, Steev Romero

Abstract

In initial university semesters, a low academic level in fundamental mathematics is evident. This article describes a didactic strategy focused on the development of the concept of function in the first university mathematics course. The strategy is based on the implementation of a classroom learning environment, guided by resources designed in dynamic software, and focused on problem-solving. The objective of this study is to present a comprehensive approach that not only addresses students' learning difficulties but also enhances professor preparation and the curricular structure. The contribution of this research lies in its focus on the integration of technology and problem solving as key tools for the teaching-learning process. The study was developed in three phases: (i) identification of the learning difficulties of students and professors, (ii) creation of a professor training space that addresses these difficulties, and (iii) implementation of the environment designed to improve student learning. The results indicate the necessity of revisiting the curricular structure, minimum course characteristics, professor preparation, and support material with the aim of proposing guidelines that, if implemented, can have a positive impact on teaching and learning.

 

Keywords: learning environments, dynamic software, activity sequences, concept of function, problem solving.

 

https://doi.org/10.55463/issn.1674-2974.51.7.13


Full Text:

PDF


References


DÍAZ-PINZÓN, J. E. Analysis of the results of the 2018 Pisa test in mathematics for the Americas. Quindío University Research Journal. 2021, 33(1), 104–114. https://doi.org/10.33975/riuq.vol33n1.463

SINAN, OLKUN. How Do We Learn Mathematics A Framework for a Theoretical and Practical Model. International Electronic Journal of Elementary Education. 2022, 14(3), 295 – 302. https://doi.org/10.26822/iejee.2022.245

DÍAZ, L. M., & CAREAGA, M. P. Analysis about the definition of mathematical problems in context: state of the art and prospective reflections. Revista espacios, 2021, 42(1). 131 – 145. https://doi.org/10.48082/espacios-a21v42n01p11

SANTOS-TRIGO, M. Mathematics education, problem solving and the use of computational tools.. Cuadernos de Investigación y Formación en Educación Matemática, CIAEM. 2011, 6(8), 35-54. https://revistas.ucr.ac.cr/index.php/cifem/article/view/6949/6635

VILLARREAL, M. E. Tecnologías y educación matemática: necesidad de nuevos abordajes para la enseñanza. Virtualidad, Educación Y Ciencia, 2012, 3(5), 73–94. https://doi.org/10.60020/1853-6530.v3.n5.3014

PALOMARES-RUIZ, A., CEBRIÁN, A., LÓPEZ-PARRA, E., & GARCÍA-TOLEDANO, E. (2020). Influence of ICTs on Math Teaching–Learning Processes and Their Connection to the Digital Gender Gap. Sustainability, 2020, 12(16), 66-92. https://doi.org/10.3390/su12166692

CEVIKBAS, M. & KAISER, G. (2021). A Systematic Review on Task Design in Dynamic and Interactive Mathematics Learning Environments. Mathematics, 2021, 9(4), 399-419. https://doi.org/10.3390/math9040399

LI, C., GARZA, T., ZHANG, S. & JIANG, Y. Constructivist learning environment and strategic learning in engineering education. Learning Environments Research, 2023, 26(3), 743-759. https://doi.org/10.1007/s10984-022-09450-w

LEÓN, O., ALFONSO, G., ROMERO, J., BRAVO-OSORIO, F. & LÓPEZ, H. Conceptual basis for learning environments. 2024, https://acacia.red/udfjc/

FERNÁNDEZ, M., GONZALEZ, N. & CARREJO, J. Evaluation of blended learning environments from the student's perspective. Revista Iberoamericana para la Investigación y el Desarrollo Educativo, 2015, 12, http://1-11.ride.org.mx/index.php/RIDESECUNDARIO/article/view/795

ISLAS-TORRES, C. Implication of ict in the learning of university students: a systemic-conectivist explanation. Revista de Medios y Educacion, 2018, 52(1), 199-215. https://hdl.handle.net/11441/69342

ARIAS-RUEDA, J.H., ARIAS-RUEDA, C.A. & BURGOS HERNÁNDEZ, C.A. Processes applied by students in mathematical problem solving: case study on the quadratic function. Gondola, Science Teaching and Learning., 2020, 15(2), 284-302. https://doi.org/10.14483/23464712.14614

BERNAL-GARZÓN, E. Contributions to the consolidation of connectivism as a pedagogical approach for the development of learning processes. Innova Educación Magazine, 2020, 2(3), 394-412. https://doi.org/10.35622/j.rie.2020.03.002

GOLDIE, J. G. S. Connectivism: A knowledge learning theory for the digital age? Medical Teacher, 2016, 38(10), 1064–1069.https://doi.org/10.3109/0142159X.2016.1173661

MUNI, J. L. A., & RABELL, L. H. Connectivism: an alternative in professional training according to the development of the information and communications technologies. Dilemas Contemporáneos: Educación, Política y Valores, 2017, 4(3), 35-50. https://dilemascontemporaneoseducacionpoliticayvalores.com/index.php/dilemas/article/view/103

MONTEAGUDO, C.D., HERNANDEZ, G. G. & RAMOS, F. R. R. The problems with text formulation at the mathematic teaching and learning process. Revista Conrado, 2020, 16(74), 276-283. https://conrado.ucf.edu.cu/index.php/conrado/article/view/1362

BUTTS, T. Posing problems properly. Problem Solving in School Mathematics, 1980, 1(1), 23-33.

POLYA, G. How to solve it? Princeton University Press, New Jersey (United States). 2014. https://www.google.com.co/books/edition/How_to_Solve_It/Zu2hEAAAQBAJ?hl=es&gbpv=1&dq=inauthor:%22G.+Polya%22&printsec=frontcover

MEN. Lineamientos curriculares de matemáticas. Ministerio de Educación Nacional. Colombia 1998. https://www.mineducacion.gov.co/1780/articles-339975_matematicas.pdf

SCHOENFELD, A. H. Problem solving in context. The Teaching and Assessing of Mathematical Problem Solving, 1988, 3(1), 82-92. https://eric.ed.gov/?id=ED307120

SANTOS-TRIGO. Problem solving, the work of Alan Schoenfeld: A proposal to consider in the learning of mathematics. Educación Matemática, 1992, 25(1), 16-24. http://www.revista-educacion-matematica.org.mx/descargas/vol4/vol4-2/vol4-2-2.pdf

HERNÁNDEZ-SABATÉ, A., ALBARRACÍN, L. & SÁNCHEZ, F. J. Graph-Based Problem Explorer: A Software Tool to Support Algorithm Design Learning While Solving the Salesperson Problem. Mathematics, 2020, 8(9), 15-95. https://doi.org/10.3390/math8091595

MIGUÉLEZ, M.M. Action-research in the classroom. Academic Agenda, 2000, 7(1), 27-39. https://icecregiondecoquimbo.cl/wp-content/uploads/2019/12/10-La-investigación-acción-en-el-aula.pdf

SANCHO, J.M. Digital backpack to the past. Notebooks of Pedagogy, 2013, 432(1), 74-77. https://diposit.ub.edu/dspace/bitstream/2445/123715/1/624816.pdf

ALBIÑANA, A.I.C., LÓPEZ, J.V.S. & GARCÍA, Ó.J. Digital competence and information processing: Learning in the 21st century. Ediciones de la Universidad de Castilla La Mancha, Ciudad Real, España, 2016. https://www.researchgate.net/publication/301230942_COMPETENCIA_DIGITAL_Y_TRATAMIENTO_DE_LA_INFORMACION_APRENDER_EN_EL_SIGLO_XXI

WONG, G. K. W., REICHERT, F. & LAW, N. Reorienting the assessment of digital literacy in the twenty-first century: a product-lifecycle and experience dependence perspective. Educational Technology Research and Development, 2023, 71(6), 2389-2412, https://doi.org/10.1007/s11423-023-10278-1

PERALES, F.J. & AGUILERA-MORALES, D. Science-Technology-Society vs. STEM: Evolution, revolution or disjunction? Journal of Science Education, 2020, 4(1), 1-15. https://doi.org/10.17979/arec.2020.4.1.5826

ARÉVALO A., CASTAÑO-MUÑOZ, M.F., RAMÍREZ-OTERO, L.F. & ROMERO-AGREDO, S. Factors causing school dropout: Application of a regression model at the Institución Universitaria Antonio José Camacho (UNIAJC). Revista Sapientía, 2019, 11 (21), 20-31. https://doi.org/10.54278/sapientia.v11i21.47

HIGGINS, K., HUSCROFT-D’ANGELO, J. & CRAWFORD, L. Effects of Technology in Mathematics on Achievement, Motivation, and Attitude: A Meta-Analysis. Journal of Educational Computing Research, 2019, 57(2), 283-319. https://doi.org/10.1177/0735633117748416

SYARIFUDDIN, H., ARNAWA, I. M., BAHRI, S., BAKAR, N. N., RAHMADYA, B., NITA, S. & ADONA, F.. How Can Blended Learning and GeoGebra Promote Students’ Achievement in Calculus during the COVID-19 Pandemic? Journal of Hunan University Natural Sciences, 2023, 50(2), 57-67. https://doi.org/10.55463/issn.1674-2974.50.2.6

CHOWDHURY, R. R. & SINGHA, A. K. Importance of integration modern technology in higher education. Knowledgeable Research: A Multidisciplinary Journal, 2023, 1(09), 71-82. https://www.doi.org/10.57067/kr.v1i09.78

CHEN, M. & ZHOU, C. The Effects of Contextualized Learning Content and Collaborative Behaviours in a Ubiquitous Learning Environment. International Conference on Intelligent Education and Intelligent Research, 2022, 22(1), 15-22. https://doi.org/10.1109/ieir56323.2022.10050066

ARÉVALO SOTO, A., CASTAÑO MUÑOZ, M.

F., RAMÍREZ OTERO, L. F., & ROMERO AGREDO, S. Determining factors of student dropout in higher education, Colombia. 2020. https://repositorio.uniajc.edu.co/handle/uniajc/1203


Refbacks

  • There are currently no refbacks.