Eliud Quintero | Instituto Tecnológico y de Estudios Superiores de Monterrey (ITESM) (original) (raw)

Papers by Eliud Quintero

En este trabajo se presenta una experiencia didactica, realizada en un primer curso del nivel sup... more En este trabajo se presenta una experiencia didactica, realizada en un primer curso del nivel superior de educacion, donde el software SimCalc MathWorlds® fue utilizado para introducir el contexto del movimiento en linea recta de modo que con este significado real se propiciara la identificacion visual de relaciones entre las graficas de velocidad y posicion. Las caracteristicas de este software dinamico permiten compartir las acciones realizadas por los estudiantes y promover el establecimiento de generalizaciones para establecer dicha identificacion. Como resultado de la secuencia que se apoya en el software, se llega a la caracterizacion visual de los puntos maximo, minimo y de inflexion de una funcion en relacion con el comportamiento de su derivada. Este resultado sugiere una reorganizacion posible del contenido del Calculo donde la representacion grafica de funciones adquiere relevancia desde el inicio del curso.

In this paper we describe a study in which we investigated the way in which linguistic and extral... more In this paper we describe a study in which we investigated the way in which linguistic and extralinguistic resources that employ students, facing with a sequence of activities, are important for the emergence and appropriation of mathematical notions. In the research, 65 students of about 18 years participated in a course of University Mathematics for Engineering that took place in 2013 at a private institution in northern Mexico. During the teaching sequence addressing qualitative relations between the graph of a function and the graph of its derivative is promoted. These notions are being interpreted by the change of position of an object that moves over a straight line and its velocity, respectively. For this, the SimCalc MathWorlds ® software is used, a dynamic environment in which students can explore mathematics of change and variation in the context of movement. In it, various representations (graphs, tables, algebraic expressions) are dynamically linked and in its design inf...

Se presenta un estudio sobre la manera en la que resultan importantes los recursos linguisticos y... more Se presenta un estudio sobre la manera en la que resultan importantes los recursos linguisticos y extralinguisticos para el surgimiento de resultados matematicos fundamentales en un curso de Calculo. Se disena un ambiente didactico mediado por el software SimCalc, en el que se abordan consecuencias graficas del Teorema Fundamental del Calculo, interpretadas en el contexto del movimiento rectilineo. Se emplea un metodo mixto de investigacion para realizar un analisis de habla y gestos que evidencia el proceso de apropiacion por parte de los estudiantes. Se disena y aplica un instrumento de evaluacion para valorar la transferencia de dicha apropiacion.

In order to take advantage of the didactic potential that Augmented Reality (AR) provides we pres... more In order to take advantage of the didactic potential that Augmented Reality (AR) provides we present an educational resource meant to help to transform the teaching and learning of Mathematics, through the creation of graphical representations for mathematical reasoning. The spatial visualization skill is a cross-curriculum content that has been taken for granted, the challenge then is to improve its development. With the design of this AR application we want to help students with this task. The application covers content that belongs to conventional courses of calculus I, II and III at college.

Digital Experiences in Mathematics Education, 2016

In this article, we discuss the dynamic digital software SimCalc MathWorlds and its potential to ... more In this article, we discuss the dynamic digital software SimCalc MathWorlds and its potential to promote dialogue in the first calculus course for engineering students at Tecnológico de Monterrey, México. Sixty students participated in a pedagogical sequence of tasks that had been designed to help them appropriate the relations between a function and its derivative. In the classroom, the software provided a visual scenario supporting the various tasks. The simulation of cartoon motion over a straight line was included during the interaction. Corresponding graphs of position and velocity gave meaning to the function and its derivative. Active and exploratory visual perception allowed the interpretation of mathematical relations being sought as affordances provided by the software. Co-action between students and mathematical knowledge through software use promoted dialogue in order to identify those relations as invariants. A qualitative method, predominantly ethnographic, was applied during the 2 weeks of the classroom experience. The results revealed the students’ appropriation of the relations by means of mathematical language. With this experience, we propose the term ‘dialogic ecosystem’ as a way to emphasize the design and performance of the pedagogical sequence, where the teacher, students and software cohabit in an environment resulting in dialogue as an important component for the acquisition of mathematical knowledge.

Digital Experiences in Mathematics Education, 2016

Procedia Computer Science, 2015

This paper presents a didactical experience taking place at 2012 in a Calculus I course with 24 c... more This paper presents a didactical experience taking place at 2012 in a Calculus I course with 24 college students. The scenario, including the simulation of uniformly accelerated motion over a straight line, is analyzed through a dynamical software. Additional to the simulation, SimCalc educational software allows the graphical interplay between velocity and position graphs, and through this visual perception, the emergence of prediction questions about the motion are promoted. Students should deal with them making use of algebraic and numeric procedures related to linear and quadratic equations. Results make us believe in the potential for the learning of calculus of a new way to deal with the visual perception of graphs, as tools for the mathematical reasoning involving numerical, algebraic and graphical representations of functions involved with the visualization of the motion scenario.

This paper presents the use of augmented reality for educational purposes within a grounded innov... more This paper presents the use of augmented reality for educational purposes within a grounded innovation process in college for the calculus curriculum. The aim of the application developed is offering students an opportunity to deal with spatial visualization skills. An activity performed in spring semester 2014 in a Calculus I course with 20 students shows the positive impact regarding the interaction with mathematics in this mode. The AR Application from 2D to 3D was provided to students in tablets prepared before with the whole activity. As part of the data collection involving the multiple source of information that a case study includes, a brief survey with open-ended questions was applied. We share the descriptive analysis of its results which make us believe that the abstraction feature of mathematics feels reachable when a virtual object stands in front of our own space and time reality.

In high school and college, the teaching and learning of Math usually lacks relating to a daily r... more In high school and college, the teaching and learning of Math usually lacks relating to a daily reality. Students live the learning of Math as a rigid routine for solving exercises, mostly in an algebraic way. The absence of meaning when we teach, makes Math something outside of our world. The Math in classroom is not an interesting subject and, as a matter of fact, the idea we leave in students about Math is not fair. Could it be possible to change this? It is our claim that today, with the emergent digital technologies, we could conceive a different way to perceive Math learning. That is the aim of our group TEAM: Tecnología Educativa para el Aprendizaje de las Matemáticas (Educational Technology for Mathematics Learning). Certainly, learning outcomes are not just a question of using technology. We are concerned with the conceptualization of a didactic strategy including technology for the student interaction with the mathematical knowledge. Understanding technology as an instrument (not as tool), should include the promotion of a thinking process to learn through technology interaction. Mathematical knowledge is now available through digital means. Today we have an opportunity to make Math a visual and tangible matter that students could reach using the kind of devices they use ordinarily. We look forward to bring a new meaning for the students' interaction with Math; one that they could better appreciate. We look forward to strengthen our educational innovation team aiming to transform the teaching and learning of Algebra, Analytic Geometry, Geometry and Calculus through the integration of digital technologies. Concerning research, we care for the promotion of mathematical cognitive skills not presented in curriculum as a content to be learned. Basic skills for understanding Math as a way of thinking the world are useful in the process of problem solving. And those skills exceed the algebraic representation of Math. Today we have an Augmented Reality Application dealing with the development of spatial visualization skills. We are also working with Kinect sensor to bring gestural aspects into the graphical representation of Math. As this two examples show, by adding digital technology to the learning process we are encouraging students to focus in visual and gestural components when interacting with mathematical content. Our purpose is to present TEAM as has been working until now. We attended several calls looking for grants that keep us together as a research group. Members of TEAM are students of the PhD Program for Innovation in Education and their thesis include the design and development of this kind of technological products for the learning of Math.

We discuss the design and development of the hybrid and flipped classroom course Introduction to ... more We discuss the design and development of the hybrid and flipped classroom course Introduction to College Mathematics supported by the Massive Open Online Course (MOOC) Math and Motion in Coursera. The experience took place with eight of eleven groups in the fall semester 2013, including seven teachers. This is a readiness course offered to students enrolled for the first time at a university in northern Mexico. The intention of the course is to give an introduction to Calculus, combining previous elements of Algebra and Analytic Geometry to foster their use in the study of linear motion. The design of the course considers linear motion context giving the chance for the learning of Calculus with a real meaning. The course included online participation of students outside the classroom, watching videos in Coursera, so they get ready for planned activities in the classroom. The goal of classroom activities was to deepen learning promoted by the videos on the MOOC. To do this, students during classroom sessions, used collaboratively different specialized software, and delivered their activity on the Blackboard course platform. Each week, one online assessment administrated by Coursera was done in the classroom, and students had the opportunity to access it twice more and improve their grades. Students also experienced a process of self-assessment for each class, to grade their own performance during classroom activity. Collaborative work done by the seven teachers, include periodic work sessions, to systematically promote decisions about the benefits of such innovative modality for the course. A diagnostic study was conducted to evaluate various dimensions of experience. Here we focus on the process of self-assessment of the student to build the course grade. The results show that there are the same proportions of students who approved with this modality, or with the conventional one, in which the teacher assigns the student grade. We share this experience to promote academic reflection on the assessment process that took place in this readiness course, a hybrid and flipped experience supported by Math and Motion MOOC. We gave an opportunity for students to take responsibility for their own performance in this course, having a strong component of technology in design, and findings showed us that we took a good decision.

Several reasons could be given to discuss about the importance of evaluating the potential of new... more Several reasons could be given to discuss about the importance of evaluating the potential of new digital technologies to incorporate visualization for the learning of mathematics. Several reasons also make this intention a difficult undertaking. In this work we aim to share the experience creating a multidisciplinary team able to give alternatives to transform mathematics curriculum to foster the development of visualization skills. The presence of emergent technologies -like Augmented Reality -is expected when the emphasis in visual aspects to trigger processes of mathematical thinking is assumed in these visualization skills.

Communications in Computer and Information Science, 2015

Lecture Notes in Computer Science, 2015

2015 ASEE Annual Conference and Exposition Proceedings, 2015

In this paper we present some results of a study conducted with 65 engineering students in a firs... more In this paper we present some results of a study conducted with 65 engineering students in a first Calculus course. SimCalc MathWorlds® software was included in the design of a didactic sequence to incorporate the scenario of the motion of an object over a horizontal straight line. The software document that was designed to work in classroom, plays an important role for analyzing the graphical behavior of position and velocity functions. By dragging the velocity graph, the software acts with the corresponding change in the position graph. The students used the software in their laptops by pairs during the two weeks didactic sequence. The aim of the sequence is to set up some relationships between the behavior of velocity graph and position graph. In a conventional curriculum those relations refer to the positive (negative) sign, and increasing (decreasing) behavior of derivative function, corresponding to the increasing (decreasing) and concave upward (downward) behavior of the function. Software brings the scenario for learning those facts analyzing the real context of linear motion. As part of the study, an assessment instrument was designed in order to appreciate the students’ appropriation of those relations. The instrument’ items are classified by corresponding to the linear motion context, or corresponding to different real contexts (no motion), or without including any real context. They also consider the posing information of the item and of the answer, being described by text or by a graphic. Application of the instrument lead us to reflect that, once the appropriation is achieved through the motion context, it could be easier for students to apply it without connection with a real context. It also reveals the difficulties for interpreting graphical information based on the derivative function. These findings are part of the overall results of a doctoral dissertation concerning with the use of digital technologies for the learning of Calculus. Keywords: Calculus learning, digital technologies, linear motion, real context, mediation.

2015 ASEE Annual Conference and Exposition Proceedings, 2015

We are part of a team of educational innovation that aims to transform the teaching and learning ... more We are part of a team of educational innovation that aims to transform the teaching and learning of Calculus through the integration of digital technologies. We are looking to foster a visual and tangible learning of Mathematics. As a team of educational research we care for developing mathematical cognitive skills that are not explicit in curriculum but have been taken for granted. Most of them is basic to the understanding of mathematics and are useful in the process of problem solving. Spatial visualization, for example, has been taken as an innate skill in students, however, experience with teaching solids of revolution, may question whether this is really the case. We identify spatial visualization as a cross-curriculum content and take the task of designing an educational technological resource to improve this skill. We have investigated the benefits of Augmented Reality technology for learning Calculus. The purpose of this paper is to present the AR Application we have developed to promote spatial visualization. Elements of its design as educational resource will be discussed in order to situate its use in ordinary Calculus I, II and III courses at college. In this paper we want to share aspects about application design as a whole, but will deepen in Calculus II level, where the visualization of solids of revolution takes place. Finally we share the kind of experience we have had with students and looking for better learning experiences for current and future generations.

Digital Experiences in Mathematics Education, 2016

Procedia Computer Science, 2015

Communications in Computer and Information Science, 2015

Lecture Notes in Computer Science, 2015

2015 ASEE Annual Conference and Exposition Proceedings, 2015