Contributions to the Development of Mathematical Thinking through Geometric Modeling and Problem Solving
DOI:
https://doi.org/10.61799/2216-0388.1288Keywords:
secondary education, geometric modeling, problem solving, Sense Making, activity system, mathematical visualization,Abstract
The development of human mathematical thinking plays a crucial role in problem solving and contributes significantly to individual and social progress. This article socializes the results obtained from a research that aimed to contribute to the development of mathematical thinking through geometric modelling and problem solving in eighth grade students of a public institution in the department of Cundinamarca. The analysis of the background of the PISA and SABER tests showed the low performance of Colombian students in problem solving and modelling. In addition, the results obtained from the implementation of two exploratory activities show that there are scarce skills in these two processes. In this framework, eight didactic activities were designed and implemented with advanced mathematical content adapted to the age and educational level, where two fundamental processes were linked: geometric modelling and problem solving, and two processes intrinsic to the fundamental ones: mathematical visualisation and Sense Making. A qualitative approach was used with a participatory action design, eight rubrics, video and audio recordings, participant observation and a final survey. The results show that students made significant progress in the development of problem-solving skills in simulated or real contexts, relying on geometric modelling and mathematical visualisation, where they constructed robust mathematical concepts giving mathematical meaning and significance. It is concluded that the organisation and planning of the practical action of mathematics teaching under the four processes contributed significantly to the robust development of students’ mathematical thinking.
Downloads
References
G. Stillman, “Applications and modelling research in secondary classrooms: What have we learnt?” In Selected regular lectures from the 12th International Congress on Mathematical Education. Springer, Cham, pp.791-805, 2015
M. Wickstrom, “Roscoe Geometric Modeling: determining the Largest Lake”, Mathematics Teacher: Learning and Teaching PK-12, vol. 113, no. 8, pp. 643-650, 2020
A. Schoenfeld, “The What and the Why of Modeling. In Affect in Mathematical Modeling”, En S. Chamberlin y B. Sriraman, Springer, Cham, pp.91-96, 2019
Programa para la Evaluación Internacional de Alumnos (PISA). Colombia. Noviembre de 2020. [Online]. Available: https://www.oecd.org/pisa/publications/PISA2018_CN_COL_ESP.pdf
S. Edo, R. Putri y Y. Hartono, “Investigating secondary school students’ difficulties in modeling problems PISA-Model Level 5 and 6”, Journal on mathematics Education, vol. 4, no. 1, pp. 41-58, 2013
J. Villa y C. López, “Sense of reality through mathematical modelling. In Trends in teaching and learning of mathematical modelling”, pp. 701-711. Springer, 2011
M. Sol, J. Giménez y N. Rosich, “Trayectorias modelizadoras en la ESO”. Modelling in Science Education and Learning, 4, pp. 329-343, 2011
M. Socas, J. Hernández y M. Palarea, “Dificultades en la resolución de problemas de Matemáticas de estudiantes para profesor de educación primaria y secundaria”, Funes, pp.145-154, 2014
D. Kadijevich, “Simple spreadsheet modeling by first-year business undergraduate students: Difficulties in the transition from real world problem statement to mathematical model”, En Blomhj, M, & Carreira, S. Proceedings of the 11th International Congress on mathematical Education. IMFUFA 461, pp. 241-248, 2009
L. Rico, “La competencia matemática en PISA”, Revista de Investigación en Didáctica de la Matemática, vol. 1, no. 2, pp. 47-66, 2007
K. Bliss y J. Libertini, Lineamientos para la evaluación e instrucción en la educación en modelación matemática, Gaimme. Society for industrial and applied mathematics (SIAM), 2020
W. Blum, P. Galbraith, H. Henn y M. Niss, “Modelling and applications in mathematics education”, vol. 10, MA: Springer US, 2007
C. Alsina, “Geometría y realidad”, Sigma, vol. 33, pp.165-179, 2008
F. Zapata, N. Cano y J. Villa, “Art and Geometry of Plants: Experience in Mathematical Modelling through Projects”, Eurasia Journal of Mathematics, Science and Technology Education, vol. 14, no. 2, pp. 585-603, 2017
P. Herbst y N. Boileau, “Geometric modeling of mesospace objects: A task, its didactical variables, and the mathematics at stake”, In Visualizing Mathematics Springer, Cham, 2018
M. Ludwig y S. Jablonski, “Doing Math Modelling Outdoors-A Special Math Class Activity designed with MathCityMap”, In HEAD 19. 5th International Conference on Higher Education Advances, Universität Politécnica de Valéncia, pp. 901-909, 2019
Entrevista Y. Baldín, 2021
L. Fonseca. “Modelo didáctico para el desarrollo del pensamiento matemático a través de la resolución de problemas y la modelación geométrica”. [Tesis de doctorado no publicada]. Universidad Antonio Nariño. Colombia, 2022
A. Balyakin y L. Chempinsky, “Experience of teaching geometric modeling at schools and universities”, In Journal of Physics: Conference Series, vol. 1691, no. 1, pp. 012042, 2020
P. Herbst, “Geometric Modeling Tasks and Opportunity to gain experience Geometry: The Ranking Triangles Task Revisited”, In Problem Solving in Mathematics Instruction and Teacher Professional Development, pp. 123-143. Springer, Cham, 2019
T. Braicovich, S. Oropeza, y V. Cerda, “Un desafío: incluir grafos en los distintos niveles educativos”, Memorias del II REPEM, pp. 70-76, 2008
G. Stanic y J. Kilpatrick. Historical perspectives in problem solving. Research Agenda for Mathematics Education: The Teaching and Assessing of Problem Solving. National Council for Teachers of Mathematics. Taylor, S. & Bogdan,1988
S. Krulik y J. Rudnick, Problem solving: A handbook for teachers. Allyn and Bacon, Inc., 7 Wells Avenue, Newton, Massachusetts 02159, 1987
M. Falk, “La enseñanza a través de problemas”, Universidad Antonio Nariño, Bogotá, Colombia. 1980
M. Diaz y Á. Poblete, “Contextualizando tipos de problemas matemáticos en el aula”. Números, 45, pp. 33-41, 2001
F. Pérez., Olimpiadas Colombianas de Matemáticas para primaria 2000 - 2004. Bogotá: Universidad Antonio Nariño, 2004
J. Sigarreta y J. Marcia, “Modelo Didáctico para la Formación Axiológica a través de la Resolución de Problemas Matemáticos”, Matemática, educación e internet, vol.4, 2003
M. Pochulu y M. Rodríguez, Educación Matemática: aportes a la formación docente desde distintos enfoques teóricos, Villa María, Argentina: Editorial Universitaria Villa María, pp. 155, 2012
R. Mesino, “Modelo pedagógico inclusivo para la enseñanza aprendizaje de la matemática a través de la resolución de problemas de niños en grado quinto con TDAH”. [Tesis de doctorado no publicada]. Universidad Antonio Nariño. Colombia, 2022
W. Zimmermann y S. Cunningham, “Editor’s introduction: What is mathematical visualization”, Visualization in teaching and learning mathematics, vol. 1, no. 8, 1991
N. Presmeg, “Research on visualization in learning and teaching mathematics: Emergence from psychology”, In Handbook of research on the psychology of mathematics education, pp. 205-235, 2006
R. Hershkowitz, Psychological aspects of learning geometry, In Mathematics and cognition, pp. 70-95, The Weizmann Institute of Science, 1990
D. Ancona, “Framing and Acting in the Unknown”, S. Snook, N. Nohria, & R. Khurana, the handbook for teaching leadership, vol. 3, no. 19, pp.198-217, 2012
T. Odden y R. Russ, “Defining sensemaking: Bringing clarity to a fragmented theoretical construct”, Science Education, vol. 103, no. 1, pp.187-205, 2019
C. Castaño Y M. Quecedo, Introducción a la metodología de investigación cualitativa, 2002
J. Mason, L. Burton, y K. Stacey, Thinking Mathematically, Harlow: Pearson, 2010
J. Brown y G. Stillman, “Developing the roots of modelling conceptions: ‘Mathematical modelling is the life of the world”, International Journal of Mathematical Education in Science and Technology, vol. 48, no. 3, pp. 353-373, 2012
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Mundo FESC Journal
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
