Aprendizaje de los n\'umeros complejos usando diferentes sistemas de c\'alculo simb\'olico y un sistema de evaluaci\'on en l\'inea en formaci\'on inicial de profesores

TL;DR

This study examines how 15 future teachers in Chile interact with complex numbers using various computer algebra systems and online evaluation tools, highlighting challenges and opportunities in their mathematical understanding.

Contribution

It explores the impact of different artifacts and task features on giving meaning to complex numbers in initial teacher training, using multiple CAS and online assessment.

Findings

Students struggled with interpreting CAS outputs due to weak prior knowledge.

Task characteristics and multiple artifacts helped students understand mathematical objects.

Difficulties were linked to interpretation issues, but artifacts facilitated meaning-making.

Abstract

En este art\'iculo se estudi\'o el trabajo matem\'atico personal de 15 profesores en formaci\'on inicial, en primer a\~no de una universidad p\'ublica en Chile, a partir de dos tareas sobre n\'umeros complejos. Estas tareas se plantearon en un CAA (Moodlle - Wiris) y se propuso resolverlas utilizando distintos CAS, como GeoGebra, Symbolab, Photomath y Wolfram Alpha entre otros. Se observaron dificultades y potencialidades en el trabajo matem\'atico de los estudiantes. En las dificultades, se observ\'o que los estudiantes ten\'ian problemas para interpretar la informaci\'on de los CAS y del feedback del CAA debido a que los conocimientos matem\'aticos previos no eran lo suficientemente solidos para hacerlo. En las potencialidades, se observ\'o que distintas caracter\'isticas de la tarea, junto con la articulaci\'on de dos o m\'as artefactos permiti\'o a los estudiantes darle significado a los objetos matem\'aticos involucrados. In this article we studied the personal mathematical work of 15 teachers in initial training, in the first year of a public university in Chile, based on two tasks on complex numbers. These tasks were presented in a CAA (Moodlle - Wiris) and it was proposed to solve them using different CAS, such as GeoGebra, Symbolab, Photomath and Wolfram Alpha, among others. Difficulties and potentialities were observed in the mathematical work of the students. In the difficulties, it was observed that the students had problems interpreting the information from the CAS and the AAC feedback because their previous mathematical knowledge was not solid enough to do so. In the potentialities, it was observed that different characteristics of the task, together with the articulation of two or more artifacts allowed students to give meaning to the mathematical objects involved.