Abstract
This paper analyzes the tasks proposed in several Portuguese mathematics textbooks from the nineteenth to the twenty-first century. A look at the nature and intended purpose of these tasks raises interesting issues about school mathematics teaching and learning. Has the meaning of terms such as “problem” and “exercise” been always the same? What other terms have been used in textbooks to designate mathematics tasks? What were the reasons for the changes? The analysis of the evolution that occurred in the terminology as well as in the nature of the tasks proposed to the students provides elements to reflect about what are the changes that have occurred in mathematics teaching and learning and how some changes are more apparent than real.
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Andrea, E. I. S. (1924). Compêndio de Álgebra. Lisboa: Imprensa Nacional de Lisboa.
Calado, J. J. G. (1960). Compêndio de Álgebra. Lisboa: Livraria Popular de Francisco Franco.
Costa, A. A., Anjos, A. O., & Lopes, A. A. (1974). Compêndio de Matemática. Porto: Porto Editora.
Costa, A. A., Anjos, A. O., & Lopes, A. A. (1983). Matemática Jovem. Porto: Porto Editora.
Cunha, A. J. (1887). Elementos de Álgebra (5th ed.). Lisboa: Livraria de António Maria Pereira.
Kilpatrick, J. (1992). A history of research in mathematics education. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 3–38). New York: Macmillan.
Kilpatrick, J., & Izsák, A. (2008). A history of algebra in the school curriculum. In C. E. Greenes & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics (pp. 3–18). Reston: NCTM.
Neves, M. A. F., Guerreiro, L., & Neves, A. (2004). Matemática 9 (1st ed.). Porto: Porto Editora.
OCDE. (2004). Learning for tomorrow’s world: First results from PISA 2003. Paris: OCDE.
Pólya, G. (1957). How to solve it: A new aspect of mathematical method (2nd ed.). New York: Doubleday.
Ponte, J. P. (2004). As equações nos manuais escolares. Revista Brasileira de História da Matemática, 4(8), 149–170.
Ponte, J. P. (2005). Gestão curricular em Matemática. In GTI (Ed.), O professor e o desenvolvimento curricular (pp. 11-34). Lisboa: APM.
Ponte, J. P., & Abrantes, P. (1982). Os problemas e o ensino da Matemática. In Ensino da Matemática: Anos 80 (pp. 201–214). Lisboa: SPM.
Ponte, J. P., Salvado, C., Fraga, A., Santos, T., & Mosquito, E. (2007). Equações do 2.° grau do fim do século XIX ao início do século XXI: Uma análise de sete manuais escolares. Quadrante, 16(1), 111–145.
Skovsmose, O. (2001). Landscapes of investigation. ZDM, 33(4), 123–132.
Stanic, G. M. A., & Kilpatrick, J. (1989). Historical perspectives on problem solving in the mathematics curriculum. In R. I. Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 1–22). Reston: NCTM e Lawrence Erlbaum.
Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3(4), 268–275.
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da Ponte, J.P. (2015). Problem Solving, Exercises, and Explorations in Mathematics Textbooks: A Historical Perspective. In: Silver, E., Keitel-Kreidt, C. (eds) Pursuing Excellence in Mathematics Education. Mathematics Education Library. Springer, Cham. https://doi.org/10.1007/978-3-319-11952-6_5
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