(a) Modelo de Barras de Singapura e seus diagramas pictóricos padrão. |
O Modelo de Barras de Singapura
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Cai, Ng e Moyer (2011), Cheong (2002)CHEONG, Y. K. The Model Method in Singapore. The Mathematics Educator, Athens, v. 6 , n. 2 , p. 47 - 64 , 2002 . Disponível em: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.555.5563&rep=rep1&type=pdf . Acesso em: 09 jan. 2021 . http://citeseerx.ist.psu.edu/viewdoc/dow...
, Collars et al . (2007), Dennis, Knight e Jerman (2016), Fong (2004)FONG , N. S. Developing algebraic thinking in early grades: Case study of the Singapore primary mathematics curriculum . 2004 . Disponível em: https://repository.nie.edu.sg/bitstream/10497/67/1/TME-8-1-39.pdf . Acesso em: 09 jan. 2021 . https://repository.nie.edu.sg/bitstream/...
, Ho e Lowrie (2014)HO , S. Y. ; LOWRIE , T. The model method: Students’ performance and its effectiveness . The Journal of Mathematical Behavior , Burnaby , v. 35 , p. 87 - 100 , 2014 . DOI: https://doi.org/10.1016/j.jmathb.2014.06.002 . https://doi.org/10.1016/j.jmathb.2014.06...
, Hoven e Garelick (2007)HOVEN, J.; GARELICK, B. Singapore math: Simple or complex?. Educational Leadership, v. 65, n. 3, p. 28, 2007 . , Kaur (2015)KAUR, B. The model method: A tool for representing and visualising relationships. 2015. Disponível em: https://repository.nie.edu.sg/handle/10497/17100 . Acesso em: 30 jan. 2021 . https://repository.nie.edu.sg/handle/104...
, Kaur (2019)KAUR , B . The why, what and how of the ‘Model’method: A tool for representing and visualising relationships when solving whole number arithmetic word problems . ZDM , Hamburg , v. 51 , n. 1 , p. 151 - 168 , 2019 . DOI: https://doi.org/10.1007/s11858-018-1000-y . https://doi.org/10.1007/s11858-018-1000-...
, Kho (1987)KHO, T. H. Mathematical models for solving arithmetic problems. In: Southeast Asian conference on mathematics education, 4, 1987, Singapore. Proceedings of the 4th Southeast Asian conference on mathematics education (ICMI-SEAMS), Singapore, 1987 , p. 345 – 351 . , Kho, Yeo e Lim (2009), Kho, Yeo e Fan (2014), Lee e Fong (2009)LEE, K.; FONG, N. S. Solving algebra word problems: The roles of working memory and the model method. In: YOONG, W. K.; YEE, L. P.; KAUR, B.; YEE, F. P.; FONG, N. S. (ed.). Mathematics education: the Singapore journey. Singapura, 2009 . p. 204 - 226 . DOI: https://doi.org/10.1142/9789812833761_0009 . https://doi.org/10.1142/9789812833761_00...
, Looi e Lim (2009)LOOI , C. K. ; LIM , K. S. From bar diagrams to letter-symbolic algebra: a technology‐enabled bridging . Journal of Computer Assisted Learning , Heerlen , v. 25 , n. 4 , p. 358 - 374 , 2009 . DOI: https://doi.org/10.1111/j.1365-2729.2009.00313.x . https://doi.org/10.1111/j.1365-2729.2009...
, Mahoney (2012)MAHONEY, K. Effects of Singapore’s model method on elementary student problem-solving performance: Single-case research. Tese (Doutorado em Educação) - Northeastern University (School of Education), Boston , 2012 . Disponível em: http://hdl.handle.net/2047/d20002962 . Acesso em: 30 mar. 2021 . http://hdl.handle.net/2047/d20002962...
, Mei e Soo (2014)MEI , L. Y. ; SOO , V. L. Mathematical Problem Solving - the Bar Model Method: A Professional Learning Workbook on the Key Problem Solving Strategy Used by Global Top Performer, Singapore. Singapura: Scholastic Education International (Singapore) Private Limited, a division of Scholastic Incorporated, 2014 . , Morin et al . (2017), Ng e Lee (2009)NG, S. F.; LEE, K. The model method: Singapore children's tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, Reston, v. 40, n. 3, p. 282-313, 2009 . DOI: https://doi.org/10.5951/jresematheduc.40.3.0282 . https://doi.org/10.5951/jresematheduc.40...
, Said e Tengah (2021)SAID , S. N. ; TENGAH , K. A. Supporting solving word problems involving ratio through the bar model . Infinity Journal , Cimahi , v. 10 , n. 1 , p. 149 - 160 , 2021 . Disponível em: http://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/view/1975 . Acesso em: 20 jan. 2021 . http://e-journal.stkipsiliwangi.ac.id/in...
e Willyarto, Pane e Chairiyani (2015). |
(b) Estudos envolvendo o Modelo de Barras na resolução de problemas e na aprendizagem de Matemática |
Modelo de Barras de Singapura na Resolução de Problemas
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Abreu (2018)ABREU, J. C. F. Construção e Gestão de Materiais Pedagógicos no Ensino da Matemática: uma adaptação do Método de Singapura no contexto da Educação Pré-Escolar e do 1. º Ciclo do Ensino Básico. 2018. Dissertação (Mestrado em Educação Pré-Escolar e Ensino do 1.º Ciclo do Ensino Básico) – Universidade dos Açores, Faculdade De Ciências Sociais e Humanas, Ponta Delgada, 2018. Disponível em: https://repositorio.uac.pt/handle/10400.3/4645 . Acesso em: 09 jan. 2021 . https://repositorio.uac.pt/handle/10400....
, Cheong (2002)CHEONG, Y. K. The Model Method in Singapore. The Mathematics Educator, Athens, v. 6 , n. 2 , p. 47 - 64 , 2002 . Disponível em: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.555.5563&rep=rep1&type=pdf . Acesso em: 09 jan. 2021 . http://citeseerx.ist.psu.edu/viewdoc/dow...
, Dennis, Knight e Jerman (2016), Empson et al. (2006), Hofer (2015)HOFER, C. The introduction of the Singapore Bar Model in year 1 problem solving: a personal reflection. The STeP Journal: Student Teacher Perspectives, London , v. 2 , n. 2 , p. 107 - 117 , 2015 . Disponível em: http://ojs.cumbria.ac.uk/index.php/step/article/view/243 . Acesso em: 16 jan. 2021 . http://ojs.cumbria.ac.uk/index.php/step/...
, Kaur (2019)KAUR , B . The why, what and how of the ‘Model’method: A tool for representing and visualising relationships when solving whole number arithmetic word problems . ZDM , Hamburg , v. 51 , n. 1 , p. 151 - 168 , 2019 . DOI: https://doi.org/10.1007/s11858-018-1000-y . https://doi.org/10.1007/s11858-018-1000-...
, Kho, Yeo e Lim (2009), Kho, Yeo e Fan (2014), Koleza (2015)KOLEZA, E. The bar model as a visual aid for developing complementary/variation problems. In: NINTH CONGRESS OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION, 9, 2015. Praga. Proceedings of CERME 9, Praga: Faculty of Education, 2015 . p. 1940 - 1946 . Disponível em: https://hal.archives-ouvertes.fr/hal-01288480/ . Acesso em: 23 jan. 2021 . https://hal.archives-ouvertes.fr/hal-012...
, Lee e Fong (2009)LEE, K.; FONG, N. S. Solving algebra word problems: The roles of working memory and the model method. In: YOONG, W. K.; YEE, L. P.; KAUR, B.; YEE, F. P.; FONG, N. S. (ed.). Mathematics education: the Singapore journey. Singapura, 2009 . p. 204 - 226 . DOI: https://doi.org/10.1142/9789812833761_0009 . https://doi.org/10.1142/9789812833761_00...
, Looi e Lim (2009)LOOI , C. K. ; LIM , K. S. From bar diagrams to letter-symbolic algebra: a technology‐enabled bridging . Journal of Computer Assisted Learning , Heerlen , v. 25 , n. 4 , p. 358 - 374 , 2009 . DOI: https://doi.org/10.1111/j.1365-2729.2009.00313.x . https://doi.org/10.1111/j.1365-2729.2009...
, Madani, Tengah e Trahmana (2018), Matzin e Mundia (2020)MATZIN , E. S. ; MUNDIA , L. Efficacy of the Bar Model Method of Teaching Mathematics to Year 7 Students: Case Study of Teachers in Brunei Darussalam . Journal of Educational Issues , Las Vegas , v. 6 , n. 1 , p. 402 - 421 , 2020 . Disponível em: https://eric.ed.gov/?id=EJ1259982 . Acesso em: 23 jan. 2021 . https://eric.ed.gov/?id=EJ1259982...
, Men, Ismail e Abidin (2019), Morin et al . (2017), Naroth e Luneta (2015)NAROTH , C. ; LUNETA , K. Implementing the Singapore mathematics curriculum in South Africa: experiences of foundation phase teachers . African Journal of Research in Mathematics, Science and Technology Education , London , v. 19 , n. 3 , p. 267 - 277 , 2015 . Disponível em: https://hdl.handle.net/10520/EJC181277 . Acesso em: 23 jan. 2021 . https://hdl.handle.net/10520/EJC181277...
, Rianasari, Budayasa e Patahuddin (2012), Said e Tengah (2021)SAID , S. N. ; TENGAH , K. A. Supporting solving word problems involving ratio through the bar model . Infinity Journal , Cimahi , v. 10 , n. 1 , p. 149 - 160 , 2021 . Disponível em: http://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/view/1975 . Acesso em: 20 jan. 2021 . http://e-journal.stkipsiliwangi.ac.id/in...
, Sharp e Dennis (2017)SHARP , E. ; DENNIS , S. M. Model drawing strategy for fraction word problem solving of fourth-grade students with learning disabilities . Remedial and Special Education , Lawrence , v. 38 , n. 3 , p. 181 - 192 , 2017 . DOI: https://doi.org/10.1177%2F0741932516678823 . https://doi.org/10.1177%2F07419325166788...
, Shin e Bryant (2017)SHIN , M. ; BRYANT , D. P. Improving the fraction word problem solving of students with mathematics learning disabilities: Interactive computer application . Remedial and Special Education , Lawrence , v. 38 , n. 2 , p. 76 - 86 , 2017 . DOI: https://doi.org/10.1177%2F0741932516669052 . https://doi.org/10.1177%2F07419325166690...
, Widyasari e Rosiyanti (2018)WIDYASARI , N. ; ROSIYANTI , H. Developing material for promoting problem-solving ability through Bar Modeling Technique . Journal of Physics: Conference Series , Singapore , v. 948 , p. 012055 , 2018 . Disponível em: https://iopscience.iop.org/article/10.1088/1742-6596/948/1/012055/meta . Acesso em: 20 jan 2021 . https://iopscience.iop.org/article/10.10...
, Willyarto, Pane e Chairiyani (2015) e Xin (2019)XIN , Y. P. The effect of a conceptual model-based approach on ‘additive’ word problem solving of elementary students struggling in mathematics . ZDM , Hamburg , v. 51 , n. 1 , p. 139 - 150 , 2019 . DOI: https://doi.org/10.1007/s11858-018-1002-9 . https://doi.org/10.1007/s11858-018-1002-...
. Trabalhos em nível nacional: Baldin (2018)BALDIN, Y. Y. Desenvolvimento do pensamento algébrico no currículo de escola básica: caso de modelagem pictórica da Matemática de Singapura. Cuadernos de Investigación y Formación en Educación Matemática, San José, v. 17, p. 31-44, 2018. Disponível em: https://revistas.ucr.ac.cr/index.php/cifem/article/view/34362 . Acesso em: 09 jan. 2021 . https://revistas.ucr.ac.cr/index.php/cif...
, Cintra (2017)CINTRA, C. C. Proposta para o Ensino de Frações para o 7 ano: do Diagnóstico à Aprendizagem Mediada por Modelo de Barras. 2017. Dissertação (Mestrado Profissional em Matemática) – Universidade Federal de São Carlos - UFSCar, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/10005 . Acesso em: 20 mar. 2021 . https://repositorio.ufscar.br/handle/ufs...
, Dotti (2016)DOTTI, T. G. P. Um estudo do modelo de barras nos livros didáticos da matemática de Singapura: fundamentação da álgebra no Ensino Eundamental I ciclo. 2016. Monografia (Trabalho de Conclusão de Curso de Licenciatura em Matemática) – Universidade Federal de São Carlos , São Carlos , 2016 . , Fontes (2019)FONTES, G. O. O modelo de barras como recurso na resolução de problemas algébricos. 2019. Dissertação (Mestrado em Ensino de Ciências Exatas) – Universidade Federal de São Carlos , São Carlos , 2019 . Disponível em: https://repositorio.ufscar.br/handle/ufscar/13376 . Acesso em: 08 maio 2021 . https://repositorio.ufscar.br/handle/ufs...
, Gois (2014)GOIS, R. C. O efeito do material concreto e do modelo de barras no processo de aprendizagem significativa do conteúdo curricular de frações pelos alunos de 7º ano do ensino fundamental. 2014. Dissertação (Mestrado em Ensino de Ciências Exatas) – Universidade Federal de São Carlos , São Carlos , 2014 . Disponível em: https://repositorio.ufscar.br/handle/ufscar/4472 . Acesso em: 09 maio 2021 . https://repositorio.ufscar.br/handle/ufs...
, Holetz (2019)HOLETZ, M. S. Utilizando a gamificação e a metodologia de ensino de Singapura para trabalhar com as operações matemáticas básicas nos anos iniciais do ensino fundamental. 2019. Dissertação (Mestrado Profissional em Educação e Novas Tecnologias) – Centro Universitário Internacional UNINTER campus Tiradentes , Curitiba , 2019 . Disponível em: https://repositorio.uninter.com/handle/1/491 . Acesso em: 06 mar. 2021 . https://repositorio.uninter.com/handle/1...
e Queiroz (2014)QUEIROZ, J. M. S. Resolução de problemas da pré-álgebra e álgebra para fundamental II do ensino básico com auxílio do modelo de barras. 2014. Dissertação (Mestrado Profissional em Matemática) – Universidade Federal de São Carlos, São Carlos, 2014. Disponível em: https://repositorio.ufscar.br/handle/ufscar/4473 . Acesso em: 20 mar. 2021 . https://repositorio.ufscar.br/handle/ufs...
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