Badatelsky orientovaná výuka matematiky na 1. stupni základního vzdělávání

Inquiry-based education means that the teacher in the classroom creates the conditions for pupils to inquire independently a part of knowledge which they are supposed to learn. This study is based on an analysis of several lessons of inquiry based mathematics education in primary classrooms, and its aim is to identify phenomena which characterize this culture of education and cause difficulties in its implementation. Problems used in our experiments had the character of (a) reviving the preconceptions of mathematical concepts that students know from everyday life, (b) using the already learned knowledge in new contexts. As an incentive for pupils’ inquiry was also used simulated incorrect solution. The process of inquiry in the classroom hinted at problems (a) with the formulation of learning objectives relevant to the valid curriculum, (b) with the management of pupils’ experiments designed to accomplish these objectives, (c) with respecting the individual differences of pupils. Implementation differed mainly according the level of autonomy the teacher allowed students, the teacher’s ability to cope with ambiguity and uncertainty, which appeared in a dialogue with the pupils, and a deeper insight into the structure of mathematics.

1. Artigue, M., & Baptist, P. (2012). Inquiry in mathematics education (resources for implementing inquiry in science and in mathematics at school). Dostupné z http://fibonacci.uni-bayreuth.de/resources/resources-for-implementing-inquiry.html

2. Artigue, M., Baptist, P., Dillon, J., Harlen, W., & Lena, P. (2011). Learning through inquiry: The Fibonacci project resources. Dostupné z http://fibonacci.uni-bayreuth.de/resources/resources-for-implementing-inquiry.html

3. Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM Mathematics Education, 45(6), 797−810. CrossRef

4. Brousseau, G. (1997). Theory of Didactical Situations in Mathematics. Kluwer academic publishers. Brousseau, G., & Novotná, J. (Eds.). (2012). Úvod do teorie didaktických situací v matematice. Praha: PedF UK.

5. Dabell, J., Keogh, B., & Naylor, S. (2008). Concept cartoons in mathematics education. Sandbach: Millgate House Education.

6. Dorier, J.-L., & Maass, K. (2014). Inquiry-based mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (s. 300−304). Dordrecht: Springer. CrossRef

7. Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht: Kluwer.

8. Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155−177. CrossRef

9. Gray, E. M., & Tall, D. O. (1994). Duality, ambiguity and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 25(2), 115−141. CrossRef

10. Hejný, M. (1999). Procept. In Zborník bratislavského seminára z teórie vyučovania matematiky (s. 40−61). Bratislava: MFF UK.

11. Hejný, M. (2004). Chyba jako prvek edukační strategie učitele. In M. Hejný, J. Novotná, & N. Stehlíková (Eds.), Dvacet pět kapitol z didaktiky matematiky, sv. 1. (s. 63−80). Praha: PedF UK.

12. Hejný, M. (2014). Vyučování matematice orientované na budování schémat: Aritmetika 1. stupně. Praha: PedF UK.

13. Janík, T. (2013). Od reformy kurikula k produktivní kultuře vyučování a učení. Pedagogická orientace, 23(5), 634−663. Dostupné z https://journals.muni.cz/pedor/article/view/1108 CrossRef

14. Polya, G. (1945). How to solve it. New Jersey: Princeton University Press.

15. Ropohl, M., Rönnebeck, S., Bernholt, S., & Köller, O. (2013). A definition of inquiry-based STM education and tools for measuring the degree of IBE (no. D2.5). Dostupné z http://pure.ipn.uni-kiel.de/portal/en/publications/a-definition-of-inquirybased-stm-education-and-tools-for-measuring-the-degree-of-ibe(4b4996b3-baa9-415e-9716-baad6618fd4e).html

16. Samková, L., Hošpesová, A., Roubíček, F., & Tichá, M. (2015). Badatelsky orientované vyučování matematice. Scientia in educatione, 6(1), 91−122. Dostupné z http://www.scied.cz/index.php/scied/article/viewFile/154/145

17. Schoenfeld, A. H., & Kilpatrick, J. (2013). A US perspective on the implementation of inquiry-based learning in mathematics. ZDM − The International Journal on Mathematics Education. Advance online publication. Dostupné z http://link.springer.com/journal/11858 CrossRef

18. Steinbring, H. (2006). What makes a sign a mathematical sign?: An epistemological perspective on mathematical interaction. Educational Studies in Mathematics, 61(1−2), 133−162. Dostupné z http://link.springer.com/10.1007/s10649-006-5892-z CrossRef

19. Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York: Free Press.

20. Van den Heuvel-Panhuizen, M. (Ed). (2008). Children learn mathematics: A learning-teaching trajectory with intermediate attainment targets for calculation with whole numbers in primary school. Rotterdam: Sense Publishers.

21. Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (s. 521−525). Dordrecht: Springer. CrossRef