University Students' Understanding of Directional Derivative: An APOS Analysis

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475802" target="_blank" >RIV/00216208:11320/23:10475802 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=gssnCwT.9q" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=gssnCwT.9q</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s40753-023-00225-z" target="_blank" >10.1007/s40753-023-00225-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

University Students' Understanding of Directional Derivative: An APOS Analysis

Popis výsledku v původním jazyce

This study reports the second research cycle on students&apos; understanding of directional derivatives of two-variable functions. We applied Action-Process-Object-Schema (APOS) Theory as theoretical framework as in the first cycle. As a result of the first research cycle, a refined genetic decomposition describing the constructions that students may do to understand directional derivatives was proposed. Following the first cycle, we used the genetic decomposition to design didactical materials (a set of activities) to help students do the proposed constructions. The APOS theory pedagogical strategy, the ACE cycle, consisting of work on the activities in collaborative groups of three or four students, followed by whole class discussion and take-home exercises, was implemented in the classroom. In this study, we empirically test the genetic decomposition and the activity set resulting from the first research cycle by performing semi-structured interviews with a group of eleven students to see whether the GD as a model and the activity set were effective, needed to be refined, or to be rejected. We validated the genetic decomposition by showing that the didactical materials and the pedagogical method were productive and supported students&apos; construction of directional derivatives. Some aspects in which students&apos; understanding can be further improved are discussed.

Název v anglickém jazyce

University Students' Understanding of Directional Derivative: An APOS Analysis

Popis výsledku anglicky

This study reports the second research cycle on students&apos; understanding of directional derivatives of two-variable functions. We applied Action-Process-Object-Schema (APOS) Theory as theoretical framework as in the first cycle. As a result of the first research cycle, a refined genetic decomposition describing the constructions that students may do to understand directional derivatives was proposed. Following the first cycle, we used the genetic decomposition to design didactical materials (a set of activities) to help students do the proposed constructions. The APOS theory pedagogical strategy, the ACE cycle, consisting of work on the activities in collaborative groups of three or four students, followed by whole class discussion and take-home exercises, was implemented in the classroom. In this study, we empirically test the genetic decomposition and the activity set resulting from the first research cycle by performing semi-structured interviews with a group of eleven students to see whether the GD as a model and the activity set were effective, needed to be refined, or to be rejected. We validated the genetic decomposition by showing that the didactical materials and the pedagogical method were productive and supported students&apos; construction of directional derivatives. Some aspects in which students&apos; understanding can be further improved are discussed.

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

International Journal of Research in Undergraduate Mathematics Education

ISSN

2198-9745

e-ISSN

2198-9753

Svazek periodika

2023

Číslo periodika v rámci svazku

2198-9745

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

30

Strana od-do

1-30

Kód UT WoS článku

001075556700001

EID výsledku v databázi Scopus

2-s2.0-85172996802