Graph Theory in Primary, Middle, and High School

Chapter
First Online:
Part of the ICME-13 Monographs book series (ICME13Mo)

Abstract

In this paper we present an experimental teaching activity conduced in some primary, middle and high schools in Sicily. The activity concerned several topics of graph theory. Here we highlight, in particular, the approach to teaching Eulerian graphs. The aim of the whole project was to present a fun, easy approach to mathematics in order to promote a good attitude towards mathematics in primary school children and to improve it in middle school kids and in high school young people. This goal is pursued also by showing some connections of mathematics with real life, making mathematics less abstract than the topics too often taught in school. Through this activity we also reach mathematical knowledge and practical abilities (related to graph theory), and above all mathematical competencies related to reasoning and mathematization, in particular by the use of graphs in mathematical models to solve problems. The teaching experiments were different, according to the different school level, but unified by the method, based on laboratorial activities, by presenting a problem to be solved together with classmates, by manipulating objects and guided by the teacher. These activities were realized by the use of artefacts: in the sense of Vygotskijan semiotic mediation, we used signs, symbols, maps, language and, in many cases, new technology’s artefacts, to mediate mathematical concepts. Lessons involved also the body as a mean to learning, especially with children, according to embodied cognition theory.

Keywords

Graph theory Mathematical modelling Eulerian trail Eulerian cycle 
This is a preview of subscription content, log in to check access.

References

  1. Aleo, M. A., Ferrarello, D., Inturri, A., Jacona, D., Mammana, M. F., Margarone, D., et al. (2009). Guardiamo il mondo con i grafi [Let’s look at the world with the graphs]. Catania: Casa editrice La Tecnica della Scuola.Google Scholar
  2. Anichini, G., Arzarello, F., Ciarrapico, L., & Robutti, O. (Eds.). (2004). La matematica per il cittadino. Attività didattiche e prove di verifica per un nuovo curricolo di Matematica (ciclo secondario). Lucca: Matteoni Stampatore.Google Scholar
  3. Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artefacts and signs after a Vygotskian perspective. In L. English, M. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (2nd ed., pp. 720–749). Mahwah, NJ: Erlbaum.Google Scholar
  4. Brown, T. (2012). Affective productions of mathematical experience. Educational Studies in Mathematics, 80, 185–199.CrossRefGoogle Scholar
  5. Chiappini, G. (2007). Il laboratorio didattico di matematica: Riferimenti teorici per la costruzione. Innovazione educativa, Inserto allegato al numero, 8, 9–12.Google Scholar
  6. DeBellis, V. A., & Rosenstein, J. G. (2004). Discrete mathematics in primary and secondary schools in the United States. ZDM Mathematics Education, 36(2), 46–55.CrossRefGoogle Scholar
  7. Euler, L. (1741). Solutio Problematis ad geometriam situs pertinentis. Commentarii academiae scientiarum Petropolitanae, 8, 128–140.Google Scholar
  8. Ferrarello, D. (2014). Primary graphs Quaderni di Ricerca in Didattica. Proceedings CIEAEM 66, 24(1).Google Scholar
  9. Ferrarello, D. (2017). Graphs in primary school: Playing with technology. In G. F. Hitt, L. Bazzini, & U. Gellert (Eds.), Mathematics and technology. A C.I.E.A.E.M. Sourcebook. Berlin: Springer.Google Scholar
  10. Ferrarello, D., & Mammana, M. F. (2017). Teoria dei grafi: Come e perchè. L’insegnamento Della Matematica E Delle Scienze Integrate, 40, 249–271.Google Scholar
  11. Ferrarello, D., Mammana, M. F., & Pennisi, M. (2014). Teaching by doing. QRDM. Proceedings of CIEAEM 2013 (Vol. 24, no. 1, pp. 429–433). Torino, Italia, 22–26 Luglio 2013.Google Scholar
  12. Lakoff, G., & Johnson, M. (1999). Philosophy in the flesh. The embodied mind and its challenge to western thought. New York: Basic Books.Google Scholar
  13. Lakoff, G., & Nunez, R. R. (2000). Where mathematics come from: How the embodied mind brings mathematics into being. New York: Basic Books.Google Scholar
  14. Levy, R. (2015). 5 Reasons to teach mathematical modeling. American Scientist. http://www.americanscientist.org/blog/pub/5-reasons-to-teach-mathematical-modeling.
  15. Mammana, M. F., & Milone, C. (2009a). I grafi: Un percorso possibile (parte prima). L’insegnamento della Matematica e delle Scienze Integrate, 32A(4), 427–440.Google Scholar
  16. Mammana, M. F., & Milone, C. (2009b). I grafi: Un percorso possibile (parte seconda). L’insegnamento della Matematica e delle Scienze Integrate, 32A(2), 109–132.Google Scholar
  17. Mammana, M. F., & Milone, C. (2010). Dal problema al modello: Una sperimentazione sul concetto di grafo nella scuola media. L’educazione matematica, IX(2), 23–36.Google Scholar
  18. MIUR. (2012). Indicazioni nazionali per il curricolo della scuola dell’infanzia e del primo ciclo d’istruzione. http://www.indicazioninazionali.it/documenti_Indicazioni_nazionali/indicazioni_nazionali_infanzia_primo_ciclo.pdf.
  19. Reggiani, M. (2008). Il laboratorio come ambiente per l’insegnamento-apprendimento della matematica: Riflessioni. L’insegnamento della Matematica e delle scienze integrate, 31B(6).Google Scholar
  20. Rosenstein, J. G. (2014). Problem solving and reasoning with discrete mathematics (preliminary edition, with accompanying activity book). Highland Park, NJ: Shiviti Publications.Google Scholar
  21. Van Hiele, P. M. (1986). Structure and insight. Orlando: Academic Press.Google Scholar
  22. Vygotskij, L. S. (1981). The genesis of higher mental functions. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 147–188). Armonk, NY: Sharpe.Google Scholar
  23. West, D. B. (2001). Introduction to graph theory. New York: Prentice Hall.Google Scholar
  24. Wilson, R. J. (1996). Introduction to graph theory. Essex: Longman Group Ltd.Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of CataniaCataniaItaly

Personalised recommendations