International Conference Proceedings
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International Conference Proceedings
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A FORUM FOR RESEARCHERS
This eleventh annual meeting of PME can be singled out for the largest
number of scientific communications ever contributed and for the widest
geographic distribution of its participants. One of the reasons for this success
must be attributed to a constant concern for improvement that can be traced
back to the early beginnings of PME. The founding members will remember that
follnwing the first meeting in Utrecht in 1977, it was decided that research reports
would be called for and that these would be published in Proceedings. At the
very next meeting, in Osnabrack, this tradition was started and has been
maintained ever since.
This concern for establishing a forum for research in mathematics education
was also reflected later on when the aims and objectives were formalized in our
constitution adopted at the Berkeley meeting in 1980, Two of the major goals
mentioned in that document are:
(1) to promote international contacts and exchange of scientific information in
the psychology of mathematics education, and
(2) to promote and stimulate interdisciplinary research In the aforesaid area
with the cooperation of psychologists, mathematicians and mathematics
teachers.
The constitution also emphasizes the importance of research in its
membership qualification, membership being *open to parsons involved inactive research in furtherance of the Group's aims or professionally interested in
the results of such research"
Over the years, several efforts have been made to change the philosophy of
PM:
. At different times there have been pressures to transform it variously into amore teacher
oriented organization, or into a general discussion group for
mathematics educators. The objectives pursued in these attempts were quitelaudable, for indeed serious thought must be given to the problem of bringingresearch to the teaching profession. Equally important is the realization that some very serious issues exist in mathematics education which are beyond the
research domain. But there are many other groups whose vocation is preciselythe discussion of these questions. On the other hand, in mathematics education,
there are no international groups other than PME where researchers can gather
and discuss their work among themselves. Evidence that our associationanswers such a need can be found in the very impressive number of researchreports in the PME-XI scientific program. Thus, It seems essential that PMEshould continue to be primarily a forum forresearchers.
This is not to say that we can ignore the more ganeral issues, such as thesignificance of constructivism for mathematical didactics, witness the fact that
this happens to be the theme of our plenary sessions. Indeed, the discussion of
such issues proves to be essential, for it provides us with an opportunity tosituate our own research in a broader perspective. And it is against thisenriched backdrop that we can exchange more profitably the results of our
individual research.
Improving the quality of our scientific exchanges has been an ongoingconcern for many years. This has been discussed at several meetings of theinternational Committee (LC.). More recently, at the London meeting of the I.C.,
there was general approval of the suggestion that the PME-XI ProgramCommittee formulate criteria for the selection of research reports. Following this,
the President, Pear la Nesher, mandated us to carry out this recommendation. At
its October 1986 meeting, the Program Committee (Behr, Bergeron, Herscov(cs,
Kieran, Nesher, Romberg) agreed to the following criteria which were publishedI
Formulating criteria for research reports was not the only innovation carriedout this year. For the first\ time, research report proposals were subjected to ablind review process. Each one was sent to two reviewers with experience inthe given domain. They were asked to use the criteria for research reports as
guidelines in evaluating the proposal and to recommend one of the following:
In evaluating these proposals, please keep in mind
that it is not always feasible to cover all the
criteria in the required 500 to 700 words.
Unconditional Acceptance indicates that the
proposal deals with significant issues in a coherent manner reflecting the suggested criteria.
Acceptance with reservation indicates that either
the proposal deals with an issue of questionable
importance or that it does not adhere to the
suggested criteria. Please make your remarks
sufficiently detailed so that we can make explicit
suggestions to the author for improving the
research paper.
Rejection indicates either that the issues dealt
with are considered in3ignificant, or that the
proposal is totally incoherent, or that it cannot
qualify as empirical or theoretical research.
Please make your remarks sufficiently detailed so
that the Organizing Committee can provide a reasoned rejection,
That the Implementation of criteria and a blind review process did not havea discouraging effect Is evidenced by the record number (185) of researchreport proposals received. The review process was carried out by 52colleagues, time constraints limiting their selection to North Americans. Thoseproposals which received unconditional acceptance (44) by both reviewerswere so accepted by us. Where one of the reviewers recommendedacceptance with reservation a: rejection, we gave the proposal a conditional
acceptance (132). Authors were provided with a copy of the reviewers'
comments and were asked to take their remarks into consideration when writingthe final version of their paper. Where both reviewers recommended rejection of
the proposal, we in turn studied each one very carefully. Only 9 proposals werenot accepted as research reports. Their authors were provided with thereviewers' comments and were urged to submit their contribution in the form of
a poster presentation or as part of a working/discussion group
The 176 accepted proposals resulted in 155 research reports, since 20proposals were withdrawn for a variety of reasons (such as lack of travel funds,
conflict with summer schools, etc.) and one paper was rejected for it did not
develop the themes announced in the proposal. We would like to have beenable to read the final drafts of the research reports to see If the suggestions of
the reviewers had been taken into account, but time did not allow it. Thus, everypaper that was not withdrawn or rejected appears in the Proceedings.
In order to continue improving the quality and scope of discussionssurrounding the paper presentations, another innovation was planned. While inthe past many contributions were grouped into subthemes (early arithmetic,
geometry, problem solving, etc.), no attempt was made at bringing the reportedresearch into perspective and suggesting future directions. Such syntheses areincluded in this year's program. Whenever the content of papers was sufficiently
related, they were grouped into subthemes warranting a synthesis. We solicitednine established authorities to comment on those grouped sets of papers. Their
task was to prepare a written response to appear in the Proceedings, present it
at the Conference, and load the ensuing discussion. In their commentary, they
were asked to address more specifically the following questions:
OUTLINE OF THE PROCEEDINGS
The Plenary Papers
As a theme for the plenary papers, we selected a broad topic of general
:nterest In the psychology of mathematics education: the theory of
constructivism. Current issues involve questions of definition and distinctionfrom other psychological theories, the status of constructivism as a theory of
knowledge acquisition, its implications for research on teaching and learning ingeneral and for research on mathematics education in particular. These issuesare addressed by four eminent scholars: Professor Hermine Sinclair who haswritten from the perspective of a psychologist, and Professor Jeremy Kilpatrick,
from that of a mathematics educator. These two perspectives are also reflectedin the two reactions given by Dr Gerard Vergnaud and Professor DavidWheeler.
HISTORY AND AIMS OF PME
PME came into existence at the Third international Congress onMathematical Education (ICME 3) held in Karlsruhe, Germany, in 1976. PME is
affiliated with the International Commission for Mathematical Instruction (ICMI).
Its past presidents have been Professor Efraim Fischbein of Tel Aviv University,
Professor Richard R. Skemp of Warwick University, Dr Gerard Vergnaud of theCentre National de la Recherche Scientifique in Paris, and Professor Kevin F.
Collis of the University of Tasmania. The ten previous annual meetings havetaken place in The Netherlands (Utrecht), West Germany, the United Kingdom(Warwick), the United States, France, Belgium, Israel, Australia, TheNNetherlands (Noordwijkerhout), the United Kingdom (London)
The major goals of the Group are:
1. To promote international contacts and the exchange of scientific
information in the psychology of mathematics education;
2. To promote and stimulate interdisciplinary research in the aforesaid areawith the cooperation of psychologists, mathematicians and mathematicsteachers;
3. To further a deeper and better understanding of the psychological aspectsof teaching and learning mathematics and the implications thereof.