Graphical construction of a local perspective on differentiation and integration

Hong, Ye; Thomas, Michael

doi:10.1007/s13394-014-0135-6

Cited by 26 publications

(36 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This research was conducted on 24 mathematics education students. Subjects were asked to solve derivative and integral graphics problems ( Figure 1) adapted from Hong & Thomas (2015). Some samples of students were interviewed to determine the translation process.…”

Section: Methodsmentioning

confidence: 99%

Alteration Representation in the Process of Translation Graphic to Graphic

Swastika

Nusantara

Subanji

et al. 2020

HSSR

View full text Add to dashboard Cite

Purpose of the study: This research aims to analyze the alteration representation in the process of translation graphic to graphic where students were asked to solve derivative and integral graphics problems. Methodology: This research used a pseudo-experimental study with Pretest-posttest nonequivalent Group Design. This research was conducted on 24 mathematics education students. Students were asked to solve derivative and integral graphics problems. Some samples of students were interviewed to determine the translation process. Main Findings: The results of the study showed that the subject used two different methods to carry out the translation process. Thus, all students perform the process of translating the graphic representation into graphs with two different methods, namely the interval and the symbolic. Applications of this study: The implications of this study indicated that the translation process can help students solve problems, especially problems with graphs and algebra, also revealed activity in the translation process different from that of other researchers before. Novelty/Originality of this study: Researchers express a new activity to the translation by calling the conversion Intermediary In the stages of Preliminary Coordination (PC) and Objective Construction (CT), S1 and S2 show different forms.

show abstract

Section: Methodsmentioning

confidence: 99%

Alteration Representation in the Process of Translation Graphic to Graphic

Swastika

Nusantara

Subanji

et al. 2020

HSSR

View full text Add to dashboard Cite

show abstract

“…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). El uso de múltiples registros permite la obtención del significado de un objeto matemático, además de que la negociación del significado es inherente a la semiosis (PRESMEG, 2006).…”

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

View full text Add to dashboard Cite

 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.

show abstract

“…They found that the zeroes of the accumulation graph and the use of colour coding for positive and negative areas served pivotal roles in the process of semiotic mediation. Hong and Thomas (2013) examined the design of a curriculum where students used digital technology to develop a more balanced dual view of calculus ideas as both process and concept. Their results called for a teaching approach incorporating frequent use of dynamic geometry technology and graphing calculators, in order to encourage versatile embodied and inter-representational thinking.…”

Section: The Learning Of Calculus In Dynamic Environmentsmentioning

confidence: 99%

Comparing Calculus Communication across Static and Dynamic Environments Using a Multimodal Approach

2016

Digit Exp Math Educ

View full text Add to dashboard Cite

In this article, a thinking-as-communicating approach is used to analyse calculus students' thinking in two environments. The first is a 'static' environment in the sense of static visual representations, such as those found in textbook diagrams, while the second is a dynamic environment as exploited by the use of dynamic geometry environments (DGEs). The purpose of the article is to compare calculus students' communication as it is facilitated by each of these two environments, and to explore the role of paper-and digital-mediated representations for positioning certain ways of thinking about calculus. The analysis provides evidence that the participants employed different modes of communicationutterances, gestures and touchscreen-dragging -and they communicated about fundamental calculus ideas differently when prompted by different types of representations. The study presents implications for teaching dynamic aspects of functions and calculus, and argues for a multimodal view of communication to capture the use of gestures and dragging for communicating dynamic and temporal mathematical relationships.

show abstract

Graphical construction of a local perspective on differentiation and integration

Cited by 26 publications

References 16 publications

Alteration Representation in the Process of Translation Graphic to Graphic

Alteration Representation in the Process of Translation Graphic to Graphic

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

Comparing Calculus Communication across Static and Dynamic Environments Using a Multimodal Approach

Contact Info

Product

Resources

About