Investigative Mathematics Tasks of High Cognitive Demand
Keywords:
Mathematics Education. Teacher Education. Mathematical Tasks. Cognitive Demand. Investigative Tasks.
Abstract
This article presents some results of a research on teacher education for teaching situations, which involve professional practices such as interpreting, anticipating and deciding. Examples of investigative tasks in Mathematics are presented with the goal of interpreting with teachers how to observe mathematical tasks, plan teaching, look at the teaching itself and interpret the mathematical thinking of students to justify new lines of action. These examples are core practices developed by the Curricular Studies Group (GECEM) and are based on the recognition and interpretation of the cognitive demand of tasks, anticipation of students' responses and decision of new courses of action based on the interpretation of students' responses and classroom events. The results indicate that teachers in initial and continuing education need to solve the tasks, reflecting on their didactic possibilities as a means of developing professional competencies that improve teaching practice.
References
BALL, Deborah Loewenberg; THAMES, Mark Hoover; PHELPS, Geoffrey Charles. Content knowledge for teaching: What makes it special?. Journal of Teacher Education, v. 59, p. 398–407, 2008.
CYRINO, Márcia Cristina de Costa Trindade; JESUS, Cristina Cirino de. Análise de tarefas matemáticas em uma proposta de formação continuada de professoras que ensinam matemática. Ciência & Educação (Bauru), v. 20, n. 3, p. 751–764, 2014.
D’ANGELO, Cynthia et al. Simulations for STEM Learning : Systematic Review and Meta-Analysis. Melo Park, CA: SRI Education, 2014.
DAMASCO, Fabiana Caldeira; GROENWALD, Claudia Lisete Oliveira; LLINARES, Salvador Ciscar. A competência docente de Observar com Sentido situações de ensino e aprendizagem na Matemática. Canoas: Editora da ULBRA, 2020. v. 1
DEMO, Pedro. Olhar do educador e novas tecnologias. Senac: a R. Educ. Prof, v. 37, n. 2, p. 15–26, 2011. Disponível em: http://pedrodemo.sites.uol.com.br.
ESCUDERO, Isabel; SÁNCHEZ, Victoria. How do domains of knowledge integrate into mathematics teachers’ practice? Journal of Mathematical Behavior, v. 4, p. 312–327, 2007.
FLORES, Cláudia Regina; WAGNER, Débora Regina; BURATTO, Ivone Catarina Freitas. Pesquisa em visualização na educação matemática : conceitos, tendências e perspectivas. Educação Matemática Pesquisa, v. 14, n. 1, p. 31–45, 2012.
GUTIÉRREZ, Ángel. Visualization in 3-Dimensional Geometry: In Search of a Framework. In: Proceedings of the 20th PME Conference, 1996. p. 3–19. Disponível em: http://www.uv.es/angel.gutierrez/archivos1/textospdf/Gut96c.pdf. Acesso em: 25 mar. 2016.
HANNA, Gila. Proof as explanation in geometry. Focus on learning problems in mathematics, v. 20, p. 4–13, 1998.
HANNA, Gila. Some pedagogical aspects of proof. Interchange, v. 21, n. 1, p. 6–13, 1990.
HOMA, Agostinho Iaqchan Ryokiti. Objetos de aprendizaje tridimensionales construidos con el software Geogebra. Revista Paradigma, v. 40, n. 1, p. 69–79, 2019.
HOMA, Agostinho Iaqchan Ryokiti. Robotics Simulators in STEM Education. Acta Scientiae, v. 21, n. 5, p. 178–191, 2019.
HOMA, Agostinho Iaqchan Ryokiti; GROENWALD, Cláudia Lisete Oliveira. Área de figuras planas com objetos de aprendizagem no Geogebra. Revista Brasileira de Ensino de Ciência e Tecnologia, v. 9, n. 123–147, 2016.
HOMA, Agostinho Iaqchan Ryokiti; GROENWALD, Claudia Lisete Oliveira. Jogos didáticos e tecnologias digitais: uma integração possível no planejamento didático do professor de Matemática. Revista do Instituto GeoGebra Internacional de São Paulo. ISSN 2237-9657, v. 9, n. 3, p. 30–45, 2020.
JESUS, Cristina Cirino de; CYRINO, Márcia Cristina de Costa Trindade; OLIVEIRA, Hélia. Análise de tarefas cognitivamente desafiadoras em um processo de formação de professores de Matemática. Educação Matemática Pesquisa, v. 20, n. 2, p. 21–46, 2018.
LLINARES, Salvador Ciscar. El desarrollo de la competencia docente “mirar profesionalmente” la enseñanza-aprendizaje de las matemáticas. Educar em Revista, v. 50, p. 17–133, 2013.
LLINARES, Salvador Ciscar et al. Mirar profesionalmente las situaciones de Enseñanza: Una competencia basada en el conocimiento. In: INVESTIGACIÓN SOBRE EL PROFESOR DE MATEMÁTICAS: PRÁCTICA DE AULA, CONOCIMIENTO, COMPETENCIA Y DESARROLLO PROFESIONAL. Salamanca: Ediciones Universidad Salamanca, 2019. p. 177–192. E-book. Disponível em: https://eusal.es/index.php/eusal/catalog/view/978-84-1311-073-8/5054/4202-1.
MISHRA, Punya; KOEHLER, Matthew J. Technological Pedagogical Content Knowledge: A Framework for Teacher Knowledge. Teachers College Record: The Voice of Scholarship in Education, v. 108, n. 6, p. 1017–1054, 2006.
NCTM. De los principios a la acción – para garantizar el éxito matemáticos para todos. México: Editando libros S.A., 2015.
NIESS, Margaret L.; GILLOW-WILES, Henry. Expanding teachers’ technological pedagogical reasoning with a systems pedagogical approach. Australasian Journal of Educational Technology, v. 33, n. 3, p. 77–95, 2017.
PENALVA, M. Carmen; LLINARES, Salvador Ciscar. Tareas Matemáticas en la Educación Secundaria. In: GOÑI, Jesus María; COLL, César (org.). Didáctica de las Matemáticas/Formación y Desarrollo Profesional del Profesorado N° 12 Vol. II. Madrid: Graó, 2011. p. 27–51.
PSOTKA, Joseph. Educational Games and Virtual Reality as Disruptive Technologies. Educational Technology & Society, v. 16, n. 2, p. 69–80, 2013.
RONAU, Robert N.; RAKES, Christopher R.; NIESS, Margaret L. Educational technology, teacher knowledge, and classroom impact: A research handbook on frameworks and approaches. Hershey, PA: IGI Global, 2012.
SMITH, Margaret Schan; STEIN, Mary Kay. 5 Practices for Orchestrating Productive Mathematics Discussions Includes Professional Development Guide. National Council of Teachers of Mathematics, 2011.
SMITH, Margaret Schan; STEIN, Mary Kay. Selecting ans Creating Mathematical Tasks: Foram Research to Practice. Matehmatics Teaching in the Middle Scholl, v. 3, p. 344–350, 1998.
STEIN, Mary Kay et al. Implementing standarts based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press, 2000.
STEIN, Mary Kay; BARBARA W. GROVER; HENNINGSEN, Marjorie. Building Student Capacity for Mathematical Thinking and Reasoning: An Analysis of Mathematical Tasks Used in Reform Classrooms. America Educational Research Journal, v. 33, n. 2, p. 455–488, 1996.
WALLS, Fiona. Challenging task-driven pedagogies of mathematics. In: 28th Annual Conference of the Mathematics Education Research Group of Australasia. Melbourne, Sydney: Merga, 2005. p. 751–758.
CYRINO, Márcia Cristina de Costa Trindade; JESUS, Cristina Cirino de. Análise de tarefas matemáticas em uma proposta de formação continuada de professoras que ensinam matemática. Ciência & Educação (Bauru), v. 20, n. 3, p. 751–764, 2014.
D’ANGELO, Cynthia et al. Simulations for STEM Learning : Systematic Review and Meta-Analysis. Melo Park, CA: SRI Education, 2014.
DAMASCO, Fabiana Caldeira; GROENWALD, Claudia Lisete Oliveira; LLINARES, Salvador Ciscar. A competência docente de Observar com Sentido situações de ensino e aprendizagem na Matemática. Canoas: Editora da ULBRA, 2020. v. 1
DEMO, Pedro. Olhar do educador e novas tecnologias. Senac: a R. Educ. Prof, v. 37, n. 2, p. 15–26, 2011. Disponível em: http://pedrodemo.sites.uol.com.br.
ESCUDERO, Isabel; SÁNCHEZ, Victoria. How do domains of knowledge integrate into mathematics teachers’ practice? Journal of Mathematical Behavior, v. 4, p. 312–327, 2007.
FLORES, Cláudia Regina; WAGNER, Débora Regina; BURATTO, Ivone Catarina Freitas. Pesquisa em visualização na educação matemática : conceitos, tendências e perspectivas. Educação Matemática Pesquisa, v. 14, n. 1, p. 31–45, 2012.
GUTIÉRREZ, Ángel. Visualization in 3-Dimensional Geometry: In Search of a Framework. In: Proceedings of the 20th PME Conference, 1996. p. 3–19. Disponível em: http://www.uv.es/angel.gutierrez/archivos1/textospdf/Gut96c.pdf. Acesso em: 25 mar. 2016.
HANNA, Gila. Proof as explanation in geometry. Focus on learning problems in mathematics, v. 20, p. 4–13, 1998.
HANNA, Gila. Some pedagogical aspects of proof. Interchange, v. 21, n. 1, p. 6–13, 1990.
HOMA, Agostinho Iaqchan Ryokiti. Objetos de aprendizaje tridimensionales construidos con el software Geogebra. Revista Paradigma, v. 40, n. 1, p. 69–79, 2019.
HOMA, Agostinho Iaqchan Ryokiti. Robotics Simulators in STEM Education. Acta Scientiae, v. 21, n. 5, p. 178–191, 2019.
HOMA, Agostinho Iaqchan Ryokiti; GROENWALD, Cláudia Lisete Oliveira. Área de figuras planas com objetos de aprendizagem no Geogebra. Revista Brasileira de Ensino de Ciência e Tecnologia, v. 9, n. 123–147, 2016.
HOMA, Agostinho Iaqchan Ryokiti; GROENWALD, Claudia Lisete Oliveira. Jogos didáticos e tecnologias digitais: uma integração possível no planejamento didático do professor de Matemática. Revista do Instituto GeoGebra Internacional de São Paulo. ISSN 2237-9657, v. 9, n. 3, p. 30–45, 2020.
JESUS, Cristina Cirino de; CYRINO, Márcia Cristina de Costa Trindade; OLIVEIRA, Hélia. Análise de tarefas cognitivamente desafiadoras em um processo de formação de professores de Matemática. Educação Matemática Pesquisa, v. 20, n. 2, p. 21–46, 2018.
LLINARES, Salvador Ciscar. El desarrollo de la competencia docente “mirar profesionalmente” la enseñanza-aprendizaje de las matemáticas. Educar em Revista, v. 50, p. 17–133, 2013.
LLINARES, Salvador Ciscar et al. Mirar profesionalmente las situaciones de Enseñanza: Una competencia basada en el conocimiento. In: INVESTIGACIÓN SOBRE EL PROFESOR DE MATEMÁTICAS: PRÁCTICA DE AULA, CONOCIMIENTO, COMPETENCIA Y DESARROLLO PROFESIONAL. Salamanca: Ediciones Universidad Salamanca, 2019. p. 177–192. E-book. Disponível em: https://eusal.es/index.php/eusal/catalog/view/978-84-1311-073-8/5054/4202-1.
MISHRA, Punya; KOEHLER, Matthew J. Technological Pedagogical Content Knowledge: A Framework for Teacher Knowledge. Teachers College Record: The Voice of Scholarship in Education, v. 108, n. 6, p. 1017–1054, 2006.
NCTM. De los principios a la acción – para garantizar el éxito matemáticos para todos. México: Editando libros S.A., 2015.
NIESS, Margaret L.; GILLOW-WILES, Henry. Expanding teachers’ technological pedagogical reasoning with a systems pedagogical approach. Australasian Journal of Educational Technology, v. 33, n. 3, p. 77–95, 2017.
PENALVA, M. Carmen; LLINARES, Salvador Ciscar. Tareas Matemáticas en la Educación Secundaria. In: GOÑI, Jesus María; COLL, César (org.). Didáctica de las Matemáticas/Formación y Desarrollo Profesional del Profesorado N° 12 Vol. II. Madrid: Graó, 2011. p. 27–51.
PSOTKA, Joseph. Educational Games and Virtual Reality as Disruptive Technologies. Educational Technology & Society, v. 16, n. 2, p. 69–80, 2013.
RONAU, Robert N.; RAKES, Christopher R.; NIESS, Margaret L. Educational technology, teacher knowledge, and classroom impact: A research handbook on frameworks and approaches. Hershey, PA: IGI Global, 2012.
SMITH, Margaret Schan; STEIN, Mary Kay. 5 Practices for Orchestrating Productive Mathematics Discussions Includes Professional Development Guide. National Council of Teachers of Mathematics, 2011.
SMITH, Margaret Schan; STEIN, Mary Kay. Selecting ans Creating Mathematical Tasks: Foram Research to Practice. Matehmatics Teaching in the Middle Scholl, v. 3, p. 344–350, 1998.
STEIN, Mary Kay et al. Implementing standarts based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press, 2000.
STEIN, Mary Kay; BARBARA W. GROVER; HENNINGSEN, Marjorie. Building Student Capacity for Mathematical Thinking and Reasoning: An Analysis of Mathematical Tasks Used in Reform Classrooms. America Educational Research Journal, v. 33, n. 2, p. 455–488, 1996.
WALLS, Fiona. Challenging task-driven pedagogies of mathematics. In: 28th Annual Conference of the Mathematics Education Research Group of Australasia. Melbourne, Sydney: Merga, 2005. p. 751–758.
Published
2023-05-18
How to Cite
HOMA, A. I. R.; GROENWALD, C. L. O.; LLINARES, S. C. Investigative Mathematics Tasks of High Cognitive Demand. Perspectivas da Educação Matemática, v. 16, n. 42, p. 1-22, 18 May 2023.
Section
Tarefas Matemáticas e a Aprendizagem Profissional Docente na Formação Inicial e
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