Žákovské konstrukce poznatků v matematice

Naďa Stehlíková; Michaela Ulrychová

doi:10.14712/18047106.22

Vol. 2 No. 2 (2011): sciED Research Reports

Pupils’ construction of knowledge in mathematics

Naďa Stehlíková, Michaela Ulrychová,

DOI: https://doi.org/10.14712/18047106.22

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Stehlíková, N., & Ulrychová, M. (2020). Pupils’ construction of knowledge in mathematics. Scientia in Educatione, 2(2), 39-58. https://doi.org/10.14712/18047106.22

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Abstract

The article concerns the question of the construction of mathematical knowledge by pupils, namely the mechanism of individual and shared construction of knowledge on the example of re-discovery of Pythagoras’ theorem within square grid paper. The theoretical background of work consists of the theory of generic models and constructivist approaches to the teaching of mathematics. A study was carried out of pupils of an 8-year secondary grammar school, working in groups and solving carefully chosen problems. The data were gathered through participation observation, field notes of the researcher and external observer, pupils’ works and mainly videorecordings. The analysis of data via techniques based on grounded theory is briefly described. The results of the experiment include the characterisation of categories of (relatively) individual and shared constructions of knowledge, including their dimensions. Concrete examples of these constructions are given. The merits and limits of the presented study are summarised and possible questions of further research outlined.

References

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BROUSSEAU, G. Theory of Didactical Situations in Mathematics. Balacheff, N., Cooper, M., Sutherland, R., Warfield, V. (Eds.). Dordrecht : Kluwer Academic Publishers, 1997. Search in Google Scholar
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HERSHKOWITZ, R., SCHWARZ, B., DREYFUS, T. Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32(2), 2001, pp. 195–222. Search in Google Scholar
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JANÍK, T. Akční výzkum jako cesta ke zkvalitňování pedagogické praxe. In MAŇÁK, J., ŠVEC, V. (ed.), Cesty pedagogického výzkumu. Brno : Paido, 2004, s. 51–68. JAWORSKI, B. Investigating Mathematics Teaching. A Constructivist Enquiry. London : The Falmer Press, 1994. Search in Google Scholar
JIROTKOVÁ, D. Cesty ke zkvalitňování výuky geometrie. Praha : PedF UK v Praze, 2010. Search in Google Scholar
MAREŠ, J. Styly učení žáků a studentů. Praha : Portál, 1998. Search in Google Scholar
PESEK, D. D., KIRSHNER, D. Interference of instrumentál instruction in subsequent relations learning. Journal for Research in Mathematics Education, 31(5), 2000, pp. 524–540. Search in Google Scholar
PRŮCHA, J., WALTEROVÁ, E., MAREŠ, J. Pedagogický slovník. Praha : Portál, 1998. Search in Google Scholar
STEHLÍKOVÁ, N. Geometrické transformace analyticky. In HEJNÝ, M., NOVOTNÁ, J., STEHLÍKOVÁ, N. (ed.), Dvacet pět kapitol z didaktiky matematiky. Praha : PedF UK v Praze, sv. 2, 2004a, s. 279–298. Search in Google Scholar
STEHLÍKOVÁ, N. Konstruktivistické přístupy k vyučování matematice. In HEJNÝ, M., NOVOTNÁ, J., STEHLÍKOVÁ, N. (ed.), Dvacet pět kapitol z didaktiky matematiky. Praha : PedF UK, sv. 1, 2004b, s. 11–21. Search in Google Scholar
STEHLÍKOVÁ, N. Structural Understanding in Advanced Mathematical Thinking. Praha : PedF UK v Praze, 2004c. Search in Google Scholar
STEHLÍKOVÁ, N. Charakteristika kultury vyučování matematice z pohledu činnosti učitele. In HOŠPESOVÁ, A., STEHLÍKOVÁ, N., TICHÁ, M. (ed.), Cesty zdokonalování kultury vyučování matematice. České Budějovice : Jihočeská univerzita, 2007, s. 13–48. Search in Google Scholar
STEINBRING, H. The construction of new mathematical knowledge in classroom interaction: An epistemological perspective. USA : Springer, 2005. Search in Google Scholar
STRAUSS, A., CORBINOVÁ, J. Základy kvalitativního výzkumu. Boskovice : Albert, 1999. Search in Google Scholar
ULRYCHOVÁ, M. Konstrukce poznatků žáky v matematice (na příkladu Pythagorovy věty). Disertační práce. Praha : PedF UK v Praze, 2011. Search in Google Scholar

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[1] BREEN, Ch. Mathematics Teachers as Researchers. In BISHOP, A. J. et al. (Eds.), Second International Handbook of Mathematics Education. Dordrecht : Kluwer Academic Publishers, 2003, pp. 523–544. Search in Google Scholar

[2] BROUSSEAU, G. Theory of Didactical Situations in Mathematics. Balacheff, N., Cooper, M., Sutherland, R., Warfield, V. (Eds.). Dordrecht : Kluwer Academic Publishers, 1997. Search in Google Scholar

[3] DAVIS, R., B., MAHER, C., A., NODDINGS, N. Constructivist Views on the Teaching and Learning of Mathematics. USA : National Council of Teachers of Mathematics, 1990. Search in Google Scholar

[4] HANUŠOVÁ, J. Cesty učitele ke konstruktivistickým přístupům. Dizertační práce. Praha : PedF UK v Praze, 2007. Search in Google Scholar

[5] HEJNÝ, M. Mechanizmus poznávacího procesu. In HEJNÝ, M., NOVOTNÁ, J., STEHLÍKOVÁ, N. (ed.), Dvacet pět kapitol z didaktiky matematiky. Praha : PedF UK v Praze, sv. 1, 2004, s. 23–42. Search in Google Scholar

[6] HEJNÝ, M., KUŘINA, F. Dítě, škola a matematika. Praha : Portál, 2001. Search in Google Scholar

[7] HERSHKOWITZ, R., HADAS, N. Abstracting Processes, from Individuals’ Constructing of Knowledge to a Group’s “Shared Knowledge”. Mathematics Education Research Journal, Vol. 19, No. 2, 2007, pp. 41–68. Search in Google Scholar

[8] HERSHKOWITZ, R., SCHWARZ, B., DREYFUS, T. Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32(2), 2001, pp. 195–222. Search in Google Scholar

[9] CHOPIN, M.-P., NOVOTNÁ, J. Contribution of the Theory of Didactical Situations to Mathematics Education: Fundamentals and main concepts. In NOVOTNÁ, J., MORAOVÁ, H. (ed.), Proccedings of SEMT 11. Praha : UK v Praze, PedF, 2011, s. 361–363. Search in Google Scholar

[10] JANÍK, T. Akční výzkum jako cesta ke zkvalitňování pedagogické praxe. In MAŇÁK, J., ŠVEC, V. (ed.), Cesty pedagogického výzkumu. Brno : Paido, 2004, s. 51–68. JAWORSKI, B. Investigating Mathematics Teaching. A Constructivist Enquiry. London : The Falmer Press, 1994. Search in Google Scholar

[11] JIROTKOVÁ, D. Cesty ke zkvalitňování výuky geometrie. Praha : PedF UK v Praze, 2010. Search in Google Scholar

[12] MAREŠ, J. Styly učení žáků a studentů. Praha : Portál, 1998. Search in Google Scholar

[13] PESEK, D. D., KIRSHNER, D. Interference of instrumentál instruction in subsequent relations learning. Journal for Research in Mathematics Education, 31(5), 2000, pp. 524–540. Search in Google Scholar

[14] PRŮCHA, J., WALTEROVÁ, E., MAREŠ, J. Pedagogický slovník. Praha : Portál, 1998. Search in Google Scholar

[15] STEHLÍKOVÁ, N. Geometrické transformace analyticky. In HEJNÝ, M., NOVOTNÁ, J., STEHLÍKOVÁ, N. (ed.), Dvacet pět kapitol z didaktiky matematiky. Praha : PedF UK v Praze, sv. 2, 2004a, s. 279–298. Search in Google Scholar

[16] STEHLÍKOVÁ, N. Konstruktivistické přístupy k vyučování matematice. In HEJNÝ, M., NOVOTNÁ, J., STEHLÍKOVÁ, N. (ed.), Dvacet pět kapitol z didaktiky matematiky. Praha : PedF UK, sv. 1, 2004b, s. 11–21. Search in Google Scholar

[17] STEHLÍKOVÁ, N. Structural Understanding in Advanced Mathematical Thinking. Praha : PedF UK v Praze, 2004c. Search in Google Scholar

[18] STEHLÍKOVÁ, N. Charakteristika kultury vyučování matematice z pohledu činnosti učitele. In HOŠPESOVÁ, A., STEHLÍKOVÁ, N., TICHÁ, M. (ed.), Cesty zdokonalování kultury vyučování matematice. České Budějovice : Jihočeská univerzita, 2007, s. 13–48. Search in Google Scholar

[19] STEINBRING, H. The construction of new mathematical knowledge in classroom interaction: An epistemological perspective. USA : Springer, 2005. Search in Google Scholar

[20] STRAUSS, A., CORBINOVÁ, J. Základy kvalitativního výzkumu. Boskovice : Albert, 1999. Search in Google Scholar

[21] ULRYCHOVÁ, M. Konstrukce poznatků žáky v matematice (na příkladu Pythagorovy věty). Disertační práce. Praha : PedF UK v Praze, 2011. Search in Google Scholar

Scientia in educatione

Pupils’ construction of knowledge in mathematics

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