Tipos de problemas que provocan la generación de argumentos inductivos, abductivos y deductivos

Referencias

ARZARELLO, F. et al. A cognitive analysis of dragging practises in Cabri environments. ZDM, Germany, v. 34, n. 3, p. 66-72, 2002. ARZARELLO, F. et al. Experimental Approaches to Theoretical Thinking: Artefacts and Proofs. In: HANNA, G.; DE VILLIERS, M. Proof and Proving in Mathematics Education. New York: Springer, 2012. p. 97-146. BACCAGLINI-FRANK, A.; MARIOTTI, M. Generating Conjectures in Dynamic Geometry: The Maintaining Dragging Model. International Journal of Computers for Mathematical Learning, Netherlands, v. 15, p. 225-253, 2010. BACCAGLINI-FRANK, A.; MARIOTTI, M.; ANTONINI, S. Different Perceptions of Invariants and Generality of Proof in Dynamic Geometry. In: TZEKAKI, M.; SAKONIDIS, H. CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION,33., 2009, Thessaloniki. Proceedings... Thessaloniki, Greece: PME, v. 2, 2009. p. 89-96. BALL, D. L.; BASS, H. Making mathematics reasonable in school. In: KILPATRICK, J.; MARTIN,W. G.; SCHIFTER, D. A research companion to Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, 2003. p. 27-44. BALL, D.; LUBIENSKI, S.; MEWBORN, D. Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In: RICHARDSON, V. Handbook of research on teaching. 4. ed. New York, NY: Macmillan, 2001. p. 433-456. BIRKHOFF, G. A set of postulates for plane geometry, based on scale and protractor. Annals of Mathematics, v. 33, n. 2, p. 329-345, 1932. Disponivel em: . Acesso em: Febrero de 2017. BOERO, P. et al. Argumentation and proof: a contribution to theoretical perspectives and their classroom implementation. In: CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION, 34., 2010, Belo Horizonte. Proceedings... Belo Horizonte, Brazil: PME, 2010. p. 179-204. CAMARGO, L. et al. Use of dragging as organizer for conjecture validation. In: CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION, 33., 2009, Thessaloniki. Proceedings... Thessaloniki, Greece: PME, 2009. p. 257-264. FELMER, P. et al. La resolución de problemas en la matemática escolar y en la formación inicial docente. Estudios de política educativa, Chile, v. 1, n. 1, p. 66-105, 2015. LABORDE, C. Dynamic Geometry Environments as a Source of Rich Learning Contexts for the Complex Activity of Proving, Netherlands, v. 44, n. 1, p. 151-161, 2000. LESH, R.; ZAWOJEWSKI, J. Problem solving and modeling. In: LESTER, F. Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age Publishing, 2007. p. 763-804. LIN, F. L. et al. Teachers’ Professional Learning of Teaching Proof and Proving. In: HANNA, G.; DE VILLIERS, M. Proof and Proving in Mathematics Education. New York: Springer, 2012. p. 327- 346. MARIOTTI, M. Proof and Proving in Mathematics Education. In: GUTIÉRREZ, A.; BOERO, P. Handbook of Research on the Psychology of Mathematics Education. Past, Present and Future. Rotterdam, The Netherlands: Sense Publishers, 2006. p. 173-204. ONUCHIC, L. R.; ALLEVATO, N. S. G. Pesquisa em Resolução de Problemas: caminhos, avanços e novas perspectivas. Bolema, Rio Claro, Brasil, v. 25, n. 41, p. 73-98, 2011. PEDEMONTE, B. How can the relationship between argumentation and proof be analysed?Educational Studies in Mathematics, Netherlands, v. 66, n. 1, p. 23-41, 2007. PERRY, P. et al. La geometría del ángulo desde otro ángulo: Una aproximación metodológica alternativa. Épsilon - Revista de Educación Matemática, España, v. 29, n. 3, p. 41-56, 2012. PERRY, P. et al. Innovación en un aula de geometría de nivel universitario. In: SAMPER, C.; MOLINA, Ó. Geometría plana: un espacio de aprendizaje. Bogotá, Colombia: Universidad Pedagógica Nacional, 2013. p. 11-34. PONTE, J. P. Investigar, ensinar e aprender. Actas do ProfMat 2003. Lisboa: APM, 2003. p. 25-39. PONTE, J. P. Problemas e investigaciones en la actividad matemática de los alumnos. In: GIMÉNEZ, J.; SANTOS, L.; PONTE, J. P. La actividad matemática en el aula. Barcelona: Graó, 2004. p. 25-34. PONTE, J. P.; FONSECA, H.; BRUNHEIRA, L. As atividades de investigação, o professor e a aulade Matemática. Actas do ProfMat 1999. Lisboa, Portugal: APM, 1999. p. 91-101. SAMPER, C. et al. Geometría dinámica: medio para el establecimiento de condicionalidad lógica. Informe de Investigación, CIUP, UPN - COLCIENCIAS: Bogotá. 2010. SAMPER, C.; MOLINA, O. Geometría Plana: un espacio de aprendizaje. Bogotá, Colombia: Universidad Pedagógica Nacional, 2013. SAMPER, C. et al. Problemas abiertos de conjeturación. In: ENCUENTRO DE GEOMETRÍA Y SUS APLICACIONES, 21., 2013b, Bogotá. Memorias... Bogotá, Colombia: Universidad Pedagógica Nacional. 2013. p. 167-170. SAMPER, C. et al. Conjeturas y organización del contenido matemático en clase. Informe de Investigación, CIUP, UPN – COLCIENCIAS. Bogotá, Colombia: 2014. SANTOS-TRIGO, M. Problem Solving in Mathematics. In: LERMAN, S. Encyclopedia of Mathematics Education. Dordrecht: Springer Science+Business Media, 2014. p. 496-500. SCHOENFELD, A. H. Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In: GROWS, D. A. Handbook of Research on Mathematics Teaching and Learning. NY: Macmillan, 1992. p. 334-370. SHERIN, M.; RUSS, R.;COLESTOCK, A. Accessing mathematics teachers’ in-the-moment noticing. In: SHERIN, M.; JACOBS, V.; PHILIPP, R. Mathematics Teacher Noticing. New York: Routledge, 2011. p. 79-94. STEFFE, L. P.; THOMPSON, P. W. Teaching experiment methodology: Underlying principles and essential elements. In: KELLY, A. E.; LESH, R. A. Handbook of research in mathematics and science education. Mahwah, EUA: Lawrence Erlbaum Associates, 2000. p. 267-306. STYLIANIDES, A.; STYLIANIDES, G. Content knowledge for mathematics teaching: The case of reasoning and proving. In: NOVOTNÁ, J., et al. CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION, 30., 2006, Prague. Proceedings.. Prague: PME, v. 5, 2006. p. 201-208. STYLIANIDES, G.; STYLIANIDES, A. Validation of solutions of construction problems in dynamic geometry environments. International journal of computer for Mathematical Learning, Netherlands, v. 10, n. 1, p. 31- 47, 2005. STYLIANIDES, J.; BALL, D. Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education, Netherlands, v. 11, n. 4, p. 307-332, 2008. YACKEL, E.; HANNA, G. Reasoning and proof. In: KILPATRICK, J.; MARTIN, W. G.; SCHIFTER, D. A research companion to Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, 2003. p. 227-236. YEVDOKIMOV, O. The place and significance of the problems for proof in learning mathematics. In: MARIOTTI, M. A. EUROPEAN RESEARCH IN MATHEMATICS EDUCATION III, 3., 2004,Bellaria. Proceedings... Bellaria: University of Pisa and ERME, 2004. Disponivel em:. Acesso em: Febrero de 2017 ZIMMERMANN, B. Improving of Mathematical Problem-Solving: Some New Ideas from Old Resources. In: FELMER, P.; PEHKONEN, E.; KILPATRICK, J. Posing and Solving Mathematical Problems. Switzerland: Springer International Publishing, 2016. p. 83-108.