RICERCA ITALIANA     

Linguistic and representation aspects of the teaching and learning of mathematics

Università degli Studi di Genova

Abstract

Based on ongoing research within the 2003-2004 National Project with the same title and the current research results and perspectives at the international level, the new Project aims at producing new knowledge about the following research themes:
- linguistic aspects of the approach to algebra and to calculus;
- verbal representation of everyday life experience, elementary mathematical modelling and construction of mathematical concepts;
- epistemological and historical studies related to linguistic and representation aspects in the teaching and learning of mathematics;
- languages and communication in the mathematics classroom.
For each of the last two themes one Operative Unit will perform specific research, but the same themes will be considered by the other O. U.s too, in connection with the first two themes.
The first and the second theme will be dealt with by different operative units according to specific research tasks in a co-ordinate way.

The Project will take into account some important needs inherent in present Italian situation in the field of mathematics education:
- the need for increasing competencies in Mathematics Education in the Italian universities involved in the new system of pre-service teacher training, as a necessary scientific background for it;
- the need for producing and disseminating (even through the Internet) scientifically based materials for mathematics teachers >>>

Principal Investigator

Paolo BOERO Università degli Studi di GENOVA

Research Objectives

FOREWORD: In order to outline the complex aspects of this Project, as well as the variety of its objectives, it seems useful to sketch a picture of the situation in which the Project has been conceived and will be (hopefully) carried on.
University mathematics educators in Italy (like in other countries) have some important challenges and societal requests to meet:
- to reach or keep a sufficiently high scientific standard (in relationship with current status of mathematics education research in the world);
- to tackle relevant research problems related to the transformations of mathematics teaching within a rapidly changing society;
- to prepare future researchers and university teachers in mathematics education;
- to provide competencies for teachers training (it started five years ago for all school levels);
- to engage in local in-service teachers' training programs, as a way to improve teachers' professional knowledge, convey mathematics education research results and get large feedback for them.
We think that ALL THESE AIMS ARE INTERCONNECTED AND IMPORTANT (though for different reasons). In particular, the fourth and fifth aims need a good research background in the universities all over Italy (since most of the in-service teacher training courses are organised at a regional level). RESEARCH FUNDING is needed for the first three aims; at present a National Project like this (which involves seven universities in seven >>>

First Results

FIRST PHASE: EXPECTED RESULTS
Expected results of the first phase will concern:
- at the very beginning (January/February 2005), re-thinking about previous research (performed within the 2003-2004 Project) and related new research questions;
- revision of the previous theoretical framework, in order to plan new experimental activities; in particular, revision of the methodology, taking the new research questions into account;
- new experimental activities aimed at collecting data related to the new research questions.
Most outcomes will be internal to the Project, with a major aim being the production of material for cross-comparison among Operative Units dealing with similar research questions (plans of teaching experiments, classroom materials, tentative analyses, etc. will be accessible on the Project website).
A number of outcomes will be external (research reports, contributions to meetings), specially aimed at comparing research perspectives and background results in national and international meetings: the PME-XXX Conference will offer a big opportunity in July, 2006 (see above).SECOND PHASE: EXPECTED RESULTS
Three kinds of scientific results are aimed at during and at the end of the second phase:
- results of a theoretical nature, which concern validating some research hypotheses about the considered themes, refining other hypotheses, formulating new research questions;
- validation of prototypes of >>>

Timescale

24 months

National and international background

SCIENTIFIC BACKGROUND

FOREWORD: In relation to the goals of the Project, by "scientific background" we mean the research performed and the results got both at the international level and by the Operative Units involved in the Project, that are useful to frame and tackle the research questions related to our programme. In the first part of this Section we will illustrate the title and present the research area, with some relevant references to international literature. In the second part we will sketch the scientific base related to the main themes of the research programme, while each operative unit in its B-model will be more detailed in showing specific previous results and references to current literature related to specific research questions. Information about the scientific base for general research methodology will close the Section.

THE TITLE OF THE PROJECT AND THE AREA OF INVESTIGATION:
Gathering in one title "languages" and "mental representations" can be justified by the narrow links that exist between mental representations and external representations in mathematical activities and learning of mathematics (as already highlighted by some authors, in Janvier, 1987; see Vergnaud, 1998 for a comprehensive development). A possible example related to such research in this project, is represented by the relationships between mental representations of properties of functions, and the representation of such properties by means of >>>