Students’ understanding of Riemann sums for integrals of functions of two variables

Martínez-Planell, Rafael; Trigueros, María

doi:10.1016/j.jmathb.2020.100791

Cited by 10 publications

(2 citation statements)

References 23 publications

(5 reference statements)

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“…The analysis of the data and evidence gathered from the students' responses were useful in reviewing and refining the corresponding elements of the GD (Martínez-Planell & Trigueros, 2020). We have designed teaching activities that will soon be applied in the classroom to begin a second research cycle on the integration of bivariate functions.…”

Section: On Students' Ideas About Integral Calculusmentioning

confidence: 99%

The need for reconstruction: students’ learning of the calculus of bivariate functions

Gaismán

Martínez-Planell

2022

epiDEMES

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This article presents a review of our research on students’ understanding of the calculus of bivariatefunctions. It summarizes findings from studies conducted during 15 years of research on the topic with the aim ofdisseminating our overall results in an accessible format. The results discussed underscore the new challenges thatstudents face when dealing with this new type of function and suggest that the belief that students can easily generalizefrom their knowledge of one-variable functions is not sustained by research, so the different foundational notionsnecessary for the context of bivariate functions need to be considered explicitly during instruction. We include researchbased suggestions that have practical value for teaching these functions, and update the state of research in thisimportant area of the didactics of mathematics, which makes the need for further research apparent. . Une revue de nos recherches sur la compréhension par les étudiants du calcul des fonctions bivariées estprésentée. Il résume les résultats des études menées tout au long de 15 ans d'activités de recherche sur le sujet. Sonobjectif est de communiquer nos résultats de recherche dans leur ensemble de manière accessible. Les résultats dontnous discutons soulignent les nouveaux défis que les étudiants rencontrent lorsqu'ils traitent ce nouveau type defonction, et suggèrent que la croyance selon laquelle les étudiants peuvent facilement généraliser à partir de leurconnaissance des fonctions à une variable, n’est pas soutenue par la recherche, de sorte que différentes notionsfondamentales qui sont nécessaires dans le contexte des fonctions bivariées, doivent donc être explicitement prises encompte lors de l'enseignement. Nous incluons la présentation de suggestions, fondées sur la recherche, qui ont unevaleur pratique pour l'enseignement des fonctions bivariées et peuvent éclairer l'état de la recherche dans ce domaineimportant de la didactique des mathématiques, ce qui rend évident la nécessité de poursuivre des recherches.

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Section: On Students' Ideas About Integral Calculusmentioning

confidence: 99%

The need for reconstruction: students’ learning of the calculus of bivariate functions

Gaismán

Martínez-Planell

2022

epiDEMES

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“…Common errors, persistent misconceptions and misunderstandings should be identified to inform and improve the teaching and learning of mathematics to facilitate student success. While researchers have documented students' understanding of various concepts in single variable calculus such as on difficulties and errors made by students in the topic of limits and integration [5,6], fewer studies exist about their understanding of multivariable calculus concepts making a case for this research study [3]. Double integration is a fundamental concept in many engineering applications and widely used in courses across the engineering disciplines.…”

Section: Introductionmentioning

confidence: 99%

Students’understanding of double integrals - implications for the engineering curriculum

Khemane¹,

Padayachee²,

Shaw³

2022

Towards a New Future in Engineering Education, New Scenarios That European Alliances of Tech Universities Open Up

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Mathematics plays a significant role in engineering students' education. To undergraduate engineering students, calculus concepts are foundational to their engineering courses. One such concept is the double integral. It is thus important to ensure that students not only learn this concept but also engage to understand it and are able to apply this knowledge in relevant engineering courses. This research paper focuses on the following two components: Firstly, the relevance of double integrals to the engineering curriculum. And secondly, students’ understanding of the double integral concept. We present the relevance of double integrals in the engineering curriculum by looking at the use of this concept in different engineering fields. We explored students’ understanding of double integrals and administered a test to 35 second year engineering students enrolled in an undergraduate Calculus III course. In a qualitative study, the performance of students was used to analyse the type of misconceptions they have in double integration. The findings reveal that the students encounter difficulties with graphical representation of surfaces and region of integration. In addition, students struggle with changing the order of integration and performing the integration process. While some of these errors are conceptual, others are really due to carelessness in the procedure.

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Multivariable calculus results in different countries

Martínez-Planell

Trigueros

2021

ZDM Mathematics Education

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Students’ understanding of Riemann sums for integrals of functions of two variables

Cited by 10 publications

References 23 publications

The need for reconstruction: students’ learning of the calculus of bivariate functions

The need for reconstruction: students’ learning of the calculus of bivariate functions

Students’understanding of double integrals - implications for the engineering curriculum

Multivariable calculus results in different countries

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