Proceedings of the Problem@Web International Conference:
Technology, creativity and affect in mathematical problem solving
Editors
Susana Carreira, Nélia Amado, Keith Jones, and Hélia Jacinto
Copyrights © 2014 left to the authors
All rights reserved
May, 2014
Faro, Universidade do Algarve
ISBN 978-989-8472-50-2
Cover Photo: Vilamoura Marina (Courtesy of the Municipality of Loulé)
Cite as:
Carreira, S., Amado, N., Jones, K., & Jacinto, H. (Eds.) (2014). Proceedings of
the Problem@Web International Conference: Technology, creativity and affect
in mathematical problem solving. Faro, Portugal: Universidade do Algarve.
Proceedings available for download at: http://hdl.handle.net/10400.1/3750.
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TABLE OF CONTENTS
Acknowledgements ………………………………………………………………………..
vii
Organizing Committee ……………………………………………………………………
viii
International Scientific Committee ………………………………………………………
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PLENARY SESSIONS
Introduction ………………………………………………………………………………..
Susana Carreira, Keith Jones
1
LECTURES
Math problem, Internet and digital mathematical performance ………………………
Marcelo Borba
4
Roles of aesthetics and affect in mathematical problem solving ……………………....
Norma Presmeg
6
The curriculum, creativity and mathematical competitions …………………………..
Jaime Carvalho e Silva
8
Multiple solution problems in computerized and non-computerized environments:
what difference does it make? …………………………………………………………....
Michal Tabach
10
PANEL
Present and future roles of online math competitions in the education of twenty-first
century young students ………………………………………………………………...….
João Pedro da Ponte, Keith Jones
ii
12
KEYNOTE ADDRESSES
Strand 1 – Technology: strategies and representations used in technology-based problem solving
approaches
The use of digital tools in web-based mathematical competitions: degrees of
sophistication in problem solving-and-expressing …………………………………..
Hélia Jacinto, Sandra Nobre, Susana Carreira, Nélia Amado
14
Strand 2 – Creativity: students’ mathematical creativity in mathematical problem solving
Highlighting creativity in children’s beyond-school mathematical problem solving
Nuno Amaral, Susana Carreira
16
Strand 3 – Affect: attitudes and emotions of students, parents and teachers regarding mathematical
problem solving
The affective relationship of youngsters and parents with mathematics and
problem solving in inclusive mathematical competitions ………………………….
Nélia Amado, Susana Carreira, Eugénia Castela, Rosa Antónia Tomás Ferreira
19
PARALLEL SESSIONS
RESEARCH PAPERS
Strand 1 – Technology: strategies and representations used in technology-based problem solving
approaches
Digital storytelling for improving mathematical literacy …………………………..
Giovannina Albano, Anna Pierri
23
Using statistical software in basic education: difficulties and affordances ………..
Cláudia Fernandes, João Pedro da Ponte
35
Correlation between different learning styles and the use of wiki in learning ……
Nashwa Ismail, Julie-Ann Edwards, Gary Kinchin
47
The role of peer and computer feedback in student´s problem solving …………...
Júlio Paiva, Nélia Amado, Susana Carreira
59
Simulating random experiments with computers in high school level teaching ….
Bernard Parzysz
71
Electronic forums: an added value when solving initial algebraic problems …….
M. Pilar Royo, Joaquin Giménez
84
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Preservice high school teachers’ construction and exploration of dynamic models
of variation phenomena ………………………………………………………………
Manuel Santos-Trigo, Matías Camacho-Machín, Carmen Olvera-Martínez
96
The role of using technology and creativity in developing positive dispositions
toward mathematical problem solving ………………………………………………
Mehmet Türegün, Luis Conde
108
Strand 2 – Creativity: students’ mathematical creativity in mathematical problem solving
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How to foster creativity in problem posing and problem solving activities ………
Cinzia Bonotto, Lisa Dal Santo
120
Mathematical problems in basic education …………………………………………
Virginia Furlanetto, Maria Madalena Dullius, Italo Gabriel Neide
133
Dimensions of mathematically creative processes in early childhood ……………..
Melanie Münz
144
Creative advantages of visual solutions to some non-routine mathematical
problems ……………………………………………………………………………….
Norma Presmeg
156
The Borrowers: Using Transportation, Addresses, and Paralelepípedos to Prompt
Creativity using Ethnomodeling ……………………………………………………..
Daniel Clark Orey, Milton Rosa
168
Creativity in mathematics class: how can it emerge? ………………………………
Sandra Pinheiro, Isabel Vale
179
Strategies used by elementary grade students in Mathematics Olympiad tests ….
Márcia Jussara Hepp Rehfeldt, Marli Teresinha Quartieri, Maria Madalena Dullius
192
Writing problem stories: developing creativity through the integration of
mathematics and language …………………………………………………………...
Fátima Sardinha, Pedro Palhares, Fernando Azevedo
204
Revealing the inner connections of math using a clock puzzle …………………….
Sabine Stöcker-Segre
217
Mathematical creativity through the eyes of future teachers ……………………...
Isabel Vale, Ana Barbosa, Lina Fonseca
229
Noticing creativity issues when future teachers analyzing problem solving
dialogues ……………………………………………………………………………….
Yuly Marsela Vanegas, Joaquin Giménez
242
Strand 3 – Affect: attitudes and emotions of students, parents and teachers regarding mathematical
problem solving
Practice in the mathematical modelling environment ……………………………...
Bárbara Cândido Braz, Lilian Akemi Kato
254
Cognitive scaffolding for problem solving: use of the practical worksheet ……….
Jaguthsing Dindyal, Eng Guan Tay, Khiok Seng Quek, Yew Hoong Leong, Tin Lam
Toh, Pee Choon Toh, Foo Him Ho
265
Affective issues in solving challenging mathematical problems within an inclusive
competition …………………………………………………………………………….
Rosa A. Tomás Ferreira, Susana Carreira, Nélia Amado
275
Identifying cognitive-affective interaction phenomena in a technological
mathematical context …………………………………………………………………
Inés M. Gómez-Chacón
288
An exploratory study on using the think-pair-share cooperative learning strategy
for students to solve mathematics problems in a Hong Kong primary school ……
Andrew P. Kwok, Alexandria Lau
300
A mathematical congress: a window to affect in problem solving ………………...
Teresa Pimentel, Isabel Vale
308
Teachers’ involvement and learning in a lesson study ……………………………..
João Pedro da Ponte, Marisa Quaresma, Mónica Baptista, Joana Mata-Pereira
321
E-POSTERS
Teaching and learning mathematics for creativity through challenging tasks …...........
Ana Barbosa, Isabel Vale, Teresa Pimentel
335
Developing positive dispositions toward mathematical problem solving ………………
Luis Conde, Mehmet Türegün
337
Posing and solving problems in mathematical modeling scenarios …………………….
Cristina Esteley, María Mina, Mónica Villarreal
338
DROIDE II – Robots in mathematics and informatics education – final results of the
project ……………………………………………………………………………………...
Elsa Fernandes
339
Problem solving: carving out spaces for creativity, communication, and perseverance
Deborah Moore-Russo, Anne Izydorczak, Harry T. O’Malley
Proof and creativity in a geometrical problem from a regional Mathematical
Olympiad …………………………………………………………………………………..
Juan Rodriguez, Nélia Amado, Susana Carreira, Sílvia Reis
340
341
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Information environment for mathematics education based on relationship
development theory ………………………………………………………………………..
Karasawa Toshimitsu
342
Problem solving in modeling scenarios with experimental activities: the role of
information and communication technologies …………………………….……………..
Mónica Villarreal, María Mina, Cristina Esteley
344
Reviewers …………………………………………………………………………………..
345
List of participants ………………………………………………………………………...
346
Sponsors ……………………………………………………………………………………
350
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ACKNOWLEDGEMENTS
This Conference was kindly supported by several sponsors and organizations. We wish
to express our special thanks to:
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Câmara Municipal de Loulé
Hotel Dom Pedro Golf
Springer
Dismel
Texas Instruments
Pelcor
Raiz Editora
Associação de Professores de Matemática (APM)
Fundação para a Ciência e a Tecnologia (FCT)
Região de Turismo do Algarve
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ORGANIZING COMMITTEE
Nélia Amado [Chair], Faculty of Sciences and Technology, University of Algarve, Portugal
Hélia Jacinto, Research Unit of the Institute of Education of the University of Lisbon, Portugal
Isa Martins, Pinheiro e Rosa Schools Grouping, Faro, Portugal
Jaime Carvalho e Silva, Faculty of Sciences and Technology, University of Coimbra,
Portugal
Juan Rodriguez, Faculty of Sciences and Technology, University of Algarve, Portugal
Nuno Amaral, Basic School 2,3 Sophia de Mello Breyner Andresen, Lisbon, Portugal
Rosa Antónia Tomás Ferreira, Faculty of Sciences, University of Porto, Portugal
Sandra Nobre, Research Unit of the Institute of Education of the University of Lisbon,
Portugal
Sílvia Reis, Schools Grouping of Valpaços, Portugal
Susana Carreira, Faculty of Sciences and Technology, University of Algarve, Portugal
INTERNATIONAL SCIENTIFIC COMMITTEE
Keith Jones [Co-chair], University of Southampton, United Kingdom
Susana Carreira [Co-chair], Faculty of Sciences and Technology, University of Algarve,
Portugal
Guida de Abreu, Oxford Brookes University, United Kingdom
Inés Gómez-Chacón, Faculty of Mathematics, Complutense University of Madrid, Spain
Isabel Vale, School of Education, Polytechnic Institute of Viana do Castelo, Portugal
Jaime Carvalho e Silva, Faculty of Sciences and Technology, University of Coimbra, Portugal
Joaquin Giménez, University of Barcelona, Spain
João Filipe Matos, Institute of Education, University of Lisbon, Portugal
João Pedro da Ponte, Institute of Education, University of Lisbon, Portugal
Marcelo Borba, State University of São Paulo, Brazil
Matías Camacho-Machín, University of la Laguna, Spain
Michal Tabach, Tel Aviv University, Israel
Nélia Amado, Faculty of Sciences and Technology, University of Algarve, Portugal
Norma Presmeg, Illinois State University (Professor Emerita), United States of America
Rosa Antónia Tomás Ferreira, Faculty of Sciences, University of Porto, Portugal
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