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Aplicaciones del concepto de derivada utilizando el programa optimizando conocimientos
(International Institute of Informatics and Systemics, IIIS, 2010-01-01) Saldarriaga R., J.M.; Esteban D., P.V.; Saldarriaga R., J.M.; Esteban D., P.V.; Universidad EAFIT. Departamento de Ciencias; Educación Matemática e Historia
Applets como herramienta para la enseñanza y el aprendizaje del cálculo vectorial
(International Institute of Informatics and Systemics, IIIS, 2010-01-01) Rojas, L.C.; Esteban, P.V.; Rojas, L.C.; Esteban, P.V.; Universidad EAFIT. Departamento de Ciencias; Educación Matemática e Historia
Collaborative and distributed augmented reality in teaching multi-variate calculus
(2006-01-01) Orozco, C.; Esteban, P.; Trefftz, H.; Orozco, C.; Esteban, P.; Trefftz, H.; Universidad EAFIT. Departamento de Ciencias; Educación Matemática e Historia
This article presents the first results of using an Augmented Reality (AR) tool, designed to support tutoring sessions in multi-variate calculus. The tool is used either in a face-to-face setting in which the instructor and the students are collocated or in a distance setting, in which the instructor and students are physically in remote places. The tool was used with two groups of students of Differential Calculus. The students had not been exposed to the concept of equations involving 3 variables and the corresponding surfaces in space. The experience explored how students generalized 2D graphics and equations with their 3D surfaces counterparts with the help of the tool.
Collaborative virtual environments for teaching physics
(SPRINGER, 2007-01-01) Giraldo, F.; Rojas, Á.M.J.; Esteban, P.; Trefftz, H.; Giraldo, F.; Rojas, Á.M.J.; Esteban, P.; Trefftz, H.; Universidad EAFIT. Departamento de Ciencias; Educación Matemática e Historia
Eafit University created a Telepresence application for distance education. It supports bidirectional audio and video and a shared virtual environment that allows the instructor and students to manipulate virtual objects in a collaborative manner, thereby reinforcing the learning process. In this paper we report the experience of creating new contents and deploying the tool in a Physics course at Universidad del Quindío. The tool was improved an extended in order to include new functionality and make it easier for development teams to create new content. Teaching for Understanding was used as pedagogical framework for course creation and also as a guide to develop the interviews that were used to capture user's perceptions and to asses the improvements in the learning process. The results showed that the use of the tool had a positive impact on the students' understanding of the topics at hand. © 2007 Springer.
Distance interaction in education processes using a Telepresence tool
(SPRINGER-VERLAG BERLIN, 2010-01-01) Giraldo, F.; Jiménez, A.; Trefftz, Helmuth; Restrepo, J.; Esteban, Pedro Vicente; Giraldo, F.; Jiménez, A.; Trefftz, Helmuth; Restrepo, J.; Esteban, Pedro Vicente; Universidad EAFIT. Departamento de Ciencias; Educación Matemática e Historia
Distance interaction among educational communities is becoming increasingly important. Courses and talks are shared among institutions and individuals who are located in different places. The Telepresence tool, developed by Eafit and Universidad del Quindío, permits course sharing among the institutions. Instructors from one institution can teach students of the other one, thereby sharing the positive features of each course. In this paper, we present the recent improvements of the Telepresence tool. We also report on the use of the tool in a Multi-Variable Calculus course, designed in accordance to the Teaching for Understanding (TFU) pedagogical framework. © 2010 Springer Science+Business Media B.V.
Technological Tools to Learn Calculus
(IEEE, 2015-01-01) Perez Gomez, Gloria Patricia; Zea Restrepo, Claudia Maria; Esteban Duarte, Pedro Vicente; Zapata Rivera, Luis Felipe; Perez Gomez, Gloria Patricia; Zea Restrepo, Claudia Maria; Esteban Duarte, Pedro Vicente; Zapata Rivera, Luis Felipe; Universidad EAFIT. Departamento de Ciencias; Educación Matemática e Historia
Online learning tools have allowed professors to carry out their classes in an interactive way, synchronic as well as asynchronic, giving them the opportunity to explore from different points of view specific themes or concepts, achieving greater dynamism in their classes through the active participation of students. This article presents the results of the implementation of an software tool for massive use designed with the objective of allowing Engineering students to strengthen their basic mathematical knowledge as well as to improve their results in courses such as Calculus I and Mathematics I. These courses are part of the first semesters of the syllabus for all undergraduate programs of the School of Engineering, and are basic courses in the formation of an engineer at Universidad EAFIT (Medellin, Colombia). This software tool for massive use allows students to selfdiagnose, to solve exercises with different levels of complexity and difficulty, to visualize academic contents such as video classes and virtual resources, and to know their evolution in the understanding of basic concepts in calculus. On one hand, this facilitates the beginning of their studies at the university. On the other, it gives the professor an initial diagnose of the level students have to start the course so that continuous analytics can be performed based on the learning process of the student. Furthermore, this article shows the results of a comparative analysis done to two groups of students, a Control group and an Experimental group, that took Calculus I as part of their undergraduate studies. The experiment lasted two months with testing done at the beginning and at the end of the course. The objective was to register the level of knowledge acquired by the students and compare the differences between the two groups, control and experimental. The testing also allowed the progress of the student between tests to be measured, taking into account that the experimental group had the opportunity to explore the platform during this two-month period. Therefore, the analysis performed served to gather information useful for evaluating the effectiveness of the proposed system in the learning process of the students at the University.
Technological tools to learn calculus
(Institute of Electrical and Electronics Engineers Inc., 2015-12-02) Gómez, G.P.P.; Restrepo, C.M.Z.; Duarte, P.V.E.; Rivera, L.F.Z.; Gómez, G.P.P.; Restrepo, C.M.Z.; Duarte, P.V.E.; Rivera, L.F.Z.; Universidad EAFIT. Departamento de Ciencias; Educación Matemática e Historia
Online learning tools have allowed professors to carry out their classes in an interactive way, synchronic as well as asynchronic, giving them the opportunity to explore from different points of view specific themes or concepts, achieving greater dynamism in their classes through the active participation of students. This article presents the results of the implementation of an software tool for massive use designed with the objective of allowing Engineering students to strengthen their basic mathematical knowledge as well as to improve their results in courses such as Calculus I and Mathematics I. These courses are part of the first semesters of the syllabus for all undergraduate programs of the School of Engineering, and are basic courses in the formation of an engineer at Universidad EAFIT (Medellin, Colombia). This software tool for massive use allows students to self-diagnose, to solve exercises with different levels of complexity and difficulty, to visualize academic contents such as video classes and virtual resources, and to know their evolution in the understanding of basic concepts in calculus. On one hand, this facilitates the beginning of their studies at the university. On the other, it gives the professor an initial diagnose of the level students have to start the course so that continuous analytics can be performed based on the learning process of the student. Furthermore, this article shows the results of a comparative analysis done to two groups of students, a Control group and an Experimental group, that took Calculus I as part of their undergraduate studies. The experiment lasted two months with testing done at the beginning and at the end of the course. The objective was to register the level of knowledge acquired by the students and compare the differences between the two groups, control and experimental. The testing also allowed the progress of the student between tests to be measured, taking into account that the experimental group had the opportunity to explore the platform during this two-month period. Therefore, the analysis performed served to gather information useful for evaluating the effectiveness of the proposed system in the learning process of the students at the University. © 2015 IEEE.
Los teoremas de green, stokes y de la divergencia matematicas en 3D
(International Institute of Informatics and Systemics, IIIS, 2010-01-01) Esteban D., P.V.; Trefftz, H.; Saldarriaga R., J.M.; Esteban D., P.V.; Trefftz, H.; Saldarriaga R., J.M.; Universidad EAFIT. Departamento de Ciencias; Educación Matemática e Historia
Understanding math concepts through computer-modeled virtual objects
(SPRINGER, 2008-01-01) Trujillo, J.; Esteban, P.; Montoya, E.; Giraldo, R.; Montoya, A.; Mejía, J.; Trefftz, H.; Trujillo, J.; Esteban, P.; Montoya, E.; Giraldo, R.; Montoya, A.; Mejía, J.; Trefftz, H.; Universidad EAFIT. Departamento de Ciencias; Educación Matemática e Historia
Information and Communication Technologies (ICT) can be used in order to motivate students to establish links between the classroom material and real life situations by modeling those situations through the course equations. This article describes the results of an experience involving a group of Multivariable Calculus at Eafit University. 3DUniversal is the program developed for the experience, which runs on Pocket PC. It allows students to interact and communicate inside the classroom. At each stage of the experience, students were asked to establish links between the classroom-covered material and real objects in their environment. © Springer Science+Business Media B.V. 2008.
USING VIRTUAL AND AUGMENTED REALITY IN THE CALCULUS CLASSROOM
(IATED-INT ASSOC TECHNOLOGY EDUCATION & DEVELOPMENT, 2020-01-01) Vega, J.; Nieto, A.; Cordoba, C.; Gil, G.; Trefftz, H.; Esteban, P.; Vega, J.; Nieto, A.; Cordoba, C.; Gil, G.; Trefftz, H.; Esteban, P.; Universidad EAFIT. Departamento de Ciencias; Educación Matemática e Historia
Education, nowadays, is going through a transition process. ``New Students'' require tools that allow them to improve their technical knowledge and, besides that, strengthen soft skills such as communication and teamwork. Developments that use Virtual Reality and Augmented Reality as a means for teaching have shown to have positive impacts on factors such as understanding, motivation and agility in the learning process of university students. In this article we describe the development of two tools, one based on Virtual Reality and one on Augmented Reality, to teach Multivariate Calculus to university students. The applications through experimentation and collaborative observation, allow them to understand concepts such as functions, quadratic surfaces, directional derivative, traces and contour lines. Both applications provide students and educators the change to experiment though digital environments used in a class in multivariate calculus. Each application includes two different roles: student and educator. The student is an observer. The professor and the students are represented through avatars that interact with each other. The educator role is more complex, allowing the user to create and modify functions and quadratic surfaces and create planes that intersect the surfaces that represent the functions. Students within the Virtual Reality environment experience ran the application on their phones. They used Virtual Reality glasses to immerse themselves in the experience and a remote Bluetooth controller to walk through the virtual environment. They were able to walk on and under the displayed mathematical functions. The instructor, on the other hand, created and modified those functions and directed the learning experience showing different interactions among planes and surfaces. The instructor ran the VR application on a computer. Meanwhile, students using the Augmented Reality application, were able to visualize functions and surfaces through the camera of their phones when pointing to the marker. Each student had the possibility of pointing to any place within the surface with a green dotted marker. They could also observe overlapping with the surfaces. The instructor had the same functionalities as in the virtual reality application. This study showed that almost all students encountered the experience satisfying and helpful. They thought it was revealing in many ways, allowing them to visualize abstract surfaces and traces easily. Also, some students pointed out their wish of including these experiences since the beginning of the course. In the full article, we plan to describe the creation of both VR and AR applications and provide data on the student perceptions.

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