Students’ geometric understanding of partial derivatives and the locally linear approach

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475897" target="_blank" >RIV/00216208:11320/23:10475897 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=7VLHaEcxx_" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=7VLHaEcxx_</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10649-023-10242-z" target="_blank" >10.1007/s10649-023-10242-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Students’ geometric understanding of partial derivatives and the locally linear approach

Popis výsledku v původním jazyce

We use Action-Process-Object-Schema (APOS) theory to study students&apos; geometric understanding of partial derivatives of functions of two variables. This study contributes to research on the teaching and learning of differential multivariable calculus and its didactics. This is an important area due to its multiple applications in science, mathematics, engineering, and technology (STEM). The study tests a previously proposed model of mental constructions students may use to understand partial derivatives through a set of activities designed to help students make the conjectured constructions. The model is based on the local linearity of differentiable two-variable functions, and the model-based activities explore the relationship between partial derivatives and tangent plane in different representations. We used semi-structured interviews with eleven students whose teacher used the three-part cycle-Activities designed with the genetic decomposition; collaborative work in small groups and Class discussion; and Exercises for home (ACE)-as pedagogical strategy. The model-based activity set based on local linearity and the ACE strategy helped students construct a geometric understanding of partial derivatives. Results led to reconsider and further refine the model. This study also resulted in improving activity sets and obtaining information on students&apos; construction of second-order and mixed partial derivatives.

Název v anglickém jazyce

Students’ geometric understanding of partial derivatives and the locally linear approach

Popis výsledku anglicky

We use Action-Process-Object-Schema (APOS) theory to study students&apos; geometric understanding of partial derivatives of functions of two variables. This study contributes to research on the teaching and learning of differential multivariable calculus and its didactics. This is an important area due to its multiple applications in science, mathematics, engineering, and technology (STEM). The study tests a previously proposed model of mental constructions students may use to understand partial derivatives through a set of activities designed to help students make the conjectured constructions. The model is based on the local linearity of differentiable two-variable functions, and the model-based activities explore the relationship between partial derivatives and tangent plane in different representations. We used semi-structured interviews with eleven students whose teacher used the three-part cycle-Activities designed with the genetic decomposition; collaborative work in small groups and Class discussion; and Exercises for home (ACE)-as pedagogical strategy. The model-based activity set based on local linearity and the ACE strategy helped students construct a geometric understanding of partial derivatives. Results led to reconsider and further refine the model. This study also resulted in improving activity sets and obtaining information on students&apos; construction of second-order and mixed partial derivatives.

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

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Educational Studies in Mathematics

ISSN

0013-1954

e-ISSN

1573-0816

Svazek periodika

2023

Číslo periodika v rámci svazku

0013-1954

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

23

Strana od-do

69-91

Kód UT WoS článku

001010691700001

EID výsledku v databázi Scopus

2-s2.0-85162125748