What does it mean for a student to understand the first-year calculus? Perspectives of 24 experts

Sofronas, Kimberly S.; DeFranco, Thomas C.; Vinsonhaler, C.; Gorgievski, Nicholas; Schroeder, Larissa B.; Hamelin, Chris

doi:10.1016/j.jmathb.2011.02.001

Cited by 34 publications

(35 citation statements)

References 52 publications

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“…Giving more attention to the procedural competence in the traditional group can be explained based on the "community of practice" phenomena. For instance, Sofronas et al (2011) stated that mathematicians trust formal notation language more in the process of proving theorems, interpreting findings, making inferences, and generalization. Besides, Pierce (1999) interprets students' finding traditional environments more reliable as a result of their lack of confidence about technological content knowledge.…”

Section: Discussionmentioning

confidence: 99%

“…Hughes-Hallett (1991) stated that for many calculus lecturers and students being competent in calculus are equal to the ability of manipulating symbols and numbers. In another study, Sofronas et al (2011) determined that after the negotiations with calculus textbook authors and well-known professors in the US, for a great majority of participants, procedural skills are the leading acquisitions of calculus, and the rate of the participants who mention technology support was limited. Based on the related literature and concordantly with the course objectives it can be understood why analytical participants remain distant to mathematics software that conceals procedural steps.…”

Section: Discussionmentioning

confidence: 99%

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Do calculus students demand technology integration into learning environment? case of instructional differences

Sevimli

2016

Int J Educ Technol High Educ

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This study evaluated how calculus students' attitudes towards usage of technology changes according to their learning environment and thinking types at the undergraduate level. Thus, the study attempted to determine the place and importance of technological support in the process of attaining the aimed and obtained acquisitions by students. Participants of the study consist of forty-three calculus students who are studying in traditional or CAS-supported teaching environments, and have different thinking types. Pre-and post-assessment tools were used in the data gathering process, and the data were evaluated with descriptive statistics. The results of the study showed that students in the traditional group place more importance on procedural skills, while students in the CAS group attach more importance to conceptual skills in terms of instructional objects. It also determined that acquisitions, which students think developed differ according to learning environment and thinking types. The main implications of the study were discussed in terms of the related literature and teaching practice.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Do calculus students demand technology integration into learning environment? case of instructional differences

Sevimli

2016

Int J Educ Technol High Educ

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“…Sin embargo, es exiguo el estudio de conexiones en el Cálculo. ISSN 1980-4415 DOI: http://dx.doi.org/10.1590/1980 No obstante, algunos estudios en el campo de la educación matemática reconocen la existencia de la conexión entre la derivada y la integral sin ser su objetivo principal (BERRY; NYMAN, 2003;HACIOMEROGLU;ASPINWALL;PRESMEG, 2010;SCHROEDER, 2011;SOFRONAS et al, 2011;DREYFUS, 2013DREYFUS, , 2014. De las metodologías propuestas para lograrlo, destacan las que proponen el manejo de distintas representaciones (MARRONGELLE, 2004;HOFFKAMP, 2011;MAMOLO;ZAZKIS, 2012;DAWKINS;MENDOZA, 2014;HONG;THOMAS, 2015) y las que promueven la modelación de situaciones en contexto (YOON;THOMAS, 2010;KLYMCHUK et al, 2010;PARK J. et al, 2013;WEBER;TALLMAN;MIDDLETON, 2015).…”

Section: Estado Del Arteunclassified

Conexiones Intramatemáticas y Extramatemáticas que se producen al Resolver Problemas de Cálculo en Contexto: un Estudio de Casos en el Nivel Superior

Flores

García‐García

2017

Bolema

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 ResumenEn el presente artículo se reporta una investigación cuyo objetivo fue identificar las conexiones que un grupo de estudiantes universitarios establecen al resolver problemas en contexto. Estos problemas pueden resolverse utilizando la relación entre la derivada y la integral establecida en el Teorema Fundamental del Cálculo. Para identificar las conexiones adoptamos el marco teórico que al respecto plantea Businskas (2008). Como método de investigación utilizamos el estudio de casos y aplicamos un cuestionario integrado por cinco problemas, de cuyas soluciones obtuvimos los datos. Los datos indican que los estudiantes establecen conexiones extramatemáticas e intramatemáticas al resolver problemas en contexto, pero principalmente utilizan las de tipo procedimental y las representaciones diferentes, además notamos una fuerte conexión con sus conocimientos previos aprendidos en los niveles de educación precedentes al nivel superior.Palabras clave: Conexiones matemáticas. Estudios de Caso. Teorema Fundamental del Cálculo. Nivel Universitario. AbstractThis paper reported a research which aims to identify connections that a university student group established to solve problems in a context. These problems can be solved using the relationship between the derivative and integral established in the Fundamental Theorem of Calculus. To identify such connections, we adopted the theoretical framework proposed by Businskas (2008). As a research method, we used the case study and applied a questionnaire which included five problems, the solutions of which we obtained the data. The data indicate that students establish extra-mathematics and intra-mathematics connections when they solve problems in a context, but mainly used the procedural type and the different representations. We also noticed a strong connection with their prior knowledge learned in previous levels of education rather than at the university level.

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“…studies that identifies students' difficulties and misconceptions with integration is described in an article by Orton (1983), which concludes that students often knew what to do, but when asked they did not know why They were doing, states that there was a set of issues related to the understanding of integration as the limit of a sum that was challenging even for the best students. Sofronas et al (2011) affirm that the integral is a fundamental mathematical concept with three important subconceptions critical for the understanding of the students and the ability to apply the calculation to a wide variety of problems: the integral as net change or accumulated total change, the integral as Integration area and techniques. Further studies, for example, Mahir (2009) and Rasslan and Tall (2002) support the idea that most students who have completed a calculus course have a very technical vision of integration and cannot explain what it means or how Interpret it in context.…”

mentioning

confidence: 99%

Understanding of university students about improper integral

Mojica

2020

IJREM

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The study of the understanding of mathematical concepts is of great interest for research in Mathematics Education. In this sense, an investigation is carried out on the understanding of the concept of improper integral, a basic concept from the first courses of Bachelor of Mathematics for subsequent courses. The objective is to characterize the understanding of this mathematical concept through a proficiency model for this purpose, an instrument was designed that was applied to second-year university students. The research is qualitative exploratory and is based on the framework of the Theory of records of semiotic representations.

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What does it mean for a student to understand the first-year calculus? Perspectives of 24 experts

Cited by 34 publications

References 52 publications

Do calculus students demand technology integration into learning environment? case of instructional differences

Do calculus students demand technology integration into learning environment? case of instructional differences

Conexiones Intramatemáticas y Extramatemáticas que se producen al Resolver Problemas de Cálculo en Contexto: un Estudio de Casos en el Nivel Superior

Understanding of university students about improper integral

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