Use of research papers in the construction of proofs in differential equations
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mathematical proficiency
higher education
problem solving
learning resources
reasoning competencia matemática
educación superior
resolución de problemas
recursos de aprendizaje

How to Cite

Landa, E. A., Ávila Vales, E. J., Sosa Moguel, L., & García Almeida, G. (2023). Use of research papers in the construction of proofs in differential equations . Nova Scientia, 15(30), 1–13.


The research goal was to analyze how the use of research papers can be a pedagogical strategy of active learning based on inquiry that helps mathematics students in the construction of proofs. The study was carried out under a qualitative methodological paradigm with an interpretive approach. The data were collected during a mathematical modeling course in a mathematician training program at a public university in southeastern Mexico. Nine students participated in this study and the course teacher. The data were analyzed based on the codification of the students' reasoning and strategies in their proof construction process in relation to the five components that structure a mathematical proficiency and the cycle of the four experiential learning modes. The use of research papers played an essential role in adaptive reasoning, the generation of arguments and the integration of students’ knowledge when constructing their mathematical proofs on the positivity of a system of differential equations solutions and even helped to overcome such difficulties like understanding some theorems involved in proofs.
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Arslan, S. (2010). Traditional instruction of differential equations and conceptual learning. Teaching Mathematics and its Applications: An International Journal of the IMA, 29(2), 94 – 107.

Baker, D., y Campbell, C. (2007). Fostering the development of mathematical thinking: observations from a proofs course. PRIMUS, 14(4), 345 – 353.

Borssoi, A. H., y de Almeida, L. M. W. (2004). Modelagem matemática e aprendizagem significativa: uma proposta para o estudo de equações diferencias ordinárias. Educação Matemática Pesquisa, 6(2), 91 – 121.

Cohen, L., Manion, L., y Morrison, K. (2007). Research Methods in Education. London and New York, NY: Routledge Falmer.

Corbin, J., y Strauss, A. (2008). Basics of Qualitative Research: Techniques and Procedures for Developing Grounded Theory. Thousand Oaks, CA: Sage.

Czocher, J. A. (2017). How can emphasizing mathematical modeling principles benefit students in a traditionally taught differential equations course? The Journal of Mathematical Behavior, 45, 78 – 94.

Czocher, J.A., Melhuish, K., y Kandasamy, S. (2020) Building mathematics self-efficacy of STEM undergraduates through mathematical modelling. International Journal of Mathematical Education in Science and Technology, 5(6), 807 – 834.

Ernst, D., Hodge, A., y Yoshinobu, S. (2017). What is inquiry -based learning? Notices of the AMS, 64(6), 570 – 574.

Flegg, J.A., Mallet, D.G., y Lupton, M. (2013). Students’ approaches to learning a new mathematical model. Teaching Mathematics and Its Applications: International Journal of the IMA, 32(1), 28 – 37.

Harel, G., y Sowder, L. (1998). Students’ proof schemes: results from exploratory studies. CBMS issues in mathematics education, 7: Research in collegiate mathematics education III (pp. 234 - 283).

He, S., Peng, Y., y Sun, K. (2020). SEIR modeling of the COVID-19 and its dynamics. Nonlinear dynamics, 101(3), 1667-1680.

Johnson, E., J. Caughman, J. Fredericks, y Gibson, L. (2013). Implementing inquirí-oriented curriculum: From the mathematicians’ perspective. The Journal of Mathematical Behavior, 32(4), 743 – 760.

Kilpatrick, J. (1998). Investigação em educação matemática e desenvolvimento curricular em Portugal: 1986-1996. Invited plenary address at “Caminhos para a investigação em educação matemática em Portugal”, Seventh Conference on Research in Mathematics Education, Mirandela, Portugal.

Kilpatrick, J., Swafford, J. y Findell, B. (Eds.) (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.

Knuth, E., Zaslavsky, O., y Ellis, A. (2019). The role and use of examples in learning to prove. The Journal of Mathematical Behavior, 53, 256 – 262.

Koirala, H.P. (2002). Facilitating student learning through math journals. Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education, 217 - 224. Descargado desde la base de datos ERIC (ED476099).

Kolb, A., y Kolb, D. (2017). The Experiential Educator. Principles and Practices of Experiential Learning. Kaunakakai, Hawaii: EBLS Press.

Laursen, S. L., Hassi, M.L., Kogan, M., y Weston, T.J. (2014). Benefits for women and men of inquiry-based learning in college mathematics: A multi-institution study. Journal for Research in Mathematics Education, 45(4), 406 – 418.

Liu, X., Li, Q., y Pan, J. (2018). A deterministic and stochastic model for the system dynamics of tumor–immune responses to chemotherapy. Physica A: Statistical Mechanics and its Applications, 500, 162 – 176.

Lockwood, E., Ellis, A. B., Dogan, M. F., Williams, C. C., y Knuth, E. (2012). A framework for mathematicians’ example-related activity when exploring and proving mathematical conjectures. En J.-J. Van Zoest, & J. L. Lo (Eds.), 34th Annual meeting of the north american chapter of the international group for the psychology of mathematics education (pp. 151–158). Kalamazoo, MI: Western Michigan University.

Lee, K. (2016). Students’ proof schemes for mathematical proving and disproving of propositions. The Journal of Mathematical Behavior, 41, 26-44.

Lozada, E., Guerrero-Ortiz, C., Coronel, A., y Medina, R. (2021). Classroom Methodologies for Teaching and Learning Ordinary Differential Equations: A Systemic Literature Review and Bibliometric Analysis. Mathematics, 9, 745.

Mejia-Ramos, J. P., y Weber, K. (2014). Why and how mathematicians read proofs: Further evidence from a survey study. Educational Studies in Mathematics, 85(2), 161 – 173.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: NCTM.

Rasmussen, C. (2001). New directions in differential equations: A framework for interpreting students’ understandings and difficulties. The Journal of Mathematical Behavior, 20(1), 55 – 87.

Rasmussen, C., y Kwon, O. N. (2007). An inquiry-oriented approach to undergraduate mathematics. The Journal of Mathematical Behavior, 26(3), 189 – 194.

Rivero-Esquivel, E., Ávila-Vales, E., y García-Almeida, G. (2016). Stability and bifurcation analysis of a SIR model with saturated incidence rate and saturated treatment. Mathematics and Computers in Simulation, 121, 109 – 132.

Rodd, M. M. (2000). On mathematical warrants: Proof does not always a warrant and a warrant may be other than a proof. Mathematical Thinking and Learning, 2(3), 221 – 244.

Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic.

Schoenfeld, A. H. (2009). The soul of mathematics. En D. Stylianou, M. Blanton, y E. Knuth (Eds.), Teaching and learning proof across the grades: A K-16 perspective (pp. xii-xvi). Mahwah, NJ: Taylor & Francis Group.

Schoenfeld, A. H. (2010). How we think. New York: Routledge.

Selden, A. (2012). Transitions and proof and proving at tertiary level. En G. Hanna & M. de Villiers (Eds.), Proof and Proving in Mathematics Education: The 19th ICMI Study (pp. 391–420). International Commission on Mathematics Instruction, Springer.

Selden, J., y Selden, A. (2009). Understanding The Proof Construction Process. En F.-L Lin, F.-J. Hsieh, G. Hanna, ve M. de Villiers (Eds.), Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education, 2. (pp. 196 – 201). Taipei, Taiwan: The Department of Mathematics, National Taiwan Normal University.

Selden, A., y Selden, J. (2015). A theoretical perspective for proof construction. CERME 9 – Ninth Congress of the European Society for Research in Mathematics Education, Charles University in Prague, Faculty of Education; ERME, Feb 2015, Prague, Czech Republic. pp.198 – 204.

Stefanowicz, A. (2014). Proofs and Mathematical Reasoning. University of Birmingham.

Stylianou, D., Blanton, M., y Rotou, O. (2015). Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof. International Journal of Research in Undergraduate Mathematics Education, 1, 91–134.

Stylianides, G., Stylianides, A., y Weber, K. (2017). Research on the teaching and learning of proof: taking stock and moving forward. En J. Cai (Ed.), Compendium for research in mathematics education, (pp. 237 – 266.). Reston, VA: National Council of Teachers of Mathematics.

Tabach, M., Hershkowitz, R., Rasmussen, C., y Dreyfus, T. (2014). Knowledge shifts and knowledge agents in the classroom. The Journal of Mathematical Behavior, 33, 192 – 208.

Weber, K. (2005). Problem-solving, proving, and learning: The relationship between problem-solving processes and learning opportunities in the activity of proof construction. The Journal of Mathematical Behavior, 24(3 – 4.), 351 – 360.

Wittmann, E.C. (2021). When Is a Proof a Proof? En Connecting Mathematics and Mathematics Education (pp. 61 – 76). Springer.

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