Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

Analysis of applications and of conceptions for an application-oriented mathematics instruction

In connection with the (revived) demand for considering applications in the teaching of mathematics, various schemata or lists of criteria have been developed since the end of the sixties, which set up requirements about closeness to the real world or about the type of mathematics being used, and which have made it possible to analyze the available applications in their light. After having stated the problem (in section 1), we present (in section 2) a sketch of some of the best known of these and of some earlier schemata, although we are not aiming for a complete picture. Then (in section 3) we distinguish among different dimensions.in the analysis of applications. With this as a basis, we develop (in section 4) our own suggestion for categorizing types of applications and conceptions for an application-oriented mathematics instruction. Then (in section 5) we illustrate our schemata by some examples of performed evaluations. Finally (in section 6), we present some preliminary first results of the analysis of teaching conceptions.

ONTIC: A Knowledge Representation System for Mathematics

Ontic is an interactive system for developing and verifying mathematics. Ontic's verification mechanism is capable of automatically finding and applying information from a library containing hundreds of mathematical facts. Starting with only the axioms of Zermelo-Fraenkel set theory, the Ontic system has been used to build a data base of definitions and lemmas leading to a proof of the Stone representation theorem for Boolean lattices. The Ontic system has been used to explore issues in knowledge representation, automated deduction, and the automatic use of large data bases.

Inputs for the incorporation of the UNESCO guidelines on ICT competency standards for teachers : the training of teachers of mathematics in Central America

Resumen tomado de la publicaci??n

Introduction to Network Mathematics

Introduction to Network Mathematics provides college students with basic graph theory to better understand the Internet

School of Mathematics Computing Guide

Guide for computing in the School of Mathematics. Intended for new staff and PG students. Originally written by Anton Prowse from a number of earlier documents.

WAIS seminar:Mathematics for Web Science Part3-1

ABSTRACT In the first two seminars we looked at the evolution of Ontologies from the current OWL level towards more powerful/expressive models and the corresponding hierarchy of Logics that underpin every stage of this evolution. We examined this in the more general context of the general evolution of the Web as a mathematical (directed and weighed) graph and the archetypical “living network” In the third seminar we will analyze further some of the startling properties that the Web has as a graph/network and which it shares with an array of “real-life” networks as well as some key elements of the mathematics (probability, statistics and graph theory) that underpin all this. No mathematical prerequisites are assumed or required. We will outline some directions that current (2005-now) research is taking and conclude with some illustrations/examples from ongoing research and applications that show great promise.

WAIS seminar:Mathematics for Web Science Part 3-2

ABSTRACT In the first two seminars we looked at the evolution of Ontologies from the current OWL level towards more powerful/expressive models and the corresponding hierarchy of Logics that underpin every stage of this evolution. We examined this in the more general context of the general evolution of the Web as a mathematical (directed and weighed) graph and the archetypical “living network” In the third seminar we will analyze further some of the startling properties that the Web has as a graph/network and which it shares with an array of “real-life” networks as well as some key elements of the mathematics (probability, statistics and graph theory) that underpin all this. No mathematical prerequisites are assumed or required. We will outline some directions that current (2005-now) research is taking and conclude with some illustrations/examples from ongoing research and applications that show great promise.

WAIS seminar: Mathematics for Web Science: Part 3-3

ABSTRACT In the first two seminars we looked at the evolution of Ontologies from the current OWL level towards more powerful/expressive models and the corresponding hierarchy of Logics that underpin every stage of this evolution. We examined this in the more general context of the general evolution of the Web as a mathematical (directed and weighed) graph and the archetypical “living network” In the third seminar we will analyze further some of the startling properties that the Web has as a graph/network and which it shares with an array of “real-life” networks as well as some key elements of the mathematics (probability, statistics and graph theory) that underpin all this. No mathematical prerequisites are assumed or required. We will outline some directions that current (2005-now) research is taking and conclude with some illustrations/examples from ongoing research and applications that show great promise.

Proyecto 'mete' (mathematics education traditions of europe) : el foco matem??tico

Se presentan los resultados de un estudio sobre las tradiciones de ense??anza en varios pa??ses europeos. Dichos pa??ses son B??lgica, Inglaterra, Hungr??a y Espa??a. Se realiza un estudio a peque??a escala en el que se emplean m??todos cuantitativos y cualitativos. A lo largo del estudio, se tiene como objetivo sacar conclusiones que mejoren la ense??anza de las Matem??ticas. Dicho objetivo es siempre m??s prioritario que la obtenci??n de generalizaciones sobre la ense??anza. Se establecen comparaciones a trav??s de los resultados de varios tests y seobtienen unas conclusiones. A partir de las conclusiones, se extraen recomendaciones para los profesores con las que mejorar su experiencia docente.

Proyecto 'mete' (mathematics education traditions of europe) : pol??gonos en primaria

Se aborda el estudio comparativo de la ense??anza de la matem??tica en varios pa??ses europeos. Se estudia la ense??anza de los pol??gonos en primaria desde un punto de vista cuantitativo y cualitativo. Para el estudio se apoya en el an??lisis de cuatro unidades did??cticas puestas en pr??ctica por profesores de los correspondientes pa??ses. Se muestra la complementariedad de ambos tipos de datos y sus posibilidades para profundizar en la ense??anza de los pol??gonos.

Foundation mathematics : teaching the early years.

Es un nuevo recurso para la etapa de tres a cinco años. Está pensado para apoyar los objetivos de aprendizaje temprano y muestra a los niños cómo usar las matemáticas en el mundo real, además para trabajar con toda la clase cálculo mental, juego de roles en escenarios que proporcionan una variedad de contextos ricos en matemáticas. Los temas estimulan en los niños los propios intereses y el sentido de la curiosidad. Cada unidad dispone de : una serie progresiva de actividades para apoyar el desarrollo de los niños desde la enseñanza preescolar. Un alto nivel de apoyo para el profesional, para desarrollar las actividades y sugerencias para apoyar a los niños con capacidades diferentes.