Aktuální změny v primárním vzdělávání: Problematika „odlišnosti“ ve třídě při výuce matematiky na prvním stupni základní školy
DOI:
https://doi.org/10.14712/23362189.2020.1668Abstrakt
V podmínkách, kdy se naše společnost transformuje na multikulturní, chceme v tomto příspěvku zkoumat situace v hodinách matematiky ve třídě, kde koexistuje respekt a odmítnutí „odlišnosti“. V případové studii sledujeme dvě skupiny žáků 4. ročníku při řešení úlohy cílené na zobecnění matematického vztahu. Zkoumáme, jak interakce mezi členy skupin odráží dvě strany stejné mince, kterou je kultura třídy, a zároveň jak odráží změny ve třídě, které vyžadují otevřenost a upřímný respekt k „odlišnosti“. Na jedné straně předvedeme dynamiku souznění, které bylo patrné mezi členy jedné ze skupin, protože „odlišnost“ nebyla překážkou, ale naopak byla zdrojem matematických myšlenek, které přispěly k řešení. Na druhé straně ukážeme, jak nedostatek otevřenosti u druhé skupiny vedl k promarnění dobrých příležitostí pro „dělání matematiky“ a k ohrožení sebevědomí jednoho z jejích členů.
Klíčová slova: rozmanitost ve třídě a konflikt, matematika v multikulturní třídě, spolupráce na řešení problémů
Reference
Adler, J. (2001). Teaching mathematics in multilingual classrooms. Dordrecht: Kluwer.
Alrø, H., & Skovsmose, O. (2002). Dialogue and learning in mathematics education: intention, reflection, critique. Dordrecht: Kluwer.
Alrø, H., Skovsmose, O., & Valero, P. (2003). Communication, conflict and mathematics education in the multicultural classroom. In M. A. Mariotti (Ed.), Proceedings of the Third Conference of the European Society for Research in Mathematics Education. Bellaria: Pisa University. Retrieved from https://www.mathematik.uni-dortmund.de
Alrø, H., Skovsmose, O., & Valero, P. (2005). Culture, diversity and conflict in landscapes of mathematics learning. In M. Bosch (Ed.), Proceedings of CERME4 (pp. 1141-1151). Sant Feliu de Guixols: Universitat Ramon Llull.
Alrø, H., Skovsmose, O., & Valero, P. (2009). Researching multicultural mathematics classroom through the lens of landscapes of learning. Nordic Research in Mathematics Education, 13(2), 329-336.
https://doi.org/10.1163/9789087907839_049
Alrø, H., Skovsmose, O., Valero, P. (2010). A learning landscape: Building perspectives on mathematics learning in multicultural classrooms. In B. Sriraman et al. (Eds.), The sourcebook on Nordic research in mathematics education (pp. 651-669). Greenwich: IAP.
Ayala-Altamirano, C., & Molina, M. (2020). Meanings attributed to letters in functional contexts by primary school pupils. International Journal of Science and Mathematics Education, 18(7), 1271-1291.
https://doi.org/10.1007/s10763-019-10012-5
Bishop, A. J. (2001). The transition experience of immigrant secondary school pupils: dilemmas and decisions. In G. de Abreu, A. J. Bishop, & N. C. Presmeg (Eds.), Transitions between contexts of mathematical practices (pp. 53-79). Dordrecht: Kluwer.
https://doi.org/10.1007/0-306-47674-6_4
Bishop, A., & Kalogeropoulos, P. (2015). (Dis)engagement and exclusion in mathematics classrooms - values, labelling and stereotyping. In A. Bishop, H. Tan, & T. Barkatsas (Eds.), Diversity in mathematics education. Towards inclusive practices (pp. 193-218). New York: Springer.
https://doi.org/10.1007/978-3-319-05978-5_12
PMid:26306705 PMCid:PMC4550077
Blanton, M. L. & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412-446.
Blanton, M., Levi, L., Crites, T., & Dougherty, B. J. (2011). Developing essential understandings of algebraic thinking for teaching mathematics in grades 3-5. In B. J. Dougherty & R. M. Zbiek (Eds.), Essential understandings series. Reston, VA: National Council of Teachers of Mathematics.
Denzin, N. K., & Lincoln, Y. S. (1998). Strategies of qualitative inquiry. Thousand Oaks, CA: Sage.
Ferguson, S. (2009). Same task, different paths: Catering for pupil diversity in the mathematics classroom. Australian Primary Mathematics Classroom, 14(2), 32-36.
Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34, 906-911.
https://doi.org/10.1037/0003-066X.34.10.906
Gorgorió, N., & Planas, N. (2005). Cultural distance and identities-in-construction within the multicultural mathematics classroom. ZDM Mathematics Education, 37(2), 64-71.
https://doi.org/10.1007/BF02655715
Gorgorió, N., Planas, N., & Vilella, X. (2002). Immigrant children learning mathematics in mainstream schools. In G. de Abreu et al. (Eds.), Transitions between contexts of mathematical practices (pp. 23-52). Dordrecht: Kluwer.
https://doi.org/10.1007/0-306-47674-6_3
Hatano, G. (1993). Time to merge Vygotskian and constructivist conceptions of knowledge acquisition. In E. A. Forman, N. Minick, & C. A. Stone (Eds.), Contexts for learning: Sociocultural dynamics in children's development (pp. 153-166). New York: Oxford University Press.
Hejný, M. (2012). Exploring the cognitive dimension of teaching mathematics through scheme-oriented approach to education. Orbis Scholae, 6(2), 41-55.
https://doi.org/10.14712/23363177.2015.39
Herzig, A. (2005). Goals for achieving diversity in mathematics classrooms. Mathematics Teacher, 99(4), 253-259.
https://doi.org/10.5951/MT.99.4.0253
Ing, M., Webb, N. M., Franke, M. L., Turrou, A. C., Wong, J., Shin, N., & Fernandez, C. H.
(2015). Pupil participation in elementary mathematics classrooms: the missing link between teacher practices and pupil achievement? Educational Studies in Mathematics, 90(3), 341-356.
https://doi.org/10.1007/s10649-015-9625-z
Kaiser, G. (2003). Learning mathematics within the context of linguistic and cultural
diversity - an empirical study. In M. A. Mariotti (Ed.), Proceedings of CERME 3, Bellaria.
Retrieved from https://www.mathematik.uni-dortmund.de/
Kostelecká, Y., Hána, D., & Hasman, J. (2017). Integrace žáků-cizinců v širším kontextu [Integration of pupils-foreigners in a wider context]. Praha: Charles University, Faculty of Education.
López Centella, E. (2019). Functional thinking of third grade pupils: a study from early algebra
framework. In J. Novotná & H. Moraová (Eds.), Proceedings of SEMT19 (pp. 251-261). Praha: Charles University.
Mayring, P. (2014). Qualitative content analysis: Theoretical foundation, basic procedures and software solution. Klangenfurt: Beltz.
https://doi.org/10.1007/978-94-017-9181-6_13
Møller, J. (2001). Identitet og kodevekslen hos unge tosprogede med dansk-tyrkisk baggrund [Identity and code exchange among bilingual young people with a Danish-Turkish background]. Kopenhagen: Danish School of Education.
Montague, M. (1992). The effects of cognitive and metacognitive strategy instruction on mathematical problem solving of middle school pupils with learning disabilities. Journal of Learning Disabilities, 25, 230-248.
https://doi.org/10.1177/002221949202500404
PMid:1573333
Rámcový vzdělávací program pro základní vzdělávání [Framework educational programme for basic education]. (2017). Praha: Ministry of Education, Youth, and Sports. Retrieved from www.nuv.cz/t/rvp-pro-zakladni-vzdelavani
Riskowski, J. L., & Olbright, G. (2010). Pupil views of diversity through a multicultural mathematics activity: Viewing transformation during the middle school years. Multicultural Education, 17(2), 2-12.
Roos, E. (2019). Inclusion in mathematics education: an ideology, a way of teaching, or both? Educational Studies in Mathematics, 100(1), 25-41.
https://doi.org/10.1007/s10649-018-9854-z
Schmidt, M. C. S. (2016). Inclusion in mathematics education: an ideology, a way of teaching, or both? Cursiv, 18, 81-105.
Seah, W. T., & Andersson, A. (2015). Valuing diversity in mathematics pedagogy through the volitional nature and alignment of values. In A. Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education: Towards inclusive practices (pp. 167-184). Cham: Springer.
https://doi.org/10.1007/978-3-319-05978-5_10
Šíp, R. (2019). Proč školství a jeho aktéři selhávají. Kognitivní krajiny a nacionalismus [Why education and its actors are failing. Cognitive landscapes and nationalism]. Brno: Masaryk University.
https://doi.org/10.5817/CZ.MUNI.M210-9378-2019
Vithal, R. (2003). In search of a pedagogy of conflict and dialogue for mathematics education. Dordrecht: Kluwer.
https://doi.org/10.1007/978-94-010-0086-4
Vithal, R., & Valero, P. (2003). Researching mathematics education in situations of social and political conflict. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 545-593). Dordrecht: Kluwer.
https://doi.org/10.1007/978-94-010-0273-8_19
Wilson, L. S. (1992). The benefits of diversity in the science and engineering work force. In M. L. Matyas & L. S. Dix (Eds.), Science and engineering programs: On target for women? (pp. 1-14). Washington, DC: National Academy Press.
