Mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Applied mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Model-based objects recognition in man-made environments

We describe a model-based objects recognition system which is part of an image interpretation system intended to assist autonomous vehicles navigation. The system is intended to operate in man-made environments. Behavior-based navigation of autonomous vehicles involves the recognition of navigable areas and the potential obstacles. The recognition system integrates color, shape and texture information together with the location of the vanishing point. The recognition process starts from some prior scene knowledge, that is, a generic model of the expected scene and the potential objects. The recognition system constitutes an approach where different low-level vision techniques extract a multitude of image descriptors which are then analyzed using a rule-based reasoning system to interpret the image content. This system has been implemented using CEES, the C++ embedded expert system shell developed in the Systems Engineering and Automatic Control Laboratory (University of Girona) as a specific rule-based problem solving tool. It has been especially conceived for supporting cooperative expert systems, and uses the object oriented programming paradigm

Modelling for Problem Solving in the Large

This a short presentation which introduces how models and modelling help us to solve large scale problems in the real world. It introduces the idea that dynamic behaviour is caused by interacting components in the system. Feedback in the system makes behaviour prediction difficult unless we use modelling to support understanding

Numeracy activities : plenary, practical and problem solving.

Es un recurso didáctico para desarrollar en los alumnos de la etapa 3 (key stage 3) del curriculo nacional inglés la comprensión de las matemáticas y las habilidades para el cálculo. Incluye actividades, que pueden fotocopiarse, y que están diseñadas para trabajar de forma individual o en grupo y para que sus respuestas, resultados y objetivos se puedan mejorar mediante la repetición y la práctica. Además, son actividades flexibles, es decir, el profesor puede ampliar o modificar su contenido según las circunstancias de los alumnos. También, es vital el uso del lenguaje, tanto oral como escrito, por los alumnos para ayudarles a comprender y dominar estos conceptos matemáticos.

100 ideas for teaching problem solving, reasoning and numeracy.

Ofrece muchas ideas para ayudar a desarrollar la resolución de problemas,el razonamiento y las habilidades numéricas en los niños de hasta más de cinco años de edad. Incluye los recursos utilizados,el tamaño del grupo y las instrucciones para cada actividad.

Mathematics across the curriculum : problem-solving, reasoning and numeracy in primary schools.

Está escrito para facilitar la enseñanza y el aprendizaje en los primeros años de la escuela y en la etapa de primaria. Las matemáticas son una asignatura troncal y su uso y aplicación en actividades de resolución de problemas es fundamental para que los niños utilicen sus conocimientos y habilidades en una amplia variedad de situaciones. Muestra, además, cómo enseñar conceptos matemáticos a través de otras materias: historia, geografía, artes, ciencia y tecnología, salud y bienestar,y desarrollo físico. También, se tratan temas de planificación y evaluación, organización y práctica en la clase y el empleo de otros recursos.

Excel at problem solving.

Recurso dirigido principalmente a profesores de alumnos entre once y dieciséis años. Cada problema se acompaña de una guía que incluye información sobre conocimientos previos, esquema de la clase y notas de soluciones. Está escrito con tres ideas principales: la resolución de problemas; el uso d e hojas de cálculo para ayudar en el planteamiento o la solución de problemas, adquisición de destrezas de aprendizaje de hoja de cálculo que pueden convertir la solución de problemas en una labor menos complicada. Trata de alentar a los alumnos a ser matemáticos en el sentido de participar en actividades de resolución de problemas; pensar y comunicar sus ideas, crear e identificar los problemas matemáticos en determinados contextos. Las veintitrés actividades se pueden trabajar con toda la clase, con los alumnos, o con grupos. En el CD-ROM se incluyen recursos complementarios.

Problem Solving Teaching Guide : its Way of Use, and the Effect on Students. 'Guía docente de resolución de problemas : su modo de uso, y el efecto en los estudiantes'.

Resumen basado en el de la publicación

Factors involved in making post-performance judgments in mathematics problem-solving

Resumen tomado de la publicaci??n

The role of schizotypy and creativity in a group problem-solving task

The well-studied link between psychotic traits and creativity is a subject of much debate. The present study investigated the extent to which schizotypic personality traits - as measured by O-LIFE (Oxford-Liverpool Inventory of Feelings and Experiences) - equip healthy individuals to engage as groups in everyday tasks. From a sample of 69 students, eight groups of four participants - comprised of high, medium, or low-schizotypy individuals - were assembled to work as a team to complete a creative problem-solving task. Predictably, high scorers on the O-LIFE formulated a greater number of strategies to solve the task, indicative of creative divergent thinking. However, for task success (as measured by time taken to complete the problem) an inverted U shaped pattern emerged, whereby high and low-schizotypy groups were consistently faster than medium schizotypy groups. Intriguing data emerged concerning leadership within the groups, and other tangential findings relating to anxiety, competition and motivation were explored. These findings challenge the traditional cliche that psychotic personality traits are linearly related to creative performance, and suggest that the nature of the problem determines which thinking styles are optimally equipped to solve it. (C) 2009 Elsevier Ltd. All rights reserved.

Worry and problem-solving skills and beliefs in primary school children

Objective. To examine the association between worry and problem-solving skills and beliefs (confidence and perceived control) in primary school children. Method. Children (8–11 years) were screened using the Penn State Worry Questionnaire for Children. High (N ¼ 27) and low (N ¼ 30) scorers completed measures of anxiety, problem-solving skills (generating alternative solutions to problems, planfulness, and effectiveness of solutions) and problem-solving beliefs(confidence and perceived control). Results. High and low worry groups differed significantly on measures of anxiety and problem-solving beliefs (confidence and control) but not on problem-solving skills. Conclusions. Consistent with findings with adults, worry in children was associated with cognitive distortions, not skills deficits. Interventions for worried children may benefit froma focus on increasing positive problem-solving beliefs.