Primary school teacher’s noticing of students’ mathematical thinking in problem solving

Professional noticing of students’ mathematical thinking in problem solving involves the identification of noteworthy mathematical ideas of students’ mathematical thinking and its interpretation to make decisions in the teaching of mathematics. The goal of this study is to begin to characterize pre-service primary school teachers’ noticing of students’ mathematical thinking when students solve tasks that involve proportional and non-proportional reasoning. From the analysis of how pre-service primary school teachers notice students’ mathematical thinking, we have identified an initial framework with four levels of development. This framework indicates a possible trajectory in the development of primary teachers’ professional noticing.

Generation of representation models for complex systems using Lagrangian functions

In this article, a new methodology is presented to obtain representation models for a priori relation z = u(x1, x2, . . . ,xn) (1), with a known an experimental dataset zi; x1i ; x2i ; x3i ; . . . ; xni i=1;2;...;p· In this methodology, a potential energy is initially defined over each possible model for the relationship (1), what allows the application of the Lagrangian mechanics to the derived system. The solution of the Euler–Lagrange in this system allows obtaining the optimal solution according to the minimal action principle. The defined Lagrangian, corresponds to a continuous medium, where a n-dimensional finite elements model has been applied, so it is possible to get a solution for the problem solving a compatible and determined linear symmetric equation system. The computational implementation of the methodology has resulted in an improvement in the process of get representation models obtained and published previously by the authors.

Enseñando a programar: un camino directo para desarrollar el pensamiento computacional

Está ampliamente aceptado que es fundamental desarrollar la habilidad de resolver problemas. El pensamiento computacional se basa en resolver problemas haciendo uso de conceptos fundamentales de la informática. Nada mejor para desarrollar la habilidad de resolver problemas usando conceptos informáticos que una asignatura de introducción a la programación. Este trabajo presenta nuestras reflexiones acerca de cómo iniciar a un estudiante en el campo de la programación de computadores. El trabajo no detalla los contenidos a impartir, sino que se centra en aspectos metodológicos, con la inclusión de experiencias y ejemplos concretos, a la vez que generales, extensibles a cualquier enseñanza de programación. En general, aunque se van desarrollado lenguajes cada vez más cercanos al lenguaje humano, la programación de ordenadores utilizando lenguajes formales no es una materia intuitiva y de fácil comprensión por parte de los estudiantes. A la persona que ya sabe programar le parece una tarea sencilla, pero al neófito no. Es más, dominar el arte de la programación es complejo. Por esta razón es indispensable utilizar todas las técnicas y herramientas posibles que faciliten dicha labor.