Problem Solving as necessary knowledge for teacher training – Mathematics for teaching

Rosilda dos Santos Morais


This paper discusses the themes «problem solving» and «Problem Solving » as topics of different natures. To do so, this research work addresses the question «Has problem solving been used as knowledge to teach «savoir à enseigner» and not as knowledge for teaching «savoir pour enseigner?». Based on methodological and theoretical references, such a question is the point when Problem Solving, in capital letters, is highlighted and claims the epistemological status of knowledge for teaching, mathematics for teaching. Moreover, it claims that such knowledge for teaching should become the central point of teacher training as regards mathematics and mathematics teaching. To support such claims, we used official Brazilian documents, such as the new Base Nacional Curricular Comum (BNCC – National Curriculum Common Base, in free translation), all of which stress the importance of using problem solving. Finally, we discuss the role played by George Polya as a teacher trainer.


Mathematics to teach; Mathematics for teach; Teacher training; History of mathematics education


Bertini, Luciane de Fátima, Rosilda dos Santos Morais and Wagner Rodrigues Valente. A Matemática a ensinar e a Matemática para Ensinar: novos estudos sobre a formação de professores. São Paulo: Livraria da Física, 2017.

Brasil, Ministério Da Educação. Base Nacional Comum Curricular (BNCC). 2ª versão. Abril. 2016. Available at:

Brownell, William. «The progressive nature of learning in mathematics». In Mathematics Teacher. 100 Years of Mathematics Teacher, NCTM, vol. 100, Special Issue, 26-35. Reston, VA: NCTM, 2006. First edition 1944.

Foucault, Michael. As palavras e as coisas. São Paulo: Martins Fontes, 1999.

Guimarães, H. M. «Polya and the Mathematical Capabilities». Educação e Matemática, APM, 2011.

Hofstetter, Rita and Bernard Schneuwly. «Saberes: Tema central para as profissões do ensino e da formação». In Saberes em (trans)formação: tema central da formação de professores, organizado por Rita Hofstetter and Wagner Rodrigues Valente, 113-172. São Paulo: Editora Livraria da Física, 2017.

Morais, Rosilda dos Santos. «O processo constitutivo da Resolução de Problemas como uma Temática da pesquisa em Educação Matemática – um inventário a partir de documentos dos ICMEs». PhD diss., Educação Matemática, Universidade Estadual Paulista “Júlio de Mesquita Filho” – UNESP, 2015.

Morais, Rosilda dos Santos and Lourdes de la Rosa Onuchic. «Uma abordagem histórica da Resolução de Problemas». In Resolução de Problemas: Teoria e Prática organized by Lourdes de la Rosa Onuchic, Norma Suely G. Allevato, Fabiane Cristina H. Nogutti and Andresa Maria Justulin, 17-34. Jundiaí: Paco Editorial, 2014.

Polya, G. Mathematical Discovery – on understanding, learning, and teaching problem solving. John Wiley& Sons: United States of America, 1962.

Rey, Bernard. «Les compétences professionnelles et le curriculum: des réalités conciliables?». In Savoirs Professionnels et curriculum de formation, organized by Yves Lenoir and Marie-Hélène Bouillier-Dutot, 83-108. Canadá: Les Presses de l’Université Laval, 2006.

Schroeder, Thomas L. and Franklin K. Lester Jr. «Developing Understanding in Mathematics via Problem Solving». In New Directions for Elementary School Mathematics, 1989 Yearbook of the NCTM, organized by Trafton, P. R. and A. P. Shulte, 31-42. Reston, VA: NCTM, 1989.

Thorndike, E. L. The new methods in Arithmetic. 1921. [S.I.]: On Available at:

Valente, W. R. «Oito temas sobre história da educação matemática». REMATEC 8, no. 12 (2013): 22-50.

Veiga-Neto, A. Foucault & a Educação. Belo Horizonte: Autêntica. 2003.



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