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Ornaments and Tessellations: Encouraging Creativity in the Mathematics Classroom

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Mathematical Creativity and Mathematical Giftedness

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

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Abstract

The presented paper focuses on encouraging creativity in mathematics lessons in heterogeneous mathematics classrooms. It is an extended version of a paper presented at ICME 2016 in Hamburg. It describes teaching experiments conducted within the frame of the project M3EaL: Multiculturalism, Migration, Mathematics Education and Language (526333-LLP-1-2012-1-IT-COMENIUS-CMP), a multilateral project whose aim was development of teaching units to support immigrant pupils and pupils from different socio-cultural backgrounds (m3eal.dm.unipi.it). The paper shows that if pre-service and in-service teachers face a situation in which they cannot rely on traditional textbooks and ways of doing mathematics—in this case a culturally heterogeneous classroom—they tend to be very creative in planning their lesson and at the same time encourage their pupils’ creativity. Thus cultural heterogeneity may be perceived as advantage as it may result in breaking down stereotypes in mathematics classrooms.

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References

  • Arslan, Ç., & Altun, M. (2007). Learning to solve non-routine mathematical problems. Elementary Education Online, 6(1), 50–61.

    Google Scholar 

  • Barton, B., Barwell, R. & Setati, M. (Eds.) (2007). Multilingualism in mathematics education. Special Issue of Educational Studies in Mathematics, 64(2).

    Google Scholar 

  • Barwell, R. (2015). Linguistic stratification in a multilingual mathematics classroom. In K. Krainer & N. Vondrová (Eds.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 1333–1339). Prague: Charles University, Faculty of Education and ERME.

    Google Scholar 

  • Barwell, R., Barton, B., & Setati, M. (2007). Multilingual Issues in mathematics education: Introduction. Educational Studies in Mathematics, 64(2), 113–119.

    Article  Google Scholar 

  • Bishop, A. J. (1988). Mathematics education in its cultural context. Educational Studies in Mathematics, 19, 179–191.

    Article  Google Scholar 

  • Cantor, G. (1867). Doctoral thesis. Berlin, Germany.

    Google Scholar 

  • César, M., & Favilli, F. (2005). Diversity seen through teachers’ eyes: Discourses about multicultural classes. In M. Bosch (Ed.), Proceedings of the 4th Conference of the European Society for Research in Mathematics Education (pp. 1153–1164). Barcelona: FUNDEMI IQS—Universitat Ramon Llull.

    Google Scholar 

  • Csikszentmihalyi, M. (1996). Creativity, flow, and the psychology of discovery and invention. New York: Harper Collins.

    Google Scholar 

  • Duval, R. (1993). Registre de représentations sémiotique et fonctionnement cognitif de la pensé. Annales de Didactique et de Sciences Cognitives, 5, 37–65.

    Google Scholar 

  • Duval, R. (2000). Basic Issues for research in mathematics education. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 55–69). Hiroshima: Hiroshima University.

    Google Scholar 

  • Einstein, A., & Infeld, L. (1938). The evolution of physics: The growth of ideas from early concepts to relativity and quanta. Cambridge: Cambridge University Press.

    Google Scholar 

  • Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 42–53). Dordrecht, Netherlands: Kluwer.

    Google Scholar 

  • Favilli, F. (Ed.) (2015). Multiculturalism, migration, mathematics education and language: Teachers‘ needs and teaching materials. Pisa, Italy: TEP, http://m3eal.dm.unipi.it. Accessed 26 Apr 2017.

  • Henrard, M. (2006). The irony in the derivatives discounting. Available from https://mpra.ub.uni-muenchen.de/3115/. Accessed 27 Sept 2017.

  • Krutetskii, V. A. (1976). In J. Kilpatrick, & I. Wirszup (Eds.) The psychology of mathematical abilities in schoolchildren (trans: Teller, J.). Chicago: The University of Chicago Press.

    Google Scholar 

  • Kynigos, C., & Theodosopoulou, V. (2001). Synthesizing personal, interactionist and social norms perspectives to analyze student communication in a computer-based mathematical activity in the classroom. Journal of Classroom Interaction, 36(2), 63–73.

    Google Scholar 

  • Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin et al. (Eds.), Creativity in mathematics and the education of gifted students (pp. 129–145). Sense Publishers.

    Google Scholar 

  • Mariotti, M. A. (2009). Artifacts and signs after a Vygotskian perspective: The role of the teacher. ZDM Mathematics Education, 41(4), 427–440.

    Google Scholar 

  • McDermott, R., & Varenne, H. (1995). Culture as disability. Anthropology & Education quarterly, 26(3), 324–348.

    Google Scholar 

  • Meany, T., & Lange, T. (2013). Learners in transition between contexts. In M. A. Clements et al. (Eds.), The third international handbook of mathematics education (Vol. 27, pp. 169–202). Springer.

    Google Scholar 

  • MIUR—Ministero dell’Istruzione, Università e Ricerca. (2012). Indicazioni nazionali per il curricolo della scuola dell’infanzia e del primo ciclo d’istruzione. Roma: MIUR, http://www.indicazioninazionali.it/documenti_Indicazioni_nazionali/indicazioni_nazionali_infanzia_primo_ciclo.pdf. Accessed 26 Apr. 2017.

  • Moraová, H., & Novotná, J. (2016). Ornaments and tessellations—Encouraging creativity in mathematics classroom. Presented in TSG 29, ICME 13, Hamburg.

    Google Scholar 

  • Moschkovich, J. N. (2007). Using two languages while learning mathematics. Educational Studies in Mathematics, Special Issue on Multilingual Mathematics Classrooms, 64(2), 121–144.

    Google Scholar 

  • Moschkovich, J. (2012). How equity concerns lead to attention to mathematical discourse, equity in discourse for mathematics? Theories, practices and policy, 89–105.

    Google Scholar 

  • MPI—Ministero della Pubblica Istruzione. (2007). The Italian way to intercultural education and the integration of Foreign pupils. Roma: MPI, http://m3eal.dm.unipi.it/images/doc/03.educational_policy/IT_educational_policy.pdf. Accessed 26 Apr. 2017.

  • MŠMT Ministerstvo školství, mládeže a tělovýchovy. (2013). Framework education programme for primary school education in the Czech Republic. Praha: MŠMT ČR.

    Google Scholar 

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

    Google Scholar 

  • Norén, E. (2008). Bilingual students’ mother tongue: A resource for teaching and learning mathematics. Nordic Studies in Mathematics Education, 13(4), 29–50.

    Google Scholar 

  • Radford, L., Bardini, C., Sabena, C., Diallo, P., & Simbagoye, A. (2005). On embodiment, artifacts, and signs: A semiotic-cultural perspective on mathematical thinking. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th PME International Conference (Vol. 4, pp. 113–120). Melbourne: PME.

    Google Scholar 

  • Sibanda, L. (2017). Do the annual national assessments in mathematics unfairly assess English Language competence at the expense of mathematical competence? In M. Graven & H. Venkat (Eds.), Improving primary mathematics education, teaching and learning. Research for development in resource-constrained contexts (pp. 147–159). London: Palgrave Macmillan.

    Google Scholar 

  • Singer, F. M., & Moscovici, H. (2008). Teaching and learning cycles in a constructivist approach to instruction. Teaching and Teacher Education, 24(6), 1613–1634.

    Google Scholar 

  • Sriraman, B. (2005). Are giftedness & creativity synonyms in mathematics? An analysis of constructs within the professional and school realms. The Journal of Secondary Gifted Education, 17, 20–36.

    Google Scholar 

  • Sullivan, P., Mousley, J., & Zevenbergen, R. (2003). The contexts of mathematics tasks and the context of the classroom: Are we including all students? Mathematics Education Research Journal, 15(2), 107–121.

    Google Scholar 

  • Tichá, M., & Hošpesová, A. (2010). Tvoření úloh jako cesta k matematické gramotnosti (Problem posing as a way to mathematical literacy, in Czech). In Jak učit matematice žáky ve věku 11 – 15 let; sborník příspěvků celostátní konference (pp. 133–145). Plzeň: Vydavatelský servis.

    Google Scholar 

  • UNICEF. https://www.unicef.org/ceecis/education_18613.html. Accessed 27 Sept 2017.

  • Winsløw, C. (2003). Semiotic and discursive variables in CAS-based didactical engineering. Educational Studies in Mathematics, 52(3), 271–288.

    Google Scholar 

  • Wittmann, E. Ch. (1995). Mathematics education as a ‘Design Science’. Educational Studies in Mathematics, 29, 355–374.

    Google Scholar 

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.

    Google Scholar 

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Acknowledgements

The authors would like to thank all the following teachers and educators who piloted the teaching units in their schools in Austria, Italy and the Czech Republic: Andreas Ulovec and Therese Tomiska (Austria), Antonella Castellini and Lucia Alfia Fazzino (Italy), Hana Moraová (Czech Republic).

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Authors and Affiliations

  1. Faculty of Education, Charles University, Prague, Czech Republic

    Hana Moraová & Jarmila Novotná

  2. CeDS, Université Bordeaux, Bordeaux, France

    Jarmila Novotná

  3. CAFRE, University of Pisa, Pisa, Italy

    Franco Favilli

Authors
  1. Hana Moraová
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  2. Jarmila Novotná
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  3. Franco Favilli
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Corresponding author

Correspondence to Hana Moraová .

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Editors and Affiliations

  1. Faculty of Letters and Science, Oil & Gas University of Ploiești, Ploiești, Romania

    Florence Mihaela Singer

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Moraová, H., Novotná, J., Favilli, F. (2018). Ornaments and Tessellations: Encouraging Creativity in the Mathematics Classroom. In: Singer, F. (eds) Mathematical Creativity and Mathematical Giftedness. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-73156-8_10

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  • DOI: https://doi.org/10.1007/978-3-319-73156-8_10

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