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.



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