On Students' Understanding of Implicit Differentiation based on APOS Theory
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10476332" target="_blank" >RIV/00216208:11320/20:10476332 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xkm-qkqo-Z" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xkm-qkqo-Z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10649-020-09991-y" target="_blank" >10.1007/s10649-020-09991-y</a>
Alternative languages
Result language
angličtina
Original language name
On Students' Understanding of Implicit Differentiation based on APOS Theory
Original language description
The Action-Process-Object-Schema (APOS) theory is applied to study student understanding of implicit differentiation in the context of functions of one variable. The APOS notions of Schema and schema development in terms of the intra-, inter-, and trans-triad are used to analyze semi-structured interviews with 25 students who had just finished taking a single-variable calculus course. Results suggest that the notions of chain rule and implicit function play a key role in the possibility of attaining implicit differentiation Schema coherence. For this, students need to construct at least a Process conception of implicit function and a chain rule Schema with coherence given by function composition. Students also need to construct relations between implicit function and each one of three components of the implicit differentiation Schema: explicit function, derivative, and differentiation rules. The study shows that students taking an introductory calculus course can be expected to have difficulty understanding the main ideas of implicit differentiation unless special activities are designed to help them make the necessary connections between components of the implicit differentiation Schema. The study suggests the need to further investigate the implementation of activities that foster the constructions proposed, in textbooks and classrooms.
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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Educational Studies in Mathematics
ISSN
0013-1954
e-ISSN
1573-0816
Volume of the periodical
2020
Issue of the periodical within the volume
0013-1954
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
17
Pages from-to
163-179
UT code for WoS article
000578460100001
EID of the result in the Scopus database
2-s2.0-85092383152