On Students' Understanding of Implicit Differentiation based on APOS Theory

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10476332" target="_blank" >RIV/00216208:11320/20:10476332 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xkm-qkqo-Z" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xkm-qkqo-Z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10649-020-09991-y" target="_blank" >10.1007/s10649-020-09991-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Students' Understanding of Implicit Differentiation based on APOS Theory

Popis výsledku v původním jazyce

The Action-Process-Object-Schema (APOS) theory is applied to study student understanding of implicit differentiation in the context of functions of one variable. The APOS notions of Schema and schema development in terms of the intra-, inter-, and trans-triad are used to analyze semi-structured interviews with 25 students who had just finished taking a single-variable calculus course. Results suggest that the notions of chain rule and implicit function play a key role in the possibility of attaining implicit differentiation Schema coherence. For this, students need to construct at least a Process conception of implicit function and a chain rule Schema with coherence given by function composition. Students also need to construct relations between implicit function and each one of three components of the implicit differentiation Schema: explicit function, derivative, and differentiation rules. The study shows that students taking an introductory calculus course can be expected to have difficulty understanding the main ideas of implicit differentiation unless special activities are designed to help them make the necessary connections between components of the implicit differentiation Schema. The study suggests the need to further investigate the implementation of activities that foster the constructions proposed, in textbooks and classrooms.

Název v anglickém jazyce

On Students' Understanding of Implicit Differentiation based on APOS Theory

Popis výsledku anglicky

The Action-Process-Object-Schema (APOS) theory is applied to study student understanding of implicit differentiation in the context of functions of one variable. The APOS notions of Schema and schema development in terms of the intra-, inter-, and trans-triad are used to analyze semi-structured interviews with 25 students who had just finished taking a single-variable calculus course. Results suggest that the notions of chain rule and implicit function play a key role in the possibility of attaining implicit differentiation Schema coherence. For this, students need to construct at least a Process conception of implicit function and a chain rule Schema with coherence given by function composition. Students also need to construct relations between implicit function and each one of three components of the implicit differentiation Schema: explicit function, derivative, and differentiation rules. The study shows that students taking an introductory calculus course can be expected to have difficulty understanding the main ideas of implicit differentiation unless special activities are designed to help them make the necessary connections between components of the implicit differentiation Schema. The study suggests the need to further investigate the implementation of activities that foster the constructions proposed, in textbooks and classrooms.

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

2020

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

2020

Číslo periodika v rámci svazku

0013-1954

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

17

Strana od-do

163-179

Kód UT WoS článku

000578460100001

EID výsledku v databázi Scopus

2-s2.0-85092383152