Analysing Profiles of Recognition in Graph Theory
Abstract
In this work, we explore the recognition skills in graph theory of undergraduate students of the degree in Computer Science-Information Technology of the University of Seville. For this purpose, we design a questionnaire that we use as an instrument for data collection, which are subsequently analysed by means of an adaptation of the methodology of the calculation of the degrees of acquisition, giving rise to different profiles of recognition in graph theory. The characteristics of these profiles allow us to give empirical support to a theoretical proposal of recognition levels in graph theory from the perspective of the Van Hiele model, as well as to draw some conclusions about aspects of teaching and learning this field of mathematics.
Keywords
Recognition, Graph theory, Levels of reasoning, Van Hiele modelReferences
Abdullah, A. H. y Zakaria, E. (2013). The effects of Van Hiele’s phases of learning geometry on students’ degree of acquisition of Van Hiele levels. Procedia-Social and Behavioral Sciences, 102, 251-266. https://doi.org/10.1016/j.sbspro.2013.10.740
Abu, M. S. y Abidin, Z. Z. (2013). Improving the levels of geometric thinking of secondary school students using geometry learning video based on Van Hiele theory. International Journal of Evaluation and Research in Education, 2(1), 16-22. https://doi.org/10.11591/ijere.v2i2.1935
Aravena, M., Gutiérrez, A. y Jaime, A. (2016). Estudio de los niveles de razonamiento de Van Hiele en estudiantes de centros de enseñanza vulnerables de educación media en Chile. Enseñanza de las Ciencias, 34(1), 107-128. https://doi.org/10.5565/rev/ensciencias.1664
Biggs, N. L. (2003). Discrete mathematics (2.ª ed.). Oxford University Press.
Gavilán-Izquierdo, J. M. y González, A. (2016). Investigación sobre el concepto de grafo a través del modelo de Van Hiele. En J. A. Macías, A. Jiménez, J. L. González, M. T. Sánchez, P. Hernández, C. Fernández, F. J. Ruiz, T. Fernández y A. Berciano (Eds.), Investigación en Educación Matemática XX (p. 597). SEIEM.
Godino, J. D., Aké, L. P., Gonzato, M. y Wilhelmi, M. R. (2014). Niveles de algebrización de la actividad matemática escolar. Implicaciones para la formación de maestros. Enseñanza de las Ciencias, 32(1), 199-219. http://dx.doi.org/10.5565/rev/ensciencias.965
González, A. y Gavilán-Izquierdo, J. M. (2017). Analizando el reconocimiento de grafos a través del modelo de Van Hiele. En Federación Española de Sociedades de Profesores de Matemáticas (Ed.), VIII Congreso Iberoamericano de Educación Matemática. Libro de actas (pp. 286-293). FESPM.
Gutiérrez, A. y Jaime, A. (1995). Towards the design of a standard test for the assessment of the student’s reasoning in geometry. En L. Meira y D. Carraher (Eds.), Proceedings of the 19th PME Conference (vol. 3, pp. 11-18). PME.
Gutiérrez, A. y Jaime, A. (1998). On the assessment of the van Hiele levels of reasoning. Focus on Learning problems in Mathematics, 20(2-3), 27-46. https://www.uv.es/angel.gutierrez/archivos1/textospdf/GutJai98.pdf
Gutiérrez, A., Jaime, A. y Fortuny, J. M. (1991). An alternative paradigm to evaluate the acquisition of the Van Hiele levels. Journal for Research in Mathematics Education, 22(3), 237-251. https://doi.org/10.2307/749076
Hart, E. W. y Sandefur, J. (Eds.) (2018). Teaching and learning discrete mathematics worldwide: Curriculum and research. Springer. https://doi.org/10.1007/978-3-319-70308-4
Hazzan, O. y Hadar, I. (2005). Reducing abstraction when learning graph theory. Journal of Computers in Mathematics and Science Teaching, 24(3), 255-272.
Jaime, A. y Gutiérrez, A. (1990). Una propuesta de fundamentación para la enseñanza de la geometría: El modelo de van Hiele. En S. Llinares y M. V. Sánchez (Eds.), Teoría y práctica en educación matemática (pp. 295-384). Alfar.
Llorens, J. L. y Pérez-Carreras, P. (1997). An extension of van Hiele’s model to the study of local approximation. International Journal of Mathematical Education in Science and Technology, 28(5), 713-726. https://doi.org/10.1080/0020739970280508
Ma, H., Lee, D., Lin, S. y Wu, D. (2015). A study of Van Hiele geometric thinking among 1st through 6th graders. Eurasia Journal of Mathematics, Science & Technology Education, 11(5), 1181-1196. https://doi.org/10.12973/eurasia.2015.1412a
Mayberry, J. (1983). The van Hiele levels of geometric thought in undergraduate preservice teachers. Journal for Research in Mathematics Education, 14(1), 58-69. https://doi.org/10.2307/748797
Medová, J., Páleníková, K., Rybanský, L. y Naštická, Z. (2019). Undergraduate students’ solutions of modeling problems in algorithmic graph theory. Mathematics, 7, 572-587. https://doi.org/10.3390/math7070572
Menzel, H. (1953). A new coefficient for scalogram analysis. The Public Opinion Quarterly, 17(2), 268-280. https://doi.org/10.1086/266460
Navarro, M. y Pérez-Carreras, P. (2006). Constructing a concept image of convergence of sequences in the van Hiele framework. En A. Selden, F. Hitt y G. Harel (Eds.), Research in Collegiate Mathematics Education VI (pp. 61-98). AMS. https://doi.org/10.1090/cbmath/013
Ouvrier-Buffet, C. (2011). A mathematical experience involving defining processes: In-action definitions and zero-definitions. Educational Studies in Mathematics, 76(2), 165-182. https://doi.org/10.1007/s10649-010-9272-3
Ouvrier-Buffet, C., Meyer, A. y Modeste, S. (2018). Discrete mathematics at university level. Interfacing mathematics, computer science and arithmetic. En V. Durand-Guerrier, R. Hochmuth, S. Goodchild y N. M. Hogstad (Eds.), Proceedings of INDRUM 2018 (pp. 255-264). University of Agder.
Perdikaris, S. C. (1997). Using the cognitive styles to explain an anomaly in the hierarchy of the Van Hiele levels. Journal of Mathematics Sciences & Mathematics Education, 6(2), 35-43.
Van Hiele, P. M. (1986). Structure and insight. A theory of mathematics education. Academic Press.
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