Mathematics primary teacher training in the context of the european higher education area

The future implementation of the European Higher Education Area requires thorough reflection on how to design and develop teacher training courses. In this reflection, it is important to reconsider, among other issues, (a) the role of prospective teachers in their own learning process and (b) the professional competencies that they must develop in the course of their higher education. Since 2003, the University of Granada has undertaken the development of pilot experiences to adapt some degree programs to this new framework. One of these degrees is Teacher in Primary Education degree, which includes several courses that focus on promoting prospective teachersÕ development of mathematical and pedagogical knowledge. In this paper how to organize future teachersÕ learning through practical activities in one of these courses is described. Firstly, the general process of adapting the course is analysed. Secondly, its theoretical and practical structure, with some examples of practical activities, are described. Finally, some results of the implementation are discussed

Introducción a la integración numérica de ecuaciones diferenciales algebraicas de índice 1

El objetivo de este trabajo es, tras introducir los conceptos y resultados básicos relacionados con las ecuaciones diferenciales algebraicas, el estudio de la integración numérica de las ecuaciones de índice 1 mediante métodos de tipo Rosenbrock. Se estudian con detalle las condiciones de orden de estos métodos, se han implementado métodos de Rosenbrock de órdenes 3 y 4, y se incluyen resultados numéricos obtenidos con dichos métodos cuando se integran las ecuaciones del péndulo y las de un amplificador con un transistor.Grado en Matemática

Errores y dificultades de estudiantes mexicanos de primer curso universitario en la resolución de tareas algebraicas

En diversas investigaciones se ha puesto de manifiesto las dificultades que presenta el aprendizaje del algebra en niveles preuniversitarios. La persistencia de errores al resolver tareas algebraicas en niveles universitarios observados en la práctica docente sugiere ampliar ese estudio a dichos niveles. En esta comunicación se recogen algunos resultados que se obtuvieron al aplicar una prueba a 153 estudiantes universitarios. Los resultados obtenidos muestran un alto índice de alumnos que presentan grandes deficiencias en sus conocimientos algebraicos básicos que no corresponden al nivel en donde se aplica la prueba. De este trabajo surge la idea de continuar con la investigación en esta dirección para profundizar el análisis de las probables causas que originan las dificultades que están en la base de esos errores

Antecedentes y fundamentación de una investigación sobre errores en la resolución de tareas algebraicas

Este artículo hace un recorrido sobre diferentes perspectivas que a través del tiempo se le han asignado a la definición del término álgebra, además de los diversos enfoques desde donde se han abierto distintas líneas de investigación con el objetivo de indagar las posibles fuentes de error en la enseñanza y aprendizaje de la misma. Finalmente, para evidenciar los errores más comunes que los estudiantes presentan al resolver distintas tareas algebraicas, se tomó en cuenta el trabajo de investigación de García (2010) realizado con un grupo de estudiantes universitarios de primer curso, con el objetivo de caracterizar las principales fuentes de errores que se presentan en las producciones de los alumnos al resolver dichas tareas

Eco‑evo‑devo and iterated learning : towards an integrated approach in the light of niche construction

In this paper we argue that ecological evolutionary developmental biology (ecoevo-devo) accounts of cognitive modernity are compatible with cultural evolution theories of language built upon iterated learning models. Cultural evolution models show that the emergence of near universal properties of language do not require the preexistence of strong specific constraints. Instead, the development of general abilities, unrelated to informational specificity, like the copying of complex signals and sharing of communicative intentions is required for cultural evolution to yield specific properties, such as language structure. We argue that eco-evo-devo provides the appropriate conceptual background to ground an account for the many interconnected genetic, environmental and developmental factors that facilitated the emergence of an organic system able to develop language through the iterated transmission of information. We use the concept of niche construction to connect evolutionary developmental accounts for sensory guided motor capacities and cultural evolution guided by iterated learning models. This integrated theoretical model aims to build bridges between biological and cultural approaches

Learning sequences of rules using classifier systems with tags

IEEE International Conference on Systems, Man, and Cybernetics. Tokyo, 12-15 October 1999.The objective of this paper was to obtain an encoding structure that would allow the genetic evolution of rules in such a manner that the number of rules and relationship in a classifier system (CS) would be learnt in the evolution process. For this purpose, an area that allows the definition of rule groups has been entered into the condition and message part of the encoded rules. This area is called internal tag. This term was coined because the system has some similarities with natural processes that take place in certain animal species, where the existence of tags allows them to communicate and recognize each other. Such CS is called a tag classifier system (TCS). The TCS has been tested in the game of draughts and compared with the classical CS. The results show an improving of the CS performance

Applying classifier systems to learn the reactions in mobile robots

The navigation problem involves how to reach a goal avoiding obstacles in dynamic environments. This problem can be faced considering reactions and sequences of actions. Classifier systems (CSs) have proven their ability of continuous learning, however, they have some problems in reactive systems. A modified CS, namely a reactive classifier system (RCS), is proposed to overcome those problems. Two special mechanisms are included in the RCS: the non-existence of internal cycles inside the CS (no internal cycles) and the fusion of environmental message with the messages posted to the message list in the previous instant (generation list through fusion). These mechanisms allow the learning of both reactions and sequences of actions. This learning process involves two main tasks: first, discriminate between rules and, second, the discovery of new rules to obtain a successful operation in dynamic environments. DiVerent experiments have been carried out using a mini-robot Khepera to find a generalized solution. The results show the ability of the system for continuous learning and adaptation to new situations.Publicad