ERIC ED453073: Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (PME 20) (20th, Valencia, Spain, July 8-12, 1996). Volume 4.

441 Pages·1996·6.2 MB·English

by  ERIC

DOCUMENT RESUME
ED 453 073
SE 064 733
AUTHOR
Puig, Luis, Ed.; Gutierrez, Angel, Ed.
TITLE
Proceedings of the Conference of the International Group for
the Psychology of Mathematics Education (PME 20)
(20th,
Valencia, Spain, July 8-12, 1996). Volume 4.
INSTITUTION
International Group for the Psychology of Mathematics
Education.
ISSN
ISSN-0771-100X
PUB DATE
1996-00-00
NOTE
440p.; For volumes 1-4 and addenda, see SE 064 730-734.
PUB TYPE
Collected Works
Proceedings (021)
EDRS PRICE
MF01/PC18 Plus Postage.
DESCRIPTORS
*Educational Change; Educational Technology; Elementary
Secondary Education; Higher Education; Knowledge Base for
Teaching; *Language; Mathematical Concepts; *Mathematics
Instruction; Problem Solving; Social Influences; Teacher
Education
ABSTRACT
The fourth volume of this proceedings contains full research
articles. Papers include:
"Conceptual and procedural approaches to
(1)
problem-solving"
(Y. Mohammad-Yusof and D. Tall);
"Teaching differential
(2)
equations to chemistry and biology students: An overview on methodology of
qualitative research. A case study"
(M. Moreno and C. Azcarate);
(3)
"Language and assessment issues in mathematics education"
(C. Morgan);
(4)
"Learning math in two languages"
"Hermeneutic
(J. Moschkovich);
(5)
experiences in constructing lessons and classroom research" (J.A. Mousley);
"Young students' informal knowledge of fractions"
(H. Murray, A. Olivier,
(6)
and P. Human);
"Tensions in the novice mathematician's induction to
(7)
mathematical abstraction"
"Students assessment of an
(E. Nardi);
(8)
alternative approach to geometry"
(L. Nasser, N. Sant'Anna, and A.P.
"Solving word problems with different mediators: How do deaf
Sant'Anna);
(9)
children perform?" (10) "Telling definition and
(T. Nunes and C. Moreno);
conditions: An ethnomethodological study of sociomathematical activity in
classroom interaction" (11) "Making sense of children's
(M. Ohtani);
(12) "Children's intuitive understanding
patterning"
(J. Orton and A. Orton);
of area measurement" (L. Outhred and M. Mitchelmore);
(13) "Responsiveness: A
key aspect of spatial problem solving"
"The first algebraic
(K. Owens);
(14)
learning. The failure of success"
(M. Panizza, P. Sadowsky, and C. Sessa);
(15) "Extending the educational conversation: Administrator's views of staff
(T. Peluso, J.R. Becker, and B.J. Pence);
development"
"The teaching of
(16)
mathematics from within the school. Teachers and principals as researchers"
(P. Perry, P. Gomezm, and P. Valero);
"Teachers' conceptions about
(17)
mathematical assessment" (G. Philippou and C. Christou);
(18) "Student
teachers' conceptions of the rational number"
(M. Pinto and D. Tall);
(19)
"Folding back to collect: Knowing you know what you need to know"
(S. Pirie,
L. Martin, and T. Kieren);
"Nouns, adjectives and images in elementary
(20)
mathematics" (D. Pitta and E. Gray);
(21) "Designing a domain for stochastic
(22) "Cord's story: An African American
abstraction"
(D. Pratt and R. Noss);
student points to the need for change in college mathematics pedagogy" (N.C.
"On dialectical relationships between signs and algebraic
Presmeg);
(23)
(24) "Exploiting understanding of data
(L. Radford and M. Grenier);
ideas"
(25) "'Wouldn't it be good if we had a
reduction" (C. Reading and J. Pegg);
Reproductions supplied by EDRS are the best that can be made
from the original document.
symbol to stand for any number': The relationship between natural language
"Enactivism
and symbolic notation in pattern description" (E. Redden);
(26)
(27) "Teaching linear algebra: Role and nature
as a methodology" (D.A. Reid);
of knowledges in logic and set theory which deal with some linear problems"
"Ways of solving algebra problems: The influence of
(M. Rogalski);
(28)
(T. Rojano, R. Sutherland, S. Ursini, S. Molyneux, and E.
school culture"
"On the introduction of real numbers in secondary school. An
Jinich);
(29)
(I. Romero and L. Rico);
action-research experience"
"Counting,
(30)
estimation and the language of uncertainty"
(T. Rowland);
"The
(31)
transformation of mathematical objects in the didactic system: The case of
(L. Ruiz Higueras and J.L. Rodriguez Fernandez);
the notion of function"
(32)
(D. Santos-Bernard);
"The use of illustrations in mathematics textbooks"
(33)
"Effects of computerized tools on prototypes of the function concept" (B.B.
Schwarz and R. Hershkowitz); "Affective constraints in mathematics
(34)
"On the ability of high-school
(B. Southwell and M. Khamis);
education"
(35)
students to cope with a self-learning task in algebra" (J. Stupp and S.
"Learning about teaching: The potential of specific mathematics
Vinner);
(36)
teaching examples, presented on interactive multimedia" (P. Sullivan and J.
(37) "Mathematical modeling in the sciences through the eyes of
Mousley);
(R. Sutherland, T. Rojano, S. Mochon, E. Jinch, and S.
Marina and Adam"
"Pre-service teachers' problem solving strategies" (M.
Molyneux);
(38)
(39) "Children's representation of the counting sequence 1-100:
Taplin);
Cognitive structural development"
(N. Thomas, J. Mulligan, and G.A. Goldin);
(M. Trigueros, S. Ursini,
(40) "College students' conceptions of variable"
(41) "Seeing is reality: How graphic calculators may influence
and A. Reyes);
the conceptualization of limits"
(L. Trouche and D. Guin); (42) "Children's
misconceptions about the independence of random generators" (J.M. Truran);
(43) "Children's use of a representativeness heuristic" (K.M. Truran);
(44)
"Two problems under one title: The case of division by zero"
(P. Tsamir);
(45) "Children's interaction and fraction learning in a computer microworld:
Construction of the iterative fraction scheme"
(46) "Precalculus
(R. Tzur);
and graphic calculators: The influence on teacher's beliefs" (P. Valero and
(47) "Conditional probability and the level of significance in the
C. Gomez);
tests of hypotheses"
(A. Vallecillos and C. Batanero);
"Students'
(48)
awareness of the distributive property" (N. Vermeulen, A. Olivier and P.
(49) "Pre-service teachers' conceptions and beliefs about the role of
Human);
real-world knowledge in arithmetic word problem solving" (L. Verschaffel, E.
(50) "Semiotics as a descriptive framework in
De Corte, and I. Borghart);
mathematical domains"
"Some psychological
(A. Vile and S. Lerman);
(51)
aspects of professional lives of secondary mathematics teachers--The
humiliation, the frustration, the hope"
(S. Vinner); "Teachers'
(52)
knowledge of pupils' errors in algebra" (E.K. Wanjala and A. Orton);
(53)
"Children's strategies for comparing two types of random generators"
(J.
Way); and (54) "Teaching to create discussion as mathematical argumentation"
(T. Wood).
(ASK)
Reproductions supplied by EDRS are the best that can be made
from the original document.
Proceedi gs of the 20th Conference of
the International Group for the
Psychology of Mathematics Edutation
o
.11
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TO THE EDUCATIONAL RESOURCES
INFORMATION CENTER (ERIC)
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4
VOL
Valencia,, Spain.
AVAILABLE
BEST COPY
Proceedings of the 20th Conference of the
International Group for the Psychology of
Mathematics Education
Volume 4
3
International Group for the Psychology of
Mathematics Education
PME 20
Proceedings of the 20th Conference of the
International Group for the Psychology of
Mathematics Education
Edited by
Luis Puig
Angel Gutierrez
Volume 4
Valencia (Spain), July 8 - 12, 1996
Universitat
Valencia
de
Dept. de Didactica de la Matematica
4
Proceedings of the 20th Conference of the International
Group for the Psychology of Mathematics Education
Volume 4
Editors:
Luis Puig
Angel Gutierrez
Dept. de Didactica de la Matematica
Universitat de Valencia
E.U. de Magisteri "Ausias March"
Apartado 22045
Valencia (Spain)
46071
Fax: 34 - 6 3864487
E-mail: [email protected]
[email protected]
Copyright © 1996 left to the Authors
All rights reserved
ISSN 0771-100X
Deposit° Legal V-2190-1996
Cover: Reproduction of the cover of a Spanish textbook (Arithmetic for the
children) written by Antonio Gallego Chaves and published by Satumino
Calleja in 1886.
Logo: The logo of the PME 20 Conference has been designed by Juan Jose
Tomero, from the Dept. de Didactica de lExpressio Musical, Plastica i
Corporal of the Universitat de Valencia.
Printed by Encuademaciones Artesanas, S.L.
Periodista Badia 5; 46010 Valencia (Spain)
5
VI
TABLE OF CONTENTS
VOLUME 4
Table of Contents
4-v
Research Reports (cont.)
Mohammad-Yusof, Y.; Tall, D.
4-3
Conceptual and procedural approaches to problem-solving
Moreno, M.; Azcarate, C.
4-11
Teaching differential equations to chemistry and biology students:
An overview on methodology of qualitative research. A case study
4-19
Morgan, C.
Language and assessment issues in mathematics education
4-27
Moschkovich, J.
Learning math in two languages
4-35
Mousley, J.A.
Hermeneutic experiences in constructing lessons and classroom
research
4-43
Murray, H.; Olivier, A.; Human, P.
Young students' informal knowledge of fractions
4-51
Nardi, E.
Tensions in the novice mathematician's induction to mathematical
abstraction
4-59
Nasser, L.; Sant'Anna, N.; Sant'Anna, A.P.
Students assessment of an alternative approach to geometry
4-67
Nunes, T.; Moreno, C.
Solving word problems with different mediators: How do deaf
children perform?
4-75
Ohtani, M.
Telling definition and conditions: An ethnomethodological study of
sociomathematical activity in classroom interaction
4-83
Orton, J.; Orton, A.
Making sense of children's patterning
4-91
Outhred, L.; Mitchelmore, M.
Children's intuitive understanding of area measurement
4-99
Owens, K.
key aspect of spatial problem solving
Responsiveness:
A
4-107
Panizza, M.; Sadowsky, P.; Sessa, C.
The first algebraic learning. The failure of success
4-115
Peluso, T.; Becker, J.R.; Pence, B.J.
Extending the educational conversation: Administrator's views of
staff development
v6
4-123
Perry, P.; Gomez, P.; Valero, P.
The teaching of mathematics from within the school. Teachers and
principals as researchers
4-131
Philippou, G.; Christou, C.
Teachers' conceptions about mathematical assessment
4-139
Pinto, M.; Tall, D.
Student teachers' conceptions of the rational number
4-147
Pirie, S.; Martin, L.; Kieren, T.
Folding back to collect: Knowing you know what you need to know
4-155
Pitta, D.; Gray, E.
Nouns, adjectives and images in elemeniary mathematics
4-163
Pratt, D.; Noss, R.
Designing a domain for stochastic abstraction
4-171
Presmeg, N.C.
Cord's story: An African American student points to the need for
change in college mathematics pedagogy
4-179
Radford, L.; Grenier, M.
On dialectical relationships between signs and algebraic ideas
4-187
Reading, C.; Pegg, J.
Exploiting understanding of data reduction
4-195
Redden, E.
"Wouldn't it be good if we had a symbol to stand for any number" :
The relationship between natural language and symbolic notation in
pattern description
4-203
Reid, D.A.
Enactivism as a methodology
4-211
Rogalski, M.
Teaching linear algebra: Role and nature of knowledges in logic and
set theory which deal with some linear problems
4-219
Rojano, T.; Sutherland, R.; Ursini, S.; Molyneux, S.; Jinich, E.
Ways of solving algebra problems: The influence of school culture
4-227
Romero, I.; Rico, L.
On the introduction of real numbers in secondary school. An action-
research experience
4-235
Rowland, T.
Counting, estimation and the language of uncertainty
4-243
Ruiz Higueras, L.; Rodriguez Fernandez, J.L.
The transformation of mathematical objects in the didactic system:
The case of the notion of function
4-251
Santos-Bernard, D.
The use of illustrations in mathematics textbooks
4-259
Schwarz, B.B.; Hershkowitz, R.
Effects of computerized tools on prOtotypes of the function concept
7
VI
Southwell, B.; Khamis, M.
4-267
Affective constraints in mathematics education
Stupp, J.; Vinner, S.
4-275
On the ability of high-school students to cope with a self-learning
task in algebra
Sullivan, P.; Mousley, J.
4-283
Learning about teaching: The potential of specific mathematics
teaching examples, presented on interactive multimedia
Sutherland, R.; Rojano, T.; Mochon, S; Jinch E.; Molyneux, S.
4-291
Mathematical modelling in the sciences through the eyes of Marina
and Adam
Taplin, M.
4-299
Pre-service teachers' problem solving strategies
Thomas, N.; Mulligan, J.; Goldin, G.A.
4-307
Children's representation of the counting sequence 1-100: Cognitive
structural development
Trigueros, M.; Ursini, S.; Reyes, A.
4-315
College students' conceptions of variable
Trouche, L.; Guin, D.
4-323
Seeing is reality: How graphic calculators may influence the
conceptualisation of limits
Truran, J.M.
4-331
Children's misconceptions about the independence of random
generators
Truran, K.M.
4-339
Children's use of a representativeness heuristic
Tsamir, P.
4-347
Two problems under one title: The case of division by zero
Tzur, R.
4-355
Children's interaction and fraction learning in a computer
microworld: Construction of the iterative fraction scheme
Valero, P.; G6mez, C.
4-363
Precalculus and graphic calculators: The influence on teacher's
beliefs
Vallecillos, A.; Batanero, C.
4-371
Conditional probability and the level of significance in the tests of
hypotheses
Vermeulen, N.; Olivier, A.; Human, P.
4-379
Students' awareness of the distributive property
Verschaffel, L.; De Corte, E.; Borghart, I.
4-387
Pre-service teachers' conceptions and beliefs about the role of real-
world knowledge in arithmetic word problem solving
NTH
4-395
Vile, A.; Lerman, S.
Semiotics as a descriptive framework in mathematical domains
4-403
Vinner, S.
Some psychological aspects of professional lives of secondary
mathematics teachers The humiliation, the frustration, the hope
4-411
Wanjala, E.K.; Orion, A.
Teachers' knowledge of pupils' errors in algebra
4-419
Way, J.
Children's strategies for comparing two types of random generators
4-427
Wood, T.
Teaching to create discussion as mathematical argumentation
9
VIII