Artifacts and Mathematical Working Space in Multiplication Complex Numbers

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.



Visualización en el área de regiones poligonales. Una metodología de análisis de textos escolares

Gustavo Adolfo Marmolejo Avenia y María Teresa González Astudillo

Abstract: Abstract: Students do not acquire the visualization ability spontaneously, therefore its development must be considered from the earliest levels. Then what content is necessary to facilitate the acquisition of this cognitive activity must be determined. The area of polygonal regions may be one of the contents suitable for the development of visualization because it resorts to the use of figures
involving the student in activities that require their use. Since textbooks are also an important resource in the classroom and they influence on how the mathematical content is taught in school, it should be considered its study and analysis. In this sense, characterizing area of polygonal regions tasks by the type of visualization that textbooks promote for its development or understanding is a first aspect to detect the role of visualization in texts. In this paper we present a methodology for analyzing tasks that allows such characterization. There have been considered five categories of analysis: visual operation, figural change, dimensional changes, bidimensional focus change, and flow change. The application of the proposed method is illustrated by analyzing a task of a first grade
math book of Compulsory Secondary Education (ESO).

Keywords: visualization, areas of plane figures, textbooks, methodology of analysis.


Recursos para el cálculo visual de integrales

Félix Martínez de la Rosa

Abstract: Visualization is one of the best resources we mathematic teachers have to facilitate teaching and learning of a subject. In this paper we show some visual methods of integration in which the symmetry of functions and the inverse functions are used, and it recovers the concept of subtangent for the visual computing of areas.

Keywords: calculus, integral, symmetries, visualization, subtangents.