University Students' Understanding of Directional Derivative: An APOS Analysis
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475802" target="_blank" >RIV/00216208:11320/23:10475802 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=gssnCwT.9q" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=gssnCwT.9q</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40753-023-00225-z" target="_blank" >10.1007/s40753-023-00225-z</a>
Alternative languages
Result language
angličtina
Original language name
University Students' Understanding of Directional Derivative: An APOS Analysis
Original language description
This study reports the second research cycle on students' understanding of directional derivatives of two-variable functions. We applied Action-Process-Object-Schema (APOS) Theory as theoretical framework as in the first cycle. As a result of the first research cycle, a refined genetic decomposition describing the constructions that students may do to understand directional derivatives was proposed. Following the first cycle, we used the genetic decomposition to design didactical materials (a set of activities) to help students do the proposed constructions. The APOS theory pedagogical strategy, the ACE cycle, consisting of work on the activities in collaborative groups of three or four students, followed by whole class discussion and take-home exercises, was implemented in the classroom. In this study, we empirically test the genetic decomposition and the activity set resulting from the first research cycle by performing semi-structured interviews with a group of eleven students to see whether the GD as a model and the activity set were effective, needed to be refined, or to be rejected. We validated the genetic decomposition by showing that the didactical materials and the pedagogical method were productive and supported students' construction of directional derivatives. Some aspects in which students' understanding can be further improved are discussed.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
50301 - Education, general; including training, pedagogy, didactics [and education systems]
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Research in Undergraduate Mathematics Education
ISSN
2198-9745
e-ISSN
2198-9753
Volume of the periodical
2023
Issue of the periodical within the volume
2198-9745
Country of publishing house
DE - GERMANY
Number of pages
30
Pages from-to
1-30
UT code for WoS article
001075556700001
EID of the result in the Scopus database
2-s2.0-85172996802