Relating the different derivatives in the development of the Geometric Differential Calculus 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%2F25%3A10504209" target="_blank" >RIV/00216208:11320/25:10504209 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Fiw0Mrx7Fj" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Fiw0Mrx7Fj</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11858-025-01728-6" target="_blank" >10.1007/s11858-025-01728-6</a>
Alternative languages
Result language
angličtina
Original language name
Relating the different derivatives in the development of the Geometric Differential Calculus Schema for two-variable functions
Original language description
This study examines students' construction of relations among the different concepts related to the rate of change of two-variable functions. It uses the notions of Schema and Schema development from APOS theory to analyze students' constructed relations between different components of the Geometric Differential Calculus Schema after they conclude a multivariable calculus course using APOS theory's didactic methodology. The course emphasized the tangent plane at a point on a surface to give meaning to the different concepts associated with function change. Results obtained contribute to research on the teaching and learning of the differential calculus of two-variable functions. This study contributes to the state of knowledge by showing how students construct relations between the tangent plane and the different derivatives defined for these functions. It also contributes to the state of knowledge by showing how using different representations helps students understand the various approaches to rates of change in this type of function. Findings inform about relations between Schema components that students can establish, those they have difficulty constructing, and about didactic strategies to help university students construct a deeper understanding of change in multivariable calculus functions.
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
2025
Confidentiality
U - Předmět řešení projektu je utajovanou skutečností podle zvláštních právních předpisů nebo je skutečností, jejíž zveřejnění by mohlo ohrozit činnost zpravodajské služby. Údaje o projektu jsou upraveny tak, aby byly zveřejnitelné
Data specific for result type
Name of the periodical
ZDM - International Journal on Mathematics Education
ISSN
1863-9690
e-ISSN
1863-9704
Volume of the periodical
2025
Issue of the periodical within the volume
1863-9690
Country of publishing house
DE - GERMANY
Number of pages
14
Pages from-to
1-14
UT code for WoS article
001555874300001
EID of the result in the Scopus database
2-s2.0-105013758764