Generalization, Covariation, Functions, and Calculus

Hitt, Fernando; González-Martín, Alejandro S.

doi:10.1007/978-94-6300-561-6_1

Cited by 14 publications

(11 citation statements)

References 44 publications

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“…From the literature review and our teaching experiences, we decided to implement DT into the preparation of the Calculus lessons for PMTs. There are several studies concerning differential or integral Calculus (e.g., [57,58]). Research concerning the use of digital technologies usually has the same structure: a comparison of the procedural abilities between the experimental and control group (in other words, a group taught with digital technologies and a group taught without digital technologies) [20,59,60].…”

Section: Implementation Dt Into Theoretical Subject-development Of Technological-content Knowledge (Tck)mentioning

confidence: 99%

Implementation of Digital Technologies into Pre-Service Mathematics Teacher Preparation

Slavíčková

2021

Mathematics

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This paper presents a long-term study of Preservice Mathematics Teachers (PMTs) at the Faculty of mathematics, physics and informatics, Comenius University in Bratislava (FMFI UK), focusing on the implementation of digital technologies (DT) into the teaching of theoretical and practical (or applied) subjects. We conducted parallel research into two aspects, one on Calculus lessons as a theoretical subject, another on the Financial Mathematics module as an applied subject. The implementation of DT and the way this was measured varied from year to year and also in the method of implementation into the aforementioned subjects. The methods of implementation and the results are briefly described, and a comparison of these two subjects in the PMTs’ preparation is also discussed.

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Section: Implementation Dt Into Theoretical Subject-development Of Technological-content Knowledge (Tck)mentioning

confidence: 99%

Implementation of Digital Technologies into Pre-Service Mathematics Teacher Preparation

Slavíčková

2021

Mathematics

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“…Por fim, enfatizamos que a prática docente que privilegia uma abordagem diferenciada para os processos de ensino e de aprendizagem dos conceitos de CDI, como por exemplo o ensino exploratório, mostra-se como um desafio para os professores do ensino superior e para pesquisadores em Educação Matemática (TREVISAN; MENDES, 2018; HITT; GONZÁLEZ-MARTÍN, 2016). Aspectos relacionados à priorização de ambientes fundamentados no ensino exploratório, que abarque o desenvolvimento de tarefas exploratórias e momentos de reflexão (STEIN et al, 2008), tendo em vista os diferentes fatores que compõem o contexto do ensino superior, como, por exemplo, a quantidade de estudantes em sala de aula e o currículo, bem como questionamentos acerca de como proporcionar experiências formativas que favoreçam aos professores do ensino superior o trabalho com tal abordagem (JAWORSKI et al, 2016), mostram-se como desafio e questões eminentes de pesquisa.…”

Section: Discussão Dos Resultados E Conclusõesunclassified

“…Nossas experiências profissionais e acadêmicas, bem como pesquisas em Educação Matemática, têm nos mostrado que a abordagem que prevalece nos processos de ensinar e de aprender Cálculo Diferencial e Integral (CDI) não se mostra satisfatória para a formação dos estudantes (JAWORSKI; MALI; PETROPOULOU, 2016), sendo assim, é necessária uma abordagem que privilegie uma formação global, crítico e reflexiva dos estudantes, que os coloquem na posição de co-construtores do conhecimento e não como meros expectadores capazes de aplicar o conhecimento em diferentes contextos (PONTE, 2014). Além disso, as dificuldades dos estudantes com a Matemática escolar refletem no seu desempenho em diferentes disciplinas do Ensino Superior (CASTRO, 2008;FARIAS, 2015), em especial, aquelas que abordam conceitos que envolvem o CDI (VERZOSA et al, 2014;HITT;GONZÁLEZ-MARTÍN, 2016;MENDES, 2018).…”

Section: Introductionunclassified

Oportunidades De Aprendizagem Do Conceito De Integral Definida Por Meio De Tarefas Matemáticas

Paulin¹,

Ribeiro²

2021

EDUCAÇÃO MATEMÁTICA

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In this paper we discuss aspects inherent to teaching practice based on inquiry-based in a university context. With this practice we aim to identify learning opportunities experienced by students of the Functions of One Variable discipline, when they develop exploratory mathematical tasks related to the calculation of areas of flat regions as introductory tools to the concept of Definite Integral and understand how these opportunities favored the teaching and learning processes of this concept. The study fits into a qualitative-interpretative research perspective, with methodological procedures inspired by Design-Based Research (DBR), developed with students from a public university in the state of São Paulo. The results show that the mathematical tasks enabled students to mobilize previous mathematical knowledge built in Basic Education, such as the calculation of the area of flat geometric figures; graphical representation of different functions; determining the domain of functions; in addition to the concept of Defined Integral itself. We also identified that the process of construction of the concept of Defined Integral, by the students when working in an inquiry-based teaching environment, took place in a collective and participatory way, in which the previous knowledge of students; group work; collective discussions; and the construction of knowledge in collaboration with peers (teachers and students).

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“…The learning of calculus draws on students' school experiences with pre-calculus notions such as functions, algebraic expressions, geometrical objects and representations (Biza, 2021;Frank & Thompson, 2021;Grant et al, 2016;Hitt & González-Martín, 2016;Thompson & Carlson, 2017). Such experiences are related to the curriculum students encounter (Biza, 2021;Byerley, 2019) and to their teachers' expectations (Ayalon & Wilkie, 2019).…”

Section: Transition Across Notions From Pre-calculus To Calculus or W...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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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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Generalization, Covariation, Functions, and Calculus

Cited by 14 publications

References 44 publications

Implementation of Digital Technologies into Pre-Service Mathematics Teacher Preparation

Implementation of Digital Technologies into Pre-Service Mathematics Teacher Preparation

Oportunidades De Aprendizagem Do Conceito De Integral Definida Por Meio De Tarefas Matemáticas

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

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