Geodesic
Grafy funkcí z pohledu žáků a studentů základních, středních a vysokých škol
Učitel matematiky, Tome 25 (2017) no. 3, pp. 129-155 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The article focuses on students' understanding of graphs of functions. Interviews were conducted with 22 students in who solved some tasks on classifications of graphs of functions. For the analysis of data, we used the theory of prototypes and the theory of exemplification and the framework of hypothetical learning trajectories. Some extracts from the interviews are given to illustrate main results. For instance, we observed that students focus on various aspects of the graph (linearity, passing through the origin of the coordinate system, etc.) and mark them as important. As students acquire more experience with graphs of functions, they focus more on the curve of the graph and the importance of aspects changes. Nevertheless, some of them stay strong (real context of the graph) during the whole process and there are important mathematical aspects (as continuity) which are systematically underestimated.
The article focuses on students' understanding of graphs of functions. Interviews were conducted with 22 students in who solved some tasks on classifications of graphs of functions. For the analysis of data, we used the theory of prototypes and the theory of exemplification and the framework of hypothetical learning trajectories. Some extracts from the interviews are given to illustrate main results. For instance, we observed that students focus on various aspects of the graph (linearity, passing through the origin of the coordinate system, etc.) and mark them as important. As students acquire more experience with graphs of functions, they focus more on the curve of the graph and the importance of aspects changes. Nevertheless, some of them stay strong (real context of the graph) during the whole process and there are important mathematical aspects (as continuity) which are systematically underestimated.
Classification : 97C30, 97i99 
@article{UM_2017_25_3_a0,
     author = {Janda, David and Pilous, Derek},
     title = {Grafy funkc{\'\i} z pohledu \v{z}\'ak\r{u} a student\r{u} z\'akladn{\'\i}ch, st\v{r}edn{\'\i}ch a vysok\'ych \v{s}kol},
     journal = {U\v{c}itel matematiky},
     pages = {129--155},
     year = {2017},
     volume = {25},
     number = {3},
     language = {cs},
     url = {http://geodesic.mathdoc.fr/item/UM_2017_25_3_a0/}
}
TY  - JOUR
AU  - Janda, David
AU  - Pilous, Derek
TI  - Grafy funkcí z pohledu žáků a studentů základních, středních a vysokých škol
JO  - Učitel matematiky
PY  - 2017
SP  - 129
EP  - 155
VL  - 25
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UM_2017_25_3_a0/
LA  - cs
ID  - UM_2017_25_3_a0
ER  - 
%0 Journal Article
%A Janda, David
%A Pilous, Derek
%T Grafy funkcí z pohledu žáků a studentů základních, středních a vysokých škol
%J Učitel matematiky
%D 2017
%P 129-155
%V 25
%N 3
%U http://geodesic.mathdoc.fr/item/UM_2017_25_3_a0/
%G cs
%F UM_2017_25_3_a0
Janda, David; Pilous, Derek. Grafy funkcí z pohledu žáků a studentů základních, středních a vysokých škol. Učitel matematiky, Tome 25 (2017) no. 3, pp. 129-155. http://geodesic.mathdoc.fr/item/UM_2017_25_3_a0/

[1] Baroody, A. J., Cibulskis, M., Lai, M., Li, X.: Comments on the use of learning trajectories in curriculum development and research. (2004). Mathematical Thinking and Learning, 6(2), 227-260.

[2] Edwards, C. J.: The historical development of the calculus. (1994). Springer.

[3] Eisenmann, P.: O experimentu se spojitostí funkce na střední škole. (1996). Učitel matematiky, 4(4). 213-219.

[4] Eisenmann, P.: Zlatý vrch nad Českou Kamenicí aneb funkce v přírodě. (2007). Matematika, Fyzika, Informatika, 16(6), 336-338.

[5] Goldstone, R. L.: The role of similarity in categorization: Providing a groundwork. (1994). Cognition, 52(2), 125-157. | DOI

[6] Hejný, M.: Vyučování matematice orientované na budování schémat: aritmetika 1. stupně. (2014). Praha: Univerzita Karlova v Praze, Pedagogická fakulta.

[7] Hejný, M., Kuřina, F.: Dítě, škola a matematika: konstruktivistické přístupy k vyučování. (2001). Praha: Portál.

[8] Hershkowitz, R.: Visualization in Geometry - Two Sides of the Coin. (1989). Focus on learning problems in mathematics, 11, 61-76.

[9] Janda, D. : Funkční myšlení žáků středních škol. (2013). Dostupné z https://is.cuni.cz/webapps/zzp/detail/119283

[10] Kopáčková, A.: Nejen žákovské představy o funkcích. (2002). Pokroky matematiky, fyziky a astronomie, 47(2), 149-161.

[11] Kopáčková, A.: Fylogeneze pojmu funkce. (2001). In J. Bečvář & E. Fuchs, Matematika v proměnách věků II (46-80). Praha: Prometheus.

[12] Lomtatidze, L.: Historický vývoj pojmu křivka. (2007). Brno: Nadace Universitas.

[13] Mervis, C. B., Rosch, E.: Categorization of natural objects. (1981). Annual review of psychology, 32(1), 89-115. | DOI

[14] Odvárko, O., Kadleček, J.: Matematika pro 7. ročník ZŠ (1.-3. díl). (1998). Praha: Prometheus.

[15] Piaget, J.: Epistemology and psychology of functions. (1977). 23. Springer Science & Business Media.

[16] Watson, A., Mason, J.: Mathematics as a constructive activity: Learners generating examples. (2006). Routledge.