Date: Wed, 1 Nov 1995 16:37:11 LISBOA
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: jaimecs@mat.uc.pt
X-Comment: Educacao em Matematica
Status: O
Eis a versao quase final do que sera' a posicao oficial da
AMERICAN MATHEMATICAL ASSOCIATION OF TWO YEAR COLLEGES
--------------------------- Original Message ---------------------------
Position Statement
of the
AMERICAN MATHEMATICAL ASSOCIATION OF TWO YEAR COLLEGES
Instructional Use of Technology in Mathematics
The American Mathematical Association of Two Year Colleges strongly
advocates the appropriate use of technology in the classroom and the
mathematics laboratory. In order to promote this objective it is essential
that mathematics departments provide students with access to the
necessary technology.
RATIONALE:
One goal of mathematics departments is to provide students with a solid
educational foundation for further personal, academic and professional
growth. A specific means of accomplishing this goal is to teach students
how to visualize and explore mathematical concepts. The appropriate
use of technology plays a key role in this instruction and in the teaching
of appropriate problem-solving skills.
RECOMMENDATIONS
- Mathematics curricula should be designed to incorporate the
pedagogical advantages of technology.
- Graphing technology, including calculators and computer algebra
systems, should be used routinely in the mathematicsclassroom.
- Mathematics departments should routinely use laboratories
equipped with appropriate technology.
- Laboratories should be scheduled both for in-lab instruction
and for sufficient open labs. Open laboratories should be
staffed by a person capable of assisting students with
the proper use of the technology.
- Mathematics faculty should have access to appropriate
technology, including calculators and computers, to facilitate
their preparation of classroom materials and presentations.
- All mathematics faculty should be provided training in the use
of technology and a forum for discussing necessary changes
in the curriculum.
- Colleges should share information regarding teaching
materials, teaching activities, and funding sources.
Mathematics departments should work with their college
administrators to obtain funding from external sources.
-
____________________________________________________________________
Brian E. Smith
Dept of Mathematics TEL: 514-931-8731 Ext 1713
Dawson College FAX: 514-931-3567
3040 Sherbrooke St. W. EMAIL: inbs@musicb.mcgill.ca
Montreal, QC, Canada H3Z 1A4
-
I would rather lose in a cause that will someday win, than win in
a cause that will someday lose -- Woodrow Wilson
-
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Jaime Carvalho e Silva
Departamento de Matematica
Universidade de Coimbra
Apartado 3008
3000 Coimbra
PORTUGAL
Phone(office): 351-39-4191199 (pbx):351-39-4191150 Fax: 351-39-32568
E-mail:jaimecs@mat.uc.pt
WWW home page: http://www.mat.uc.pt/~jaimecs/index.html
Portugal Cultural: http://www.di.uminho.pt/WWWcontrib/cultura.html
Date: Tue, 21 Nov 1995 13:59:06 LISBOA
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: ajmachia@fc1.fc.up.pt
X-Comment: Educacao em Matematica
Status: RO
As 7:38 PM 11/17/95, Luis Sanchez escreveu:
*Recordo que no meu texto eu exprimia duvidas
* sobre como iria ser encarada essa abordagem ''informal'' em compendios e
* no dia a dia das aulas.
Podem sempre levantar-se duvidas relativamente a forma como um curriculo
vai funcionar na pratica, seja ele qual for.
*Os professores que temos estao a par dos resultados da investigacao sobre o
*assunto?
Infelizmente nao existe divulga=E7=E3o suficiente sobre os resultados de
investiga=E7=E3o em educa=E7=E3o matem=E1tica. Torna-se pertinente a existencia de
"um guia" sobre concep=E7=F5es alternativas dos alunos. Um guia escrito com o
objectivo de levar a voz dos alunos a quem ensina.
* objeccao por mim formulada tinha a ver com a faixa etaria a que se
* destina a materia em causa. O conceito em analise vai ser ensinado, na
* actaual reestruturacao, a beira da idade adulta (17 anos). Foi sobre esta
* faixa que as investigacoes indicadas foram feitas?
EM- sim!!
EM- Nesses estudos "tudo" foi tentado para que os alunos aceitassem a
defini=E7=E3o de Weierstrass e as conclus=F5es levam-nos a pensar que os alunos
t=EAm de ter tempo para :
-clarifica=E7=E3o de linguagem usada no ensino de limites;
-transi=E7=E3o de modelos dinamicos para o modelo estatico de Weierstrass
EM- Se a abordagem nao for feita de forma informal de que forma podem os
alunos compreender a definicao formal? Recusando os modelos informais que
defendem? Dessa forma nao resulta, Os estudos feitos mostram que os modelos
informais nao sao abandonados mesmo quando a definicao formal parece ter
sido "aprendida" para fins de avaliacao (obter respostas certas num teste).
* Tambem faco notar que mesmo no nivel universitario (a partir dos 18 anos,
* portanto...) e bem conhecida dos professores a resistencia de nao poucos
* estudantes ao conceito de limite; justificara isso que se distorca o seu
* ensino a este nivel?
EM- Se o conceito for tratado informalmente dando tempo ao aluno de adoptar
a definicao formal como instrumento de grande utilidade na teoria de
limites da analise standard talvez o aluno nao apresente a resistencia de
que se queixa.
* Finalmente gostaria de acrescentar que acho admissivel um ensino informal
* do conceito de limite e das derivadas (tanto mais justificavel quanto mais
* cedo esse
* ensino e realizado). Julgo que e preciso muito trabalho para o tornar
* eficiente e preferivel ao tradicional. Julgo que ele se justificara com
* vista a uma absorcao durante um periodo de aprendizagem relativamente
* longo (um ciclo do ensino) e com possibilidade de se prestar a aplicacoes
* suficientemente interessantes.
EM- Acho esta proposta interessante. Quero ouvir mais e j=E1 agora: Abaixo
com a 4 horas semanais!!
Eduarda
Date: Wed, 22 Nov 1995 19:03:15 LISBOA
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: JDVIEIRA@mat.ua.pt
X-Comment: Educacao em Matematica Status: RO Ausente, so agora vi mensagens sobre limites (dias 16,17 e 21). Que o assunto e delicado todos o sabemos. Naeo me pronuncio para ja sobre a discussaeo em causa - como introduzir o conceito no ensino secundario -, pois naeo conheco o artigo , ou a proposta de EM (ja agora, e possivel obter uma copia do artigo de Moura,E. referido na mensagem do dia 16?) . Desde ha cerca de 4 anos que venho dedicando alguma atencaeo , de modo sistematico, ao modo como os nossos alunos assimilam tal conceito. Tenho dados relativos a alunos do 1o ano universitario, do 3o ano (apos frequencia de Topologia), do 5o ano (alunos do seminario - lic. Ensino) e relativos a professores do ensino secundario que fizeram o favor de colaborar. Os dados recolhidos merecem, no meu entender, alguma reflexaeo. Uma percentagem enorme de alunos daeo respostas simplesmente assombrosas no que respeita a definicaeo formal de limite. Em 1994 no dep. de matem. da Univ. de Aveiro e em 1995 em Coimbra (SPM), em ilhavo e na Guarda apresentei algumas reflexoees sobre o tema em encontros de professores e julgo que a reaccaeo tem sido positiva. Espero arranjar tempo para terminar um artigo a partir dos dados que recolhi. Sobre o modo de atresentar o conceito a nivel elementar ja tive algumas certezas, mas hoje saeo mais as duvidas do que as certezas. E preciso reflectir, experimentar e voltar a reflectir. J.David Vieira +---------------------------------- | Joao Carlos David Vieira | Dep. Matematica | Universidade de Aveiro | Email : jdvieira@samantha.mat.pt | Fax : (034) 382014 | Telef : 370200 EXT 3407 +----------------------------------
Date: Thu, 23 Nov 1995 07:46:31 LISBOA
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: ejp@cc.fc.ul.pt
X-Comment: Educacao em Matematica -----INFORMACAO------ Mini-Curso de Investigaco em Educacao Matematica Convidam-se todos os interessados a participar neste mini-curso, organizado pelo Centro de Matematica da Universidade do Porto, o qual se ira realizar nos dias 4, 5, 6 e 7 de Dezembro, sobre a orientacao da Doutora Michele Artigue. Dos topicos do curso constam: Desenvolvimento da investigacao em Educacao Matematica em Franca Quadros de referencia teoricos e metodologias Alguns exemplos de investigacao As sessoes do curso terao lugar das 18:00 as 19:30 horas, na sala Gomes Teixeira, no Edificio Central da Faculdade de Ciencias da Universidade do Porto. Para mais informacoes contactar Candida Moreira, do Grupo de Matematica Pura. ************************************************* Joao Pedro da Ponte Departamento de Educacao da Faculdade de Ciencias Universidade de Lisboa Edificio C1-Campo Grande-1700 LISBOA-PORTUGAL fax office (351-1)-757-3624 tel. office (351-1)-7573141 ext 1103 or 2012 tel. home (351-1)-3630861 *************************************************
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: Augusto.Oliveira@individual.puug.pt
>Um dos comentarios deste forum afirmava que >"Sejamos honestos: nao h'a suficiente trabalho de investigacao no ambito da did'actica da Matem'atica a este nivel (sobre limites) que avalize um tal salto no escuro sem ter o cuidado de prevenir os possiveis efeitos negativos." >Devo informar o participante deste forum que investigacao em educacao matematica sobre as concepcoes alternativas de limite dos alunos mostra que os alunos t^em serias dificuldades com a definicao formal de limite (isto e' a de Weierstrass). Sem elaborar aqui sobre os resultados da investigacao existente posso referir contudo que os alunos n=E3o abandonam as suas concepcoes em favor da definicao formal em quase nenhuma situacao . A literatura no assunto revela por exemplo situacoes em que : -os alunos eram melhores que o standard e a instrucao foi mais cuidada que o habitual; >- foram criadas situacoes didacticas com o objectivo de confrontar os alunos com exemplos conflituosos com as suas concepcoes >Em nenhuma das situacoes acima os alunos aceitaram a definicao formal abandonando as suas concepcoes. >Posso fornecer ao forum uma lista de trabalhos publicados sobre concepcoes alternativas dos alunos sobre limites para quem estiver interessado: >Cornu, B. (1991). 'Limits' em Advanced Mathematical Thinking, Editado por David Tall.. Mathematics Education Library. Kluwer Academic Press Publishers. P. O. Box #22, 3300 AH Dordrecht, The Netherlands. >Cornu, B. (1981). Apprentissage de la notion the limite: mod=E8les spontan= =E9s >et mod=E8les propres. International Conference for the Psychology of Mathematics Education. Grenobe, France. >Davis, R. B. & Vinner, S. (1986). The Notion of Limit: Some Seemingly Unavoidable Misconceptions Stages. Journal of Mathematical Behavior, 5, 281-303. >Lakatos, I. (1978). Cauchy and the Continuum: The significance of Non-Standard Analysis For The History And Philosophy Of Mathematics. Mathematics Inttelligencer, I:3, 151-161. >Monaghan, J. (1991). Problems With the Language of Limits. For the Learning of Mathematics, 11, 3, pp. 20-24. Canada. >Robert, A. (1982). L'Acquisition de la Notion de Convergence des Suites Numeriques dans L'Enseignement Superior. Recherces en Didactique des Math=E9matiques, vol 3 N=BA3, pp. 307-341, 1982. >Sierpinska, A. (1987). Humanities Students And Epistemological Obstacles Related to limits. Educational Studies in Mathematics, 18, 371-397. >Sierpinska, A. (1989). Sur un Programme de Recherche Li=E9 =E0 la Notion D'obstacle =C9pist=E9mologique. Colloque International Obstacle =C9pist=E9mo= logique >et Conflict Socio-Cognitiff. Cirade, Universit=E9 du Qu=E9bec =E0 Montr=E9a= l. >Tall, D. & Vinner, S. (1981). Concept Image and Concept Definition In Mathematics with Particular Reference To Limits and Continuity. Educational Studies in Mathematics, 12, 151-169. >Moura, E. Student's alternative frameworks about the notion of limit. Quadrante, vol. 4 (1), 1995. >Moura e Costa (1995)Concepcoes dos alunos sobre converg=EAncias de sucessoes= : >uma revis=E3o de literatura. SIEM VI. =C9vora, 1995. >Williams, S. R. Models of limit held by COLLEGE CALCULUS STUDENTS. Journal of research in mathematics education, 1991, vol. 22, 3, 219-236. >Podemos ainda encontrar literatura relativa =E0s concepcoes dos alunos sobre infinito que retrate situacoes diferentes das dos limites est=B4a relacionad= a >com limites. >Eduarda Moura Permito-me sugerir alguns itens bibliograficos suplementares sobre a questao do ensino dos 'limites' ou alternativas: - o livro de H.J. Keisler "Elementary Calculus", Prindle W & S, 2nd ed.1986; -A. Deledicq & V. Gautheron "Cours elementaire d'Analyse Non-standard", a publicar, sobre o qual baseei o mini-curso "O verdadeiro calculo infinitesimal" no ultimo Profmat em Evora (a org. tem as notas do curso); -acabado de publicar brevemente na Pitman "Developments in Nonstandard Mathematics". AJFO. AJFO
Date: Mon, 27 Nov 1995 16:51:19 LISBOA
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: ejp@cc.fc.ul.pt
X-Comment: Educacao em Matematica Esta e uma informacao veiculada por Eduardo Veloso - Seguem-se alguns enderecos interessantes na Internet sobre educacao matematica. Pode ser que isto seja util para alguem menos informado - ****The Geometry Forum***** - Julgo que se trata de um dos melhores *sites* da Internet para ed. mat. Trata sobretudo de questoes de geometria, mas receberam recentemente um subsidio para formar outro forum dedicado a ed. mat. em geral, The Math =46orum, que abrir=E1 dentro de algum tempo. Seguem-se os Forum Highlights de hoje, 17 de Novembro - Forum Highlights While these items are also listed elsewhere on this site we wanted to make it easy for people who were used to our previous home page or who were looking for only Geometry Forum resources. Forum Projects and Offerings --Forum Web-based Lessons and Units The Forum is experimenting with the use of the Web for instruction and with involving Forum users in the creation of materials. --Newsgroups Moderated discussions of geometry, research, and math education. --Hot Topics -featured discussions posted to the Web from our geometry.pre-college newsgroup --Ask Dr. Math Elementary and high school students and their teachers can submit math questions to our math doctors. -- Problem of the Week and Project of the Month The Geometry Forum's Problem of the Week and Project of the Month are posted in the geometry.pre-college newsgroup. -- MathMagic MathMagic is a K-12 telecommunications project developed in El Paso, Texas.Challenges are posted in each of four categories (k-3, 4-6, 7-9 and 10-12). School teams are paired in a problem-solving dialog. -- The Internet Resource Collection (Steve's Dump) A well-developed, searchable collection of Web resources for teachers and mathematicians. The Internet Geometry Hunt A monthly project consisting of questions about math and mathematicians, often related to geometry, to which the answers can be found on the Internet. -- NCTM-L An active mailing list devoted to discussions on current math education, currently hosted by the Forum. -- Dynamic Geometry Software Sketchpad and Cabri software and sketch archives. -- The Forum News Gateway Netnews on the WWW. You can learn more about it, and even give it a try. -- Learning and Math Discussions A Forum series discussing current research in mathematics education. -- Workshops Geometry and the Internet: weekend workshops and summer institutes. -- Internet software Up-to-date Macintosh email, news, ftp, gopher, and www softwar= e. -- FTP Archives Math software, bibliographies, past discussions, reference materials, and more. -- Outposts The Geometry Forum Newsletter. - O endereco WWW e=B4 http://forum.swarthmore.edu Manteem variados newsgroups. Os dois melhores sao geometry-software-dynamic, com muitas novidades, sketches etc. para o CABRI II e para o Geometer's Sketchpad, e o geometry-pre-college com muitas discuss=F5es e problemas de geometria, alguns interessantes. Quem usa o Netscape ou outro browser do mesmo tipo, pode ver isso em newsgroups. Quem apenas tem e-mail, pode subscrever. Para isso basta enviar uma mensagem para majordomo@forum.swarthmore.edu sem assinatura e sem assunto dizendo apenas o seguinte subscribe geometry-software-dynamic ou subscribe geometry-pre-college ou os dois ou ainda o mesmo para os outros newsgroups, geometry-college geometry-puzzles geometry-forum geometry-research geometry-institutes geometry-announcements - ****MacTutor History of Mathematics Archive***** -------------- Este eh um local mantido por dois professores da Un. de St. Andrews, na Escocia, que tem imenso interesse, nao apenas relativamente a historia da matematica - biografias de 1000 matematicos, que podem ser pesquisadas de varios modos. A descricao que fazem de si proprios eh a seguinte: - This History of Mathematics archive is part of the Mathematical MacTutor system developed at the School of Mathematical and Computational Sciences University of St Andrews for learning and experimenting with mathematics. The archive contains the biographies of more than 1000 mathematicians. About 200 of these biographies are fairly detailed and most are accompanied by pictures of the mathematicians themselves. You can access the long biographies by either an Alphabetical Index or a Chronological Index. The other shorter biographies are grouped together by the initial letter or letters of the mathematician's names and can be accessed by the Short Biographies Index. Each page of shorter biographies starts with a list of those appearing on it. About 300 of the shorter biographies are accompanied by pictures. The pages of shorter biographies also contain links to all the mathematicians with long biographies and so can act as an Index to the whole collection. We have written some articles on the development of mathematical ideas cross-referenced to the biographies. You can access these using the History Topics Index. There is a new article giving an Overview of the History of Mathematics. There is a collection of more than 60 Famous Curves which have been extensively studied by mathematicians, giving their history as well as pictures of the curves and various curves (evolutes, inverses, caustics etc.) which are associated with them. There is a Chronology showing the overlapping lives of the mathematicians who have long biographies in our archive. We have a Mathematicians of the day page which contains details of the mathematicians who were born or died on today's date and another file: Anniversaries for the year containing details for all dates. You may like to try our Birthplace Map. This shows the birthplaces of those Western European mathematicians in our list of long biographies and allows one to access the whole of our list by country of birth. We have written some other Miscellaneous material of historical interest. Instructions on how to operate the system are available. There is a Search Form (or a Simple Search Form for browsers without forms) which allows you to find references to keywords throughout the archive. You may like to try some of our Search Suggestions. More details of the Mathematical MacTutor system are available. There are other good sources of information concerning the history of mathematics available on the web. - O enderesso www eh http://www-groups.dcs.st-and.ac.uk:80/~history/Information.html e daqui pode partir-se para muitos outros locais na Internet sobre historia da matematica: - basta usar os links que sao dados na pagina chamada *Other Web sources on the history of mathematics* --History of Mathematics maintained by David E. Joyce (Clark University, USA= ) Including a comprehensive chronology of mathematicians --History of Mathematics Web Resources maintained by David E. Joyce (Clark University, USA) A good place to find more general information -- Bright SPARCS list of Mathematicians (ANU, Canberra, Australia) A large database of scientists --WWW Virtual Library, History of Science Technology and Medicine maintained by Tim Sherratt -- (ASAP, Australia) A more general history of science -- The History of Mathematics maintained by D. R. Wilkins (Trinity College, Dublin, Ireland) -- Including excerpts from W. W. Rouse Ball's A short account of the history= of mathematics -- Biographies of Women Mathematicians maintained by Larry Riddle (USA) Contains some detailed biographies and images of women mathematicians -- Ancient Mathematics at the Library of Congress Vatican Exhibit some interesting articles mainly about Greek Mathematics --Catalog of the Scientific Community: 16th and 17th Centuries at the Galileo Project a searchable database of scientists including information on over 164 mathematicians. -- A History of Sciences related to Astronomy maintained by Wolfgang R. Dick (IFAG, Potsdam,Germany) including references to astronomers -- A Brief History of Algebra and Computing: An Eclectic Oxonian View by Jonathan Bowen (Oxford University Computing Laboratory, UK) A hypertext article with hyperlinks to the MacTutor History of Mathematics archive. -- The Mathematical Quotations Server maintained by Mark Woodard Quotations by mathematicians or about mathematics -- Favourite Mathematical Constants maintained by Steven Finch Information on a collection of well-known, and some more obscure constants -- The Hooke Museum of the History of Science at the University of Oxford The Geometry Center with some excellent interactive web applications The Yahoo Mathematics Page A page of other Maths related sites - ****Eisenhower National Clearinghouse for Mathematics and Science Education*= *** - Este eh um ponto de partida para muitos outros recursos em ed. mat. Uma descricao dada pelos proprios: - ENC Overview The Eisenhower National Clearinghouse for Mathematics and Science Education (ENC) is funded through a contract with the U. S. Department of Education to provide K-12 teachers with a central source of information on mathematics and science curriculum materials. ENC was established in 1992 at The Ohio State University and is located in Columbus, Ohio. The purpose of the Eisenhower National Clearinghouse is to encourage the adoption and use of K-12 curriculum materials and programs which support state and national efforts to improve teaching and learning in mathematics and science. It provides better access to resources by creating, maintaining, and cataloging a comprehensive, multi-media collection of materials and programs. The ENC catalog and other products are distributed nationally using both traditional formats and advanced computing and telecommunications technologies. Specifically, ENC provides the following products and services: -- A catalog of mathematics and science curriculum materials from Federal government agencies and many other sources. The Resource Finder includes print, other media (e.g., video, audio, graphic images, and software), kits, and online electronic resources. Catalog entries include a wealth of information, such as an abstract, cost of the item, and information on availability. The catalog database is available online via Internet, through modem access with a toll-free number, and, beginning in late 1995, on CD-ROM. -- ENC Online. Users can readily access a variety of Internet resources, including the ENC Resource Finder, resources from other education databases, and information and materials on education reform. This resource is available through modem access using the toll-free number, telnet, Gopher, and the World Wide Web. -- Twelve Demonstration Sites located in conjunction with the ten Eisenhower Regional Consortia, at the Capital Collection & Demonstration Site, and at ENC. Demonstration sites provide both the opportunity for users to preview ENC Online and a variety of software and other materials available at each site. -- A repository of the complete collection of curriculum materials in Columbus, Ohio, for educators and others to examine the complete ENC collection and a smaller repository, the Capital Collection & Demonstration Site, in Washington, DC, at George Washington University. Visitors to ENC in Columbus can view curriculum materials at the ENC Reference Desk. -- A variety of print materials including topical catalogs on selected materials in the ENC collection, information about Federal programs serving mathematics and science education, and informational materials about ENC. -- Beginning in late 1995, two CD-ROM collections per year. One will include materials that support education reform, such as curriculum frameworks and information on standards, assessment, and professional development, and the second will make print and software curriculum materials available for classroom use. Each disk will also include the complete ENC Resource Finder and an Internet directory which can be used to demonstrate the benefits of Internet access. - O endereco do ENC eh http://www.enc.org/ - A partir destes tres locais pode praticamente chegar-se a todos os outros, pois cada um deles contem links para outros locais. E e' tudo por hoje Eduardo Veloso Eduardo Veloso Av. D. Rodrigo da Cunha, 11 3=BA D 1700 Lisbon Portugal tel. & Fax.: (351) (1) 8483046 e-mail: veloso@telepac.pt ************************************************* Joao Pedro da Ponte Departamento de Educacao da Faculdade de Ciencias Universidade de Lisboa Edificio C1-Campo Grande-1700 LISBOA-PORTUGAL fax office (351-1)-757-3624 tel. office (351-1)-7573141 ext 1103 or 2012 tel. home (351-1)-3630861 *************************************************
Date: Mon, 27 Nov 1995 16:51:19 LISBOA
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: ejp@cc.fc.ul.pt
X-Comment: Educacao em Matematica Esta e uma informacao veiculada por Eduardo Veloso -------- Seguem-se alguns enderecos interessantes na Internet sobre educacao matematica. Pode ser que isto seja util para alguem menos informado ---------- ****The Geometry Forum***** ---------- Julgo que se trata de um dos melhores *sites* da Internet para ed. mat. Trata sobretudo de questoes de geometria, mas receberam recentemente um subsidio para formar outro forum dedicado a ed. mat. em geral, The Math =46orum, que abrir=E1 dentro de algum tempo. Seguem-se os Forum Highlights de hoje, 17 de Novembro ------ Forum Highlights While these items are also listed elsewhere on this site we wanted to make it easy for people who were used to our previous home page or who were looking for only Geometry Forum resources. =46orum Projects and Offerings --Forum Web-based Lessons and Units The Forum is experimenting with the use of the Web for instruction and with involving Forum users in the creation of materials. --Newsgroups Moderated discussions of geometry, research, and math education. --Hot Topics -featured discussions posted to the Web from our geometry.pre-college newsgroup --Ask Dr. Math Elementary and high school students and their teachers can submit math questions to our math doctors. -- Problem of the Week and Project of the Month The Geometry Forum's Problem of the Week and Project of the Month are posted in the geometry.pre-college newsgroup. -- MathMagic MathMagic is a K-12 telecommunications project developed in El Paso, Texas.Challenges are posted in each of four categories (k-3, 4-6, 7-9 and 10-12). School teams are paired in a problem-solving dialog. -- The Internet Resource Collection (Steve's Dump) A well-developed, searchable collection of Web resources for teachers and mathematicians. The Internet Geometry Hunt A monthly project consisting of questions about math and mathematicians, often related to geometry, to which the answers can be found on the Internet. -- NCTM-L An active mailing list devoted to discussions on current math education, currently hosted by the Forum. -- Dynamic Geometry Software Sketchpad and Cabri software and sketch archives. -- The Forum News Gateway Netnews on the WWW. You can learn more about it, and even give it a try. -- Learning and Math Discussions A Forum series discussing current research in mathematics education. -- Workshops Geometry and the Internet: weekend workshops and summer institutes. -- Internet software Up-to-date Macintosh email, news, ftp, gopher, and www softwar= e. -- FTP Archives Math software, bibliographies, past discussions, reference materials, and more. -- Outposts The Geometry Forum Newsletter. --------------- O endereco WWW e=B4 http://forum.swarthmore.edu Manteem variados newsgroups. Os dois melhores sao geometry-software-dynamic, com muitas novidades, sketches etc. para o CABRI II e para o Geometer's Sketchpad, e o geometry-pre-college com muitas discuss=F5es e problemas de geometria, alguns interessantes. Quem usa o Netscape ou outro browser do mesmo tipo, pode ver isso em newsgroups. Quem apenas tem e-mail, pode subscrever. Para isso basta enviar uma mensagem para majordomo@forum.swarthmore.edu sem assinatura e sem assunto dizendo apenas o seguinte subscribe geometry-software-dynamic ou subscribe geometry-pre-college ou os dois ou ainda o mesmo para os outros newsgroups, geometry-college geometry-puzzles geometry-forum geometry-research geometry-institutes geometry-announcements -------------- ****MacTutor History of Mathematics Archive***** -------------- Este eh um local mantido por dois professores da Un. de St. Andrews, na Esc=F3cia, que tem imenso interesse, nao apenas relativamente a historia da matematica - biografias de 1000 matematicos, que podem ser pesquisadas de varios modos. A descricao que fazem de si proprios eh a seguinte: ------------ This History of Mathematics archive is part of the Mathematical MacTutor system developed at the School of Mathematical and Computational Sciences University of St Andrews for learning and experimenting with mathematics. The archive contains the biographies of more than 1000 mathematicians. About 200 of these biographies are fairly detailed and most are accompanied by pictures of the mathematicians themselves. You can access the long biographies by either an Alphabetical Index or a Chronological Index. The other shorter biographies are grouped together by the initial letter or letters of the mathematician's names and can be accessed by the Short Biographies Index. Each page of shorter biographies starts with a list of those appearing on it. About 300 of the shorter biographies are accompanied by pictures. The pages of shorter biographies also contain links to all the mathematicians with long biographies and so can act as an Index to the whole collection. We have written some articles on the development of mathematical ideas cross-referenced to the biographies. You can access these using the History Topics Index. There is a new article giving an Overview of the History of Mathematics. There is a collection of more than 60 Famous Curves which have been extensively studied by mathematicians, giving their history as well as pictures of the curves and various curves (evolutes, inverses, caustics etc.) which are associated with them. There is a Chronology showing the overlapping lives of the mathematicians who have long biographies in our archive. We have a Mathematicians of the day page which contains details of the mathematicians who were born or died on today's date and another file: Anniversaries for the year containing details for all dates. You may like to try our Birthplace Map. This shows the birthplaces of those Western European mathematicians in our list of long biographies and allows one to access the whole of our list by country of birth. We have written some other Miscellaneous material of historical interest. Instructions on how to operate the system are available. There is a Search Form (or a Simple Search Form for browsers without forms) which allows you to find references to keywords throughout the archive. You may like to try some of our Search Suggestions. More details of the Mathematical MacTutor system are available. There are other good sources of information concerning the history of mathematics available on the web. ------------------------- O enderesso www eh http://www-groups.dcs.st-and.ac.uk:80/~history/Information.html e daqui pode partir-se para muitos outros locais na Internet sobre historia da matematica: - basta usar os links que sao dados na pagina chamada *Other Web sources on the history of mathematics* --History of Mathematics maintained by David E. Joyce (Clark University, USA= ) Including a comprehensive chronology of mathematicians --History of Mathematics Web Resources maintained by David E. Joyce (Clark University, USA) A good place to find more general information -- Bright SPARCS list of Mathematicians (ANU, Canberra, Australia) A large database of scientists --WWW Virtual Library, History of Science Technology and Medicine maintained by Tim Sherratt -- (ASAP, Australia) A more general history of science -- The History of Mathematics maintained by D. R. Wilkins (Trinity College, Dublin, Ireland) -- Including excerpts from W. W. Rouse Ball's A short account of the history= of mathematics -- Biographies of Women Mathematicians maintained by Larry Riddle (USA) Contains some detailed biographies and images of women mathematicians -- Ancient Mathematics at the Library of Congress Vatican Exhibit some interesting articles mainly about Greek Mathematics --Catalog of the Scientific Community: 16th and 17th Centuries at the Galileo Project a searchable database of scientists including information on over 164 mathematicians. -- A History of Sciences related to Astronomy maintained by Wolfgang R. Dick (IFAG, Potsdam,Germany) including references to astronomers -- A Brief History of Algebra and Computing: An Eclectic Oxonian View by Jonathan Bowen (Oxford University Computing Laboratory, UK) A hypertext article with hyperlinks to the MacTutor History of Mathematics archive. -- The Mathematical Quotations Server maintained by Mark Woodard Quotations by mathematicians or about mathematics -- Favourite Mathematical Constants maintained by Steven Finch Information on a collection of well-known, and some more obscure constants -- The Hooke Museum of the History of Science at the University of Oxford The Geometry Center with some excellent interactive web applications The Yahoo Mathematics Page A page of other Maths related sites ---------------- ****Eisenhower National Clearinghouse for Mathematics and Science Education*= *** --------------------- Este eh um ponto de partida para muitos outros recursos em ed. mat. Uma descricao dada pelos proprios: ---------- ENC Overview The Eisenhower National Clearinghouse for Mathematics and Science Education (ENC) is funded through a contract with the U. S. Department of Education to provide K-12 teachers with a central source of information on mathematics and science curriculum materials. ENC was established in 1992 at The Ohio State University and is located in Columbus, Ohio. The purpose of the Eisenhower National Clearinghouse is to encourage the adoption and use of K-12 curriculum materials and programs which support state and national efforts to improve teaching and learning in mathematics and science. It provides better access to resources by creating, maintaining, and cataloging a comprehensive, multi-media collection of materials and programs. The ENC catalog and other products are distributed nationally using both traditional formats and advanced computing and telecommunications technologies. Specifically, ENC provides the following products and services: -- A catalog of mathematics and science curriculum materials from Federal government agencies and many other sources. The Resource Finder includes print, other media (e.g., video, audio, graphic images, and software), kits, and online electronic resources. Catalog entries include a wealth of information, such as an abstract, cost of the item, and information on availability. The catalog database is available online via Internet, through modem access with a toll-free number, and, beginning in late 1995, on CD-ROM. -- ENC Online. Users can readily access a variety of Internet resources, including the ENC Resource Finder, resources from other education databases, and information and materials on education reform. This resource is available through modem access using the toll-free number, telnet, Gopher, and the World Wide Web. -- Twelve Demonstration Sites located in conjunction with the ten Eisenhower Regional Consortia, at the Capital Collection & Demonstration Site, and at ENC. Demonstration sites provide both the opportunity for users to preview ENC Online and a variety of software and other materials available at each site. -- A repository of the complete collection of curriculum materials in Columbus, Ohio, for educators and others to examine the complete ENC collection and a smaller repository, the Capital Collection & Demonstration Site, in Washington, DC, at George Washington University. Visitors to ENC in Columbus can view curriculum materials at the ENC Reference Desk. -- A variety of print materials including topical catalogs on selected materials in the ENC collection, information about Federal programs serving mathematics and science education, and informational materials about ENC. -- Beginning in late 1995, two CD-ROM collections per year. One will include materials that support education reform, such as curriculum frameworks and information on standards, assessment, and professional development, and the second will make print and software curriculum materials available for classroom use. Each disk will also include the complete ENC Resource Finder and an Internet directory which can be used to demonstrate the benefits of Internet access. --------------- O endereco do ENC eh http://www.enc.org/
Date: Tue, 28 Nov 1995 14:28:36 LISBOA
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: ejp@cc.fc.ul.pt
Joao David Vieira disse em 22-11-95: <<Tenho dados realtivos a alunos do 1=BA ano universitario, do 3 ano (apos frequencia da Topologia), do 5 ano (alunos do seminario - lic em Ensino) e realtivoa a profesores do ensino sencundario... Uma percentagem assombrosa de alunos dao respostas simplesmente assombrosas no que respeita a definicao formal de limite. Pela minha parte nao fico nada admirado. Eu proprio fiz uma pequena investigacao a proposito da aprendizagem do conceito de vector, que ha cerca de 15 anos era ensinado como classe de equivalencia de segmentos orientados a alunos de 12 anos... Os resultados mostraram claramente que quase todos os alunos tinham uma ideia de vector que nao tinha nada a ver com a definicao formal. Se os alunos do Joao David Vieira, apos tantos anos de ensino universitario continuam com dificuldades nesta materia e porque qualquer coisa esta errada neste ensino. Tudo indica que as definicoes formais, se a sua necessidade nao e compreendida, nao sao verdadeiramente assimiladas. E para se compreender uma definicao formal, e a sua necessidade, normalmente e preciso comprender primeiro uma definicao informal. Provavelmente neste ponto estaremos todos de acordo. A questao que se poe e como tornear o problema. Ha varias hipoteses: 1--trabalhar durante mais tempo com definicoes informais 2--mudar, parcial ou substancialmente o tipo de ensino (por exemplo, de modo a que deixe de ser exclusivamente expositivo e comece a ter uma componente de investigacao autonoma por parte do aluno) 3--fazer 1 e 2 em simultaneo. Penso que serao necessarias mais investigacoes que ponham em pratica 1, 2 ou 3 e que avaliem os respectivos resultados. Essas investigacoes para serem crdiveis tem de usar metodologias adequadas. Seria interessante que nelas participaseem investigadores de educacao matematica, professores e matematicos. Entretanto, precisamos de ter alguma coisa nos curriculos. Parece-me que a proposta de reajustamento do ensino secundario, sem ser a ideal (ja sabemos que nos espartilho das 4 horas semanais tal seria impossivel), assume uma posicao razoavel nesta materia. Joao Pedro ************************************************* Joao Pedro da Ponte Departamento de Educacao da Faculdade de Ciencias Universidade de Lisboa Edificio C1-Campo Grande-1700 LISBOA-PORTUGAL fax office (351-1)-757-3624 tel. office (351-1)-7573141 ext 1103 or 2012 tel. home (351-1)-3630861 *************************************************
Date: Tue, 28 Nov 1995 16:22:48 LISBOA
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: Augusto.Oliveira@individual.puug.pt
X-Comment: Educacao em Matematica >Joao David Vieira disse em 22-11-95: ><<Tenho dados realtivos a alunos do 1=3DBA ano universitario, do 3 ano= (apos >frequencia da Topologia), do 5 ano (alunos do seminario - lic em Ensino) e realtivoa a profesores do ensino sencundario... Uma percentagem assombrosa de alunos dao respostas simplesmente assombrosas no que respeita a definicao formal de limite. >Pela minha parte nao fico nada admirado. Eu proprio fiz uma pequena investigacao a proposito da aprendizagem do conceito de vector, que ha cerca de 15 anos era ensinado como classe de equivalencia de segmentos orientados a alunos de 12 anos... Os resultados mostraram claramente que quase todos os alunos tinham uma ideia de vector que nao tinha nada a ver com a definicao formal. >Se os alunos do Joao David Vieira, apos tantos anos de ensino universitario continuam com dificuldades nesta materia e porque qualquer coisa esta errada neste ensino. Tudo indica que as definicoes formais, se a sua necessidade nao e compreendida, nao sao verdadeiramente assimiladas. E para se compreender uma definicao formal, e a sua necessidade, normalmente e preciso comprender primeiro uma definicao informal. >Provavelmente neste ponto estaremos todos de acordo. A questao que se poe e como tornear o problema. Ha varias hipoteses: >1--trabalhar durante mais tempo com definicoes informais 2--mudar, parcial ou substancialmente o tipo de ensino (por exemplo, de modo a que deixe de ser exclusivamente expositivo e comece a ter uma componente de investigacao autonoma por parte do aluno) 3--fazer 1 e 2 em simultaneo. >Penso que serao necessarias mais investigacoes que ponham em pratica 1, 2 ou 3 e que avaliem os respectivos resultados. Essas investigacoes para serem crdiveis tem de usar metodologias adequadas. Seria interessante que nelas participaseem investigadores de educacao matematica, professores e matematicos. >Entretanto, precisamos de ter alguma coisa nos curriculos. Parece-me que a proposta de reajustamento do ensino secundario, sem ser a ideal (ja sabemos que nos espartilho das 4 horas semanais tal seria impossivel), assume uma posicao razoavel nesta materia. >Joao Pedro >************************************************* >Joao Pedro da Ponte >Departamento de Educacao da Faculdade de Ciencias Universidade de Lisboa >Edificio C1-Campo Grande-1700 LISBOA-PORTUGAL fax office (351-1)-757-3624 >tel. office (351-1)-7573141 ext 1103 or 2012 tel. home (351-1)-3630861 >************************************************* Penso que a nocao intuitiva ou informal de limite e=B4 uma nocao suficientemente clara para ser assimilada pelos alunos. Ja=B4experimentaram perguntar aos alunos para explicarem a nocao utilizando, sem receio, os seus proprios termos e sem pretenderem reproduzir uma definicao formal que nunca entenderam? O que esta' realmente mal, muito mal, e=B4 a definicao formal=B4(dita a`Cauchy, mas formalizada por Weierstrass nos anos 60 do sec. passado), na medida em que parece nada corresponder a` nocao informal. Claro que sabemos que corresponde, bla bla bla apos muitos anos de pratica frustrada de tentativa de ensino... Mas ha=B4 uma definicao formal alternativa (Ah! Ah! Ah!) que nao tem os inconvenientes da weierstrassiana, e' a da Analise Nao-standard! AJFO. AJFO
Date: Tue, 28 Nov 1995 16:57:28 LISBOA
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: ajmachia@fc1.fc.up.pt
At 3:37 95/11/23, Joao David Vieira wrote: (...) Benvindo a discussao! Gostaria de saber sobre os dados que recolheu, nao demore a escrever o artig= o. Quanto ao meu artigo, esta' publicado na quadrante vol 4 no. 1, 1995, publica=E7=E3o APM (mais barato para socios...) Se me der a sua morada eu envio-lhe uma copia! Nesse artigo nada e' proposto em termos curriculares. Tudo o que tenho feito ate agora e' tentar compreender as concepcoes alternativas dos alunos sobre limites. Eduarda
Date: Tue, 28 Nov 1995 16:50:46 LISBOA
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: ajmachia@fc1.fc.up.pt
* Permito-me sugerir alguns itens bibliograficos suplementares sobre a ques= tao * do ensino dos 'limites' ou alternativas: * - o livro de H.J. Keisler "Elementary Calculus", Prindle W & S, 2nd ed.19= 86; * -A. Deledicq & V. Gautheron "Cours elementaire d'Analyse Non-standard", a * publicar, sobre o qual baseei o mini-curso "O verdadeiro calculo * infinitesimal" no ultimo Profmat em Evora (a org. tem as notas do curso); * -acabado de publicar brevemente na Pitman "Developments in Nonstandard * Mathematics". AJFO. * AJFO Obrigado pela indica=E7=E3o bibliografica. O Professor Carlos Sa tinha-me emprestado os seus apontamentos e eu come=E7ei a l=EA-los, no entanto fiquei encalhada quase logo no principio pois uma das propriedades dos reais que enuncia e a seguinte: "que a soma de um numero infinitamente grande de apreciaveis e' um =20infinitamente grande". Ora eu pensei por exemplo numa serie (com soma) que pode somar a um apreciavel. Mas se este exemplo nao serve entao o cardinal dos numeros naturais nao e um infinitamente grande? Fiquei muito desiludida! No espirito de Leibniz ou de Cauchy (se eles tivessem pensado nisso) acha que eles considerariam o cardinal dos numeros naturais um infinitamente grande? Ser=E1 que a analise nao standard se adapta mais as concepcoes dos alunos do que a analise standard? E uma questao por responder... Eduarda
Date: Wed, 29 Nov 1995 09:30:40 LISBOA
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: secje@ua.pt
--============_-1394485128==_============ Content-Type: text/plain; charset="us-ascii" Tenho andado a travar algumas lutas, utilizando pequenas influencias para exigir que os organismos mostrem antecipadamente que tipo de coisas esperam dos estudantes do ensino secundario. Em muitos aspectos, tenho de escrever por fora da matematica. Mas tenho algum interesse em defender as minhas opinioes tambem para dentro da matematica. Envio um dos textos ( word - texto so com mudanca de linha) agarrado a esta mensagem. Se nao o receberem ou nao o conseguirem ler, informem. Tentarei de novo e de outra maneira. Arselio --============_-1394485128==_============ Content-Type: application/mac-binhex40; name="C1.doc" Content-Disposition: attachment; filename="C1.doc" --============_-1394485128==_============ Content-Type: text/plain; charset="us-ascii" ********************************** Arse'lio de Almeida Martins ********************************** Escola Secunda'ria de Jose' Este^va~o Avenida 25 de Abril 3810 AVEIRO PT Ph: 351 34 23813 Fax 351 34 24330 ********************************** Urbanizaca~o Chave, Lote 18, 3. Dir. .3810 AVEIRO PT Ph: 351 34 26439 ********************************** No idea is really bad, unless we are uncritical. What is really bad is to to have no idea at all. (Polya) --============_-1394485128==_============-- Attachment converted: Macintosh HD:C1-a (WDBN/MSWD) (00007170)
Date: Wed, 29 Nov 1995 15:11:22 LISBOA
Reply-To: sem@cc.fc.ul.pt Originator: sem@cc.fc.ul.pt Sender: sem@cc.fc.ul.pt Precedence: bulkFrom: aguiar@gama.isr.ist.utl.pt
>Envio um dos textos ( word - texto so com mudanca de linha) agarrado a esta mensagem. Se nao o receberem ou nao o conseguirem ler, informem. Tentarei de novo e de outra maneira. >Arselio caro Arselio, tenho interesse no seu texto. seria possivel envia-lo em ascii para que quem nao usa word, como eu, possa le-lo ? muito obrigado. pedro aguiar
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