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. i
TABLE OF CONTENTS Acknowledgements.. Organizing Committee International Scientific Committee vii viii viii PLENARY SESSIONS Introduction.. Susana Carreira, Keith Jones 1 LECTURES Math problem, Internet and digital mathematical performance Marcelo Borba Roles of aesthetics and affect in mathematical problem solving... Norma Presmeg The curriculum, creativity and mathematical competitions.. Jaime Carvalho e Silva Multiple solution problems in computerized and non-computerized environments: what difference does it make?... Michal Tabach 4 6 8 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 12 ii
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 Using statistical software in basic education: difficulties and affordances.. Cláudia Fernandes, João Pedro da Ponte Correlation between different learning styles and the use of wiki in learning Nashwa Ismail, Julie-Ann Edwards, Gary Kinchin The role of peer and computer feedback in student s problem solving... Júlio Paiva, Nélia Amado, Susana Carreira Simulating random experiments with computers in high school level teaching. Bernard Parzysz Electronic forums: an added value when solving initial algebraic problems. M. Pilar Royo, Joaquin Giménez 23 35 47 59 71 84 iii
Preservice high school teachers construction and exploration of dynamic models of variation phenomena Manuel Santos-Trigo, Matías Camacho-Machín, Carmen Olvera-Martínez The role of using technology and creativity in developing positive dispositions toward mathematical problem solving Mehmet Türegün, Luis Conde 96 108 Strand 2 Creativity: students mathematical creativity in mathematical problem solving How to foster creativity in problem posing and problem solving activities Cinzia Bonotto, Lisa Dal Santo Mathematical problems in basic education Virginia Furlanetto, Maria Madalena Dullius, Italo Gabriel Neide Dimensions of mathematically creative processes in early childhood.. Melanie Münz Creative advantages of visual solutions to some non-routine mathematical problems. Norma Presmeg The Borrowers: Using Transportation, Addresses, and Paralelepípedos to Prompt Creativity using Ethnomodeling.. Daniel Clark Orey, Milton Rosa Creativity in mathematics class: how can it emerge? Sandra Pinheiro, Isabel Vale Strategies used by elementary grade students in Mathematics Olympiad tests. Márcia Jussara Hepp Rehfeldt, Marli Teresinha Quartieri, Maria Madalena Dullius Writing problem stories: developing creativity through the integration of mathematics and language... Fátima Sardinha, Pedro Palhares, Fernando Azevedo Revealing the inner connections of math using a clock puzzle. Sabine Stöcker-Segre Mathematical creativity through the eyes of future teachers... Isabel Vale, Ana Barbosa, Lina Fonseca Noticing creativity issues when future teachers analyzing problem solving dialogues. Yuly Marsela Vanegas, Joaquin Giménez 120 133 144 156 168 179 192 204 217 229 242 iv
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 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 Affective issues in solving challenging mathematical problems within an inclusive competition. Rosa A. Tomás Ferreira, Susana Carreira, Nélia Amado Identifying cognitive-affective interaction phenomena in a technological mathematical context Inés M. Gómez-Chacón 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 A mathematical congress: a window to affect in problem solving... Teresa Pimentel, Isabel Vale Teachers involvement and learning in a lesson study.. João Pedro da Ponte, Marisa Quaresma, Mónica Baptista, Joana Mata-Pereira 254 265 275 288 300 308 321 E-POSTERS Teaching and learning mathematics for creativity through challenging tasks... Ana Barbosa, Isabel Vale, Teresa Pimentel Developing positive dispositions toward mathematical problem solving Luis Conde, Mehmet Türegün Posing and solving problems in mathematical modeling scenarios. Cristina Esteley, María Mina, Mónica Villarreal DROIDE II Robots in mathematics and informatics education final results of the project... Elsa Fernandes 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 335 337 338 339 340 341 v
Information environment for mathematics education based on relationship development theory.. Karasawa Toshimitsu Problem solving in modeling scenarios with experimental activities: the role of information and communication technologies... Mónica Villarreal, María Mina, Cristina Esteley 342 344 Reviewers.. 345 List of participants... 346 Sponsors 350 vi
ACKNOWLEDGEMENTS This Conference was kindly supported by several sponsors and organizations. We wish to express our special thanks to: 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 vii
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 viii