identificação do projecto “learn: matemática, tecnologia e ... · identificação do projecto...

Identificação do Projecto “LEARN: Matemática, Tecnologia e Sociedade Referência PTDC/CED/65800/2006

Área científica principal Main Area

Education Sciences

Área científica Secundária Secondary area

(vazio) (void)

Título do projecto (em português) Project title (in portuguese)

APRENDER: Matemática, Tecnologia e Sociedade

Título do projecto (em inglês) Project title (in english)

LEARN: Mathematics, Technology and Society

Palavra-chave 1 Keyword 1

Aprendizagem Learning


Educação Education


Matemática Mathematics


Tecnologias de Informação e Comunicação Information and Communication Technologies

Objectivos sócio-económicos Socio-economic objectives

Social Development And Services Data de início do projecto Starting date

Duração do projecto em meses Duration in months

01-09-2007 36

Instituição Proponente Principal Contractor

Fundação da Faculdade de Ciências (FFC/FC/UL)

Campo Grande - Edificio C7 -1º Piso 1749-016Lisboa

Instituições Participantes Participating Institutions

(vazio) (void)

Unidade de Investigação Principal Research Unit

Centro de Investigação em Educação da Faculdade de Ciências da Universidade de Lisboa (CIE/FC/UL)

Campo Grande - Edifício C1 - PISO 2 1749-016Lisboa

Instituição de Acolhimento Host Institution

Faculdade de Ciências da Universidade de Lisboa (FC/UL)

Campo Grande - Edifício C5 1700-000Lisboa

Orçamento

Fundação da Faculdade de Ciências

DESCRIÇÃO DESCRIPTION 2007 2008 2009 2010 2011 TOTAL

Recursos Humanos Human resources

0 0 0 0 0 0

Missões Missions

15300 46190 22400 0 0 83890

Consultores Consultants

1430 2860 1430 0 0 5720

Aquisição de serviços e manutenção Acquisition of services and maintenance

2400 2450 2500 0 0 7350

Outras despesas correntes Other current expenses

3020 1550 1730 0 0 6300

Despesas gerais Overheads

7599 10610 5612 0 0 23821

Equipamento Equipment

15845 0 0 0 0 15845

TOTAL 45594 63660 33672 0 0 142926

Plano de financiamento Finance plan

DESCRIÇÃO DESCRIPTION 2007 2008 2009 2010 2011

TOTAL

Financiamento solicitado à FCT Requested funding

38514 23468 28980 0 0 90962

Financiamento próprio Own funding

0 0 0 0 0 0

Outro financiamento público Other public-sector funding

0 0 0 0 0 0

Outro financiamento privado Other private funding

0 0 0 0 0 0

Total do Projecto Total of the project

38514 23468 28980 0 0 90962

Justificação do orçamento

-

4.1. Justificação dos recursos humanos 4.1. Human ressources justification (vazio) (void)

4.2. Justificação de missões 4.2. Mission justification

Tipo Local Nº de deslocações Custo envolvido (€)

Participação em congressos Portugal - PROFMAT 36 13120

Justificação

Participation in 2007, 2008 e 2009 in the annual meeting of the Association of Teachers of Mathematics (Associação de Professores de Matemática - ProfMat) for presentation of 6 communications and 3 workshops to mathematiocs teachers. Participation of 12 members x 3 years = 36 participations. Cost includes registration and accommodation for 3 days.


Participação em congressos Portugal- SIEM 12 2450

Justificação

Participation in 2007, 2008 and 2009 in the Seminar for Research in Mathematics Education (SIEM) promoted by the Association of Teachers of Mathematics (Associação de Professores de Matemática) for presentation of 6 communications. Participation of 4 members of the team x 3 years = 12 participations. Cost includes only registration and accomoation for 2 days given that the Seminar takes place each year at the same location of the meeting ProfMat.


Participação em congressos Seul, South Korea (PME31) 8 10320

Justificação

Participation in July 2007 in the 31st Conference for the Psychology of Mathematics Education presenting 1 research report, 2 communications and 1 poster. Participation of 8 members of the team. Cost includes registration, air fare and dayly support.


Participação em congressos Morelia, Mexico (PME32) 10 16800

Justificação

Participation in July 2008 in the 32nd Conference for the Psychology of Mathematics Education (PME32) for presentation of 1 research report, 2 communications and 2 posters. Participation of 10 members. Cost includes registration, air fare and dayly support.


Participação em congressos Athens, Greece 8 17000

Justificação

Participation in July 2009 in the 33rd Conference for the Psychology of Mathematics Education (PME33) for presentation of 3 research reports, 2 communications and 1 poster. Participation of 8 members. Cost includes registration, air fare and dayly support.


Participação em congressos Mexico City, Mexico (ICME) 10 8000

Justificação

Participation in July 2008 in the 11th International Conference on Mathematics Education (ICMI 11) (the world largest conference in Mathematics Education) for presentation of the Project, 2 research reports, 1 workshop and 2 posters. Participation of 10 members of the team. Cost includes only registration and dayly support (given that the PME32 Conference is held at the same country during the week before).


Participação em congressos Portugal - MES5 12 6600

Justificação

Participation in Februray 2008 in the 5th Conference foir Mathematics Education and Society for a session presentation of the Project as a whole, of 2 research reports and 2 posters. Participation of 12 members. Cost includes registration and accomodation.


Trabalho de campo Portugal 120 9600

Justificação

12 members of the team will make 10 visits to each specific site where empirical data are collected. The average cost for each visit is €80 for day support. The total cost is 12 x 10 x 80 = 9600

Custo total: 83890

4.3. Justificação de consultores 4.3. Consultants justification

Nome Instituição Fase do projecto

Custo envolvido

(€)

Ole Skovsmose

Aalborg University, Denmark http://www.learning.aau.dk/dk/institut/medarbejdere/ole_skovsmose.htm

All phases

2860

Justificação

Professor Ole Skvosmose is an international authority in the field of mathematics education specially in the area of critical mathematics education. He will act in the four phases of the Project as critical reader and as resource both for the empirical and the theoretical field of research. The consultant will be responsible for giving feedback on each (scientific) deliverable of the Project. Cost refer to 4 visits to the Project and will be paid to the consultant in four parts after each visit.

Nome Instituição Fase do projecto

Custo envolvido

(€)

Stephen Lerman

South Bank University, London, United kingdom http://myweb.lsbu.ac.uk/~lermans/

All phases

2860

Justificação

Professor Stephen Lerman is an international expert in the socio-cultural perspectives of learning mathematics, specially in semiotic mediation. He has previous experience of working with the Principal researcher in a past research project funded by FCT. He will act in the four phases of the Project as critical reader and as resource both for the empirical and the theoretical field of research. The consultant will be responsible for giving feedback on each (scientific) deliverable of the Project. Cost refer to 4 visits to Project and will be paid to consultant in four parts after each visit.

Custo total: 5720

4.4. Justificação de aquisição de serviços e manutenção 4.4. Acquisition of services and maintenance justification

Tipo Custo envolvido (€) Construction and maintenance of data basis 3100 Justificação

A data basis will be created from the very beginning to support the storing and acess of data from all the researchers in the team. The data basis will include text, video clips, photographs and audio files. This will be crucial for the storing and cross-analysis of data from different sites. Maintenance will be in a case to case basis. The cost is estimated according to previous experience in this kind of work and points to €1300 in 2007, €900 in 2008 and €900 in 2009.

Tipo Custo envolvido (€) Maintenance of computing, printer, video and audio devices 4250

Justificação

The equipment will have a rather frequent use during the project therefore we antecipate the need to have maintenance of the printer and computing and of the new equipment in the 3rd year of the project (once the guarantee is expired)

Custo total: 7350

4.5. Justificação de outras despesas correntes 4.5. Current expenses justification

Tipo de despesa Custo envolvido (€) Bibliography 2850 Justificação

Key books to be available to all the 15 members of the team (5 copies each): 2007: €1200 2008: €900 2009: €750

Tipo de despesa Custo envolvido (€) Consumables 3450 Justificação

Toner for printer for 3 years: €1305 Paper for the printer for 3 years: €945 4Gb Memory Pen for 14 members of the team (year 1): €1200

Custo total: 6300

4.6. Justificação do Equipamento 4.6. Equipment justification

4.6.1. Equipamento já disponível para a execução do projecto 4.6.1 Available equipment

Tipo de equipamento Fabricante Modelo Ano

Computer TOSHIBA Satellite 1900-303 2000

Computer Asus P4-B 2002

Printer Hewlett Packard Laserjet 400N 1999

Scanner Hewlett Packard Scanjet 5470 2002

4.6.2. Discriminação do equipamento a adquirir 4.6.2. List of new equipment requested

Tipo de equipamento Fabricante Modelo Custo envolvido (€)

Memo tape recorder SONY JCD-P330F 90

Justificação

The memo tape recorder will be used to collect data in interviews in each site to be observed and to edit material to produce examples and illustrations for the Guidelines for the design of scenarios for learning mathematics. Each tape recorder will be used by subgroups of 3 researchers and kept in the Project Office.

Memo tape recorder SONY JCD-P330F 90 Justificação

The memo tape recorder will be used to collect data in interviews in each site to be observed and to edit

material to produce examples and illustrations for the Guidelines for the design of scenarios for learning mathematics. Each tape recorder will be used by subgroups of 3 researchers and kept in the Project Office.



Video projector SONY VPL-CS20 1165 Justificação

During the Project meetings it wll be crucial to have the possibility of projecting the data and documents being discussed and analysed. The projector will serve also for presentations in workshops where this material is not available in Portugal. The video projector will be kept in the Project Office and for exclusive use of the Project team.

Computer SONY VAIO VGN-BX197XP 2430 Justificação

The computer will be used to produce reports, write articles and communications, edit and analyse video and audio records, edit and publish documents in the website of the Project. A portable computer allows members of the team to manage flexible forms of work. Data suggest that 4 computers are needed for the 15 members of the research team.







Video camera SONY DCR-DVD505E 1150 Justificação

The video camera will be used to collect data in each site to be observed and to edit and compose material to produce examples and illustrations for the Guidelines for the design of scenarios for learning mathematics. Each video camera will be used by subgroups of 3 researchers and kept in the Project Office.









Custo total: 15845

Equipa de investigação

-

5.1 Lista de membros (15) 5.1. Members list (15) Nome Name

Função Role

Grau académico Academic degree

%tempo%time

João Filipe Lacerda Matos Inv. Responsável AGREGAÇÃO 40 Mônica Maria Borges Mesquita Investigador MESTRADO 25 Madalena Pinto dos Santos Investigador DOUTORAMENTO 25 Susana Paula Graça Carreira Investigador DOUTORAMENTO 25 Maria Teresa Santos Faria Investigador MESTRADO 25 Isabel Maria Vieira Amorim da Silva Investigador MESTRADO 25 Neuza Sofia Guerreiro Pedro Investigador LICENCIATURA 25 Elsa Maria Santos Fernandes Investigador DOUTORAMENTO 25 Helena Isabel Pereira da Silva Gerardo Investigador MESTRADO 35 Maria Teresa Godinho Pereira da Silva Investigador LICENCIATURA 35 Alexandre José Santos Pais Investigador MESTRADO 35 Margarida Maria Sales Henriques Belchior Investigador MESTRADO 25 Nélia Maria Pontes Amado Investigador MESTRADO 35 Ana Sofia Pereira Alves Investigador LICENCIATURA 35 Rita Freitas Brito Mestre Investigador MESTRADO 25

Indicadores previstos -

Indicadores de realização previstos para o projecto Expected output indicators

DESCRIÇÃO DESCRIPTION 2007 2008 2009 2010 2011 Total

A - Publicações Publications

Livros Books

0 0 1 0 0 1

Artigos em revistas internacionais Papers in international journals

2 5 10 0 0 17

Artigos em revistas nacionais Papers in national journals

5 8 12 0 0 25

B - Comunicações Communications

Comunicações em encontros científicos internacionais Communications in international meetings

3 12 5 0 0 20

Comunicações em encontros científicos nacionais Communications in national meetings

5 5 8 0 0 18

C - Relatórios Reports

1 1 1 0 0 3

D - Organização de seminários e conferências Organization of seminars and conferences

0 1 1 0 0 2

E - Formação avançada Advanced training

Teses de Doutoramento PhD theses

0 0 4 0 0 4

Teses de Mestrado Master theses

0 2 2 0 0 4

Outras Others

0 0 0 0 0 0

F - Modelos Models

0 0 0 0 0 0

G - Aplicações computacionais Software

0 0 0 0 0 0

H - Instalações piloto Pilot plants

0 0 0 0 0 0

I - Protótipos laboratoriais Prototypes

0 0 0 0 0 0

J - Patentes Patents

0 0 0 0 0 0

L - Outros Other

0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

Acções de divulgação da actividade científica Scientific activity spreading actions (Estimula-se a apresentação e propostas neste âmbito que possibilitem a aproximação da actividade científica ao grande público) (It is strongly desired the presentation of proposals within this subject that will approach science to the general public.)

Members of the research team of Project have for a long time a tradition of spreading mathematical ideas and processes for a variety of audiences – from children in primary school to teachers in science and mathematics and adults who seek for formal recognition of competences. However, within this Project an effort will be made to turn into simple forms the results of the research providing examples in order to show evidence how people use and learn mathematics in the practices where they are involved in their lives (from pupils to pre-service teachers and other professionals). In doing this, we aim to deconstruct the formal and distant character of mathematics bringing it to the everyday of people through applications and modelling. The web-based materials that will be developed and published will also contribute to spread a social vision of mathematics.

8.1 Resumo

Resumo (em português) Abstract (in portuguese)

O Projecto adopta uma estratégia que coloca em diálogo o campo teórico e o campo empírico da investigação em quatro fases: 1) especificação de uma 1ª versão do esquema conceptual para aprendizagem matemática tomando como base trabalho anterior de membros da equipa; 2) análise de tendências existentes na aprendizagem matemática numa variedade de práticas e produção de 4 etnografias das práticas observadas para identificar e caracterizar aquelas tendências (e.g. interacção horizontal entre participantes numa mesma prática conduzindo a aprendizagens matemáticas); 3) consideração dos resultados da fase 2 na reelaboração do esquema conceptual desenvolvido sobre aprendizagem matemática dando origem a uma 2ª versão; 4) desenvolvimento, a partir daquele esquema, de um conjunto de linhas orientadoras para o design de cenários para aprendizagem matemática (em forma de hipertexto incluindo exemplos extraídos das etnografias). O esquema teórico baseia-se numa perspectiva situada da aprendizagem articulada com a educação matemática crítica e mediação semiótica. Isto permitirá utilizar o conhecimento produzido em projectos anteriores (Projecto Mathematical Thinking, Projecto Pensar a Aprendizagem e Projecto WebLabs). A base empírica será concretizada em 4 etnografias de práticas em que a aprendizagem matemática é significativa a fim de identificar e caracterizar (i) os artefactos usados pelas pessoas nas suas práticas e o seu papel mediador na aprendizagem matemática e no desenvolvimento de competências matemáticas (com especial atenção às TIC); (ii) o reportório partilhado nas práticas, em particular a sua natureza matemática; (iii) a organização social das práticas; (iv) o desenvolvimento dinâmico das identidades dos participantes e do seu sentido de pertença às comunidades. Será objecto de observação um conjunto de locais para recolha de dados, incluindo: práticas escolares em matemática (2 locais em turmas entre o 3º e o 9º ano de escolaridade), formação inicial de professores de matemática em estágio (1 local), orientação de projectos envolvendo matemática e TIC em desenvolvimento em escolas (1 local), e matemática do espaço de trabalho (2 locais tais como enfermagem e restauração). A recolha de dados terá lugar através da imersão dos subgrupos de investigadores no terreno adoptando uma abordagem etnográfica

e utilizando gravadores vídeo e áudio uma vez acauteladas todas as questões de natureza ética envolvidas. O trabalho no terreno terá lugar durante cerca de 6 meses em cada local dado que o elemento tempo constitui um factor crítico na qualidade dos dados recolhidos. As sessões de análise de dados subsequentes têm como objectivo (i) produzir 4 ‘etnografias da prática’, e (ii) produzir evidência, aperfeiçoar e consolidar a 2ª versão do esquema conceptual para aprendizagem matemática. As etnografias constituirão narrativas analíticas de práticas específicas e actuarão como casos que mostrarão evidência de como a participação nas práticas se desenvolve e como a aprendizagem matemática ocorre e se torna visível. Estas etnografias alimentarão igualmente o desenvolvimento de materiais e exemplos para apoiar o uso do esquema conceptual e das linhas orientadoras para o design de cenários para a aprendizagem matemática. A infra-estrutura do Projecto colocará em articulação a competência de investigadores seniores e de jovens investigadores em conjunto com o uso de uma plataforma colaborativa (em Moodle) como forma de trabalho conjunto e repositório de versões sucessivas de documentos a elaborar no seio do Projecto. No final, o site e a plataforma serão adaptados à forma de um portal em Educação Matemática e Sociedade. Algumas questões chave de investigação orientarão o trabalho de forma a mantê-lo focado, tais como: como são socialmente constituídas nas práticas as competências matemáticas? como é que a aprendizagem matemática se articula com as formas de participação das pessoas nas diversas práticas? que artefactos, em especial de natureza tecnológica, (e.g. ferramentas diárias de trabalho, plataformas para colaboração, etc) estão envolvidos como elementos de mediação e que papel têm na aprendizagem matemática? que implicações se pode tirar para o design de cenários para aprendizagem matemática? O Projecto terá um impacto assinalável num número elevado de profissionais da educação (nomeadamente em professores de matemática e em outros profissionais ligados à formação como por exemplo em Centros de Reconhecimento e Certificação de Competências e Centros de Competência) quer através das comunicações, workshops e posters quer através dos artigos e demais publicações previstas. O website do Projecto servirá como recurso para tomada de contacto com o esquema conceptual e as linhas orientadoras para o design de cenários para aprendizagem matemática criando condições para a valorização de uma visão da aprendizagem e das competências matemáticas que tenham em consideração a sua dimensão social e tecnológica. 

Resumo (em inglês) Abstract (in english)

Project Learn adopts a strategy that puts in dialogue the theoretical field and the empirical field of research in four phases: 1) elaboration of 1st version of the theoretical framework for mathematical learning taking as a basis previous research of several members of the team; 2) analysis of learning processes and practices in a variety of sites in the empirical field, with production of 4 ethnographies of practices, making possible to identify and characterize common trends in learning (e.g. a trend to horizontal interaction between practitioners, leading to learning mathematics); 3) results of phase 2 will feed into the theoretical framework giving birth to a 2nd version of the framework; 4) drawing on that framework, a set of guidelines for the design of learning scenarios in mathematics will be produced (hypertext document together with examples under the form of web-based materials). The theoretical framework will draw on a situated perspective on learning articulated with a perspective of critical mathematics education and using tools of semiotic mediation theory. This will allow taking on board previous results of research projects of the senior researchers (projects Mathematical Thinking, Reflecting on Learning and WebLabs). The empirical basis of the project will be 4 ethnographies of practices where mathematics has a significant role in order to identify and characterize (i) the artefacts used by people in their practices and its mediating role in mathematical learning and development of mathematical competences (with special attention to ICT), (ii) the shared repertoires of the practices, in particular its mathematical nature, (iii) the social organization of the practices, (iv) the dynamic development of participants’ identities and sense of belonging to communities. A set of sites will be addressed as empirical field for observation and data collection, including: schooling practices in mathematics (2 sites in classes between 3rd and 9th grade), mathematics pre-service teachers’ education (1 site), supervising mathematics-ICT projects developing in schools (1 site), workplace (2 sites, such as nursery practice and restaurant service). Data collection will take place through an immersion of subgroups of researchers in the selected sites, adopting an ethnographic stance and using video and audio digital recording devices after assuring all the ethical issues that may be involved. Field work is planned to take an average duration of 6 months in each site as time shows to be a crucial factor in quality of data collected. The analysis workshops will address the data collected aiming to (i) produce 4 ‘ethnographies of the practices’ that will be published as independent booklets, and (ii) to produce evidence, improve and consolidate the conceptual framework for learning. The ethnographies are self-contained analytical narratives of specific practices and will act as case studies showing evidence how participation in practices develops and how learning occurs and is visible. These ethnographies will also feed in the development of examples and suggestions to support users of the conceptual framework and of the design for mathematical learning. The infrastructure of the Project will put together the expertise of senior and young researchers together with the use of a web-based platform (on Moodle) as medium for

interaction and work of participants and repository of all types of materials produced within the Project by the research team. Coming to the end of the Project this platform will be redesigned as a portal on Mathematics, Education and Society. Key research questions will serve as orientations to keep the team focused, such as: how is mathematical competence socially constituted and constructed in practices? how does mathematical learning articulate with forms of participation in the practices? What artefacts, specially of technological nature (e.g. everyday computational tools, platforms for collaboration, etc) are involved as mediators and what role do they have in mathematics learning? what are the implications for the design of learning scenarios in mathematics? It is expected that the project has a relevant and direct impact on a number of professionals in education (namely on mathematics teachers and other professionals dealing with education and training in mathematics such as Centres for Recognition and Certification of Competences in adults, Competence Centres for ICT in Education) both through articles and communications in Conferences, workshops and posters and publications with the results of the Project. The Project website will serve both during the Project and at its end, as a resource for practitioners to get in touch and use the conceptual framework and Guidelines developed thus creating conditions for valuing a perspective on mathematics learning and competences that consider its social and technological dimensions. 

8.2. Objectivos 8.2. Objectives Descrição dos Objectivos do Projecto Project Objectives (description)

Objectives: a) iteratively develop a framework for mathematical learning, and b) elaborate a set of guidelines for the design of learning scenarios in mathematics with emphasis on the relationships to information technology and society. This development will draw on previous research of members of the project and will follow four phases: elaboration of 1st iteration of the framework; identification and analysis of trends on learning in a variety of practices (including school); 2nd iteration of the framework; elaboration of guidelines for the design of learning scenarios. The project will produce (i) booklet with key principles of the framework, (ii) set of guidelines for the design of scenarios for learning mathematics with technological and social dimensions, (iii) set of web-based materials to help users make sense of the design and to support its use, and (iv) set of ethnographies of practices, papers, Seminars and workshops to disseminate the results among researchers and teachers.

Descrição dos Objectivos do Investigador Responsável Principal Investigator Objectives (description)

This project is central in the Research Program Learn 2006-2012: Mathematics, Technology and Society aiming to consolidate and expand the previous research program Learning 1996-2006 – a constellation of projects who explored possibilities to approach learning in mathematics bringing in the social and cultural dimensions. Goals for Research Program Learn 2006-2012 are: (i) to refine, empirically document and disseminate a framework for the design of learning mathematics, (ii) to develop human capital (7 to 9 PhD and 14 to 16 MSc researchers) to elaborate further developments and implementation of the framework and learning design, (iii) to implement and sustain a portal on the web providing materials, guidelines and advise to newcomers in the field of mathematics education, technology and society, (iv) produce a PhD Program on ICT and Mathematics Education to be submitted to the Univ. of Lisbon, and (v) to produce recommendations for curriculum development in mathematics.

8.3. Estado da Arte 8.3. State of the Art Descrição do Estado da Arte State of the Art (description)

A considerable body of work has been and is being produced within the mathematics education international community that focuses on mathematical learning. We refer to areas such as problem solving, geometry with ICT, advanced mathematical thinking, etc. and such work is apparent in publications such as the recent Journal of Mathematical Thinking and Learning. Piaget’s enormous contribution to the study of learning is well known and his influence can be found in many studies of developmental psychology in mathematics education. However, its orientation has been, in the main, to identify what is particular about mathematical learning as distinct from other areas of the curriculum and to elaborate on how best to enable or facilitate this in students. Most of this work has drawn on analysis of mathematics itself and/or on psychology. Structures of mathematical thinking for abstraction, for problem posing and solving as well as classroom strategies have been developed and became key texts and key strategies in the teaching and learning of mathematics around the world.

In the field of mathematics education research, more and more authors bring in social aspects of learning mathematics (Matos et al., 2001). While analyzing what is taking place for an individual as he/she learns mathematics, one looks also at individuals interacting with others in learning, even if in this final activity ‘others’ are in the form of texts, or other people as virtual conversational partners. For example, drawing on a situated perspective on learning (Lave & Wenger, 1991; Wenger, 1998), Santos (2004) has shown how mathematics – while domain that lives within a variety of practices – takes form as knowledge in the interaction with the structuring resources of the practices where it is used. These resources are not confined to artefacts (e.g. calculator, tables, school procedures) and to the resources of the practice that seem to be immediately connected to mathematics (e.g. currency system). In fact, she found evidence that there is a relevant dimension of structuring in elements such as the status of the participants in the practice, the explicit presence that mathematics has in the story of the practice (e.g. its visibility in the repertoire shared by participants in the practice), the importance recognized to mathematics as a resource used to get access to positions of power, and the meaning of belonging to the community where the practice unfolds. Putting participation as the core of learning of people in action (as agents of activity and members of communities) and bringing in the complex relationships of participation to the social world (with its meanings, structure and constitutive order), Santos (2004) recognizes participation in activities in context (with its structuring resources, artefacts, discourses, history and systems of activities) as the key issue to learning. It is this orientation that led us to ask in this Project research questions strongly framed by a situated perspective on learning in order to establish a rather solid basis for the construction of the framework. The notion of semiotic mediation brings together the social origins of consciousness, the function of language as cultural artefact of the practice and the meaning-making process based on prior network of experiences (captured in the semiotic triad of Peirce). As in the learning of a second language, the process of learning scientific concepts in any setting stands on a range of meanings previously developed and originated within daily experiences. Such knowledge spontaneously produced becomes a mediator in the learning of new knowledge (Carreira & Lerman, 2006). A fundamental issue to be taken from Vygotsky is that scientific concepts require for their production and development a certain basis of spontaneous concepts. Furthermore, one important condition for the learning of scientific concepts (such as in mathematics) is the need to make them consciously the object of thinking, manipulation and use. The learning of a scientific concept is not a straightforward process. It takes a history that eventually will place it within a conceptual system. Its function is not the ´defeat´ of spontaneous concepts, as poor and distorted structures to be overcome, but instead it will rehabilitate such concepts as equally powerful in the active and often creative production of meaning (Carreira & Lerman, 2006). For every scientific concept, the relationship with objects is mediated from the very start by some other concept. As semiotic mediation proved to be a rather useful tool for analysis of leaning, it is brought in the framework of this Project. The ideas emerging from the work of Núñez, Edwards & Matos (1999) contain several implications that are of clear relevance in the plane of mathematics education. Perhaps one of the strongest is their claim that regardless of all the efforts to give mathematics a rigorous and formalist dimension, independent of the nature of human reasoning, mathematics and mathematicians can not do without metaphorical ideas like the number line or the natural continuum sense for a continuous function. In the field of mathematics education, mathematical models and metaphors have also been the subject of inquiry. The apparent closeness between model and metaphor stimulates the approach to mathematical models and modelling from the point of view of metaphor. In producing a mathematical model we would be creating a web that connects and brings closer different conceptual domains. Through such a web relationships between separated domains become possible. A mathematical model reveals itself as a model of something when its metaphorical matrix is unpacked and put into action (Carreira, 1998). Metaphorisation becomes, as such, an essential part of thinking mathematically and of the process of making mathematical ideas mean something both within mathematics and outside it. As people work on mathematical models of different phenomena the metaphorical matrix of a model works as a mathematical artefact. Mathematics can therefore work as a way of ´seeing as´. The meaning of mathematical concepts and processes becomes a double-anchored meaning. Unpacking a metaphorical matrix directs our attention to who does the unpacking and what constitutes appropriate unpacking in any specific context, and hence the notion of mediation. Here the core of metaphorisation is the invitation to interpretation and to the production of alternative views. In that sense, it means an extension of interpretative chains in the semiotic process.

Although being quite common to assert the importance of mathematics in the development of the modern society, as recent international studies show (e.g. PISA) most of the people who benefit from learning mathematics in school only use a very small part of what they learnt and are too far away of taking a critical stance when facing the ways mathematical models affect their life. Mathematics supports the modulation and constitution of a wide range of social phenomena, and in this way mathematics becomes part of reality (Skovsmose, 2005). Our everyday integrates a model-supported virtual reality with an already constructed reality in a mix that has no parallel in history and in doing this such information technology materialises in ‘packages’ containing mathematics as a key defining ingredient. Thus, mathematics being so embedded in technology and society would be enough to justify why bringing in technology (specially ICT) in this Project. Although we find a large body of research in science education dealing with a perspective coined as Science, Technology Society (Bauchspies et al., 2006) this is not the case in mathematics education. Therefore, it is apparent a need to fill in the existing gap in the development of research in this area. Although we find in the international mathematics education community a relevant development in terms of mathematics, technology and society, in Portugal we are making the first steps and we count no more then 5 the number of pieces of research in the field. In conclusion, there is a lack of theoretical frameworks that approach mathematics education from a social /semiotic / situated point of view. Thus, based on consolidated work from several members of the research team, the Project aims to develop such a theoretical framework and guidelines for the design of scenarios for learning mathematics – including dimensions of technology and taking into consideration the relationships between Mathematics and Society. References: Bauchspies, W., Croissant, J. & Restivo, S. (2006). Science, Technology, and Society: A Critical Introduction. Oxford: Blackwell Publishing. Carreira, S. (1998). Significado e Aprendizagem da Matemática: Dos Problemas de Aplicação à Produção de Metáforas Conceptuais. Unpublished Doctoral Dissertation, University of Lisbon. Carreira, S. & Lerman, S. (2006). Semiotic Mediation and Metaphor in Teaching and Learning Mathematics. Unpublished paper. Lave, J. & Wenger, E. (1991). Situated Learning – legitimate peripheral participation. New York: Cambridge University Press. Matos, J.F., Carreira, S., Santos, M., Lerman, S., Evans, J. & Tsatsaroni, A. (2001). Researching School Mathematical Thinking and Practices. Unpublished Final Report of Project Mathematical Thinking. Núñez, R., Edwards, L. & Matos, J.F. (1999). Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, (39), pp. 45-65. Santos, M. (2004). Encontros e Esperas com os Ardinas em Cabo Verde: Aprendizagem como Participação em Práticas Sociais. PhD Thesis, Mathematics Education, University of Lisbon. Skovsmose, O. (2005).Travelling Trough Education: uncertainty, mathematics, responsibility. London: Sense Publishers Wenger, E. (1998). Communities of practice – learning, meaning and identity. Cambridge: Cambridge University Press.

8.4. Resultados e Repercussões 8.4. Results and Repercussions Divulgação de Resultados (descrição) Diffusion of Results (description)

From the early beginning of the Project LEARN the research team will open a site and a platform (based on Moodle). This will allow the permanent diffusion of the Project through the documents published on the platform for the general public, News and Resources for people who register and become regular visitors of the Project platform. Diffusion will include also the presentation of the Project in the annual meeting of the Association of Teachers of Mathematics, of communications, workshops and posters in both national and international Conferences and Seminars. This will assure the diffusion of the Project both at a national and an international level. A number of publications will contribute to the diffusion of the Project: articles in mathematics journals of reference, 4 booklets with ethnographies and 1 booklet with Learning Framework and Guidelines (collected in a book at the end of the Project) together with multimedia web-based versions. All the documents produced

will be available on the website of the Project.

Repercussões (descrição) Repercussions (description)

The project will impact on three levels: 1) Impact on mathematics teachers’ practices in schools and other professionals dealing with mathematics education. A number estimated as 3500 to 4000 teachers will be directly exposed (both in national meetings and in paper and web publications) to (i) a theoretical framework that takes learning mathematics as inherent to participation in meaningful practices and (ii) to Guidelines for the design of scenarios for learning mathematics with a technology and society dimension (see Diffusion of the Project). Previous work with teachers using ideas for such a framework has shown that it is plausible that many of the teachers will take onboard relevant aspects of the framework given that it makes a step forward if compared with traditional constructivist approaches to teaching and learning mathematics. In particular, the Guidelines for design of scenarios will contain ideas, examples and suggestions that will have repercussion in the practices of a number of teachers and other practitioners. 2) Impact on the research team. The group of researchers that form the research team includes 11 young researchers. At the moment of submission of this proposal, it is guaranteed that from those, 4 will develop and complete their doctoral dissertations (the all 4 are registered in July 2006 in a doctoral program) and 4 will develop and complete their Master thesis within the project. From the 4 doctors/PhD senior researchers included in the team 2 of them are in the process of preparing the creation of research programs in the field of mathematics education to be started after 2010 in their institutions (University of Madeira and University of Algarve). This suggests the development of a critical mass in the area of mathematics education and society in Portugal with links to the international community. 3) Impact on the resources available for mathematics educators and teachers. As a side-product, the project will put together seminal documents that we can not find today in Portugal (in particular a Learning Framework, Guidelines and examples for the design of scenarios for the learning of mathematics including a dimension of technology and society). Those resources will be organized in a portal aimed to constitute a reference for the Portuguese speaking mathematics teachers and educators – thus constituting an element with rather strong potential impact on the intended audience. When the project comes to an end the principal researcher will seek for solutions for the sustainability of the portal addressing the Centre for Research in Education.

8.5. Regionalização 8.5. Regionalization Região Region

Percentagem Percent

Norte 0 Centro 10 Lisboa e Vale do Tejo 55 Alentejo 0 Algarve 20 Região Autónoma dos Açores 0 Região Autónoma da Madeira 15 Descrição Description It is anticipated that the project will have impact in the institutions of some of the researchers involved and in teachers and other professionals related to those institutions. Besides the researchers working in the area of Lisbon, there is: - 2 members of the Project team are teachers at the University of Algarve with large contacts with schools in the area - 1 member of the Project team is teacher at the University of Madeira with close relationships with schools in the area and with local educational authorities.

Thus, the regionalization will go both trough the participation of educationally influent people from different areas of Portugal and through the impact of the actions of the project in the populations (mostly teachers and children).

8.6. Tarefas 8.6. Tasks Descrição da tarefa

Designação da tarefa

Task 1: Project Management Data de início

Data de fim

Duração (em meses)

Pessoas * mês nesta tarefa

01-09-2007 31-08-2010 36 9 Resultados esperados Expected results Objectives: - Set in place effective and efficient conditions and management structure to include project coordination and financial management - Monitoring progress of deliverables. Milestones and expected results: Month 1: Project infrastructure Every 2 months: Meetings of the whole Project team will be held in general every two months although it is expected that for some tasks it will be necessary to have extra meetings. The Project will organize groups of team members that will be allocated to work in specific tasks. The use of the Project platform on Moodle will allow researchers to interact at distance and in asynchrony mode sharing drafts and co-writing documents in Wiki. Annual reports will be submitted in months 12, 24 and 36 (together with Final Report). Annual auditing (with the two consultants) will feed into the following year’s planning. Result: conditions of work, effective and efficient scientific and financial management procedures in place. Descrição da tarefa Task description Task 1.1 will be to set-up in place structures (including a website and a Moodle platform for collaborative work on the web) and appoint a coordinator to management of the financial procedures. This will be done on month 1. It will be allocated to the project the room C.3.2.11 at Building C3 of the Faculty of Sciences of the University of Lisbon (around 36 m2) in use for several years for research projects coordinated by the Principal Researcher. That room will serve as Project Office with the facilities already in use (namely 2 computers, laser printer, scanner, phone and fax line, 4 points of internet connection); all the equipment and bibliography of the Project and folders with data collected will be kept in the Project Office for the three years of the work. Meetings of the whole research team will be held at room C4.1.17 at Building C4 of FCUL. Task 1.2 will be to manage the project and monitor progress and deliverables. The Principal Researcher will coordinate all the scientific aspects of the project. The person appointed to manage the project will take charge of all the financial and material aspects of the project including preparing cost statements, storing and managing data collected for the Project, draft copies of field reports, articles, web-based materials and resources, logs of meetings of the research team, etc. A log of evolving decisions will be setup on month 1 and will be maintained along the 36 months. This will be logged at the project website and Moodle platform which will include also detailed description of the work being done in each Task. Task 1.3 will be concerned with production of reports to the funding agency FCT taking into account the tasks done, the deliverables prepared and the results achieved (including the annual scientific auditing of the project by the two consultants).

Deliverables: D1.1.1. Project infrastructure (working space, website and Moodle platform for the project) D1.2.1. cost statements (every 6 months or according to the specified rules of FFC-UL) D1.3.1. progress report year 1 D1.3.2. progress report year 2 D1.3.3. final report (together with progress report year 3)


Task 2: Learning framework (1st iteration) Data de início

Data de fim



01-09-2007 30-02-2008 6 20 Resultados esperados Expected results Objective: Specify a framework to address mathematical learning in society (including when appropriate a dimension of technology) drawing on situated approaches to learning, critical mathematics education and semiotic mediation literature Milestones and expected results: Month 2, 4 and 6: workshops Month 6: completion of deliverables D2.1.1., D2.1.2. and D2.1.3. Result: specification of 1st version of the theoretical framework for learning mathematics with a dimension of society and technology. Descrição da tarefa Task description Task 2.1. will be updating and critically reviewing the literature concerning learning from a situated point of view, a critical mathematics education approach and a semiotic mediation perspective. Although some of the members of the research team have a deep understanding of the situated perspective of learning, the critical mathematics education perspective and the semiotic mediation approach, there is a need to establish a basis for the framework that serves as reference for further development. On the other side, it is quite important that all the members of the team (specially the young researchers) come into a common understanding of the key concepts of the basic framework. A set of key papers and chapters will be selected for reading and analysis from groups of the research team. Presentations in subgroups will be prepared for the workshops of Task 2.2. Task 2.2. will be organizing and putting in action a set of three workshops for discussion and organization of the core ideas of the theoretical perspectives brought in. All the members of the project team will be involved in this task participating in the writing and/or acting as critical readers of parts of the framework (together with one or two consultants in the 3rd workshop). All members of the research team will be involved in the tasks working in groups of 3 or 4 for the purpose of exploring, elaborating and organizing particular aspects of the framework. Deliverables: D2.1.1. delineation and description of 1st iteration of the theoretical framework D2.1.2. map of concepts D2.1.3. table of key categories for analysis coming out from the framework D2.2.1. three workshops for delineating the core ideas of the theoretical framework


Task 3: Preparation and methodology for field work Data de início

Data de fim



01-01-2008 31-03-2008 3 10 Resultados esperados Expected results Objectives: - Identify a set of sites to be used as empirical field in the Project - Specify a methodology for data collection under an ethnographic perspective including ethical issues, tools and strategies for field work - Specify a methodology for data analysis and for the construction of an ‘ethnography of practice’ including organizing strategies and tools Milestones and expected results: Month 6: completion of deliverables D3.1.1. and D3.2.1. Month 7: completion of deliverables D3.3.1., D3.3.2. and D3.4.1. Results: identification of sites to serve as empirical field, specification of methodology for data collection and analysis Task 3.1. will comprise the identification of sites for data collection. These sites will be chosen according to a set of criteria which include (i) the access to the practice (as a participant observer), (ii) the existence of mathematics in the practice to be observed (even if not immediately identified by the participants as mathematical), (iii) a guarantee that the practice will run for the period foreseen for data collection, (iv) the existence of a variety of types of sites in terms of domain of practice (e.g. mathematics classes in school, mathematics teacher in-service education, development of projects on mathematics and ICT in schools, nurses’ activities in hospital, restaurant service). Members of the research team will be allocated to sites in groups of 2 or 3 people. Task 3.2. will be to specify strategies and procedures to approach sites, to get the necessary authorizations and to firm an agreement with people responsible in each site, to identify key informants in each site and plan the field work according to a specific schedule. Task 3.3. will be to specify guidelines and procedures for data collection and storing which include: (i) recording with video cameras of relevant segments of the practice observed in a site, (ii) audio record of informal / semi-structured interviews with key informants in the context of the practice being observed, (iii) collecting and /or photographing artefacts used in the practice. Task 3.4. comprises the specification of forms of analysis of the data collected and the basic layout for writing the ethnographies. This task is two fold: (i) to organize data in order to produce the ethnography of the practice observed, and (ii) to produce evidence to feed in and develop the 2nd iteration of the learning framework in Task 4. All the members of the research team will be involved in these tasks. For Tasks 3.1. and 3.3. subgroups of 2 or 3 people will be formed according to the specificity of the sites to be addressed. For tasks 3.2. and 3.4. the team will work in subgroups of 4 to 5 people. Deliverables: D3.1.1. list of sites to be addressed as empirical field together with names of members of the research team involved in the observation of each specific site D3.2.1. delineation of procedures to approach sites for field work D3.3.1. guidelines for participant observation and data collection using video recording cameras D3.3.2. guidelines for interview and data collection using audio tape recording D3.4.1. delineation of procedures for organizing, reducing and analyzing data collected and of basic layout for the ethnographies


Task 4: Field data collection Data de início

Data de fim



01-03-2008 31-12-2008 10 34 Resultados esperados Expected results Objectives: Collect data in a variety of sites orientated to produce ethnographies of the practices observed Milestones and expected results: Month 7 and 8: immersion in the sites where develop the practices to be observed; report on the approach taken Month 7 to 16: collection of data according to the guidelines defined in Task 3 Month 8, 10, 12 , 14: reporting on the development of the field work in each site Month 16: a set of folders organized with data collected in the various sites observed. Results: empirical organized data from a variety of practices in different sites including mathematics (with a dimension of technology) that will serve as the raw material for the production of ethnographies of practice and evidence for the 2nd version of the leaning framework. Descrição da tarefa Task description Task 4.1. will be the approach to sites and negotiation of ethical issues and conditions for participant observation of practices and the tentative inclusion of practitioners of the site in the process of data collection (and if possible in the preliminary analysis) Task 4.2. comprises the immersion of subgroups of 2 or 3 members of the research team in each site where the selected practices are to be analyzed, collection of video records and photographs of segments of the practice observed, interviews to key informants in each site, collection of artefacts used in the practice and finally the closing of the ‘visit’ to the site ensuring that both researchers and practitioners got the most of the research procedure Task 4.3. will be the organization of data being collected into a form that allows other members of the research team to inspect and analyze the material collected. This is accomplished through storing key segments of video clips, audio and text into a data basis-like system in the Moodle platform of the project for further analysis by other members of the research team. All members of the research team will be involved in the tasks. Subgroups will be formed according to the specificity of the sites to be approached (regarding Tasks 4.1. and 4.2.). For Task 4.3. the subgroups will share common forms of organization of data collected and will meet in plenary sessions for organization. Deliverables: D4.1.1. reports on the success of the approach taken to each site D4.2.1. reports on the situation of data collection through the participation of the researcher in the practice observed (every 2 months) D4.3.1. folders including data collected organized by site and report listing all data collected


Task 5: Data analysis Data de início Start date

Data de fim End date

Duração (em meses) Duration (in months)

Pessoas * mês nesta tarefa Person * month in this task

01-01-2009 31-12-2009 12 34 Resultados esperados Expected results Objectives: - Analysis of data collected for identification of learning trends in people participating in the practices and the associated contextual factors. - Production of a set of 4 ethnographies of practice - Delineate results to feed the 2nd iteration of the learning framework (see Task 6) Milestones and expected results: Raw data will be organized and analyzed in subgroup workshops including the team members who collected data in the field. Essential results will be produced using the learning framework and the table of categories and the map of concepts (see Task 2) including for example the meaning and role of mathematical artefacts in the practice, the forms of participation, the shared repertoire and its mathematical nature. Result: a corpus of results from the empirical data showing evidence of the forms of learning in different practices and how mathematics permeate learning; as products the project will produce a set of four ethnographies of the practices observed Descrição da tarefa Task description Task 5.1. Data analysis will follow a model based on three phases. First, data from each site will be organized as a narrative with identification of key informants, relevant bounded episodes and possible trajectories of learning and participation in the practice observed. Second, a systematic search for evidence for the criteria defined in the theoretical framework will be put in place and marked as possible partial results. Third, a cross-site view will provide evidence for similarities and differences together with situated explanations for it. The key issue in this analysis is the identification of learning trends in people participating in the practices and the associated contextual factors. Special attention is paid to mathematical aspects of the practice including dimensions of technology (such as the use of computational tools, collaborative platforms, etc). Task 5.2. As a way of making more public the analysis and putting it in context, 4 sites will be selected (according to the quality of the data collected and in a variety of domains) and for each one of those 4 it will be elaborated an ethnography of the correspondent practice in that site. The ethnography of the practice is an analytical description of the practice (average size of 12000 words) including the key elements coming from the analysis done in Task 5.1. The ethnographies will be developed according to a basic layout defined by the team in Task 3.There will be a paperback version and a web-based version of the ethnographies including short illustrative video clips and excerpts of dialogues hyperlinked to the analysis. All members of the team will be involved in the tasks of analysis and production of results. The writing of each one of the 4 ethnographies will involve directly one or two researchers in each and the others will act as critical readers. Deliverables: D5.1.1. six subgroups’ workshops for the analysis and two workshops of the whole research team for discussion of trends identified in learning D5.1.2. summaries of the results produced with explicit reference to exhibits showing evidence of those results D5.2.1. set of 4 ethnographies of practices involving mathematics and a technological dimension (to be published at the end of the Project).


Task 6: Learning framework (2nd and final version) Data de início

Data de fim



01-01-2010 31-05-2010 5 11,2 Resultados esperados Expected results Objectives: Specify a 2nd version of the theoretical framework to address mathematical learning drawing on a situated approach to learning, perspective of critical mathematics education and semiotic mediation literature putting the 1st version in dialogue with the results obtained in Task 5 Milestones and expected results: Month 28: completion of deliverables D6.1.1., D6.1.2. and D6.1.3. Result: specification of 2nd version of the theoretical framework. Descrição da tarefa Task description Task 6.1. will be develop a 2nd version of the elaboration of the theoretical framework based on the 1st version and the results from the empirical field. This will be accomplished through the systematic test of evidence and results from the empirical field against the 1st version of the framework. It is expected that the framework is refined in terms of more specific relationships between concepts such as, for example, adding complexity to the web of relations between participation and reification of practices in mathematical artefacts used by people, extending previous concepts to new meanings, adding forms of representation through new uses of artefacts and refining the map of concepts produced in 1st iteration together with a refined table of key categories. This will involve a set of two workshops of the whole team (at least one including the two consultants) to establish the agreed final version of the framework. As in Task 2 (1st version of the framework), all members of the research team will be involved in these tasks working in groups of 3 or 4 for the purpose of elaborating and reorganizing particular aspects of the framework. Deliverables: D6.1.1. 2nd and final version of the conceptual framework (whose publication will be proposed to the Centre for Research in Education of FCUL at the end of the Project) D6.1.2. 2nd version of the map of concepts D6.1.3. 2nd version of table of key categories coming out of the framework


Task 7: Guidelines for design of learning scenarios Data de início

Data de fim



01-04-2010 31-08-2010 5 11,2 Resultados esperados Expected results Objectives: Specify a set of guidelines for the design of mathematics learning with web-based examples Organize the web-based examples in a portal on mathematics education, technology and society Milestones and expected results: Month 36: completion of deliverables D7.1.1., D7.1.2. and D7.2.1. Result: guidelines for design of learning scenarios in mathematics. Descrição da tarefa Task description Task 7.1. will consist of the elaboration of a set of guidelines for the design of scenarios that promote mathematics learning. This will involve the preparation and implementation of a set of three workshops of the whole team (the last one involving also at least one of the 2 consultants) to devise the structure of the guidelines, the relations to the conceptual map, the forms of exemplification through short cases (taken from the ethnographies) illustrated by transcripts and short video clips and an helpdesk for users to be provided on the platform. Task 7.2. will be filling in examples (including short video clips and illustrative texts and excerpts from interviews hyperlinked to the guidelines) giving them a final form as a web portal for Mathematics Education and Society. All members will be involved in Task 7.1.. A first draft of the guidelines will be prepared by a subgroup and the other members will act as critical readers. A second subgroup will be in charge of Tasks 7.2. including the organization and articulation of the examples with the guidelines and giving final form to be web-resources in the form of a portal. Deliverables: D7.1.1. guidelines for the design of learning scenarios for mathematics (to be published together with D6.1.1.) D7.1.2. set of web-based materials for virtual exploration in mathematics (including learning objects and video clips) in connection to technology and real world situations in society at large D7.2.1. portal including all the materials developed within the project under the name Mathematics Education and Society


Task 8: Dissemination of results Data de início

Data de fim



01-02-2008 31-08-2010 30 29 Resultados esperados Expected results Objectives: Make public the intermediate and final products of the project, specially to intended audiences of mathematics teachers, teacher trainers, other professionals involved in mathematics education and researchers Milestones and expected results: During the project the key documents produced will be published at the website. The number of articles written by members of the research team (from month 6 on) will increase according to the development of the framework for learning mathematics and the guidelines for the design of scenarios. Month 6 to month 36: deliverables D8.1.1. Month 36: deliverables D8.1.2. to D8.1.5. Result: Dissemination of the Project through a set of communications presented in national and international Seminars and Conferences; deep participation in the scientific program of the 5th edition of the Mathematics Education and Society Conference; a set of articles in national and international journals; a set of 4 booklets including the ethnographies produced and a booklet with the final version of the framework and the guidelines for the design of learning scenarios for mathematics (collected in a book at the end of the Project); a web-based site and platform coming into the form of portal by the end of the project. Descrição da tarefa Task description Task 8.1. will be the systematic dissemination of the intermediate and final products of the project through three key forms: (i) participation of the team members in national and international Seminars and Conferences presenting communications and posters (including the Annual Seminar for Research in Mathematics Education organized by the Association of Teachers of Mathematics in Portugal, the Meeting for Research in Mathematics Education organized by the Portuguese Society for Sciences of Education, the annual Conference of the International Group for the Psychology of Mathematics Education - PME, the 5th Mathematics Education and Society Conference – MES5, the 11th International Conference on Mathematics Education – ICME-11); (ii) publication of a set of 4 booklets with ethnographies of practices; (iii) publication of a set of articles in national and international journals (with referee) including Quadrante, Revista Educação e Matemática, Revista de Educação, Revista Portuguesa de Educação, Educational Studies in Mathematics, Journal for Mathematical Thinking and Learning, For the Learning of Mathematics, Journal for Research in Mathematics Education; (iv) systematic dissemination of intermediate products on the project web site and Moodle platform (making it a portal by the end of the project); (v) organizing the scientific programme and presenting in rather extensive form the Project in the 5th International Conference for Mathematics Education and Society to be held in 2008 in Portugal and the Seminar to be promoted by the Centre for Research in Education of FCUL in 2009 at the end of the Project; (vi) publication (which will be proposed in 2009 to the Centre for Research in Education of FCUL) of a book including a summary of the final version of the Conceptual Framework and the Guidelines for design of learning scenarios in mathematics and the four Ethnographies produced. All members of the team will be involved from the very beginning in the diffusion and dissemination of the Project and its results and ideas. It will be encouraged that members of the research team form small groups to prepare articles, communications, workshops and posters both on specific aspects of the project as well as in key issues and global results. It is expected that all members be involved in presenting communications in national conferences and between 8 and 12 directly involved in each international conference where the

Project will participate. Deliverables: D8.1.1. set of articles, paper presentations and posters D8.1.2. set of four booklets with ethnographies D8.1.3. book for the final version of the learning framework and guidelines for learning scenarios in mathematics (and including the four ethnographies) D8.1.4. portal for Mathematics Education, Technology and Society D8.1.5. 5th Conference on Mathematics Education and Society D8.1.6. Seminar at the Centre for Research in Education of the Faculty of Sciences of the University of Lisbon – public presentation of final report

8.7. Referências Bibliográficas Ano Year

Publicação Publication

1996

Matos, J.F., Estudos Etnográficos em Educação Matemática: Implicações da Análise de Estudos Realizados em Portugal [Ethnographic Studies in Mathematics Education: implications of Portuguese cases]. In J. Ponte et al. (Eds), Desenvolvimento Profissional dos Professores de Matemática — Que Formação? (pp. 213-231). Lisboa: Sociedade Portuguesa de Ciências da Educação

1998 Santos, M. & Matos, J.F., School mathematics learning: participation through appropriation of mathematical artifacts. In A. Watson (Ed), Situated Cognition and the Learning of Mathematics., Centre for Mathematics Education Research, University of Oxford, pp. 106-126

1999 Núñez, R., Edwards, L. & Matos, J.F., Embodied cognition as grounding for situatedness and context in mathematics education, Educational Studies in Mathematics, (39), pp. 45-65

2001 Matos, J.F. & Santos, M., Thinking about mathematical learning with the ardinas in Cabo Verde, In A. Bishop, G. Abreu e N. Presmeg (Eds), Transitions Between Contexts for Mathematics Learning. Dordrecht: Kluwer, pp. 213-242

2001 Carreira, S., Where There´s a Model, There´s a Metaphor: Metaphorical Thinking in Students´ Understanding of a Mathematical Model. Mathematical Thinking and Learning, Vol. 3, No. 4: pages 261-287

8.8. Artigos Anteriores Ano Year

Artigo (endereço na Internet - URL) Paper (Link in the Internet - URL)

2003 http://www.educ.fc.ul.pt/docentes/jfmatos/papers_learn/paper1.pdf





identificação do projecto “learn: matemática, tecnologia e ... · identificação do projecto...

Documents