Where Calculus and Engineering Converge: an Analysis of Curricular Change in Calculus for Engineers

Ellis, Brittney; Larsen, Sean; Voigt, Matthew; Vroom, Kristen

doi:10.1007/s40753-020-00130-9

Cited by 10 publications

(6 citation statements)

References 24 publications

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“…Czocher (2017), for example, reports on a differential equations course for NMPs taught with modelling principles. Regarding tailored calculus courses for engineers, to gain more insight on what can make these courses successful, Ellis et al (2021) analyzed two calculus courses in two US universities. One of the courses was successful while the other was discontinued.…”

Section: Nmps' (Non) Use Of Content and Approaches From Calculus Cour...mentioning

confidence: 99%

“…We still have very little information about adaptations of calculus courses to specific disciplines and the rationales behind these adaptations. Furthermore, more research is needed on what characteristics make calculus courses adapted to specific disciplines successful (e.g., Ellis et al, 2021). Again, we anticipate that joint teams across disciplines will provide important insights towards the design and the evaluation of these courses.…”

Section: Attending To the Scaffolding And Filtering Roles Of Calculus...mentioning

confidence: 99%

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‘Scaffolding’ or ‘Filtering’: A Review of Studies on the Diverse Roles of Calculus Courses for Students, Professionals and Teachers

Biza

González-Martín

Pinto

2022

Int. J. Res. Undergrad. Math. Ed.

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Calculus courses have been attracting the attention of mathematics education researchers over the last decades. Recent publications and special issues dedicated to calculus highlight the diverse roles of calculus courses in the pathways for STEM studies within and across educational levels, as well as issues related to the academic preparation of future STEM professionals, including mathematicians, non-mathematics professionals (NMPs) and teachers. In this paper, we review recent literature, mostly since 2015, to identify and characterize explicit references to such diverse roles of calculus courses. The review highlights an intrinsic tension between two institutional roles of calculus: scaffolding and filtering. We find nuanced yet substantial variation in how the dual role of calculus is experienced and managed across different groups of students and stakeholders. With regard studies on calculus for mathematics students, recent studies attend to changes in the rules underpinning calculus notions and processes, and highlight the scaffolding potential of calculus courses towards abstraction and reasoning. In contrast, studies on calculus for NMPs report that such courses often promote filtering rather than scaffolding and question transferability and relevance of those courses for NMPs. Finally, studies challenge the perception that traditional tertiary calculus courses scaffold school teaching and underline the need for empirical research that would explain the nature of this scaffolding and how it can be realized in practice. We conclude that further empirical research, in particular theory development, is needed to address the diverse roles of calculus at the intersection of institutions, disciplines and communities.

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Section: Nmps' (Non) Use Of Content and Approaches From Calculus Cour...mentioning

confidence: 99%

Section: Attending To the Scaffolding And Filtering Roles Of Calculus...mentioning

confidence: 99%

‘Scaffolding’ or ‘Filtering’: A Review of Studies on the Diverse Roles of Calculus Courses for Students, Professionals and Teachers

Biza

González-Martín

Pinto

2022

Int. J. Res. Undergrad. Math. Ed.

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“…Mathematics, renowned for its pervasive influence, assumes a pivotal role across various domains encompassing science, technology, and everyday applications (Rohmah & Sutiarso, 2018). Particularly, its mastery lays the groundwork for subsequent academic pursuits, notably within natural sciences, engineering, and education (Tasman & Ahmad, 2018;Ayebo et al, 2017;Boz & Adnan, 2017;Rasmussen et al, 2014;Ellis et al, 2021). A proficient understanding of mathematics is paramount, given its fundamental significance in shaping the educational trajectory of learners.…”

Section: Introductionmentioning

confidence: 99%

Error Analysis of Learners’ Problem-Solving Abilities in Mathematics Courses: A Newman Error Analysis (NEA) Approach

Ekasari,

Putra

2024

J. Pendidik. Sains

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This study endeavors to systematically discern the spectrum of learner errors manifesting in problem-solving processes within the domain of mathematics, specifically focusing on the intricacies of integration, utilizing Newman Error Analysis (NEA) as the guiding framework. The cohort under investigation comprises 14 first-year students hailing from the Department of Physics Education at Musamus University, Merauke. Employing a descriptive methodology underscored by a qualitative orientation, this research incorporates tests and interviews as primary instruments for data collection. The tests are designed to meticulously evaluate the array of errors committed by learners, as per the tenets of Newman's model. Additionally, a subset of four participants is selected for in-depth interviews aimed at elucidating the underlying challenges encountered during problem-solving endeavors, which ultimately contribute to the genesis of learner errors. Analysis of the findings underscores the prevalence of comprehension errors, transformation errors, process errors, and encoding errors amongst learners grappling with problems centered on the subtopic of integration.

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“…El papel del cálculo en el desempeño profesional del ingeniero justifica que la mayoría de los programas de ingeniería lo incluyan como asignatura obligatoria, buscando proporcionar a los estudiantes herramientas que utilizarán durante el resto de su formación (Ellis, Larsen, Voigt y Kristeen, 2021;González-Martín, 2021). Así, desde los planes de estudio de ingeniería se insiste en que el ingeniero llegue a "asumir una concepción científica del mundo al interpretar los conceptos del Cálculo Diferencial e Integral", "caracterizar, interpretar, comunicar y aplicar los conceptos y principales resultados de la disciplina, mediante una correcta utilización del lenguaje matemático en sus formas: analítica, gráfica, numérica y verbal, centrando la atención en los modelos matemáticos" y desarrollar la capacidad de razonamiento y de las formas del pensamiento matemático, la comprensión de la demostración de teoremas, la identificación e interpretación de los conceptos matemáticos, la argumentación lógica de propiedades y "la demostración de resultados teóricos sencillos, mediante el empleo de los métodos analíticos, gráficos y/o numéricos" (Ministerio de Educación Superior, 2017, p. 28;2018, p. 54).…”

Section: Introductionunclassified

Significados intuitivos y formales de la integral definida en la formación de ingenieros

García¹,

Burgos²,

Godino³

et al. 2023

Relime

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La integral definida es un concepto central en las aplicaciones del cálculo a las ciencias experimentales e ingeniería por lo que es un tema de investigación didáctica relevante. En este trabajo se analizan los diversos significados de la integral definida aplicando herramientas teóricas del Enfoque ontosemiótico del conocimiento y la instrucción matemática, en particular, la interpretación del significado en términos de sistemas de prácticas operativas y discursivas relativas a la resolución de tipos de problemas y el modelo de niveles de algebrización de la actividad matemática. Se identifican tipos de situaciones-problemas y configuraciones de prácticas, objetos y procesos que permiten caracterizar y articular los diversos significados parciales de la integral definida (geométrico-intuitivo, como límite de sumas de Riemann y función acumulativa) así como de sus extensiones al caso de integral dobles (como caso particular de las múltiples) y de línea, desde los más intuitivos a los más formales. El análisis permite identificar los grados de generalidad de los objetos del cálculo integral y el papel del álgebra en la caracterización de los significados de la integral definida, que deben considerarse en la planificación y gestión de los procesos de enseñanza y aprendizaje del cálculo integral en las carreras de ingeniería.

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Where Calculus and Engineering Converge: an Analysis of Curricular Change in Calculus for Engineers

Cited by 10 publications

References 24 publications

‘Scaffolding’ or ‘Filtering’: A Review of Studies on the Diverse Roles of Calculus Courses for Students, Professionals and Teachers

‘Scaffolding’ or ‘Filtering’: A Review of Studies on the Diverse Roles of Calculus Courses for Students, Professionals and Teachers

Error Analysis of Learners’ Problem-Solving Abilities in Mathematics Courses: A Newman Error Analysis (NEA) Approach

Significados intuitivos y formales de la integral definida en la formación de ingenieros

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