Armando Solares

• PhD
• Researcher at Centro de Investigación y de Estudios Avanzados (Cinvestav) (Mexico)

Our research examines how children construct meanings about their territory when faced with disputes and displacement due to socio-ecological devastation. To do this, we took a territorial and spatial approach and asked elementary school students to create maps of their communities' environment. We focused on the work of children from two schools i...

Contribución desde los investigadores en didáctica de la matemática de la Pontificia Universidad Católica de Valparaíso a la comunidad de Educación Matemática de habla hispana centrado en los Pensamientos: -Pensamiento Probabilístico -Pensamiento Matemático -Pensamiento Variacional -Pensamiento Matemático Avanzado -Pensamiento Infinitesimal -Pensam...

In this theoretical article, we argue that the imminent collapse of earth systems that sustain life forms calls for mathematics education as a field to reflect on and re-evaluate its priorities and thus practices. We consider both what ecological collapse means for mathematics education and whether mathematics education might offer meaningful gestu...

experiencia de co-construcción didáctica entre saberes escolares, comunitarios y científicos en torno al río Atoyac

Este libro ofrece un panorama de investigaciones desarrolladas en México y en Latinoamérica en torno a los conocimientos y procesos de aprendizaje que tienen lugar en contextos escolares y extraescolares, tanto en el campo de la lengua como en el de las matemáticas. Desde sus particulares perspectivas teóricas y metodológicas, los estudios presenta...

Este libro ofrece un panorama de investigaciones desarrolladas en México y en Latinoamérica en torno a los conocimientos y procesos de aprendizaje que tienen lugar en contextos escolares y extraescolares, tanto en el campo de la lengua como en el de las matemáticas. Desde sus particulares perspectivas teóricas y metodológicas, los estudios presenta...

Resumen Presentamos una comparación de tendencias sobre la modelización matemática entre Latinoamérica y el resto del mundo a través de un análisis documental de 561 escritos, publicados entre 1980 y mediados de 2021, entre artículos de las principales revistas de investigación a nivel internacional y capítulos de libros. El análisis se centró en l...

We offer an analysis of the mathematical modelling literature identifying local and global tendencies and the diversity of approaches to mathematical modelling. The review comprises 502 documents from two source types: articles published in relevant journals and specific books from the International Community of Teachers of Mathematical Modelling a...

We focus on the role of transformational aspects of algebraic activity and the construction of meaning (or signification processes) during the process of appropriating the structure sense of algebraic texts. For such purpose, we use the basis of analysis of the productions of two students when working with the Expression Machine (described in chapt...

International assessment studies generally contribute to curriculum reform by highlighting certain aspects of curriculum needing improvement, usually attained though the recognition and application of some studies’ components. By focusing on the question “How have international studies driven school mathematics curriculum reforms?”, this chapter ex...

Como una manera de concientizar a la población sobre los problemas desde la Comunidad Escolar, se impulsó en la escuela primaria Xicohténcatl de San Rafael Tenanyecac, Nativitas, con el acompañamiento de la Red Comunidad, Ciencia y Educación, la Coordinadora por un Atoyac con Vida y el Centro Fray Julián Garcés de Derechos Humanos, una propuesta ed...

We report our progress on the “River Memorial Museum” didactic intervention project developed with schools, in the basin of the Atoyac River in Mexico, that are significantly impacted by the pollution produced through industrialisation. The teachers of the elementary schools in these communities, environmental scientists, educators, and community a...

This article explores the complex relational landscape of international partnerships where local and transnational education objectives are entangled. We present a methodological practice for experimenting with diagrams and maps. Our emphasis on spatial rendering of local/global relationality is intended to invite discussion about the postcolonial...

El sistema educativo mexicano promueve desde las políticas educativas y el currículo el uso de tecnologías para la enseñanza y el aprendizaje del álgebra. Para aplicarlo en las aulas, los profesores cuentan con una red compleja de conocimientos y prácticas relacionados con las matemáticas y su didáctica. Sin embargo, las condiciones en las que los...

We present the progress in the UKRI “Community, Science and Education” project (EP/T003545/1), developed through a network of mathematics and science educators, environmental and health scientists, teachers, and community leaders. This project aims to construct ways to bring education close to the concerns and needs of communities located in the At...

In t his document we present the design of a teaching sequence for the introduction of an algebraic method for the solution of two unknowns linear equations systems through a mathematical modelling task. The application of this sequence aims to characterize moments of sense production and construction of meanings that first high school students (be...

In this theoretical research report we propose a socio-ecological perspective, as relevant for research in mathematics education that takes account of our complex, precarious present and imagined future, while recognising its historical roots. We discuss briefly work that considers the social, political and ecological, and build from this scholarsh...

We present some results of an ethnographic perspective-based study of mathematically significant knowledge of Hñañu women embroiderers from Valle del Mezquital (Mexico). In this contribution, we focus on an interview throughout where one embroiderer and the researchers encounter and dialogue about the realization of embroideries ordered by the clie...

This article explores the complex relational landscape of international partnerships where local and transnational education objectives are entangled. We present a methodological practice for experimenting with diagrams and maps. Our emphasis on spatial rendering of local/global relationality is intended to invite discussion about the postcolonial...

This poster prepares the groundwork for a project that focuses on high school students’ construction of scientific knowledge through computer simulation. The activity “The infection game” simulates the diffusive dynamics of an infectious disease in close connection with the students (e. g. catching a cold). It is expected to characterize the action...

Palabras clave: Introducción: La situación socioambiental en México y en América del Sur requiere la construcción de formas de acercar la educación a las preocupaciones y necesidades de las comunidades marginadas, compartiendo conocimientos entre educadores, científicos, maestros, líderes comunitarios y formuladores de políticas. En el departamento...

We aim to dialogue with and support a network of scholars working around the theme of how mathematics education may be(come) relevant − locally and globally − in a changing world and how we, as researchers, might develop and employ methodologies that are suitably agile to operate with and within this world. We ask these questions while also troubli...

The paper describes briefly the current state-of-the-art on the teaching and learning of mathematical modelling. The lines of development are identified along the discussions, which have been taken place mainly at past ICMEs or ICTMAs and are enriched by an extensive additional literature review of the most recent discussion on mathematical modelli...

Presentamos una investigación centrada en el diseño de un Recorrido de Estudio e Investigación (REI), enmarcada en el paradigma del Cuestionamiento del mundo (Chevallard, 2013). Exponemos el trabajo realizado en una escuela telesecundaria de una comunidad rural de México y usamos la noción de inter-institucionalidad para estudiar un problema signif...

Este proyecto fue sometido a un concurso internacional en la convocatoria 2018 del Global Challenges Research Fund de UK (GCRF), y revisado por investigadores especialistas en el tema. Tiene financiamiento del Engineering and Physical Sciences Research Council (EPSRC) del British Research Council, UK. El objetivo es construir soluciones educativas...

Identificamos y analizamos conocimientos matemáticos que los estudiantes construyen mediante el uso de simulaciones computacionales para la modelación de fenómenos de las ciencias y las matemáticas. Investigadores participantes: Dra. Ana Isabel Sacristán (DME, Cinvestav), Dr. Paulino Preciado-Babb, Enrique Hernández (investigador postdoctoral) (Uni...

Social Sciences and Humanities. Research Council of Canada (SSHRCC). Grant Award No. 430-2019-00382.

A lo largo de los años la modelación matemática ha ganado gran atención internacional, no sólo en la investigación sino también en el desarrollo de propuestas curriculares y en su implementación en salones de clases. Pero, a pesar de la muy extensa cantidad de publicaciones, existen pocas revisiones de literatura sistemáticas. En este reporte prese...

Mathematical modelling has a long tradition in mathematics education and has been gaining international attention, not only in research and practice, but also in official perspectives reflected explicitly in programs of studies around the world. Despite extensive publications on diverse aspects of mathematical modelling, systematic literature surve...

Mathematical modelling has a long tradition in mathematics education and has been gaining international attention, not only in research and practice, but also in official perspectives reflected explicitly in programs of studies around the world. Despite extensive publications on diverse aspects of mathematical modelling, systematic literature surve...

Newton Moblity Grants 2017 RD2, University of Bristol, UK (NMG2R/170058). Esta propuesta tiene como objetivo mejorar los niveles básicos de matemáticas entre niños de comunidades marginadas en México. Hay una necesidad urgente para conectar matemática educativa que se ofrece a estos niños, a su experiencia fuera de la escuela en su vida cotidiana....

resentamos los resultados del análisis de los conocimientos puestos en acción por una maestra de matemáticas de secundaria en su práctica en el aula. Éstos toman forma y se despliegan como estrategias didácticas específicas para gestionar su clase cuando incorpora Computer Algebra Systems. A partir de observaciones no participantes de clases cotidi...

En este estudio buscamos estudiar la manera en que los estudiantes se apropian de las herramientas algebraicas. El análisis se centró en las dificultades y los avances de estudiantes de primer grado de secundaria al seguir una secuencia de problemas que, a parVr del estudio de fenómenos lineales, introdujo la simbolización algebraica como una más d...

We identified mathematical knowledge involved in embroidery activities of the Hñahñu culture from Valle del Mezquital (Mexico) from a cultural-semiotic approach. The motivation that led to this research was to test the viability of a teaching model (Filloy, Rojano & Puig, 2008), which considers the social and cultural aspects of the embroidery acti...

In this paper we analyze a variety of ways of teaching from work activities that involved mathematical knowledge. These activities are given in the rural environment of Sonora state as well as in the surroundings of the Mexico City conurbation. We present the results of two independent research projects that, in the quest for mathematical knowledge...

This workshop was motivated by both current developments in the learning sciences (in particular embodied cognition) and recent shifts of how mathematics knowledge for teachers is conceptualized. We perceived a need for research mathematicians to join with grade-school mathematics educators, working together to interrogate, elaborate, and format th...

In this paper we analyze a variety of ways of teaching from work activities that involved mathematical knowledge. These activities are given in the rural environment of Sonora state as well as in the surroundings of the Mexico City conurbation. We present the results of two independent research projects that, in the quest for mathematical knowledge...

The notion of equality, roughly meaning “sameness”, is one that may seem natural to teachers and practitioners of mathematics. However, to students who have not had the benefit of years of experience and practice with the concept, it can seem confusing and arbitrary. For example, an elementary school student first encountering numbers, who has just...

Este libro contribuye a la construcción de aproximaciones alternativas y complementarias a los aún dominantes y extendidos métodos mecanicistas y algoritmos de la enseñanza de las matemáticas. Los autores aportan nuevas perspectivas para el estudio del contenido y la naturaleza del conocimiento matemático.

Our study concerns the conceptual mathematical knowledge that emerges during the resolution of tasks on the equivalence of polynomial and rational algebraic expressions, by using CAS and paper-and-pencil techniques. The theoretical framework we adopt is the Anthropological Theory of Didactics (Chevallard 19:221–266, 1999), in combination with semio...

Our study concerns the conceptual mathematical knowledge that emerges during the resolution of tasks on the equivalence of polynomial and rational algebraic expressions, by using CAS and paper-and-pencil techniques. Our findings highlight the mathematical knowledge (technological discourse) constructed in the process of confronting, differentiating...

Little is known about the ways in which teachers take on research-based resources and adapt them to their own needs. This study focused on the manner in which three teachers who were participating in a research project on the learning of algebra with Computer Algebra System (CAS) technology spontaneously adapted the resources that were designed spe...

En este trabajo se abordan las dificultades en la enseñanza y el aprendizaje de los productos notables, comúnmente identificados como: binomio al cuadrado, binomios conjugados y binomios de tercer grado con un término común. El objetivo fue desarrollar una propuesta de intervención pedagógica para fortalecer la comprensión del concepto de productos...

Teachers participating in a research project on the learning of algebra with CAS technology spontaneously adapted the resources designed specifically by the researchers for the project. Analysis of the classroom-based observations of teaching practice showed that adaptive shaping occurred with respect to all three key features (the mathematics, the...

This article centers on studying the progress of algebraic syntax once students have surmounted initial obstacles found in the transition toward symbolic algebra. It specifically analyzes students' progress concerning the operation on the unknown, when the latter is represented by an expression that involves a 2nd unknown. In curricular terms, stud...

This article centers on studying the progress of algebraic syntax once students have surmounted initial obstacles found in the transition toward symbolic algebra. It specifically analyzes students' progress concerning the operation on the unknown, when the latter is represented by an expression that involves a 2nd unknown. In curricular terms, stud...

En el presente trabajo se planteó el problema del uso del CAS en la enseñanza de ecuaciones lineales con una incógnita. La investigación se realizó con niños de primer y segundo grado de secundaria e incluyó actividades en las que se resolvieron ecuaciones con lápiz y papel y usando el CAS. Para ello se utilizó como marco teórico metodológico tanto...

En la educación secundaria la enseñanza de los sistemas de ecuaciones lineales es un problema complejo, ya que los estudiantes deben emplear el lenguaje algebraico y realizar transformaciones de las ecuaciones dadas para lograr llegar a una solución. Estas acciones implican grandes dificultades, tales como: traducción del lenguaje común al lenguaje...

We studied the progress of algebraic syntax, once students have overcome the initial

We studied the progress of algebraic syntax, once students have overcome the initial obstacles of the transition toward symbolic algebra. We analyzed the progress on the line of operation of the unknown, but when said unknown is represented by an expression involving a second unknown. One of the first times in the curriculum that this situation ari...

En esta investigación se aborda el tema del progreso en la sintaxis algebraica, una vez que los alumnos han remontado los primeros obstáculos de la transición hacia el álgebra simbólica. Específicamente se analiza el progreso en la misma línea de operación de la incógnita, pero cuando esta aparece representada por una expresión que involucra una se...

Coordinación académica de los libros de texto de Matemáticas para Telesecundaria. Libros del maestro, libros del alumno de los tres grados. Así como recursos didácticos (TIC)producidos y en uso en el Sistema Educativo Nacional de Telesecundaria.

We deal with the study of the senses and the meanings generated in the representation of the unknowns in the resolution of word problems involving two unknown quantities. The discussed cases show the difficulties that the students beginning the algebra learning have to deal with when using the equality between "unknown things". For them, applying t...

In this paper we analyze the meanings of the "equal" sign as generated by sense production of the methods of substitution and comparison for solving problems and systems of equations of two unknowns. These methods are usually introduced through an extension process of the syntax and meanings recently learned by students in order to solve problems u...

In Filloy and Rojano (1989) we introduced the use of concrete models for the teaching of solving linear equations and studied the abstraction processes that take place when such models are put in work by 12-13 years olds. In this paper we discuss M and V cases where, on the face elements provided by the same “concrete” model for the operation of th...

In this paper we discuss how concrete modeling in algebra influences the way children in the arithmetic/algebra transition can learn to solve word problems. We discuss the stage in which the algebraic syntax developed to solve equations has just been acquired and then used to traslate the word problems into algebraic code.