Dr. Alvarado-Martínez, Hugo

This paper aims to characterize the subfields of problems emerging from problem-situations of the derivative in university textbooks proposed for the training of civil and commercial engineers. Thirteen textbooks used for the teaching of the derivative in the syllabi of different Chilean universities were qualitatively analyzed. The notion of epistemic configuration of the onto-semiotic approach to mathematical knowledge and education was used for this purpose. It is observed that a complex approach to the derivative is adopted in the textbooks considered. A total of 21 subfields of problems appear, although not all the textbooks extensively use subfields of derivative problems. The findings of this research establish relevant guidelines for the design of a specific didactic proposal to learn the construction of the derivative in engineering courses.

Se evalúa la asignación de valores a situaciones de incertidumbre desde las intuiciones probabilísticas en 41 estudiantes de secundaria (16-17 años) por medio de un cuestionario de once ítems cerrados. A continuación, se implementa un ciclo formativo de veinte horas cronológicas de probabilidades y sus representaciones en la vida cotidiana, y analizan los cambios producidos en las argumentaciones en dos ítems por los estudiantes. Los resultados indican mayor variabilidad en las intuiciones postest de los estudiantes en situaciones de contexto habitual y mejora significativa en conocimientos con argumentos probabilísticos. En consecuencia, se promueve una enseñanza de probabilidad, a temprana edad, de las intuiciones a la confrontación con el conocimiento formal y que tenga en consideración la experimentación, variadas argumentaciones, y las conexiones entre los significados de la probabilidad.

En este trabajo se analizan las intuiciones y heurísticas sobre la probabilidad en 331 estudiantes de primaria (12-13 años) por medio de un cuestionario de seis ítems cerrados, y se examinan las argumentaciones en dos ítems abiertos. Los resultados muestran una alta variación en la intuición probabilística en situaciones aleatorias y la existencia de razonamientos acerca de nociones informales de probabilidad bajo una condición. Se considera pertinente para la enseñanza en este nivel educativo favorecer un acercamiento a la comprensión con distintas situaciones de incertidumbre mediante la profundización de los significados intuitivo y clásico de la probabilidad.

Working with statistical data from real contexts has become fundamental in school-level statistics, because it enables the development of statistical reasoning. In this regard, the notion of the random variable is fundamental to statistical data analysis. Thus, the aim of this research was to characterise the meanings of the concept of the random variable that are promoted in the Chilean mathematics curriculum for secondary education. To achieve this, we examined the representativeness of the meanings of the random variable intended by the curriculum in relation to the meanings of reference for this concept, using theoretical and methodological notions from the onto-semiotic approach. The findings show that the meanings of reference were not fully represented in the textbooks and the national curriculum, and that the most promoted meaning was that of the random variable as a variable of interest. Regarding the types of representation, it was observed that the graphical and tabular representations were neglected. Lastly, it was noticed that definitions of the concept of variable, its classifications, and differences were omitted almost entirely from the textbooks.