The role of topology in the construction of students' optimization schema for two-variable functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475799" target="_blank" >RIV/00216208:11320/23:10475799 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=m7nT8MUOgQ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=m7nT8MUOgQ</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmathb.2023.101106" target="_blank" >10.1016/j.jmathb.2023.101106</a>
Alternative languages
Result language
angličtina
Original language name
The role of topology in the construction of students' optimization schema for two-variable functions
Original language description
This study uses Action-Process-Object-Schema theory (APOS) to examine students' understanding of two-variable function optimization. A genetic decomposition (GD) based on the notion of Schema is proposed. This is a conjecture of mental structures and relations that students may construct to understand the optimization of these functions. The GD was tested with semi-structured interviews with eleven students who had just finished an introductory multivariable calculus course. Results show that giving explicit attention during instruction to the topological structure of the domain of the function to be optimized and the use of GD-based activities was effective in promoting students' understanding of two-variable function optimization. On the theoretical side, the study contributes to a better understanding of the APOS notions of Schema, Schema-triad, and types of relations between Schema components that have not been used extensively in the literature and that proved to be a powerful tool to model students' learning.
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
Journal of Mathematical Behavior
ISSN
0732-3123
e-ISSN
1873-8028
Volume of the periodical
2023
Issue of the periodical within the volume
0732-3123
Country of publishing house
GB - UNITED KINGDOM
Number of pages
20
Pages from-to
1-20
UT code for WoS article
001128643100001
EID of the result in the Scopus database
2-s2.0-85178162946