Students’ Understanding of Riemann Sums and Double Integrals: The Case of Task Design in APOS Theory

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10490328" target="_blank" >RIV/00216208:11320/24:10490328 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8vi8deql9e" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8vi8deql9e</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s40753-024-00250-6" target="_blank" >10.1007/s40753-024-00250-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Students’ Understanding of Riemann Sums and Double Integrals: The Case of Task Design in APOS Theory

Popis výsledku v původním jazyce

In this study, we investigate students&apos; understanding of the relation between a double integral of a continuous function over a rectangle and the corresponding Riemann sums. To do so, we explore the relation between (1) a proposed model (genetic decomposition) of mental constructions that students may do to understand the relation between Riemann sums and double integrals, (2) tasks designed to help students make these constructions, and (3) the results of semi-structured interviews with eleven students who completed the tasks. We focus on the construction differences between students who engaged in tasks designed according to the genetic decomposition and those in a previously studied lecture-based course. The study aimed to underscore the task&apos;s effect on students&apos; learning in order to refine the genetic decomposition if needed. This study contributes a set of tasks that enable students to relate Riemann sums and double integrals. The results showed that students using the proposed materials in class and a collaborative didactical strategy provided evidence of constructing the structures proposed in the genetic decomposition. The tasks are based on a genetic decomposition, so the study also contributes by showing that it is an effective model to guide instruction. The constructions inferred from students&apos; work are discussed in detail and compared to those proposed in the genetic decomposition and those resulting from previous research.

Název v anglickém jazyce

Students’ Understanding of Riemann Sums and Double Integrals: The Case of Task Design in APOS Theory

Popis výsledku anglicky

In this study, we investigate students&apos; understanding of the relation between a double integral of a continuous function over a rectangle and the corresponding Riemann sums. To do so, we explore the relation between (1) a proposed model (genetic decomposition) of mental constructions that students may do to understand the relation between Riemann sums and double integrals, (2) tasks designed to help students make these constructions, and (3) the results of semi-structured interviews with eleven students who completed the tasks. We focus on the construction differences between students who engaged in tasks designed according to the genetic decomposition and those in a previously studied lecture-based course. The study aimed to underscore the task&apos;s effect on students&apos; learning in order to refine the genetic decomposition if needed. This study contributes a set of tasks that enable students to relate Riemann sums and double integrals. The results showed that students using the proposed materials in class and a collaborative didactical strategy provided evidence of constructing the structures proposed in the genetic decomposition. The tasks are based on a genetic decomposition, so the study also contributes by showing that it is an effective model to guide instruction. The constructions inferred from students&apos; work are discussed in detail and compared to those proposed in the genetic decomposition and those resulting from previous research.

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

2024

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

2024

Číslo periodika v rámci svazku

2198-9745

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

29

Strana od-do

1-29

Kód UT WoS článku

001282061900001

EID výsledku v databázi Scopus

2-s2.0-85200228557