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X-Comment:  Educacao em Matematica


Esta e uma compilacao feita por Tommy Dreyfus, que podera ser de interesse
para muitos membros da lista.

Joao Pedro da Ponte

>
>----------------------------- ESM TOC --------
>
>EDUCATIONAL STUDIES IN MATHEMATICS
>________________________________
>
>VOLUME 31, NOS. 1/2, SEPTEMBER 1996
>
>PETER CHARLES TAYLOR / Mythmaking and Mythbreaking in the Mathematics
>Classroom
>11--33
>
>MARIA G. BARTOLINI BUSSI / Mathematical Discussion and Perspective Drawing
>in Primary School
>35--65
>
>BILL BARTON / Making Sense of Ethnomathematics: Ethnomathematics is Making
>Sense
>67--99
>
>CATHERINE A. BROWN, MARY KAY STEIN and ELLICE ANN FORMAN / Assisting
>Teachers and Students to Reform the Mathematics Classroom
>101--131
>
>KATHRYN CRAWFORD / Vygotskian Approaches in Human Development in The
>Information Era
>133--152
>
>ROBYN ZEVENBERGEN / Constructivism as a Liberal Bourgeois Discourse
>153--171
>
>JOANNA O. MASINGILA, SUSANA DAVIDENKO and EWA PRUS-WISNIOWSKA / Mathematics
>Learning and Practice in and Out of School: A Framework for Connecting
>These Experiences
>173--198
>
>TONY BROWN / The Phenomenology of the Mathematics Classroom
>199--233
>
>
>VOLUME 30, NO. 4, JUNE 1996
>
>DOUGLAS H. CLEMENTS, MICHAEL T. BATTISTA, JULIE SARAMA and SUDHA SWAMWATHAN
>/ Development of Turn and Turn Measurement Concepts in a Computer-Based
>Instructional Unit
>313-337
>
>SARA HERSCHKOVITZ and PEARLA NESHER / The Role of Schemes in Designing
>Computerized Environments
>339-365
>
>ANTOINE DAGHER / Apprentissage dans un environnement informatique:
>Possibilite, nature, transfert des acquis
>367-398
>
>HEATHER MCLEAY and DAVID PIGGINS / The Mental Manipulation of 2-D
>Representations of Knots as Deformable Structures
>399-414
>
>
>VOLUME 30, NO. 3, APRIL 1996
>
>PAUL COBB and JOY W. WHITENACK / A Method for Conducting Longitudinal
>Analyses of Classroom Videorecordings and Transcripts
>213-228
>
>MERRILY GOOS and PETER GALBRAIH / Do It This Way! Metacognitive Strategies
>in Collaborative Mathematical Problem Solving
>229-260
>
>GERARD SENSEVY / Fabrication de problemes de fraction par des eleves a la
>fin de l'enseignement elementaire
>261-288
>
>WOO-HYUNG WHANG / The Influence of English-Korean Bilingualism in Solving
>Mathematics Word Problems
>289-312
>
>
>VOLUME 30, NO. 2, MARCH 1996
>
>ROSA MARIA BOTTINO and FULVIA FURINGHETTI / The Emerging of Teachers'
>Cenceptions of New Subjects Inserted in Mathematics Programs: The Case of
>Informatics
>109-134
>
>LYN D. ENGLISH and PATRICK V. SHARRY / Analogical Reasoning and the
>Development of Algebraic Abstraction
>135-157
>
>TED HODGSON / Students' Ability to visualize Set Expressions: An Initial
>Investigation
>159-178
>
>JOE RELICH / Gender, Self-Concept and Teachers of Mathematics: Effects on
>Attitudes to Teaching and Learning
>179-195
>
>MARTIN A. SIMON / Beyond Inductive and Deductive Reasoning: The Search for
>a Sense of Knowing
>197-210
>
>
>VOLUME 30, NO. 1, JANUARY 1996
>
>ANNE PITKETHLY and ROBERT HUNTING / A Review of Recent Research in the Area
>of Initial Fraction Concepts
>5-38
>
>LIORA LINCHEVSKI and NICOLAS HERSCOVICS / Crossing the Cognitive Gap
>between Arithmetic and Algebra: Operating on the Unknown in the Context of
>Equations
>39-65
>
>GRAYSON H. WHEATLEY and ANNE REYNOLDS / The Construction of Abstract Units
>in Geometric and Numeric Settings
>67-83
>
>TERRY WOOD / Events in Learning Mathematics: Insights from Research in
>Classrooms
>85-105
>
>
>




>




>

*************************************************
Joao Pedro da Ponte
Dep Educacao-Fac Ciencias-Univ Lisboa
Edificio C1-Campo Grande
1700 LISBOA-PORTUGAL

fax office  (351-1)-750-0082
tel. office (351-1)-757-3141 ext 1103/2012/2522
tel. home   (351-1)-363-0861
*************************************************

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X-Comment:  Educacao em Matematica


Esta e uma compilacao feita por Tommy Dreyfus, que podera ser de interesse
para muitos membros da lista.

Joao Pedro da Ponte

>
>----------------------------- JRME TOC --------
>
>JOURNAL FOR RESEARCH IN MATHEMATICS EDUCATION
>__________________________________________
>
>JRME Volume 27 Number 1, January 1996
>
>ARTICLES
>
>Talking About Rates Conceptually, Part II: Mathematical Knowledge for  Teaching
>Alba G. Thompson and Patrick W. Thompson, pp. 2-24.
>
>Children's Understanding of the Principles of Covariation and Compensation
>in Part-Whole Relationships
>Kathryn C. Irwin, pp. 25-40.
>
>Identification of Multiplicative Thinking in Children in Grades 1-5
>Faye B. Clark and Constance Kamii, pp. 41-51.
>
>Intention and Significance in the Teaching and Learning of Mathematics
>Tony Brown, pp. 52-66.
>
>Inhibiting Factors in Generating Examples by Mathematics Teachers and
>Student Teachers: The Case of Binary Operation
>Orit Zaslavsky and Irit Peled, pp. 67-78.
>
>Conceptual Knowledge in Introductory Calculus
>Paul White and Michael Mitchelmore, pp. 79-95.
>
>BRIEF REPORT
>Results of Research Studies on Causal Predominance Between Achievement and
>Attitude in Junior High School Mathematics of Japan
>Saburo Minato and Tsugio Kamada, pp. 96-99.
>
>REVIEW
>One Very Complete View (Though Only One) of How Children Learn
>Mathematics--A Review of Children's Mathematical Development: Research and
>Practical Applications, by David C. Geary
>Robert B. Davis, pp. 100-106.
>
>
>JRME Volume 27 Number 2, March 1996
>
>Editorial
>Frank K. Lester, Jr., pp. 130-132.
>
>ARTICLES
>
>INTERSUBJECTIVITY IN MATHEMATICS LEARNING: A CHALLENGE TO THE RADICAL
>CONSTRUCTIVIST PARADIGM?
>Stephen Lerman, pp. 133-150.
>
>INTUITIVE STRATEGIES AND PRECONCEPTIONS ABOUT ASSOCIATION IN CONTINGENCY TABLES
>Carmen Batanero, Antonio Estepa, Juan D. Godino, and David R. Green, pp.
>151-169.
>
>THE DEVELOPMENT OF UNITIZING: ITS ROLE IN CHILDREN'S PARTITIONING STRATEGIES
>Susan J. Lamon, pp. 170-193.
>
>THE DEVELOPMENT OF THE IDEA OF MATHEMATICAL PROOF: A 5-YEAR CASE STUDY
>Carolyn A. Maher and Amy M. Martino, pp. 194-214.
>
>GENDER-RELATED DIFFERENCES IN SELF-REFERENCED COGNITIONS IN RELATION TO
>MATHEMATICS
>Gerard Seegers and Monique Boekaerts, pp. 215-240.
>
>REVIEW
>The Mathematics of Popular Consumption--A Review of Popular Culture,
>Educational Discourse, and Mathematics, by Peter Appelbaum
>Suzanne K. Damarin, pp. 241-243.
>
>
>JRME Volume 27 Number 3, May 1996
>
>ARTICLES
>
>STUDENTS' UNDERSTANDING OF THREE-DIMENSIONAL RECTANGULAR ARRAYS OF CUBES
>Michael T. Battista and Douglas H. Clements, pp. 258-292.
>
>POSING MATHEMATICAL PROBLEMS: AN EXPLORATORY STUDY
>Edward A. Silver, Joanna Mamona-Downs, Shukkwan S. Leung and Patricia Ann
>Kenney, pp. 293-309.
>
>MULTIDIGIT NUMBER SENSE: A FRAMEWORK FOR INSTRUCTION AND ASSESSMENT
>Graham A. Jones, Carol A. Thornton, Ian J. Putt, Kevin M. Hill, A. Timothy
>Mogill, Beverly S. Rich and Laura R. Van Zoest, pp. 310-336.
>
>ASSESSMENT OF A PROBLEM-CENTERED MATHEMATICS PROGRAM: THIRD GRADE
>Terry Wood and Patricia Sellers, pp. 337-353.
>
>ENGAGING WHOLE-NUMBER KNOWLEDGE FOR RATIONAL-NUMBER LEARNING USING A
>COMPUTER-BASED TOOL
>Robert P. Hunting, Gary Davis and Catherine A. Pearn, pp. 354-379.
>
>
>JRME Volume 27 Number 4, July 1996
>
>ERIC's RESEARCH ON MATHEMATICS EDUCATION REPORTED IN 1995, p. 386
>
>ARTICLES
>
>EFFICACY AND TEACHING MATHEMATICS BY TELLING: A CHALLENGE FOR REFORM
>John P. Smith III , pp. 387-402.
>
>A LONGITUDINAL STUDY OF LEARNING TO USE CHILDREN'S THINKING IN MATHEMATICS
>INSTRUCTION
>Elizabeth Fennema, Thomas P. Carpenter, Megan L. Franke, Linda Levi,
>Victoria R. Jacobs, and Susan B. Empson pp. 403-434.
>
>COORDINATING VISUAL AND ANALYTIC STRATEGIES A STUDY OF STUDENTS'
>UNDERSTANDING OF THE GROUP D4;
>Rina Zazkis, Ed Dubinsky, and Jennie Dautermann , pp. 435-457.
>
>SOCIOMATHEMATICAL NORMS, ARGUMENTATION, AND AUTONOMY IN MATHEMATICS
>Erna Yackel and Paul Cobb, pp. 458-477.
>
>EXPLORING THE ORIGINS, USES, AND INTERACTIONS OF STUDENT INTUITIONS:
>COMPARING THE LENGTHS OF PATHS
>Ming Ming Chiu, pp. 478-504.
>
>TELEGRAPHIC REVIEWS, pp. 505-506.
>
>LETTER TO THE EDITOR, pp. 507-508.
>
>ANNOUNCEMENT, p. 509.
>
>
>MANUSCRIPTS ACCEPTED FOR PUBLICATION
>
>At its 1996 Spring meeting the JRME Editorial Panel recommended that a
>listing of all articles accepted for and awaiting publication should be
>added to the current home page. The Panel hopes that such a list would be
>of use to the mathematics education community by providing advance notice
>of the topics and themes of research pending actual publication.
>
>AN ANALYSIS OF ARITHMETIC PROBLEM POSING BY MIDDLE SCHOOL STUDENTS
>Edward A. Silver, University of Pittsburgh
>Jinfa Cai, University of Delaware
>
>DIVISIBILITY AND MULTIPLICATIVE STRUCTURE OF NATURAL NUMBERS: PRESERVICE
>TEACHERS' UNDERSTANDING
>Rina Zazkis and Stephen Campbell, Simon Fraser University, Burnaby,
>Bristish Columbia
>
>ELEMENTARY STUDENTS' CONSTRUCTION AND COORDINATION OF UNITS IN AN AREA SETTING
>Anne Reynolds, University of Oklahoma
>Grayson H. Wheatley, Florida State University
>
>THE IMPLEMENTATION OF A "FUNCTION" APPROACH TO INTRODUCTORY ALGEBRA: A CASE
>STUDY OF TEACHER COGNITIONS, TEACHER ACTIONS, AND THE INTENDED CURRICULUM
>David H. Haimes, Trent University, Peterborough, Ontario
>
>ASSESSING THE RELATIONSHIP BETWEEN ATTITUDE TOWARD MATHEMATICS AND
>ACHIEVEMENT IN MATHEMATICS: A META-ANALYSIS
>Xin Ma and Nand Kishor, The University of British Columbia
>
>YOUNG CHILDREN'S PERCEPTIONS OF MATHEMATICS IN PROBLEM-SOLVING ENVIRONMENTS
>Megan Loef Franke, University of California, Los Angeles
>Deborah Carey, University of Maryland, College Park
>
>STUDENTS' DEVELOPMENT OF LENGTH MEASUREMENT CONCEPTS IN A LOGO-BASED UNIT
>ON GEOMETRIC PATHS
>Douglas H. Clements, State University of New York at Buffalo
>Michael T. Battista, Kent State University
>Julie Sarama, State University of New York at Buffalo
>Sudha Swaminathan, State University of New York at Buffalo
>Sue McMillen, D'Youville College
>
>CONCEPTUAL UNITS ANALYSIS OF PRESERVICE ELEMENTARY SCHOOL TEACHERS'
>STRATEGIES ON A RATIONAL-NUMBER-AS-OPERATOR TASK
>Merlyn J. Behr, Northern Illinois University
>Helen A. Khoury, Northern Illinois University
>Guershon Harel, Purdue University
>Thomas Post, University of Minnesota
>Richard Lesh, University of Massachusetts - Dartmouth
>
>CHILDREN'S CONCEPTUAL STRUCTURES FOR MULTIDIGIT NUMBERS AND METHODS OF
>MULTIDIGIT ADDITION AND SUBTRACTION
>Karen C. Fuson, Northwestern University
>Diana Wearne, University of Delaware
>James Hiebert, University of Delaware
>Hanlie Murray, University of Stellenbosch, South Africa
>Piet Human, University of Stellenbosch, South Africa
>Alwyn Olivier, University of Stellenbosch, South Africa
>Tom Carpenter, University of Wisconsin - Madison
>Elizabeth Fennema, University of Wisconsin - Madison
>
>DEEPENING THE ANALYSIS: LONGITUDINAL ASSESSMENT OF A PROBLEM-CENTERED
>MATHEMATICS PROGRAM
>Terry Wood and Patricia Sellers, Purdue University
>
>ASSESSMENT AND GRADING IN HIGH SCHOOL MATHEMATICS CLASSROOMS
>Sharon L. Senk, Michigan State University
>Charlene E. Beckmann, Grand Valley State University
>Denisse R. Thompson, University of South Florida
>
>DEVELOPING RATIO AND PROPORTION SCHEMES: A STORY OF A FIFTH GRADER
>Jane-Jane Lo, Cornell University
>Tad Watanabe, Towson State University
>
>THE CHANGING ROLE OF THE MATHEMATICS TEACHER
>Doug M. Clarke, Australian Catholic University
>
>RESULTS OF THIRD-GRADE STUDENTS IN A REFORM CURRICULUM ON THE ILLINOIS
>STATE MATHEMATICS TEST (Brief Report)
>William M. Carroll, University of Chicago School Mathematics Project
>
>YOUNG CHILDREN'S INTUITIVE MODELS OF MULTIPLICATION AND DIVISION
>Joanne T. Mulligan and Michael C. Mitchelmore, Macquarie University, Sydney
>
>FACILITATING STUDENTS' INTERACTIONS IN A COOPERATIVE LEARNING SETTING OF
>MATHEMATICS
>Roza Leikin and Orit Zaslavsky, Technion - Israel Institute of Technology
>
>REFLECTIVE DISCOURSE AND COLLECTIVE REFLECTION
>Paul Cobb, Vanderbilt University
>Ada Boufi, National and Capodistrian University of Athens, Greece
>Kay McClain, Vanderbilt University
>Joy Whitenack, University of Missouri
>
>TEACHERS' EVOLVING CONCEPTIONS OF ONE-TO-ONE TUTORING: A THREE-TIERED
>TEACHING EXPERIMENT
>Richard Lesh, University of Massachusetts - Dartmouth
>Anthony E. Kelly, Rutgers, The State University of New Jersey
>
>INCREASED KNOWLEDGE IN GEOMETRY AND INSTRUCTIONAL PRACTICE
>Jane O. Swafford, Graham A. Jones, and Carol A. Thornton, Illinois State
>University
>
>LISTENING FOR DIFFERENCES: AN EVOLVING CONCEPTION OF MATHEMATICS TEACHING
>Brent A. Davis, The University of British Columbia
>
>DESIGNING REPRESENTATIONS: REASONING ABOUT FUNCTIONS OF TWO VARIABLES
>Michal Yerushalmy, University of Haifa, Israel
>
>FAMILIES AND MATHEMATICS: A STUDY OF PARENT-CHILD INTERACTIONS
>Ann Anderson, The University of British Columbia
>
>TEACHING REALISTIC MATHEMATICAL MODELING IN THE ELEMENTARY SCHOOL: A
>TEACHING EXPERIMENT WITH FIFTH GRADERS
>Lieven Verschaffel and Erik De Corte, University of Leuven, Belgium
>
>INCONSISTENCY BETWEEN A BEGINNING ELEMENTARY TEACHER'S MATHEMATICS BELIEFS
>AND TEACHING PRACTICE
>Anne M. Raymond, Keene State College
>
>MATHEMATICAL TASKS AND STUDENT COGNITION: CLASSROOM-BASED FACTORS THAT
>SUPPORT AND INHIBIT HIGH-LEVEL MATHEMATICAL THINKING AND REASONING
>Marjorie Henningsen and Mary Kay Stein, University of Pittsburgh,
>Pittsburgh, PA
>
>AN INVESTIGATION OF AFRICAN-AMERICAN STUDENTS' MATHEMATICAL PROBLEM SOLVING
>Carol E. Malloy and M. Gail Jones, University of North Carolina, Chapel
>Hill, NC
>
>CHILDREN'S PROBLEM POSING WITHIN FORMAL AND INFORMAL CONTEXTS
>Lyn D. English, Queensland University of Technology, Brisbane, QLD Australia
>
>THE EVOLUTION WITH AGE OF PROBABILISTIC, INTUITIVELY BASED, MISCONCEPTIONS (BR)
>Efraim Fischbein and Ditza Schnarch, Tel Aviv University, Tel Aviv Israel
>
>COMPUTER-INTENSIVE ALGEBRA AND STUDENTS' CONCEPTUAL KNOWLEDGE OF FUNCTIONS
>Brian R. O'Callaghan, Southeastern Louisiana University, Hammond, LA
>
>THE CONSTRUCTION OF THE SOCIAL CONTEXT OF MATHEMATICS CLASSROOMS: A
>SOCIOLINGUISTIC ANALYSIS
>Bill Atweh, Robert E. Bleicher, and Tom Cooper, Queensland University of
>Technology, Red Hill, QLD Australia
>
>INVENTION AND UNDERSTANDING IN THE DEVELOPMENT OF MULTIDIGIT ADDITION AND
>SUBTRACTION PROCEDURES: A LONGITUDINAL STUDY
>Tom Carpenter, University of Wisconsin, Madison, WI
>Megan L. Franke, UCLA
>Victoria R. Jacobs and Elizabeth Fennema, University of Wisconsin
>
>MAKING SENSE OF INSTRUCTIONAL DEVICES: THE EMERGENCE OF TRANSPARENCY IN
>MATHEMATICAL ACTIVITY
>Luciano Meira, Universidade Federal de Pernambuco, Recife, PE Brazil
>
>OPEN AND CLOSED MATHEMATICS APPROACHES AND SITUATED COGNITION
>Jo Boaler, King's College, London UK
>
>KINDERGARTEN STUDENTS' ORGANIZATION OF COUNTING IN JOINT COUNTING TASKS AND
>THE EMERGENCE OF COOPERATION
>Heide G. Wiegel, University of Georgia, Athens, GA
>
>PRESCHOOLERS' COUNTING AND SHARING
>Kristine L. Pepper, Donburn Primary School
>Robert P. Hunting, La Trobe University, Bundoora, VIC Australia
>
>SUPPORTING INNOVATION: THE IMPACT OF A TEACHER'S CONCEPTIONS OF FUNCTIONS
>ON HIS IMPLEMENTATION OF A REFORM CURRICULUM
>Gwendolyn M. Lloyd and Melvin R. Wilson, University of Michigan, Ann Arbor, MI
>
>PROSPECTIVE SECONDARY SCHOOL MATHEMATICS TEACHERS' STRATEGIES FOR
>DEVELOPING AND VALIDATING FUNCTIONS AS MATHEMATICAL MODELS IN THE PRESENCE
>OF COMPUTING TOOLS
>Rose Mary Zbiek, University of Iowa, Iowa City, IA
>
>SUPPORTING STUDENTS' MATHEMATICAL INQUIRIES THROUGH READING
>Marjorie Siegel, Columbia University, New York, NY
>Raffaella Borasi and Judith M. Fonzi, University of Rochester
>
>USING CONCEPT MAPS TO ASSESS CALCULUS STUDENTS' KNOWLEDGE OF FUNCTION
>Carol G. Williams, Abilene Christian University, Abilene, TX
>
>
>




>




>

*************************************************
Joao Pedro da Ponte
Dep Educacao-Fac Ciencias-Univ Lisboa
Edificio C1-Campo Grande
1700 LISBOA-PORTUGAL

fax office  (351-1)-750-0082
tel. office (351-1)-757-3141 ext 1103/2012/2522
tel. home   (351-1)-363-0861
*************************************************

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X-Comment:  Educacao em Matematica

Largest Known Prime Found by SGI/Cray Supercomputer

EAGAN, Minn., September 3, 1996 -- Computer scientists at Silicon
Graphics's Cray Research unit, have discovered the largest known prime
number while conducting tests on a CRAY T90 series supercomputer.

The new prime number has 378,632 digits. Printed in newspaper-sized
type, the number would fill approximately 12 newspaper pages.

In mathematical notation, the new prime number is expressed as
2^1257787-1 , which denotes two, multiplied by itself 1,257,787 times,
minus one. Numbers expressed in this form are called Mersenne prime
numbers after Father Marin Mersenne, a 17th century French monk who
spent years searching for prime numbers of this type.

Prime numbers can be divided evenly only by themselves and one. Examples
include 2, 3, 5, 7, 11 and so on. The Greek mathematician Euclid proved
that there are an infinite number of prime numbers. But these numbers do
not occur in a regular sequence and there is no formula for generating
them. Therefore, the discovery of new primes requires randomly
generating and testing millions of numbers.

Silicon Graphics employees have been at the leading edge for prime
number discoveries since 1978. The last 10 records for the largest known
prime belong to people who are now working at Silicon Graphics:
Prime   Digits  Year  SGI Employee

2^21701-1    6533  1978  Landon Curt
Noll
          (with Laura Nickel)
2^23209-1    6987  1979  Landon Curt
Noll
2^44497-1   13395  1979  David Slowinski
          (with Harry
Nelson)
2^86243-1   25962  1982  David Slowinski
2^132049-1   39751
1983  David Slowinski
2^216091-1   65050  1985  David Slowinski
391591 *
  65087  1989  Landon Curt Noll
   2^216193-1         John Brown

  Sergio Zarantonello
          (with Joel & Gene Smith, Bodo Parady)

2^756839-1  227832  1992  David Slowinski
          Paul Gage
2^859433-1
 258716  1994  David Slowinski
          Paul Gage
2^1257787-1  378632
1996  David Slowinski
          Paul Gage
"Finding these special numbers is a true 'needle-in-a-haystack'
exercise, but we improve our odds by using a tremendously fast computer
and a clever program," said David Slowinski, a Cray Research computer
scientist. and fellow Cray Research computer scientist Paul Gage
developed the program that found the new prime number. Mathematician
Richard Crandall (of NeXT), independently verified that the number
Slowinski and Gage found is prime.

Prime numbers have applications in cryptography and computer systems
security. Huge prime numbers like those discovered most recently are
principally mathematical curiosities, but the process of searching for
prime numbers does have several practical benefits.

For instance, the "prime finder" program developed by Slowinski and Gage
is used by Silicon Graphics's Cray Research unit as a quality assurance
test on all new supercomputer systems. A core element of this program is
a routine that involves squaring a number repeatedly. As this process
continues, it eventually involves multiplying immense numbers -- numbers
of hundreds of thousands of digits -- by themselves.

"This acts as a real 'torture test' for a computer," said Slowinski.
"The prime finder program rigorously tests all elements of a system --
from the logic of the processors, to the memory, the compiler and the
operating and multitasking systems. For high performance systems with
multiple processors, this is an excellent test of the system's ability
to keep track of where all the data is." Slowinski said the recent CRAY
T90 series supercomputer test in which the new prime number was
discovered would run for over 6 hours on one central processing unit of
the system. "If a machine can complete this exhaustive run-through, we
can be confident everything is working as it should," said Slowinski.

In addition, Slowinski said, techniques used to speed up the performance
of the prime finder can also be used to enhance the performance of
programs customers use on real-world problems such as forecasting the
weather and searching for oil. "Through our work on the prime finder
program, we learn new techniques for speeding up certain kinds of
mathematical operations. These operations are often key elements of the
most computation-intensive portions of software programs our customers
run on their systems," said Slowinski.

Slowinski compared running the prime finder on supercomputers and
continually "tuning" the program to building and racing exotic cars.
"There aren't many practical uses for dragsters or Formula 1 race cars.
But some things engineers do to make those cars perform better
eventually find their way into cars you and I drive," said Slowinski.

Slowinski noted that with the discovery of the new prime number, a new
perfect number can also be generated. A perfect number is equal to the
sum of its factors. For example, 6 is perfect because its factors -- 1,
2 and 3 -- when added together, equal 6. Mathematicians don't know how
many perfect numbers exist. They do know, however, that all perfect
numbers have a direct relationship to Mersenne primes. The new perfect
number generated with the new Mersenne prime is the 34th known perfect
number and has 757,263 digits.

------------


Mais informacoes na WEB em:

http://www.utm.edu/research/primes/notes/1257787.html
http://www.sjmercury.com/business/compute/prime.htm
http://reality.sgi.com/csp/ioccc/noll/prime/prime_press.html
http://ourworld.compuserve.com/homepages/justforfun/prime.htm
http://www.utm.edu/research/primes/
http://www.utm.edu/research/primes/largest.html


----



----
Jaime Carvalho e Silva, Univ. Coimbra, Portugal
http://www.mat.uc.pt/~jaimecs/index.html

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X-Comment:  Educacao em Matematica

-------

                       POR FAVOR DISTRIBUIR

A 30 de Setembro deste ano vai realizar-se em Lisboa a
EuroAIED- Conferencia Europeia de Inteligencia Artificial aplicada
'a Educacao (em geral- Ensino Assistido por Computador).

O prazo limite para a  inscricao na conferencia e'
o dia 15 de Setembro (ao pre,co menos caro).

Esta conferencia esta' organizada em torno de sessoes de trabalho
das quais se podem  destacar topicos tais como: Multimedia Educacional,
Sistemas Autores, Sistemas de Ensino basedados em Simulacoes,
Modelacao de Alunos, Ambientes Virtuais de Ensino, etc.

Para obter informacoes sobre a conferencia e' favor de consultar:
   http://cbl.leeds.ac.uk/~euroaied/EuroAIED/EuroAIED.html

Alguma outra informacao relativamente 'a conferencia, podem
contactar-me directamente (INESC-tel 3100219) ou por mail
(amp@minerva.inesc.pt).

Ate' breve na Gulbenkian!

A. Paiva
------


               EUROPEAN CONFERENCE ON AI IN EDUCATION

            Fundacao Calouste Gulbenkian, Lisbon, Portugal
                    September 30 - October 2, 1996

                       Still time to register!

All the details of the working sessions (including most of the papers),
timetable, travel, list of delegates, Lisbon, etc. are on the WWW page:
http://www.cbl.leeds.ac.uk/conferences/EuroAIED
A form for registration is given below.

General Information
-------------------
You are cordially invited to participate in EuroAIED (the European
Conference on Artificial Intelligence in Education), to be held in
Lisbon from September 30th to October 2nd 1996.  About sixty papers
will be presented and discussed in a workshop-like atmosphere
within the stimulating environment of the world-famous Gulbenkian
Centre.
EuroAIED is intended to provide an opportunity for researchers to
develop principles for the design of systems to support learning.
The "principles" may be derived from artificial intelligence,
cognitive science, human-computer interaction, and related fields;
the "systems" include tutoring systems, learning environments,
simulations, multimedia systems, WWW-based systems, etc.; and
"learning" includes learning by schoolchildren, university students
and industrial trainees.

EuroAIED will be organised as a set of 'working sessions',
enveloped within opening and closing addresses given by Joost Breuker
(University of Amsterdam) and Ben du Boulay (University of Sussex),
respectively.  The usual format of a working session will be: some short
presentations of submitted papers addressing a set of pre-specified
questions, followed by a general discussion, and then (in a plenary
session) a synthesis presentation of the conclusions of the working
session.

The working session topics are:
        Instructional planning     Cognitive science
        Simulation-based learning  Machine learning
        Virtual reality            Virtual learning environments
        Educational multimedia     Student modelling
        Natural language           Qualitative reasoning
        Distributed cognition      Motivation
        Authoring systems          External representations
        Collaborative learning     Self-explanation

Travel and Accommodation
------------------------

Lisbon airport is just twenty minutes from the centre of Lisbon and less
from the hotels mentioned below.  You will find that airfares are
considerably less if you include a Saturday night stay (EuroAIED is
Monday
to Wednesday).  For details of the special airfare deal please consult
the WWW page.

Participants are entirely responsible for making their own accommodation
arrangements.  We reserved rooms at the Ibis Hotel and Novotel within a
few minutes walk of the conference centre.  Although these reservations
have now lapsed we understand that there are still rooms available
there.
These hotels are close to the Palhava metro station, which is convenient
for getting into the centre of Lisbon.  The Lisbon information (from our
WWW page) contains details of other hotels in Lisbon if you should
need them.

The details of the hotels mentioned above are as follows:

IBIS
Address: Av. Jose' Malhoa, 1000 Lisboa
Tel : 351.1.7273181
fax : 351.1.7273287

Prices: single room with breakfast - 8 950 esc.
        double room with breakfast - 9 700 esc.

NOVOTEL
Address: Av. Jose' Malhoa, 1642, 1000 Lisboa.
Tel: 351.1.7266022
Fax: 351.1.7266496

Prices: single or double room with breakfast- 10 500 esc.


------------------------- CUT HERE -----


Registration
-----------

Delegate details

Title.............First name.....................Last
name...................

Address......................................................................

............................................................................

Phone (work)..........................(home)
...............................

Fax.................................
Email..................................

Affiliation (for
badge)......................................................

Please indicate any special needs
..........................................

............................................................................

Signature
..................................................................

Registration fees

Conference
Includes entry to all sessions, a copy of proceedings, and coffee
breaks.
All prices are in ECUs.


              Early (before Sept 15)       On-site
Regular       190                          230
Student       130                          160               ...... ECU

Student fees are only granted to full-time students.  A letter from
the department head certifying status must accompany registration.

Dinner at Castelo de Sao Jorge: 40 ECU
Please tick here ... if vegetarian and here ... if vegan.
                                                             ...... ECU

Extra proceedings (to collect at the conference): 30 ECU
                                                             ...... ECU

Total fee
                                                             ...... ECU


Cancellation/Refund Policy: A notification of cancellation must be
sent in writing to the address below.  If the cancellation is received
before
September 10th the registration fee, less a 50 ECU handling fee, will
be refunded.

Payment:
Payments are requested in ECU, except that Non-European citizens may pay
in US dollars, using a fixed exchange rate of 1 ECU = 1.25 US dollars,
UK citizens may pay in sterling, using a fixed exchange rate of
1 ECU = 0.82 pounds, and Portuguese citizens may pay in escudos, using
a fixed exchange rate of 1 ECU = 196 escudos.

  *  Money transfer in ECU:
     Ask your bank for a SWIFT transfer to the National Westminster
     bank, code NW BK BG 2L, quoting
       National Westminster Bank, Account No 310/02504847
       Sort Code 60-60-05, quoting EuroAIED
       Leeds City Office, 8 Park Row, Leeds LS1 1QS

  (for Non-European citizens)
  *  $-Cheque made payable to EuroAIED, University of Leeds

  (for UK citizens)
  *  Money transfer in pounds to:
       National Westminster Bank, Account No 86577220
       Sort Code 60-60-05, quoting EuroAIED
       Leeds City Office, 8 Park Row, Leeds LS1 1QS
  *  Pound-Cheque made payable to EuroAIED, University of Leeds

  (for Portuguese citizens)
  *  Money transfer in escudos (PTE) to:
       Conferencia EuroAIED
       NIB - 0013 9955 02100162438 02
       BNU, Agencia Arco do Cego
       Av. Duque de  Avila, 2-A, 1000 Lisboa
  *  Escudos (PTE)-Cheque made payable to "Conferencia EuroAIED"

Please send to:
        EuroAIED Secretariat
        Computer Based Learning Unit
        University of Leeds
        Leeds LS2 9JT
        England

        phone: +44 (0)113 233 4626
        fax: +44 (0)113 233 4635
        email: euroaied@cbl.leeds.ac.uk

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X-Comment:  Educacao em Matematica

Formacao de professores para o 3 Ciclo: Algumas (muitas...) questoes

Um dos aspectos que se tem discutido bastante ultimamente e a possibilidade
das Escolas Superiores de Educacao poderem formar professores do 3 Ciclo do
Ensino Basico. 
Varios tem sido os argumentos que poem em causa esta possibilidade.

Afirma-se, por exemplo, que um professor sera menos qualificado so por ser
formado por uma Escola Superior de Educacao. Sera que o facto de ser formado
numa qualquer Universidade, e uma garantia de qualidade? 
Sera que as instituicoes sao "iguais" por blocos: todas as Universidades
fazem formacao de professores de qualidade e todas as ESES fazem formacao de
professores sem qualidade? 

Sera que em todas as Universidades os futuros professores sao formados por
doutorados? Por exemplo, quantos doutorados ha em Portugal nas diferentes
areas das Ciencias da Educacao? Desde quando existem? Onde e que trabalham?

Refere-se que as Escolas Superiores de Educacao nao foram concebidas para
formar professores do 3 Ciclo. E as Universidades? Foram concebidas para
formar professores de algum nivel de ensino? Para que as Universidades
pudessem formar professores e criar condicoes para isso, nao tiveram que se
ir reestruturando, redefinindo os seus principios, investindo na formacao do
seu corpo docente, criando novos espacos e formas de organizacao? Porque e
que se poe em causa que as ESEs tenham capacidade para fazer o mesmo? 

Consideramos indiscutivel que os professores de qualquer nivel de ensino
devam possuir uma formacao cientifica solida. E pensamos que quer as
Universidades quer as ESEs devem, por todos os meios ao seu alcance,
garantir a possibilidade dessa formacao. Colocam-se, no entanto, varias
questoes. Como se processa e como de devera processar a articulacao dessa
formacao cientifica com a formacao pedagogica/didactica? Sera que esta
articulacao e feita com qualidade em qualquer Universidade? Por professores
pedagogicamente habilitados, onde? Sera que a formacao cientifica que e
feita em muitas Universidades e adequada a futuros professores? 

A questao dos docentes das ESEs fazerem ou nao investigacao e tambem muito
polemica. Porque e que normalmente os projectos de investigacao apresentados
por ESEs nao sao financiados? 
Nao sera que as condicoes que as ESEs e as Universidades tem para fazer
investigacao sao de tal forma diferentes que privilegiam estas ultimas?
Ja se investigou qual o numero de professores que fazem investigacao nas
Universidades (no ambito de Mestrados, Doutoramentos, Projectos,...) e que
pertencem ao corpo docente de ESEs?

No debate que tem sido feito em torno da questao da formacao de professores
para o 3 Ciclo tem sempre estado presentes, de uma forma implicita ou
explicita, questoes relacionadas com a afirmacao das diferentes instituicoes
envolvidas. Como professoras do Ensino Superior Politecnico, interessa-nos
mais reflectir sobre o que podera ser uma formacao de qualidade para os
futuros professores do Ensino Basico, consistente com os principios
orientadores estabelecidos na Lei de Bases do Sistema Educativo. 
Pensamos que a formacao de professores e suficientemente importante para
justificar uma resposta ao desafio que aqui deixamos:

Que formacao de professores para o seculo XXI? 
 
Ana Boavida, Joana Porfirio, Lurdes Serrazina

Reply-To: sem@cc.fc.ul.pt
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X-Comment:  Educacao em Matematica
Status: RO

>Formacao de professores para o 3 Ciclo: Algumas (muitas...) questoes
>
>Um dos aspectos que se tem discutido bastante ultimamente e a possibilidade
>das Escolas Superiores de Educacao poderem formar professores do 3 Ciclo do
>Ensino Basico. 
>Varios tem sido os argumentos que poem em causa esta possibilidade.
>
>Afirma-se, por exemplo, que um professor sera menos qualificado so por ser
>formado por uma Escola Superior de Educacao. Sera que o facto de ser formado
>numa qualquer Universidade, e uma garantia de qualidade? 
>Sera que as instituicoes sao "iguais" por blocos: todas as Universidades
>fazem formacao de professores de qualidade e todas as ESES fazem formacao de
>professores sem qualidade? 
>
>Sera que em todas as Universidades os futuros professores sao formados por
>doutorados? Por exemplo, quantos doutorados ha em Portugal nas diferentes
>areas das Ciencias da Educacao? Desde quando existem? Onde e que trabalham?
>
>Refere-se que as Escolas Superiores de Educacao nao foram concebidas para
>formar professores do 3 Ciclo. E as Universidades? Foram concebidas para
>formar professores de algum nivel de ensino? Para que as Universidades
>pudessem formar professores e criar condicoes para isso, nao tiveram que se
>ir reestruturando, redefinindo os seus principios, investindo na formacao do
>seu corpo docente, criando novos espacos e formas de organizacao? Porque e
>que se poe em causa que as ESEs tenham capacidade para fazer o mesmo? 
>
>Consideramos indiscutivel que os professores de qualquer nivel de ensino
>devam possuir uma formacao cientifica solida. E pensamos que quer as
>Universidades quer as ESEs devem, por todos os meios ao seu alcance,
>garantir a possibilidade dessa formacao. Colocam-se, no entanto, varias
>questoes. Como se processa e como de devera processar a articulacao dessa
>formacao cientifica com a formacao pedagogica/didactica? Sera que esta
>articulacao e feita com qualidade em qualquer Universidade? Por professores
>pedagogicamente habilitados, onde? Sera que a formacao cientifica que e
>feita em muitas Universidades e adequada a futuros professores? 
>
>A questao dos docentes das ESEs fazerem ou nao investigacao e tambem muito
>polemica. Porque e que normalmente os projectos de investigacao apresentados
>por ESEs nao sao financiados? 
>Nao sera que as condicoes que as ESEs e as Universidades tem para fazer
>investigacao sao de tal forma diferentes que privilegiam estas ultimas?
>Ja se investigou qual o numero de professores que fazem investigacao nas
>Universidades (no ambito de Mestrados, Doutoramentos, Projectos,...) e que
>pertencem ao corpo docente de ESEs?
>
>No debate que tem sido feito em torno da questao da formacao de professores
>para o 3 Ciclo tem sempre estado presentes, de uma forma implicita ou
>explicita, questoes relacionadas com a afirmacao das diferentes instituicoes
>envolvidas. Como professoras do Ensino Superior Politecnico, interessa-nos
>mais reflectir sobre o que podera ser uma formacao de qualidade para os
>futuros professores do Ensino Basico, consistente com os principios
>orientadores estabelecidos na Lei de Bases do Sistema Educativo. 
>Pensamos que a formacao de professores e suficientemente importante para
>justificar uma resposta ao desafio que aqui deixamos:
>
>Que formacao de professores para o seculo XXI? 
> 
>Ana Boavida, Joana Porfirio, Lurdes Serrazina


   Uma pergunta que deve ser muito inocente:
   
   E se as ESE's se concentrassem a fundo na investigac,a~o e ensino das
a'reas pedago'gicas e dida'cticas, e as Universidades se concentrassem a
fundo na investigac,a~o e ensino das a'reas "cienti'ficas", melhor dizendo
(pois a Pedagogia e a Dida'ctica tambe'm sa~o Cie^ncias de pleno direito),
especi'ficas, no nosso caso matema'ticas (mas provavelmente o mesmo se
passa com a Fi'sica, a Qui'mica, etc., etc.,....)?

   E uma sugesta~o que deve ser ainda mais inocente:

   E se as "cabecinhas pensadoras" da nossa prac,a  arranjassem maneira de
os futuros professores adquirirem a sua formac,a~o "cienti'fica" nas
Universidades e a sua formac,a~o pedago'gica nas ESE's, frequentando parte
do seu curso superior numa Universidade e parte numa ESE?  Na~o se
conseguira~o articular protocolos ou redigir e aprovar legislac,a~o nesse
sentido? 

   Ou serei um colega maldito se vos disser a minha opinia~o, `a boa
maneira da frontalidade que se usa no primeiro mundo (Portugal ja' lhe
pertencera'?). E a minha opinia~o e' esta: as Universidades na~o te^m nem
tera~o vocac,a~o para preparar pedagogos, as ESE's na~o te^m nem tera~o
vocac,a~o para preparar professores nas respectivas a'reas cienti'ficas.

   E enquanto na~o nos conhecermos a no's pro'prios, viva o corporativismo
e viva o folclore!!!

        J. M. S. Simo~es Pereira 
Nome (Name):         J.M.S.Simo~es Pereira
Enderec,o (Address): Departamento de Matema'tica
                     Universidade de Coimbra
                     PT-3000 Coimbra (PORTUGAL)                            
                
Teleco'pia (Fax): +351 39 32568    Telefone (Phone): +351 39 7003191       
                                     
Enderec,o electro'nico (E-mail): siper@matuc2.mat.uc.pt

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X-Comment:  Educacao em Matematica
Status: RO



Respondendo as nosas colegas das ESEs e ao colega da Universidade de
Coimbra, sobre a formacao de professores...


Nao me parece que exista neste momento uma definicao consensual do que e
uma "formacao inicial de qualidade" -- em todas as suas dimensoes. Mas
parece-me que esse tipo de formacao, no que respeita a futuros professores
de Matematica do 3 ciclo e secundario (e pelos vistos tambem do 2 ciclo)
tem de ter necessariamente uma componente cientifica forte. Sou dos que
acreditam que nao e possivel ensinar Matematica sem saber (bastante) de
Matematica. Se acharem que eu estou errado, expliquem-me porque.

Essa formacao deve ser feita tanto quanto possivel por pessoas que sabem
realmente de Matematica. O doutoramento e, mais do que isso, provas dadas
atraves do trabalho de investigacao, sao indicadores importantes de
capacidade cientifica. Isso e hoje aceite dum modo geral em todas as
sociedades desenvolvidas. Se tiverem outros criterios melhores para avaliar
esta capacidade, digam-me.

Tambem nao me parece que neste momento as ESEs tenham possibilidde (em
termos de recursos humanos) para proporcionar a formacao cientifica (nao so
na Matematica mas em muitas outras disciplinas). O pais nao esta tao bem de
recursos que possa dar-se ao luxo de destruir Departamentos univeristarios
de formacao de professores (no Minho, em Aveiro, em Evora, em Letras e
Ciencias de Lisboa, etc) para ir gastar um dinheirao a desenvolver novas
instituicoes. Pode parecer bonito a quem la esta mas nao sera razoavel em
termos do pais que temos.

E por outro lado... nao existe uma divisao absoluta entre "ciencia" e
"pedagogia", nem a formacao de professores se reduz A formula
"ciencia+pedagogia". Trata-se de perspectivas mais do que ultrapassadas em
toda a parte. Alias, comeca-se a perceber que as certezas da ciencia
precisam de uma boa dose de critica epistemologica, ao mesmo tempo que se
alargam as areas de estudos cientificos de suporte a actividade educativa.

Pode haver varias solucoes para a formacao de professores. Por mim,
continuo convencido que a melhor seria a de integrar as ESEs nas
Univerisdades, como escolas de indole profissionalizante e fazer a formacao
de professores (do primeiro, segundo, terceiro ciclos e secundario) em
colaboracao com os Departamentos universitarios das areas correspondentes.
So um mal-entendido atirou as ESEs para os politecnicos. Elas nao tem nada
a ver (ou nao deviam ter) com a nocao de cursos de baixa qualificacao,
curtos, de cunho essencialmente tecnicizante proprios do Politecnico. E
talvez a altura de corrigir esse erro e repor a situacao mais natural para
a formacao de professores em Portugal.


um abraco e os votos de bom trabalho

Joao Pedro

*************************************************
Joao Pedro da Ponte
Dep Educacao-Fac Ciencias-Univ Lisboa
Edificio C1-Campo Grande
1700 LISBOA-PORTUGAL

fax office  (351-1)-750-0082
tel. office (351-1)-757-3141 ext 1103/2012/2522
tel. home   (351-1)-363-0861
*************************************************

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X-Comment:  Educacao em Matematica
Status: RO

>Respondendo as nosas colegas das ESEs e ao colega da Universidade de
>Coimbra, sobre a formacao de professores...
>
>
>Nao me parece que exista neste momento uma definicao consensual do que e
>uma "formacao inicial de qualidade" -- em todas as suas dimensoes. Mas
>parece-me que esse tipo de formacao, no que respeita a futuros professores
>de Matematica do 3 ciclo e secundario (e pelos vistos tambem do 2 ciclo)
>tem de ter necessariamente uma componente cientifica forte. Sou dos que
>acreditam que nao e possivel ensinar Matematica sem saber (bastante) de
>Matematica. Se acharem que eu estou errado, expliquem-me porque.
>
>Essa formacao deve ser feita tanto quanto possivel por pessoas que sabem
>realmente de Matematica. O doutoramento e, mais do que isso, provas dadas
>atraves do trabalho de investigacao, sao indicadores importantes de
>capacidade cientifica. Isso e hoje aceite dum modo geral em todas as
>sociedades desenvolvidas. Se tiverem outros criterios melhores para avaliar
>esta capacidade, digam-me.
>
>Tambem nao me parece que neste momento as ESEs tenham possibilidde (em
>termos de recursos humanos) para proporcionar a formacao cientifica (nao so
>na Matematica mas em muitas outras disciplinas). O pais nao esta tao bem de
>recursos que possa dar-se ao luxo de destruir Departamentos univeristarios
>de formacao de professores (no Minho, em Aveiro, em Evora, em Letras e
>Ciencias de Lisboa, etc) para ir gastar um dinheirao a desenvolver novas
>instituicoes. Pode parecer bonito a quem la esta mas nao sera razoavel em
>termos do pais que temos.
>
>E por outro lado... nao existe uma divisao absoluta entre "ciencia" e
>"pedagogia", nem a formacao de professores se reduz A formula
>"ciencia+pedagogia". Trata-se de perspectivas mais do que ultrapassadas em
>toda a parte. Alias, comeca-se a perceber que as certezas da ciencia
>precisam de uma boa dose de critica epistemologica, ao mesmo tempo que se
>alargam as areas de estudos cientificos de suporte a actividade educativa.
>
>Pode haver varias solucoes para a formacao de professores. Por mim,
>continuo convencido que a melhor seria a de integrar as ESEs nas
>Univerisdades, como escolas de indole profissionalizante e fazer a formacao
>de professores (do primeiro, segundo, terceiro ciclos e secundario) em
>colaboracao com os Departamentos universitarios das areas correspondentes.
>So um mal-entendido atirou as ESEs para os politecnicos. Elas nao tem nada
>a ver (ou nao deviam ter) com a nocao de cursos de baixa qualificacao,
>curtos, de cunho essencialmente tecnicizante proprios do Politecnico. E
>talvez a altura de corrigir esse erro e repor a situacao mais natural para
>a formacao de professores em Portugal.
>
>
>um abraco e os votos de bom trabalho
>
>Joao Pedro
>
>*************************************************
>Joao Pedro da Ponte
>Dep Educacao-Fac Ciencias-Univ Lisboa
>Edificio C1-Campo Grande
>1700 LISBOA-PORTUGAL
>
>fax office  (351-1)-750-0082
>tel. office (351-1)-757-3141 ext 1103/2012/2522
>tel. home   (351-1)-363-0861
>*************************************************


   Ressalvando embora a minha fuga a ana lises profundas sobre "diviso~oes
absolutas entre cie^ncia e pedagogia" (que eu pro'prio nunca afirmei
existirem), e a "cri'ticas epistemolo'gicas" ou outras hiper-meta-coisas
deste ge'nero que por eu na~o ter preparac,a~o em Filosofia reconhec,o na~o
poder abordar,  permito-me contudo acrescentar mais uma nota ao que eu ja'
disse e que em parte motivou o colega Joa~o Pedro da Ponte:
 
     A ideia dele de integrar as ESE's nas Universidades obtem a minha
imediata concorda^ncia: e' uma forma mais radical de implementar a minha
sugesta~o de que se estabelec,am protocolos para colaborac,a~o entre umas e
outras ou se crie legislac,a~o para formalizar uma preparac,a~o dos
professores recorrendo a ambas: afinal o essencial da minha anterior
mensagem. Embora mais difi'cil de vir a tornar-se realidade, talvez os que
pensam como no's (eu e o Pedro da Ponte) so' assim acredita'ssemos numa
eficaz e produtiva colaborac,a~o.

      Bom trabalho para todos!

          Simo~es Pereira

    
Nome (Name):         J.M.S.Simo~es Pereira
Enderec,o (Address): Departamento de Matema'tica
                     Universidade de Coimbra
                     PT-3000 Coimbra (PORTUGAL)                            
                
Teleco'pia (Fax): +351 39 32568    Telefone (Phone): +351 39 7003191       
                                     
Enderec,o electro'nico (E-mail): siper@matuc2.mat.uc.pt

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