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Pregled bibliografske jedinice broj: 1042501

Asymptotes and Asymptotic Behaviour in Graphing Functions and Curves: an Analysis of the Croatian Upper Secondary Education Within the Anthropological Theory of the Didactic


Čižmešija, Aleksandra; Katalenić, Ana; Milin- Šipuš, Željka
Asymptotes and Asymptotic Behaviour in Graphing Functions and Curves: an Analysis of the Croatian Upper Secondary Education Within the Anthropological Theory of the Didactic // International Journal of Science and Mathematics Education, 18 (2020), 1185-1205 doi:.org/10.1007/s10763-019-10020-5 (međunarodna recenzija, članak, znanstveni)


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Naslov
Asymptotes and Asymptotic Behaviour in Graphing Functions and Curves: an Analysis of the Croatian Upper Secondary Education Within the Anthropological Theory of the Didactic

Autori
Čižmešija, Aleksandra ; Katalenić, Ana ; Milin- Šipuš, Željka

Izvornik
International Journal of Science and Mathematics Education (1571-0068) 18 (2020); 1185-1205

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Asymptotes and asymptotic behaviour ; Anthropological Theory of the Didactic (ATD) ; Didactic transposition ; Function graph ; Secondary mathematics education

Sažetak
In this paper, we will examine the mathematical knowledge that prospective mathematics teachers draw upon when graphing function graphs and curves, with a special focus on the occurrence of asymptotes. Three tasks which involved a graph of a rational and exponential function and a hyperbola as a conic section were designed and administered to students. We performed this study within the framework of Anthropological Theory of the Didactic to examine the relationship of prospective mathematics teachers’ available knowledge with the knowledge to be taught in upper secondary schools and scholarly knowledge relevant for teaching. By studying prospective mathematics teachers’ knowledge, we aim to understand the feasibility of our proposed reference epistemological model for graphing functions and curves in the upper secondary school. Our findings reveal students’ shortcomings with respect to the choice of the appropriate graphing praxeology for given tasks. Students’ graphing strategies relied mostly on plotting points obtained by evaluating a formula, which is a dominant approach in the textbooks we analysed. Plotting points did not lead students to examine asymptotic behaviour, along with the observed monotonicity of a function. Their graphing strategies were found to be predominantly dependent on the particular setting in which the task was presented. Additionally, in our study, the idea of an asymptote as a tangent line at infinity in the geometric setting was questioned.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Obrazovne znanosti (psihologija odgoja i obrazovanja, sociologija obrazovanja, politologija obrazovanja, ekonomika obrazovanja, antropologija obrazovanja, neuroznanost i rano učenje, pedagoške discipline)



POVEZANOST RADA


Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb,
Fakultet za odgojne i obrazovne znanosti, Osijek

Citiraj ovu publikaciju

Čižmešija, Aleksandra; Katalenić, Ana; Milin- Šipuš, Željka
Asymptotes and Asymptotic Behaviour in Graphing Functions and Curves: an Analysis of the Croatian Upper Secondary Education Within the Anthropological Theory of the Didactic // International Journal of Science and Mathematics Education, 18 (2020), 1185-1205 doi:.org/10.1007/s10763-019-10020-5 (međunarodna recenzija, članak, znanstveni)
Čižmešija, A., Katalenić, A. & Milin- Šipuš, Ž. (2020) Asymptotes and Asymptotic Behaviour in Graphing Functions and Curves: an Analysis of the Croatian Upper Secondary Education Within the Anthropological Theory of the Didactic. International Journal of Science and Mathematics Education, 18, 1185-1205 doi:.org/10.1007/s10763-019-10020-5.
@article{article, year = {2020}, pages = {1185-1205}, DOI = {doi.org/10.1007/s10763-019-10020-5}, keywords = {Asymptotes and asymptotic behaviour, Anthropological Theory of the Didactic (ATD), Didactic transposition, Function graph, Secondary mathematics education}, journal = {International Journal of Science and Mathematics Education}, doi = {doi.org/10.1007/s10763-019-10020-5}, volume = {18}, issn = {1571-0068}, title = {Asymptotes and Asymptotic Behaviour in Graphing Functions and Curves: an Analysis of the Croatian Upper Secondary Education Within the Anthropological Theory of the Didactic}, keyword = {Asymptotes and asymptotic behaviour, Anthropological Theory of the Didactic (ATD), Didactic transposition, Function graph, Secondary mathematics education} }
@article{article, year = {2020}, pages = {1185-1205}, DOI = {doi.org/10.1007/s10763-019-10020-5}, keywords = {Asymptotes and asymptotic behaviour, Anthropological Theory of the Didactic (ATD), Didactic transposition, Function graph, Secondary mathematics education}, journal = {International Journal of Science and Mathematics Education}, doi = {doi.org/10.1007/s10763-019-10020-5}, volume = {18}, issn = {1571-0068}, title = {Asymptotes and Asymptotic Behaviour in Graphing Functions and Curves: an Analysis of the Croatian Upper Secondary Education Within the Anthropological Theory of the Didactic}, keyword = {Asymptotes and asymptotic behaviour, Anthropological Theory of the Didactic (ATD), Didactic transposition, Function graph, Secondary mathematics education} }

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Social Science Citation Index (SSCI)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


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