Papers by Gisela Hernandes Gomes
Le Centre pour la Communication Scientifique Directe - HAL - SHS, Sep 12, 2020
This paper provides an overview of the various stages of our research, which seeks to better unde... more This paper provides an overview of the various stages of our research, which seeks to better understand the use of calculus in university engineering courses. We first illustrate the use of integrals in a classic task (sketching a bending moment diagram) in a Strength of Materials course, showing that although integrals appear in the theoretical block, they are not explicitly used in the practical block. Our analysis of the course's reference book shows that this situation is replicated for all notions defined as integrals. This leads us to seek further information by examining teaching practices and by considering mathematical and didactic praxeologies. Our preliminary results indicate that, although integrals are present in the knowledge block of the course, their presence in the practical block and in the evaluation is significantly weaker.
CERME 10, Feb 1, 2017
Research has shown that mathematics courses in engineering programmes present students with a num... more Research has shown that mathematics courses in engineering programmes present students with a number of difficulties, some of which stem from a disconnection between mathematics course content and the professional activity of engineers. Using tools from the anthropological theory of the didactic (ATD), we examine how the drawing of bending-moment diagrams is introduced in a classic textbook used in engineering programs. Although the notion of integral is used to teach this topic, the techniques used rely mostly on geometrical considerations (and not on integral techniques or theorems), and the justifications provided are a mix of (incomplete) mathematical discourse and professional justifications, with implications for students' learning.
Le Centre pour la Communication Scientifique Directe - HAL - Archive ouverte HAL, Feb 4, 2015
The debate surrounding the teaching of mathematics in Engineering courses has inspired research f... more The debate surrounding the teaching of mathematics in Engineering courses has inspired research for more than a century. However, Engineering students still have difficulties in recognizing the mathematics required to solve problems in non-mathematical contexts. In order to study the vision of mathematics adopted by Engineering teachers and understand its role in shaping teaching practices, we interviewed two Engineering teachers with different backgrounds: one with BSc in Mathematics and MSc and PhD in Engineering, and another with BSc, MSc and PhD in Engineering. Our data reveal differences in the way these teachers approach topics such as mathematical rigor and approximation, and identify challenges faced by their students when working with modelling.
The notion of integral is usually first introduced to engineering students in their calculus cour... more The notion of integral is usually first introduced to engineering students in their calculus courses before later being used in their professional engineering courses. In this paper we analyse the textbooks used as main references in two engineering courses: a calculus course and a mechanics of solids course. Specifically, we compare how each textbook presents the task of sketching the graph of an antiderivative in the context of kinematics. Our results indicate that the mechanics of solids course presents this task by emphasising the notion of area and basic geometric calculations, using different notation and rationale than in the calculus course. We discuss the possible impact of these differences on the training of engineers.
The purpose of this research was to investigate the transition from academic mathematics to real-... more The purpose of this research was to investigate the transition from academic mathematics to real-life, engineering situations. In particular, through a case study, we investigate what mathematics content Brazilian undergraduate engineering students at private university use in order to develop their final course project. Theoretically, we use aspects of mathematical thinking raised in the literature reviewed. The methodological approach includes phases of grounded theory. Data collection included students’ written documents as well as videotaped interviews with students and their professors. Results revealed that to accomplish their projects students relied engaged in mathematical modeling and used specific software. Moreover, students showed that they were able to cope with mathematical situations that were not taught in their engineering courses.
In this paper we seek to further investigate whether having different backgrounds influences Engi... more In this paper we seek to further investigate whether having different backgrounds influences Engineering teachers' views of Calculus and shapes their opinion of how the subject should be taught, and whether these views affect their actual teaching practices. Our research is based on an institutional perspective and employs Chevallard's Anthropological Theory of the Didactic (ATD), in particular the notion of personal relationship, and we analyse the possible impacts of institutional choices on an individual's practices. Our data seem to indicate that even when they occupy the same position in the same institution, teachers with different academic backgrounds hold quite different personal relationships with the contents of their Calculus course, and that this has a significant impact on their practices.
… DE EDUCAÇÃO MATEMÁTICA, 2011
A preocupação com o ensino da Matemática em cursos de Engenharia tem sido objeto de atenção desde... more A preocupação com o ensino da Matemática em cursos de Engenharia tem sido objeto de atenção desde a criação da International Commission on Mathematical Instruction (ICMI), em 1908. E continua em recentes estudos que apontam a dificuldade encontrada pelos alunos de ...
Page 1. Gisela Hernandes Gomes UM ESTUDO DE ÁREAS COM ALUNOS DA 6ª SÉRIE DO ENSINO FUNDAMENTAL Di... more Page 1. Gisela Hernandes Gomes UM ESTUDO DE ÁREAS COM ALUNOS DA 6ª SÉRIE DO ENSINO FUNDAMENTAL Dissertação apresentada à Banca Examinadora da Pontifícia Universidade Católica de São Paulo, como exigência parcial para obtenção do título de ...
Methods for teaching Engineering processesdemand previous knowledge of mathematical tools,introdu... more Methods for teaching Engineering processesdemand previous knowledge of mathematical tools,introduced in courses basic cycles. Some tools, however,might have not been learnt beforehand. A solution for thisdifficulty is to encourage students to learn themathematical tool inductively via problem-basedlearning. The paper reports the pedagogical experienceof performing spectral analysis on a sea-level time serieswith a Civil Engineering undergraduate class. The serialmoving average is computed to estimate tide-oscillationtrend, so making students familiar to these concepts.Calculations are performed via electronic spreadsheet,using formulae programmed by students themselves. Themotivation caused by the problem and the appeal tointuition could better fix concepts, and shorten learningtime – from six to three teaching hours (although datatyping and data organization took an extra homeworkhour). Finally, the computer lab workshop environment(with targets and deadlines) demonstrated the valu...
ABSTRACT En términos generales los estudiantes tienen dificultades para entender los conceptos de... more ABSTRACT En términos generales los estudiantes tienen dificultades para entender los conceptos de la disciplina Cálculo Diferencial e Integral. En el presente trabajo presentamos algunos cuestionamientos sobre la aplicación de una actividad para los estudiantes del curso de Ingeniería Civil en lo que respecta a la representación de la recta tangente y recta normal en un punto particular de una función. Para el desarrollo de esta actividad fue indicado el uso de la Tecnología de Computación mediante la utilización del software Winplot. Los ejercicios resueltos presentados por los estudiantes muestran algunas incoherencias en la solución. Estos resultados nos llevaron a cuestionar el uso de una herramienta tecnológica para ayudarlos, e al mismo tiempo, investigar las fallas conceptuales que obstaculizan la percepción del estudiante en la solución correcta del problema.
Research in Mathematics Education
Resumo_Este artigo relata os estudos que um grupo de pesquisa em Ensino de Engenharia da Universi... more Resumo_Este artigo relata os estudos que um grupo de pesquisa em Ensino de Engenharia da Universidade Presbiteriana Mackenzie (UPM) tem desenvolvido com o ambiente virtual de aprendizagem chamado Virtual Math Teams, desenvolvido pela Drexel University. O objetivo deste trabalho é descrever e discutir as atividades elaboradas no Virtual Math Teams e analisar a resolução de problemas das disciplinas Pesquisa Operacional e Álgebra Linear dos cursos de Engenharia Civil e de Engenharia de Produção, na qual emergem ideias e conceitos matemáticos inseridos nessa resolução. Os resultados apontam que o ambiente Virtual Math Teams facilita a discussão e resolução de problemas que envolvam elementos matemáticos, cada qual com suas peculiaridades. Palavras-chave_Virtual Math Teams; ambiente virtual; conceitos matemáticos.
En términos generales los estudiantes tienen dificultades para entender los conceptos de la disci... more En términos generales los estudiantes tienen dificultades para entender los conceptos de la disciplina Cálculo Diferencial e Integral. En el presente trabajo presentamos algunos cuestionamientos sobre la aplicación de una actividad para los estudiantes del curso de Ingeniería Civil en lo que respecta a la representación de la recta tangente y recta normal en un punto particular de una función. Para el desarrollo de esta actividad fue indicado el uso de la Tecnología de Computación mediante la utilización del software Winplot. Los ejercicios resueltos presentados por los estudiantes muestran algunas incoherencias en la solución. Estos resultados nos llevaron a cuestionar el uso de una herramienta tecnológica para ayudarlos, e al mismo tiempo, investigar las fallas conceptuales que obstaculizan la percepción del estudiante en la solución correcta del problema.
Resumo_Este artigo relata os estudos que um grupo de pesquisa em Ensino de Engenharia da Universi... more Resumo_Este artigo relata os estudos que um grupo de pesquisa em Ensino de Engenharia da Universidade Presbiteriana Mackenzie (UPM) tem desenvolvido com o ambiente virtual de aprendizagem chamado Virtual Math Teams, desenvolvido pela Drexel University. O objetivo deste trabalho é descrever e discutir as atividades elaboradas no Virtual Math Teams e analisar a resolução de problemas das disciplinas Pesquisa Operacional e Álgebra Linear dos cursos de Engenharia Civil e de Engenharia de Produção, na qual emergem ideias e conceitos matemáticos inseridos nessa resolução. Os resultados apontam que o ambiente Virtual Math Teams facilita a discussão e resolução de problemas que envolvam elementos matemáticos, cada qual com suas peculiaridades. Palavras-chave_Virtual Math Teams; ambiente virtual; conceitos matemáticos.
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Papers by Gisela Hernandes Gomes