{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T08:13:28Z","timestamp":1775290408771,"version":"3.50.1"},"publisher-location":"Cham","reference-count":45,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319998602","type":"print"},{"value":"9783319998619","type":"electronic"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-3-319-99861-9_9","type":"book-chapter","created":{"date-parts":[[2018,11,30]],"date-time":"2018-11-30T08:26:14Z","timestamp":1543566374000},"page":"187-217","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Mathematical Problem Solving Beyond School: A Tool for Highlighting Creativity in Children\u2019s Solutions"],"prefix":"10.1007","author":[{"given":"Susana","family":"Carreira","sequence":"first","affiliation":[]},{"given":"Nuno","family":"Amaral","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,12,1]]},"reference":[{"key":"9_CR1","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/S0360-1315(99)00029-9","volume":"33","author":"S Ainsworth","year":"1999","unstructured":"Ainsworth, S. (1999). The functions of multiple representations. Computers & Education, 33, 131\u2013152.","journal-title":"Computers & Education"},{"key":"9_CR2","first-page":"1270","volume-title":"Proceedings of the Eighth Congress of European Research in Mathematics Education (CERME 8)","author":"E Aizikovitsh-Udi","year":"2013","unstructured":"Aizikovitsh-Udi, E. (2013). Creativity and critical thinking in solving non-routine problems among talented students. In B. Ubuz, \u00c7. Haser, & M. A. Mariotti (Eds.), Proceedings of the Eighth Congress of European Research in Mathematics Education (CERME 8) (pp. 1270\u20131271). Ankara, Turkey: European Society for Research in Mathematics Education."},{"issue":"2","key":"9_CR3","first-page":"176","volume":"8","author":"CR Aldous","year":"2007","unstructured":"Aldous, C. R. (2007). Creativity, problem solving and innovative science: Insights from history, cognitive psychology and neuroscience. International Education Journal, 8(2), 176\u2013186.","journal-title":"International Education Journal"},{"key":"9_CR4","unstructured":"Amaral, N. (2016). A criatividade matem\u00e1tica no contexto de uma competi\u00e7\u00e3o de resolu\u00e7\u00e3o de problemas. Doctoral Thesis. Lisboa: Instituto de Educa\u00e7\u00e3o, Universidade de Lisboa."},{"key":"9_CR5","first-page":"1584","volume-title":"Pre-Proceedings of the 12th International Congress on Mathematical Education (ICME 12)\u00a0\u2013 Topic Study 3","author":"N Amaral","year":"2012","unstructured":"Amaral, N., & Carreira, S. (2012). An essay on students\u2019 creativity in problem solving beyond school\u00a0\u2013 Proposing a framework of analysis. In Pre-Proceedings of the 12th International Congress on Mathematical Education (ICME 12)\u00a0\u2013 Topic Study 3 (pp. 1584\u20131593). Seoul, South Korea: ICMI."},{"issue":"59","key":"9_CR6","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1590\/1980-4415v31n59a02","volume":"31","author":"N Amaral","year":"2017","unstructured":"Amaral, N., & Carreira, S. (2017). A Criatividade Matem\u00e1tica nas Respostas de Alunos Participantes de uma Competi\u00e7\u00e3o de Resolu\u00e7\u00e3o de Problemas. Bolema, 31(59), 880\u2013906.","journal-title":"Bolema"},{"issue":"2","key":"9_CR7","doi-asserted-by":"crossref","first-page":"230","DOI":"10.54870\/1551-3440.1073","volume":"4","author":"M Andresen","year":"2007","unstructured":"Andresen, M. (2007). Introduction of a new construct: The conceptual tool \u201cflexibility\u201d. The Montana Mathematics Enthusiast, 4(2), 230\u2013250.","journal-title":"The Montana Mathematics Enthusiast"},{"key":"9_CR8","volume-title":"An\u00e1lise de Conte\u00fado","author":"L Bardin","year":"2004","unstructured":"Bardin, L. (2004). An\u00e1lise de Conte\u00fado (3rd ed.). Lisboa: Edi\u00e7\u00f5es 70.","edition":"3"},{"issue":"1\u20132","key":"9_CR9","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s11858-008-0143-7","volume":"41","author":"RA Beghetto","year":"2009","unstructured":"Beghetto, R. A., & Kaufman, J. C. (2009). Do we all have multicreative potential? ZDM\u00a0\u2013 International Journal on Mathematics Education, 41(1\u20132), 39\u201344.","journal-title":"ZDM\u00a0\u2013 International Journal on Mathematics Education"},{"key":"9_CR10","first-page":"137","volume-title":"Proceedings of the 30th conference of the International Group for the Psychology of mathematics education","author":"P Benko","year":"2006","unstructured":"Benko, P., & Maher, C. A. (2006). Students constructing representations for outcomes of experiments. In J. N. H. Moraov\u00e1, M. Kr\u00e1tk\u00e1, & N. Stehl\u00edkov\u00e1 (Eds.), Proceedings of the 30th conference of the International Group for the Psychology of mathematics education (Vol. 2, pp. 137\u2013143). Prague, Czech Republic: PME."},{"key":"9_CR11","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/978-3-319-17187-6_6","volume-title":"Selected regular lectures from the 12th international congress on mathematical education","author":"S Carreira","year":"2015","unstructured":"Carreira, S. (2015). Mathematical problem solving beyond school: Digital tools and students mathematical representations. In J. S. Cho (Ed.), Selected regular lectures from the 12th international congress on mathematical education (pp. 93\u2013113). New York: Springer."},{"key":"9_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-24910-0","volume-title":"Youngsters solving mathematical problems with technology: The results and implications of the problem@web project","author":"S Carreira","year":"2016","unstructured":"Carreira, S., Jones, K., Amado, N., Jacinto, H., & Nobre, S. (2016). Youngsters solving mathematical problems with technology: The results and implications of the problem@web project. New York: Springer."},{"key":"9_CR45","doi-asserted-by":"crossref","unstructured":"Freiman, V. (2006). Problems to discover and to boost mathematical talent in early grades: A challenging situations approach. The Mathematics Enthusiast, 3(1), 51\u201375.","DOI":"10.54870\/1551-3440.1035"},{"key":"9_CR13","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1163\/9789087909352_023","volume-title":"Creativity in mathematics and the education of gifted students","author":"V Freiman","year":"2009","unstructured":"Freiman, V. (2009). Mathematical e-nrichement: Problem-of-the-week model. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 367\u2013381). Rotterdam: Sense Publishers."},{"key":"9_CR14","first-page":"203","volume-title":"Proceedings of the 33rd conference of the International Group for the Psychology of mathematics education","author":"V Freiman","year":"2009","unstructured":"Freiman, V., & Applebaum, M. (2009). Involving students in extra-curricular school mathematical activity: Virtual mathematical marathon case study. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd conference of the International Group for the Psychology of mathematics education (Vol. 1, pp. 203\u2013206). Thessaloniki, Greece: PME."},{"key":"9_CR15","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/s11858-008-0118-8","volume":"41","author":"V Freiman","year":"2008","unstructured":"Freiman, V., & Lirette-Pitre, N. (2008). Building a virtual learning community of problem solvers: Example of CASMI community. ZDM - International Journal on Mathematics Education, 41, 245\u2013256.","journal-title":"ZDM - International Journal on Mathematics Education"},{"key":"9_CR16","first-page":"447","volume-title":"Proceedings of the 28th conference of the International Group for the Psychology of mathematics education","author":"A Gagatsis","year":"2004","unstructured":"Gagatsis, A., & Elia, I. (2004). The effects of different modes of representation on mathematical problem solving. In M. H\u00f8ines & A. Fuglestad (Eds.), Proceedings of the 28th conference of the International Group for the Psychology of mathematics education (Vol. 2, pp. 447\u2013454). Bergen, Norway: PME."},{"issue":"1","key":"9_CR17","first-page":"31","volume":"7","author":"JG Gomez","year":"2007","unstructured":"Gomez, J. G. (2007). What do we know about creativity? The Journal of Effective Teaching, 7(1), 31\u201343.","journal-title":"The Journal of Effective Teaching"},{"key":"9_CR18","unstructured":"Guerra, E. C. S. (2007). Creatividad y desarrolo professional docente en matem\u00e1ticas para la educaci\u00f3n prim\u00e1ria. Doctoral Thesis. Barcelona: Universidad de Barcelona."},{"key":"9_CR19","volume-title":"Pesquisa Qualitativa e An\u00e1lise de Conte\u00fado\u00a0\u2013 Sentidos e forma de uso","author":"IC Guerra","year":"2006","unstructured":"Guerra, I. C. (2006). Pesquisa Qualitativa e An\u00e1lise de Conte\u00fado\u00a0\u2013 Sentidos e forma de uso. Estoril, Portugal: Princ\u00edpia Editora."},{"issue":"5","key":"9_CR20","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1007\/s11858-009-0214-4","volume":"41","author":"A Heinze","year":"2009","unstructured":"Heinze, A., Star, J. R., & Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education. ZDM\u00a0\u2013 International Journal on Mathematics Education, 41(5), 535\u2013540.","journal-title":"ZDM\u00a0\u2013 International Journal on Mathematics Education"},{"key":"9_CR21","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s11858-012-0467-1","volume":"45","author":"M Kattou","year":"2013","unstructured":"Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. ZDM\u00a0\u2013 International Journal on Mathematics Education, 45, 167\u2013181.","journal-title":"ZDM\u00a0\u2013 International Journal on Mathematics Education"},{"key":"9_CR22","first-page":"286","volume-title":"Creativity in mathematics and the education of gifted students","author":"B Koichu","year":"2009","unstructured":"Koichu, B., & Andzans, A. (2009). Mathematical creativity and giftedness in out-of-school activities. In R. A. Berman & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 286\u2013307). Rotterdam: Sense Publishers."},{"key":"9_CR23","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1163\/9789087909352","volume-title":"Creativity in mathematics and the education of gifted students","author":"R Leikin","year":"2009","unstructured":"Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 130\u2013144). Rotterdam: Sense Publishers."},{"key":"9_CR24","unstructured":"Mann, E. L. (2005). Mathematical creativity and school mathematics: Indicators of mathematical creativity in middle school students. Doctoral thesis. University of Connecticut, USA."},{"key":"9_CR25","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1017\/CBO9780511606915.010","volume-title":"Creativity and reason in cognitive development","author":"RE Mayer","year":"2006","unstructured":"Mayer, R. E. (2006). The role of domain knowledge in creative problem solving. In J. C. Kaufman & J. Baer (Eds.), Creativity and reason in cognitive development (pp. 145\u2013158). Cambridge, New Jersey: Cambridge University Press."},{"key":"9_CR26","first-page":"150","volume-title":"Creativity in mathematics and the education of gifted students","author":"RM Milgram","year":"2009","unstructured":"Milgram, R. M., & Hong, E. (2009). Talent loss in mathematics: Causes and solutions. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 150\u2013163). Rotterdam: Sense Publishers."},{"issue":"37","key":"9_CR27","first-page":"7","volume":"22","author":"R Moraes","year":"1999","unstructured":"Moraes, R. (1999). An\u00e1lise de conte\u00fado. Revista Educa\u00e7\u00e3o, 22(37), 7\u201332.","journal-title":"Revista Educa\u00e7\u00e3o"},{"key":"9_CR28","unstructured":"NCTM. (2014). Procedural fluency in mathematics: A position of the National Council of Teachers of Mathematics. [Article]. Available at http:\/\/www.nctm.org\/about\/content.aspx?id=42833"},{"issue":"3","key":"9_CR29","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1007\/s11858-009-0189-1","volume":"41","author":"AA Nistal","year":"2009","unstructured":"Nistal, A. A., Van Dooren, V., Clarebout, G., Elen, J., & Verschaffel, L. (2009). Conceptualising, investigating and stimulating representational flexibility in mathematical problem solving and learning: A critical review. ZDM\u00a0\u2013 International Journal on Mathematics Education, 41(3), 627\u2013636.","journal-title":"ZDM\u00a0\u2013 International Journal on Mathematics Education"},{"key":"9_CR30","doi-asserted-by":"crossref","unstructured":"Pehkonen, E. (1997). The state-of-art in mathematical creativity. ZDM \u2013 International Journal on Mathematics Education, 29(3), 63\u201367.","DOI":"10.1007\/s11858-997-0001-z"},{"key":"9_CR31","first-page":"35","volume-title":"Handbook of creativity","author":"J Plucker","year":"1999","unstructured":"Plucker, J., & Renzulli, J. (1999). Psychometric approaches to the study of human creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 35\u201361). Cambridge: Cambridge University Press."},{"issue":"1","key":"9_CR32","doi-asserted-by":"crossref","first-page":"38","DOI":"10.5951\/MTMS.9.1.0038","volume":"9","author":"R Preston","year":"2003","unstructured":"Preston, R., & Garner, A. S. (2003). Representation as a vehicle for solving and communicating. Mathematics Teaching in the Middle School, 9(1), 38\u201343.","journal-title":"Mathematics Teaching in the Middle School"},{"key":"9_CR33","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1146\/annurev.psych.55.090902.141502","volume":"55","author":"MA Runco","year":"2004","unstructured":"Runco, M. A. (2004). Creativity. Annual Review of Psychology, 55, 657\u2013687.","journal-title":"Annual Review of Psychology"},{"key":"9_CR34","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1080\/10400419.2012.650092","volume":"24","author":"MA Runco","year":"2012","unstructured":"Runco, M. A., & Jaeger, G. J. (2012). The standard definition of creativity. Creativity Research Journal, 24, 92\u201396.","journal-title":"Creativity Research Journal"},{"key":"9_CR35","volume-title":"Eminent creativity, everyday creativity, and health","author":"MA Runco","year":"1998","unstructured":"Runco, M. A., & Richards, R. (1998). Eminent creativity, everyday creativity, and health. Norwood, NJ: Ablex."},{"key":"9_CR36","first-page":"62","volume-title":"Handbook of creativity","author":"MA Runco","year":"1999","unstructured":"Runco, M. A., & Sakamoto, S. (1999). Experimental studies of creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 62\u201392). Cambridge: Cambridge University Press."},{"issue":"3","key":"9_CR37","doi-asserted-by":"crossref","first-page":"154","DOI":"10.5951\/TCM.7.3.0154","volume":"7","author":"SJ Russell","year":"2000","unstructured":"Russell, S. J. (2000). Principles and standards: Developing computational fluency with whole numbers. Teaching Children Mathematics, 7(3), 154\u2013158.","journal-title":"Teaching Children Mathematics"},{"key":"9_CR38","doi-asserted-by":"crossref","unstructured":"Selter, C. (2009). Creativity, flexibility, adaptivity, and strategy use in mathematics. ZDM \u2013 International Journal on Mathematics Education, 41(5), 619\u2013625.","DOI":"10.1007\/s11858-009-0203-7"},{"key":"9_CR39","doi-asserted-by":"crossref","unstructured":"Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM \u2013 International Journal on Mathematics Education, 29(3), 75\u201380.","DOI":"10.1007\/s11858-997-0003-x"},{"key":"9_CR40","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1108\/978-1-60752-838-820251005","volume-title":"Creativity giftedess, and talent development in mathematics","author":"B Sriraman","year":"2008","unstructured":"Sriraman, B. (2008). Are mathematical giftedness and mathematical creativity synonyms? A theoretical analysis of constructs. In B. Sriraman (Ed.), Creativity giftedess, and talent development in mathematics (pp. 85\u2013112). Charlotte, NC: IAP."},{"key":"9_CR41","doi-asserted-by":"crossref","unstructured":"Steele, D. (2008). Seventh-grade students\u2019 representations for pictorial growth and change problems. ZDM \u2013 International Journal on Mathematics Education, 40, 97\u2013110.","DOI":"10.1007\/s11858-007-0063-y"},{"key":"9_CR42","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1142\/9789812770868_0001","volume-title":"Creativity: A handbook for teachers","author":"R Sternberg","year":"2007","unstructured":"Sternberg, R. (2007). Creativity as a habit. In A. Tan (Ed.), Creativity: A handbook for teachers (pp. 3\u201325). Singapore: World Scientific."},{"issue":"20","key":"9_CR43","first-page":"181","volume":"8","author":"I Vale","year":"2012","unstructured":"Vale, I. (2012). As Tarefas de Padr\u00f5es na Aula de Matem\u00e1tica: Um Desafio para Professores e Alunos. Intera\u00e7\u00f5es, 8(20), 181\u2013207.","journal-title":"Intera\u00e7\u00f5es"},{"key":"9_CR44","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/978-94-6091-439-3_2","volume-title":"The elements of creativity and giftedness in mathematics","author":"X Yuan","year":"2011","unstructured":"Yuan, X., & Sriraman, B. (2011). An exploratory study of relationships between students\u2019 creativity and mathematical problem-posing abilities. In B. Sriraman & K. H. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 5\u201328). Rotterdam: Sense Publishers."}],"container-title":["Research in Mathematics Education","Broadening the Scope of Research on Mathematical Problem Solving"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-99861-9_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T07:39:06Z","timestamp":1775288346000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-99861-9_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783319998602","9783319998619"],"references-count":45,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-99861-9_9","relation":{},"ISSN":["2570-4729","2570-4737"],"issn-type":[{"value":"2570-4729","type":"print"},{"value":"2570-4737","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018]]}}}