Autor: somidem

Experimentos de enseñanza e investigación. Una dualidad en la práctica del formador de profesores de matemáticas

  Por

Salvador Llinares

Resumen: Este artículo se centra en el papel que pueden desempeñar los experimentos
de enseñanza y la investigación sobre el aprendizaje del profesor de matemáticas en la
práctica de formar profesores. En primer lugar, se describen los fundamentos que justifican
la integración de determinadas tareas profesionales en los entornos de aprendizaje
que configuran los experimentos de enseñanza. En segundo lugar, se constata cómo
las investigaciones han permitido identificar algunas características sobre qué y cómo
aprenden los estudiantes para profesor en estos entornos de aprendizaje. Finalmente,
las actividades descritas muestran la dependencia mutua entre los diferentes roles del
formador de profesores de matemáticas como docente, diseñador e investigador.

Palabras clave: aprendizaje del profesor, experimentos de enseñanza, construcción
del conocimiento, interacción.

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El futuro de las tecnologías digitales en la educación matemática: prospectiva a 30 años de investigación intensiva en el campo

  Por

Teresa Rojano

Resumen: Se plantea una prospectiva de investigación futura, a partir de un recuento
de los resultados de estudios empíricos y teóricos sobre entornos tecnológicos de
aprendizaje en matemáticas, llevados a cabo a lo largo de tres décadas. También se
analizan los factores favorables y los obstructores potenciales para la implementación
de un currículo de matemáticas que incorpore a las tecnologías digitales como agentes
de cambio, tanto a nivel de contenidos como de prácticas de aula. El artículo se enfoca
sobre todo en el uso de la tecnología en la educación básica y media, y se intenta dar
una visión panorámica internacional (sin pretender que ésta sea exhaustiva).

Palabras clave: tecnologías digitales y educación matemática, análisis retrospectivo,
visión prospectiva, literatura especializada internacional.

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The etymological definition of Ethnomathematics and its implications for Mathematics Education

  Por

Author: Armando Aroca Araujo

Abstract : Several authors have referred to the apparent roots of the mathemaand
-tics roots of the word ethnomathematics in a rather superficial way and
without deepening in its analysis and their actual and potential implications
In this paper, these roots are etymologicaly revised and to related to trends in
current research in the Ethnomathematics Program. A literature review is conducted
that includes both journal and conference papers. It is concluded that
the aforementioned roots have been interpreted differently, and that several
of those interpretations have little to do with the etymology and with current
research trends in the Ethnomathematics Program.

Key words: Etymology, mathema, tics, research trends, ethnomathematics.

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Teachers’ knowledge of mathematics teaching when they exemplify and help in linear algebra classes

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Authors: Leticia Sosa Guerrero, Eric Flores-Medrano, José Carrillo Yáñez

Abstract : This paper examines the kind of mathematical knowledge, which lies
behind the use of examples and provision of support for students by two Baccalaureate
(16-18) teachers in Spain. The methodological approach is that of a
qualitative instrumental case study within an interpretative paradigm. Analysis
is carried out through the Mathematics Teacher’s Specialised Knowledge model,
with particular focus on one of the sub-domains of pedagogical content knowledge,
Knowledge of Mathematics Teaching. The detailed consideration of the
types of examples used and their particular features sheds light on the teachers’
awareness of the potential these have in the educational context. At the same
time, the use of various scaffolding techniques on the part of the teachers points
to knowledge about the variety of learner support available and how this focuses
on specific aspects.

Key words: Mathematics teachers, exemplification in mathematics, mathematics
learning support, pedagogical content knowledge, knowledge base for
teaching.

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Infinite iterative processes and transcendent objects: A model of construction of mathematical infinity from the APOS Theory

  Por

Authors: Diana Paola Villabona Millán, Solange Roa Fuentes

Abstract: The present study aims to examine the mental structures that a person
can develop to construct the mathematical concept of infinity in two particular contexts: “the paradox of Achilles and the tortoise” and the “Sierpin´ ski triangle”.
Based on the genetic generic decomposition of the infinite, proposed by
Roa-Fuentes and Oktaç (2014), this investigation focuses on the study of the
particular characteristics, mechanisms and structures produced by each context.
The analysis of data from work done by postgraduate students (in Mathematics
and Mathematics Education) shows how from the infinite iterative process
(potential infinity) advances towards to a transcend object (actual infinity).
Furthermore, the results reflect the importance of the coordination mechanism
in the construction of infinite iterative process.

Key words: APOS theory, paradoxes, Sierpin´ ski triangle, infinite iterative processes,
transcendent objects.

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Artifacts and Mathematical Working Space in Multiplication Complex Numbers

  Por

Authors: Macarena Flores González, Elizabeth Montoya Delgadillo

Abstract: The representation of multiplication in the number system of the
Complex Numbers is usually presented with a strong emphasis in the algebraic
aspect that brings a partial comprehension of this property. On the basis of the
foregoing, the current study investigates the learning process of the multiplication
of complex numbers in order to teach this content facilitating the graphic register
according to the theory of Mathematical Working Space. In this qualitative
research, there has been implemented a learning proposal that includes 34
engineering students in the first stage and 4 mathematics students in the second
stage; both groups of students are in their first year at university (18-19 years
old). Based on the results it is clear that carrying out processes and conversions
between the semiotic registers used with a software artefact not only permit
the activation of certain genesis of the ETM, but also produce circulations in the
personal ETM of a student which leads to a better comprehension of the mathematical
object in question.

Key words: Mathematical working space, multiplication of complex numbers,
artefact, visualization.

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Cycles of understanding about the concepts of function and variation

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Authors: Verónica Vargas Alejo, Aarón Víctor Reyes Rodríguez, César Cristóbal Escalante

Abstract : In this paper we analyze the relationship between the conceptual tools
(representations) used by students enrolled in a college tourism program, to
model a situation about cost of sending packages, and the cycles of understanding
that the students develop about the concepts of step function, function, and
variation. Based on the perspective of Models and Modeling, the questions that
guide the discussion are: What kind of representations did first semester students
use to describe and analyze problematic situations where the underlying model
is a step function? To what extent did the representations support the development
of different cycles of understanding of the concepts of function and variation?
The results show multiple representations that students construct, analyze, modify,
and refine. The representations helped to acquire meaning of mathematical
concepts as function and variation.

Key words: Understanding cycles, functions, step functions, modeling and variation.

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Blind source separation: a bridge between linear algebra and signal analysis

  Por

Authors: Rita Vázquez,  Avenilde Romo, Rebeca Romo-Vázquez,  María Trigueros

Abstract: The aim of this paper is to present a praxeological analysis in the frame
of the anthropological theory of didactics (ATD) of an engineering method known
as Blind Source Separation (BSS). In the method we found praxeologies that can
be transposed to the first year mathematics courses in engineering education,
particularly in Linear Algebra. The analysis shows that BSS is a potential tool to
generate modelling activities that reduce the gap between mathematical theory
and engineering practice. We present a proposal of a research and study path
based on BSS.

Key words: Engineering education, mathematical models, linear algebra, BSS,
anthropological theory of didactics.

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When praxeologies travel from one institution to another: a “boundary crossing” epistemological approach

  Por

Corine Castela

Abstract: The focus of this paper is on vocational training programs, which means
previous investigation about mathematics in vocational settings. We start by
explaining the term ‘boundary crossing’ in relation with the cultural, historical,
activity theory approach. We then present a way to address the same issue within
the anthropological theory of the didactic, using the key concepts of institution
and praxeology. We develop an analysis grid of knowledge produced by users
when they employ a mathematical technique and a general model of the changes
human knowledge is submitted to when moving from one institution to another.
Our approach is relevant to any level of professional qualification, from engineering
to professions socially viewed as poorly qualified.
Key words: Anthropological theory of the didactic, technology of a technique,
inter-institutional circulation, transposition.

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La definición etimológica de Etnomatemática e implicaciones en Educación Matemática

  Por

DOI 10.24844/EM2802.07

Autor: Armando Aroca Araujo

Resumen: El objetivo de este escrito fue hacer una reflexión sobre las raíces
etimológicas mathema y tica de la palabra etnomatemática y sobre el distanciamiento
que hay entre las interpretaciones de éstas con su etimología y su
relación con las tendencias investigativas del Programa Etnomatemática. El
problema que se encontró es que se han venido utilizando las raíces de mathema
y tics o tica sin un análisis más a fondo sobre las mismas y sus potenciales
y reales implicaciones. Para poder analizar la relación de la definición etimológica
con las tendencias investigativas se hizo un estudio de carácter documental (de
ponencias y artículos), mediante análisis del discurso. Como conclusión, se
encontró que las interpretaciones de dichas raíces son diversas, y que guardan
poca relación con la etimología y las tendencias actuales de investigación en
el Programa Etnomatemática.

Palabras clave: Etimología, mathema, tics o tica, tendencias investigativas,
etnomatemáticas.

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