Lluís Albarracín

PROBLEMAS DE ESTIMACIÓN DE GRANDES CANTIDADES: MODELIZACIÓN E INFLUENCIA DEL CONTEXTO

En este articulo introducimos los problemas de estimacion de grandes cantidades. Nos proponemos estudiar la presencia de procesos de modelizacion matematica y la influencia del contexto de estos problemas en las propuestas de resolucion de alumnos de Educacion Secundaria. A partir de un analisis cualitativo de diferentes dimensiones de las propuestas recogidas (respuesta orientada a la pregunta, estrategias, exito en la resolucion), estudiamos la existencia de relaciones entre las estrategias propuestas por los alumnos y los contextos planteados en las situaciones de los enunciados de los problemas, y la modelizacion de las situaciones planteadas. De los datos recogidos en nuestro estudio se deduce que el contexto puede influir en las propuestas de resolucion que hacen los alumnos. Concluimos que este tipo de problemas pueden ser utilizados para introducir la modelizacion en las aulas.

On the Role of Inconceivable Magnitude Estimation Problems to Improve Critical Thinking

In this chapter, we introduce inconceivable magnitude estimation problems as a subgroup of Fermi problems. The problems we use in our study require counting the amount of people in different situations. Based on the experience of a classroom activity carried out with 15-year-old students, we describe the process they went through to solve the problems, and discuss in which ways these problems provide knowledge to critically analyse the information that appears in the media.

Modelling with Statistical Data: Characterisation of Student Models

This chapter reports on the solutions of 22 groups of Year 10 students (15–16 years old) to a model-eliciting activity involving interpretation of data, namely, lists of salaries from five companies. Students were asked to see what could be ascertained about the structure of the company based on their mathematical or statistical analysis of the data. The students had no previous modelling experience but some understanding of statistics. Solutions based on the concepts and the processes involved in the models are represented in a graph. This analysis tool allowed distinguishing of significant differences between students’ responses. Results show a wide range of concepts and mathematical procedures were used. The activity promoted mathematical modelling and could be the first of a didactic sequence aimed at working on data distribution and dispersion.

Design and Implementation of a Tool for Analysing Student Products When They Solve Fermi Problems

In this chapter, we present a tool for analysing the work of secondary-level students from two different schools when they solve a type of Fermi problem. The tool is based on the characterisation of the concepts, procedures and language used to construct the models. Our results show that the proposed tool is useful to describe the models and to distinguish different aspects between the models produced by students without any previous modelling experience and those obtained by students who were already acquainted with working on modelling activities.

EyeMath: Identifying Mathematics Problem Solving Processes in a RTS Video Game

Video games are promising tools in educational environments since they have features that can promote learning in a playful environment. Formerly, we identified mathematics learning opportunities in a real time strategy video game. Going further, in order to precisely understand which information the students use to solve the challenges provided by the video game, this paper presents an eye tracker based tool to identify processes of mathematics problem solving while playing the game. The first preliminary results show the potential of the tool to further identify metacognitive and mathematics problem solving processes.

Problematizing the estimation of large numbers: Modeling and the influence of context

En este articulo introducimos los problemas de estimacion de grandes cantidades. Nos proponemos estudiar la presencia de procesos de modelizacion matematica y la influencia del contexto de estos problemas en las propuestas de resolucion de alumnos de Educacion Secundaria. A partir de un analisis cualitativo de diferentes dimensiones de las propuestas recogidas (respuesta orientada a la pregunta, estrategias, exito en la resolucion), estudiamos la existencia de relaciones entre las estrategias propuestas por los alumnos y los contextos planteados en las situaciones de los enunciados de los problemas, y la modelizacion de las situaciones planteadas. De los datos recogidos en nuestro estudio se deduce que el contexto puede influir en las propuestas de resolucion que hacen los alumnos. Concluimos que este tipo de problemas pueden ser utilizados para introducir la modelizacion en las aulas.