Ana Isabel Sacristán

Center for Research and Advanced Studies of the National Polytechnic Institute | Cinvestav · Departamento de Matemática Educativa

The advent of technology has done more than merely increase the range of resources available for mathematics teaching and learning: it represents the emergence of a new culture—a virtual culture with new paradigms—which differs crucially from preceding cultural forms. In this chapter, the implications of this paradigm shift for policies concerning...

The significant development and use of digital technologies has opened up diverse routes for learners to construct and comprehend mathematical knowledge and to solve problems. This implies a revision of the pedagogical landscape in terms of the ways in which students engage in learning, and how understandings emerge. In this chapter we consider how...

In this paper, we describe the design and implementation of computer programming activities aimed at introducing young students (9–13years old) to the idea of infinity, and in particular, to the cardinality of infinite sets. This research was part of the WebLabs project where students from several European countries explored topics in mathematics a...

In this paper, we describe a design experiment aimed at helping students to explore and develop concepts of infinite processes and objects. Our approach is based on the design and development of a computational microworld, which afforded students the means to construct a range of representational models (symbolic, visual and numeric) of infinity-re...

This chapter focuses on teaching the use of programming technology for pure or applied mathematics investigation projects to university mathematics students and future mathematics teachers. We investigate how the theoretical frame of instrumental orchestration contributes to our understanding of this teaching. Our case study is situated within the...

Resultados del "Cuestionario sobre el uso de recursos tecnológicos digitales (TD) en la enseñanza de la Estadística y Probabilidad". Diseñado durante la fase de diagnóstico del trabajo doctoral de Perla Marysol Ruiz Arias.

In this paper, we turn to the notion of networking theories with the aim of contrasting two theoretical mathematics education perspectives inspired by Vygotsky’s work, namely, the Theory of Objectification and the Documentational Approach to Didactics. We are interested in comparing/contrasting these theories in accordance with the following three...

Presentamos resultados parciales de una investigación que indaga cómo estudiantes de ocho años interpretan, en una representación (fotografía) de un macroespacio, la ubicación de objetos y sujetos, y cómo establecen relaciones de proximidad entre ellos: tareas integradas a una trayectoria de aprendizaje que fomenta el tránsito entre distintos espac...

We are interested in understanding how university students learn to use programming as a tool for “authentic” mathematical investigations (i.e., similar to how some mathematicians use programming in their research work). The theoretical perspective of the instrumental approach offers a way of interpreting this learning in terms of development of sc...

In this paper, we present an empirical study examining challenges undergraduate mathematics students (N=73) encounter when engaging in programming-based mathematics inquiry projects, and how they handle these challenges. Results suggest that a majority of students find the programming or the programming of mathematics the most challenging aspect of...

During their school life, students learn mathematical topics that can be considered essential for the understanding of the property of density in the set of real numbers. It is thus that we felt the need to design a sequence of tasks and define a Hypothetical Learning Trajectory that can help promote the learning of this property. This report prese...

This chapter aims to make more explicit the grounded or ‘pragmatic theories’ that inform the design of mathematics teachers’ professional development (PD) to exploit technological affordances. It uses aspects of some representative projects that took place in four countries (Colombia, Italy, Mexico, and Portugal) to illustrate lessons learned (e.g....

In this article, we seek to understand how university students learn to use programming as an instrument for ‘authentic’ mathematical investigations. We use the instrumental approach as a framework, focusing on how the transformation of the programming language into an instrument requires that the user develops or mobilizes multiple schemes at diff...

Spatial reasoning skills are necessary to perform activities at school, at work and in everyday life, in general. Different studies indicate the importance of its development at an early age, since it allows the reading of a three-dimensional world and its interpretation in two-dimensional representations. Our research focuses on the design of acti...

The instrumental approach is a useful theoretical lens for understanding students' learning processes with a main focus on the transformation of an artefact (a human design for a goal-directed activity) into a meaningful instrument (i.e. an artefact and schemes developed by the student). In this paper, we articulate the instrumental approach for co...

Introduction (front matter) to the section (Part III). -------------- (Free to download as "FrontMatter" to Part III on SpringerLink using DOI or through: https://link.springer.com/content/pdf/bfm%3A978-3-030-19741-4%2F3%2F1.pdf) -------------- Integrating digital technologies for learning, including in mathematical education, is a foremost issue...

In this paper, we study the selection process of resources for teaching geometry, of a 5th Grade primary-school teacher in Colombia. For that, we use some concepts from the Documentational Approach to Didactics (DAD), such as “resource system” and “scheme”; and from the Mathematical Work Space (MWS) theory, the “geometrical paradigms” defined by Ku...

This paper centers on the use and integration of resources in mathematics classrooms. It presents an experienced teacher's use of GeoGebra and of worksheets in a class with 11th grade high-school students, and contrasts it with his reflection during a semi-structured interview that took place after the class. We aim to show how this teacher structu...

Sacristán, A. I. (2017). Digital technologies in mathematics classrooms: barriers, lessons and focus on teachers. In E. Galindo & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 90–99). Indianapolis, IN: Hoosier Association of Mathemat...

In the 1980s and 90s, the idea of engaging in computer programming for learning and exploring mathematical concepts became popular in mathematics education at basic levels, in what is now known as the constructionism paradigm. However, the teaching and learning of mathematics in high- er levels was rarely influenced by that approach. Here I present...

In 2011, the European Mathematical Society stated that a third pillar of scientific inquiry of complex systems has emerged in the form of a combination of modelling, simulation, optimization and visualization. This paper presents a naturalistic case study of an undergraduate student enrolled in a sequence of three programming, project-based mathema...

This work is part of a research project that aims to enhance engineering students’ learning of how to apply mathematics in modelling activities of real-world situations, through the construction (design and programming) of videogames. We want also for students to relate their mathematical knowledge with other disciplines (e.g., physics, computer sc...

We present two case studies from a research that focuses on the selection and orchestration of digital resources by primary-school teachers experienced in the use of technological tools. The case studies (of teachers from a public school in Colombia of 1 st and 5 th grades, respectively) describe the paths that each of these teachers followed when...

For the past 4 years, we have been involved in a project that aims to enhance the teaching and learning of experimental analysis and statistics, of environmental and biological sciences students, through computational programming activities (using R code). In this project, through an iterative design, we have developed sequences of R-code-based act...

Pretelín-Ricárdez, A., & Sacristán, A. I. (2016). Programming videogames with models of physical parameters: some examples. In Arnan Sipitakiat & Nalin Tutiyaphuengprasert (Eds.), Constructionism in Action: Conference Proceedings Constructionism 2016 (pp. 208–215). Bangkok, Thailand: Suksapattana Foundation. ISBN (E-Book) 978-616-92726-0-1 -----...

Pretelín-Ricárdez, A., & Sacristán, A. I. (2016). Videogame construction with models of physical parameters (Workshop). In Arnan Sipitakiat & Nalin Tutiyaphuengprasert (Eds.), Constructionism in Action: Conference Proceedings Constructionism 2016. (pp. 369–370). Bangkok, Thailand: Suksapattana Foundation. ISBN (E-Book) 978-616-92726-0-1 Retrieved f...

http://www.mii.lt/informatics_in_education/htm/infedu.2015.15.htm We present some results of an ongoing research project where university engineering students were asked to construct videogames involving the use of physical systems models. The objective is to help them identify and understand the elements and concepts involved in the modelling pro...

Este artículo corresponde a un avance de investigación, donde se describe un estudio cualitativo con estudiantes de ingeniería, abordado desde una visión construccionista (Papert & Harel, 1991), donde se explora, cómo a través de la implementación de un micromundo (Hoyles & Noss, 1987) donde se diseñan y programan videojuegos, los estudiantes puede...

Open peer commentary on the article “Learning about Learning with Teachers and (from) Young Children” by Chrystalla Papademetri-Kachrimani. Upshot: The activities that Papademetri-Kachrimani presents in her stories create situations that lead to unexpected results, thus opening the potential for learning about learning in teachers’ professional dev...

Sacristán A. I., & Pretelín-Ricárdez, A., (2015). Learning to apply mathematics in engineering modelling through constructing virtual sensory systems in maze-videogames. In Amado, N., & Carreira, S. (Eds.) Proceedings of the 12th International Conference on Technology in Mathematics Teaching, Pp. 509-517. Faro, Portugal: Universidade do Algarve. IS...

We present some results of an ongoing research project where university engineering students are asked to construct videogames where they need to use models of physical systems; the purpose of this is to help them learn more about modelling processes and the elements and concepts involved. That is, a constructionist approach of game design is used...

We will present some results of a research project where university engineering students (in their 5th year of studies) are asked to construct videogames as a means to help them develop their conceptions and skills related to the modeling of physical systems. For example, students had to build a game modeling liquid water behavior. Learning how to...

In this paper, we react to Lagrange and Kynigos’s contribution to this special issue, in which they present some of their experiences from two cross-case studies in the ReMath project (associated respectively with the use of two dynamic digital artefacts, Casyopée and Cruislet). They described how the project, which involved teams from three differ...

Resumen: En esta era de tecnologización digital, las reformas educativas realizadas durante las últimas dos décadas en las escuelas de nuestro país, enfatizan el uso de herramientas tecnológicas como apoyo didáctico y en la necesidad de formación docente para lograr este objetivo. Esta investigación se centra en observar los tipos de tecnologías di...

La investigación que presenta este artículo busca poner a prueba un modelo teórico y metodológico para promover procesos de reflexión en comunidades de práctica (CoP) de educadores matemáticos, como complemento o alternativa a su desarrollo profesional. Exhibimos algunos resultados de un proceso de reflexión de profesores de matemática de educación...

En este taller los participantes diseñarán y programarán videojuegos serios (Serious Games) como una actividad de construcción que permita aprender conceptos de modelación matemática de sistemas físicos. Los participantes se organizaran en equipos de unas tres personas para construir juegos serios dentro de un micromundo de aprendizaje. Se utilizar...

We discuss here the collaborative aspect of online explorations of videos of free-fall phenomena, by five adult students enrolled in a continuing education course on "Physics and its algebra". These explorations are part of an ongoing research project on promoting mathematical learning via the process of building math models in a context of rich ex...

This paper describes part of a proposal for college students to design and program Serious Games for the learning of certain concepts involved in some mechanical systems. The aim of this is to use the design and programming activity for promoting learning according to a constructionist view; therefore these activities are considered part of a learn...

It is common for engineering lecturers at undergraduate level to face questions by students on how mathematical concepts and tools relate to the real world in which they will work. These questions arise often when the mathematics that is being taught is not placed in the context in which it will be used. We thus wanted to relate and contextualize t...

This paper considers the work carried out by online teacher educators and their professional development. We use the theoretical perspective of the documentational approach that focuses, in this case, on the interaction between teacher educators and the resources they use for their online training work. We thus study the following issues: (1) What...

At ICTMT 9, we presented results from a long-term professional development Master’s programme for in-service teachers that focussed on the incorporation of technologies for mathematics teaching and learning. In the past five years, we have had the opportunity to document the impact of the programme on the participants’ academic lives. In the previo...

In this digital era, there is a need to incorporate technologies into educational practices. In our country (Mexico), there have been many policy and educational reforms with this aim. However, many factors create a gap between this political will and the reality of school teachers, particularly in non-developed countries, where resources, access t...

This report summarizes the intent and conclusions of the Discussion Group 27: “How is technology challenging us to re-think the fundamentals of mathematics education?” that took place during the 11th International Congress on Mathematical Education, held in Monterrey, Mexico, July 6 - 13, 2008. The group’s contributions and discussion documents ar...

Access to and implementation of digital technologies for mathematics teaching and learning across and within countries and regions display similarities and differences. This chapter is derived from regional presentations made at the ICMI Study 17 Conference held in Vietnam in December 2006. The descriptions of the situations in four countries (Russ...

This introduction sets the scene for the volume section 2 on the theme of learning and assessing mathematics with and through digital technologies. It first describes the section’s points of departure. Then each of the chapters of the section is briefly addressed. The introduction ends with a short reflection on the section as a whole, noting that...

Here we give an overview of the Mexican experience of a national program, begun in 1997, of gradual implementation of computational tools in the lower secondary-school classrooms (children 12-15 years-old) for mathematics and science. This project illustrates, through the benefit of long-term hindsight, the successes and difficulties of large-scale...

In this paper we present a school project where students constructed three-dimensional pyramids using the Logo programming language, complemented with paper-and-pencil, dynamic geometry (Cabri) and spreadsheet (Excel) investigations. The aim of this project was to give, through a fun and meaningful way, and using a constructionist approach, junior...

Since 1997, an ongoing national programme called Teaching Mathematics with Technology (EMAT) has been introduced in Mexican lower-secondary mathematics classrooms (children 12-15 year-old). The programme introduces a pedagogical model aimed to foster exploratory and collaborative learning through the use of computational tools. In this article, we...

In the past decade, the Mexican Ministry of Education has been making intense efforts for incorporating digital technologies. One of such efforts is the Enciclomedia programme which provides teachers with a system of computer interactive resources and activities designed to be used mainly on electronic interactive whiteboards. We were asked to desi...

n during a CAS-based activity to develop a general factorization for 1 − n x . We illustrate how he attributes a meaning to the ellipsis symbol related to his experience of "terms cancelling out" rather than the taken-for-granted meaning of an undefined continuing process. We show his associated difficulties in making sense of the sequence of decre...

Logo is a powerful language that allows for explorations of advanced mathematical topics such as that of infinite sequences and series. In this paper, I revisit the design of a computer microworld for the exploration of such infinite processes. In this microworld, students of different ages (some as young as 14) constructed and investigated graphic...

We present a proposal of a course designed to introduce Fractal Geometry, in a meaningful way, to graduate students of Graphic Design, using Logo-based activities; we also present some results of the study we carried out to evaluate this proposal. The implementation of Fractals to Graphic Design responds to the need to handle new tools for the grap...

We present results from an on-going research studying the implementation of technological tools in middle-school (children 12-15 yrs. old) mathematics classrooms, focusing in particular on the importance of the teachers’ role for students learning. This research is part of a national project sponsored, since 1997, by the Mexican Ministry of Educati...

We present results from a study which investigated the influence of dynamic geometry-based activities in the development of proving skills (in geometry) in high-school students (15-16 years of age). After a 12-week course on Cabri and the writing of conjectures and proofs, students were asked to write and prove conjectures based on their observatio...

The research literature has pointed to difficulties encountered by students in interpreting and establishing links between different types of representational registers. Here I present results from a study where a Logo-based computational microworld for the exploration of infinity and infinite processes, was meant to facilitate the construction and...

This paper presents some results from a study whose main concern was to investigate students' developing conceptions of infinity and infinite processes as mediated by a Logo- based environment or microworld. The general findings of the study indicate that the environment and its tools shaped these students' understanding s of the infinite in rich w...

In this paper, I present the design of a computer microworld for the exploration of infinite processes such as infinite sequences and series. The activities of the microworld use the Logo programming language as a means to construct diverse types of representations (symbolic, visual, and numeric) for such infinite processes. The environment and the...

Resumen Este trabajo forma parte de un proyecto cuyo propósito general es explorar el comportamiento cognitivo de un estudiante cuando trabaja dentro de un entorno computacional. Para el diseño de estrategias didácticas propias del medio computacional, es importante entender las diferencias de fondo que él tiene con respecto a los medios tradiciona...

Activities intended to enhance the theoretical framework and the methodology of mathematical education have intensified during the last decade. We have witnessed, for instance, the publication of diverse cognitive and epistemological studies - in both books and journals - converging to constructivist stances. See [6], [9]. However, it is still nece...

(ISSN 0187-8298) Los conceptos matemáticos vinculados con el infinito y su operatividad —en los diferentes contextos en los cuales se presentan— muestran consistentemente ser fuente de dificulta-des y conflictos para el estudiante. Nuestro interés se centra en el estudio de posibles obstrucciones al aprendizaje de ciertos conceptos matemáticos que...