Relating the different derivatives in the development of the Geometric Differential Calculus Schema for two-variable functions

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Relating the different derivatives in the development of the Geometric Differential Calculus Schema for two-variable functions

Popis výsledku v původním jazyce

This study examines students&apos; 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&apos; constructed relations between different components of the Geometric Differential Calculus Schema after they conclude a multivariable calculus course using APOS theory&apos;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.

Název v anglickém jazyce

Relating the different derivatives in the development of the Geometric Differential Calculus Schema for two-variable functions

Popis výsledku anglicky

This study examines students&apos; 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&apos; constructed relations between different components of the Geometric Differential Calculus Schema after they conclude a multivariable calculus course using APOS theory&apos;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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50301 - Education, general; including training, pedagogy, didactics [and education systems]

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

ZDM - International Journal on Mathematics Education

ISSN

1863-9690

e-ISSN

1863-9704

Svazek periodika

2025

Číslo periodika v rámci svazku

1863-9690

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

14

Strana od-do

1-14

Kód UT WoS článku

001555874300001

EID výsledku v databázi Scopus

2-s2.0-105013758764