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How Hungarian teachers think about combinatorics and its teaching

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Teachers’ attitudes and beliefs have a fundamental influence on the way of teaching and the efficiency of learning. This topic was also brought up in the didactic research in recent years, in connection with mathematics teachers as well.– To the best of our knowledge, however, a study that investigates this specific area (combinatorics) was not included. As combinatorics has a special role in connecting the development of mathematical thinking and teaching different areas, our short-time Project (Didactics Grant of the Hungarian Academy: Complex Mathematics Education in the 21st Century) focused on the teaching of combinatorics in Hungary. Our aim was to examine some aspects of this field in connection with Tamás Varga’s method and also teachers’ beliefs towards combinatorics with the help of a questionnaire. The main results of this survey are discussed below.
Twórcy
autor
  • Loránd Eötvös University in Budapest Faculty of Science, Mathematics Institute H-1117 Budapest, Pázmány P. s. 1/c
autor
  • Loránd Eötvös University in Budapest Faculty of Science, Mathematics Institute H-1117 Budapest, Pázmány P. s. 1/c
autor
  • Loránd Eötvös University in Budapest Faculty of Science, Mathematics Institute H-1117 Budapest, Pázmány P. s. 1/c
Bibliografia
  • [1] G. Ambrus, Ö. Vancsó. Ist eine schnelle tiefgehende (und nachhaltige) Änderung in der Vorstellung von Mathematiklehrern möglich? - Reflexion der Erfahrungen eines Fortbildungskurses im Bereich der mathematischen Modellierung. TMCS, 13 (1), (2015) 1–20.
  • [2] H. Burkhardt, – with contributions by H. Pollak. Modelling in Mathematics Classrooms: reflections on past developments and the future. ZDM, (38) (2006), 178–195.
  • [3] E. Deák. Die besondere Verflechtung der mathematischen Forschung, des Mathematik-Unterrichts und der Mathematikdidaktik Ungarns im 19. und 20. Jahrhundert. Mitteilungen der GDM, Nr. 74 (2002)
  • [4] I. Eglesz I, Cs. Kovács, J. Radnainé Szendrei, V. Sztrókayné Földvári. Matematika 5. Tanári Kézikönyv, Tankönyvkiadó, Budapest, (1981).
  • [5] A. Eichler. Statistics teachers and Classroom practices. In. C. Batanero, G. Burril & C. Reading (Eds.). Teaching statistics in school mathematics-challenges for teaching and teacher education, New ICMI study series, Vol. 15, Heidelberg/New York: Springer, (2011), 175–186.
  • [6] A. Eichler, R. Ehrens. Domain-specific belief systems of secondary mathematics teachers. In. Pepin, Birgit et al. (Eds.). From beliefs to dynamic affect systems in mathematics education. Exploring a mosaic of relationships and interactions. Cham: Springer, (2015), 179–200.
  • [7] R. Ehrens, A. Eichler. Teachers’ curricular beliefs referring to calculus. In. Proceedings of the 12th International Congress on Mathematics Education (ICME), Seoul, Korea (2012).
  • [8] F. Furinghetti, E. Pehkonen. Rethinking Characterizations of Beliefs. In. G. Leder, E. Pehkonen, G. Törner (Eds.). Beliefs: A hidden variable in mathematics education? Dordrecht: Kluwer Academic Publishers, (2002), 39–57.
  • [9] M. Glaymann, T. Varga. Zwischen unmöglich und sicher: Exemplarische Kapitel der Kombinatorik, Wahrscheinlichkeitsrechnung und Simulation im Unterricht der Sekundarstufe I. Freiburg: Herder (1975).
  • [10] S. Grigutsch, U. Raatz, G. Törner. Einstellungen gegenüber Mathematik bei Mathematiklehrer, Journal für Mathematik-Didaktik, (19) (1998) 3–45.
  • [11] M. S. Hannula. Exploring new dimensions of mathematics-related affect: embodied and social theories. Research in Mathematics Education 14 (2), (2012) 137–161.
  • [12] A. Hoffmann. Vergleich der Problemlösefähigkeit von Primar-und Sekundarstufenschülern im Hinblick auf Lerneffekte während eines Interviews, Journal für Mathematik-Didaktik, 26 (3/4), (2005), 176–199.
  • [13] S. Klein. The Effects of Modern Mathematics, Akadémiai Kiadó, Budapest (1987).
  • [14] S. Kuntze, L. Zöttl. Auf Aufgaben bezogene Überzeugungen und übergreifende Beliefs von Lehramtsstudierenden, Beiträge zum Mathematikunterricht, (2007).
  • [15] K. Maaß. How can teachers’ belief affect their professional development? ZDM (43) (2011) 573–586.
  • [16] K. Maaß, J. Gurlitt. Designing a Teacher-Questionnaire to Evaluate Professional Development about Modelling, Conference-Volume der CERME, (2009), Lyon.
  • [17] F. M. Pajares. Teachers‘ Belief and Educational Research: Cleaning up a Messy Construct. Review of Educational Research, 62(3), (1992) 307–332.
  • [18] V. Richardson. The Role of Attitudes and Beliefs in Learning to Teach, In. J. Sikula (Ed.).Handbook of research on teacher education;second edition, New York: Macmillan. (1996) 102–119
  • [19] L. Shulman. Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), (1986) 4 -14.
  • [20] P. Szebenyi (Ed.). Az általános iskolai nevelés és oktatás terve 1978, [Mathematics syllabus for primary school, 1978], Országos Pedagógiai Intézet, Budapest, (1978).
  • [21] J. Szendrei. In memory of Tamás Varga (2007) http://www.cieaem.org/?q=system/files/varga.pdf
  • [22] A. G. Thompson. Teachers’ beliefs and conceptions: a synthesis of the research Handbook of research on mathematics teaching and learning, A. Douglas (Ed.) Grouws, Macmillan Publishing Company, (1992) 127–146.
  • [23] G. Törner. Mathematical beliefs – A search for a Common Ground. In. Leder G., E. Pehkonen, G. Törner (Eds.) Beliefs: A Hidden variable in Mathematics Education? Dordrecht: Kluwer. (2002) 73 – 94.
  • [24] T. Varga. Mathematics Education in Hungary Today, Educational Studies in Mathematics 19 (1988), 291–298.
  • [25] T. Varga, M. Dumon. Combinatoire Statistiques et Probabilités de 6 á 14 ans. Fiches de travail. Guide at Commentaires. O.C.D.L. Paris (1973).
  • [26] T. Varga. Combinatorics and probability for young children, I. Sherbrooke Mathematics Project. Canada, University of Sherbrooke, (1967).
  • [27] T. Varga. Notes on mathematics reform in Hungarian schools. Pilot work in Budapest. Higher mathematics in lower grades. Prepubescent Mathematical Learning. New York, London, Paris, Gordon and Breach Science Publishers, (1969).
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Bibliografia
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