Constructing a schema: The case of the chain rule?

Clark, Julie Margaret; Cordero, Francisco; Cottrill, Jim; Czarnocha, Bronisław; DeVries, David J.; John, Dennis St; Tolias, Georgia; Vidakovic, Draga

doi:10.1016/s0732-3123(97)90012-2

Cited by 95 publications

(99 citation statements)

References 15 publications

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“…En su estudio definen un esquema desarrollado -tematizado -como una colección coherente de acciones, procesos, objetos y otros esquemas, previamente construidos, que son coordinados y sintetizados por el individuo para formar estructuras utilizadas en la resolución de problemas matemáticos y que muestran la coherencia del esquema al discernir cuando el esquema es aplicable o no. De esta manera, el desarrollo de un esquema SÁNCHEZ-MATAMOROS, G.; GARCÍA, M.; LLINARES, S. a través de los niveles intra, inter, trans se caracteriza por el tipo de relación -coordinación de operaciones en términos piagetianos -que los estudiantes son capaces de establecer entre los elementos matemáticos del esquema cuando resuelven un problema (BAKER; COOLEY; TRIGUEROS, 2000;CLARK et al, 1997;LLINARES, 2006).…”

Section: Marco Teóricounclassified

Algunos indicadores del desarrollo del esquema de derivada de una función

Sánchez-Matamoros

García

Llinares

2013

Bolema

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ResumenEl objetivo de esta investigación es caracterizar algunos indicadores del desarrollo del esquema de derivada en estudiantes de pos-secundaria. Usamos los niveles intra, inter y trans del desarrollo de un esquema propuestos por Piaget y García para caracterizar el uso flexible que los estudiantes hacen de la equivalencia lógica entre diferentes elementos matemáticos cuando resuelven un problema, como un indicador del desarrollo del esquema de derivada. Este indicador ayuda a explicar la transición entre los niveles inter y trans de desarrollo del esquema derivada.Palabras claves: Desarrollo de la Comprensión. Esquema. Fases del Desarrollo de un

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Section: Marco Teóricounclassified

Algunos indicadores del desarrollo del esquema de derivada de una función

Sánchez-Matamoros

García

Llinares

2013

Bolema

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“…Mathematical education researchers report that, although student routine performance on differentiation items is usually adequate, most of them have little intuitive or conceptual understanding of the derivative concept [1][2][3][4][5][6]. Many calculus students are, for example, proficient at differentiating a function and finding its critical values.…”

Section: Introductionmentioning

confidence: 99%

Application of Grey Numbers to Assessment of the Understanding the Graphical Representation of the Derivative

Voskoglou¹

2017

EDUCATION

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Grey numbers, which are defined with the help of the real intervals, are very useful in the everyday life for handling approximate data. In the present paper grey numbers are used as a tool for assessing, with linguistic expressions, the student understanding of the graphical representation of the derivative. Although the proposed new assessment method is proved to be equivalent with an analogous method using Triangular Fuzzy Numbers developed in earlier works, the required computational burden is significantly reduced. A classroom application is also presented illustrating our results.

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“…Their attempt to use the APOS theory resulted in insufficiency by itself therefore they included the schema development idea of Piaget et al (1989). Clark et al (1997) used triad classification after realization of not being able to apply the APOS theory. Similar to Clark et al (1997) APOS theory appears to be inappropriate for evaluating the research question in this work because students' responses didn't reflect a proper setting to apply the APOS theory; therefore, participating students' responses are analyzed by using the schema development idea.…”

Section: Schema Developmentmentioning

confidence: 99%

Evaluation of Engineering & Mathematics Majors' Riemann Integral Definition Knowledge by Using APOS Theory

Tokgoz¹

2016 ASEE Annual Conference &Amp; Exposition Proceedings

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University of Oklahoma. His pedagogical research interest includes technology and calculus education of STEM majors. He worked on an IRB approved pedagogical study to observe undergraduate and graduate mathematics and engineering students' calculus and technology knowledge in 2011. His other research interests include nonlinear optimization, financial engineering, facility allocation problem, vehicle routing problem, solar energy systems, machine learning, system design, network analysis, inventory systems, and Riemannian geometry.c American Society for Engineering Education, 2016 Evaluation of Engineering & Mathematics Majors' Riemann Integral Definition Knowledge by Using APOS TheoryIn this study senior undergraduate and graduate mathematics and engineering students' conceptual knowledge of Riemann's definite integral definition is observed by using APOS (Action-ProcessObject-Schema) theory. Seventeen participants of this study were either enrolled or recently completed (i.e. 1 week after the course completion) a Numerical Methods or Analysis course at a large Midwest university during a particular semester in the United States. Each participant was asked to complete a questionnaire consisting of calculus concept questions and interviewed for further investigation of the written responses to the questionnaire. The research question is designed to understand students' ability to apply Riemann's limit-sum definition to calculate the definite integral of a specific function. Qualitative (participants' interview responses) and quantitative (statistics used after applying APOS theory) results are presented in this work by using the written questionnaire and video recorded interview responses. Participants are asked to calculate the definite integral of the function f(x) = x 2 on the interval [1, 2] by using the limit definition of Riemann integral. Missing conceptual knowledge of the participants in calculus are observed when they were incapable of determining the solution to the problem.

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Constructing a schema: The case of the chain rule?

Cited by 95 publications

References 15 publications

Algunos indicadores del desarrollo del esquema de derivada de una función

Algunos indicadores del desarrollo del esquema de derivada de una función

Application of Grey Numbers to Assessment of the Understanding the Graphical Representation of the Derivative

Evaluation of Engineering & Mathematics Majors' Riemann Integral Definition Knowledge by Using APOS Theory

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