The role of topology in the construction of students' optimization schema for two-variable functions

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The role of topology in the construction of students' optimization schema for two-variable functions

Popis výsledku v původním jazyce

This study uses Action-Process-Object-Schema theory (APOS) to examine students&apos; 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&apos; 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&apos; learning.

Název v anglickém jazyce

The role of topology in the construction of students' optimization schema for two-variable functions

Popis výsledku anglicky

This study uses Action-Process-Object-Schema theory (APOS) to examine students&apos; 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&apos; 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&apos; learning.

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

Journal of Mathematical Behavior

ISSN

0732-3123

e-ISSN

1873-8028

Svazek periodika

2023

Číslo periodika v rámci svazku

0732-3123

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

20

Strana od-do

1-20

Kód UT WoS článku

001128643100001

EID výsledku v databázi Scopus

2-s2.0-85178162946