Categoría: Volumen 26

Daniel Eudave Muñoz

Abstract: The purpose of this research is to analyze the social workers’ activities involving
the generation and processing of numerical and statistical data and how they deal with
these tasks and how they solve them. The work focuses on the analysis of activities,
situations and conceptual structure, following the approach of the French educational
training (didactique professionnelle). We report the use of statistics for the social workers
in Aguascalientes City, Mexico, and the pragmatical concepts that give meaning and
order to their professional knowledge.

Keywords: pragmatical concept, situated learning, education and work, statistical
education, social work.

María Trigueros

Abstract: The goal of this paper is to describe how the use of modeling in a differential
equations course contributes to foster a change in students’ understanding of first order
differential equation and solution set. The design and results of a research experience
based on APOS theory are presented. The focus of the paper is the description of those
results related with the use of different representations and others that seem to play an
important role in the changes observed in students’ understanding.

Keywords: modeling, differential equations, APOS theory, representations, understanding.

Luis Moreno Armella

Abstract: There is a force that goes through the teaching of Calculus: The tension between
the intuitive and the formal. Calculus continues to be taught as if it were natural
to introduce the study of change and accumulation by means of formalized concepts
known as the mathematics of e and d. It is frequently considered as a failure that
“students still seem to conceptualize limits via the imagination of motion.” This kind of
assertions shows the tension created by traditional teaching between students’ intuitions
and a misdirected formalization. The internal connections of the intuition of change and
accumulation are not correctly translated into that arithmetical approach of e and d.

Keywords: intuition, formalization, infinitesimal, analog cognition, symbol, metaphor,
embodied knowledge, digital medium, mediation.

Guardar

María Dolores Lozano

Abstract: In this article I present the enactivist perspective (Maturana and Varela, 1984)
as a theoretical alternative that can be used to investigate and clarify the teaching and
learning of mathematics. The biological roots of the theory are introduced, including fundamental
ideas such as autopoiesis and structural determinism. In addition, the theory’s
ideas on cognition as embodied action are discussed and some of its uses in mathematics
education are exemplified. Finally, I conclude by inviting the reader to use the ideas
exposed in order to investigate, in a complex manner and considering a multiplicity of
dimensions, the phenomena related to the teaching and learning of mathematics.

Keywords: enactivism, autopoiesis, embodied cognition, mathematics education.

Guardar

Gelsa Knijnik

Abstract: The paper aims at discussing aspects of mathematics education, which is
understood as the educational processes that happen inside or outside the school
space. Specifically it problematizes the no recognition of the existence of other ways to
mathematize, different from those usually taught in school. This problematization has
as theoretical bases what is called Ethnomatematics Perspective, a theoretical toolbox
built with the interlocution of Wittgenstein’s late ideas and the theorizations of Michel
Foucault. From the empirical side, the paper presents examples of mathematical language
games of different forms of life. The discussion done shows the productivity of
such Ethnomathematics Perspective to increase the possibilities of school mathematics.

Keywords: ethnomatematics perspective, Wittgenstein, Foucault, mathematics education.

Guardar

Guardar

Luis Radford

Abstract: In this article, I discuss some aspects of the manner in which phenomenology
has dealt with the question of the nature of objects of knowledge and the knowability of
such objects. I focus on Kant’s phenomenology and consider in particular some ontological
presuppositions that make Kant’s phenomenology both Platonist and anti-Platonist.
Then, I make a brief incursion into Hegel’s phenomenological approach and Marx’s
critique of Hegel, Kant, and German idealism in general. In the last part of the article,
I comment on Marx’s idea of praxis as an entirely new path to tackle the question of
the nature and knowability of objects of knowledge. I discuss some of the implications
of such an idea for mathematics education. I end up sketching a Hegelian dialectic
materialist concept of knowledge that provides room for understanding knowledge as
something ineluctably embedded in cultural praxis.

Keywords: phenomenology, sense, sensation, mathematical objects, praxis, dialectical
materialism.

Guardar