24 SES 05.5 PS, General Poster Session
General Poster Session
This poster reports on a learning experience aiming to present and analyze the work produced by 5th grade students in solving a mathematical task with investigative characteristics.
Creating stimulating learning environments implies the diversification of the type and nature of mathematical tasks in the classroom, in the perspective of the valuation of mathematical experience through problem solving, investigations and other situations involving students in the processes of mathematical thinking and communication. Thus, the tasks proposed to the students should (i) appeal to their intelligence, (ii) develop understanding and their mathematical skills, (iii) stimulate them to make connections and develop a coherent framework for mathematical ideas, (iv) appeal to the mathematical reasoning and formulating and solving problems, (v) promote the communication about mathematics, (vi) show mathematics as a permanent human activity, based on different experiences, and (vii) promote the development of students’ mathematical competence (National Council of Teachers of Mathematics, 2000).
Mathematical tasks, according to their type and nature, can provide different ways of understanding or doing mathematics (Pires, 2011). The tasks may appeal to routine processes or be a challenge to exploration or discovery, require a repetitive or a creative reasoning, allow a uniformity of learning rhythms or foster the diversification, have a convergent or a divergent character, reinforce a static view of mathematics as “end product” or point to a dynamic view as “construction”, establishing mathematical connections and providing more meaningful mathematical experiences.
Mathematical investigations appear as an expression of a non-routine work, referring to complex mathematical processes and involving a strongly problematic activity (Martins, Maia, Menino, Rocha & Pires, 2002). These tasks may provide a divergent activity that encourages students to be curious, to search for alternative strategies, to consider what would happen if certain conditions change or to generalize the situation (Chamoso & Rawson, 2001). Usually the investigations require a similar work to the one produced by mathematicians: towards a particular situation that must be answered, the students have to ask questions, to make and test conjectures, to justify these conjectures based on mathematical arguments and to validate the results (Ponte, Ferreira, Brunheira, Oliveira & Varandas, 1998).
This process of testing and validation is also a social practice (Boavida, 2005) because the students have to argue and communicate their results to the others, possibly argue against, so that the results may be validated by all. Assigning a central role to the “practice of argumentation” (National Council of Teachers of Mathematics, 2000) in the classroom means empowering all students not only to present and explain their reasonings, but also to understand and accept the others’ argumentation.
Boavida, A. M. (2005). A argumentação na aula de matemática: Olhares sobre o trabalho do professor. In J. Brocardo, F. Mendes & A. M. Boavida (Orgs.), XVI SIEM – Atas (pp. 13-43). Setúbal, Portugal: Associação de Professores de Matemática. Bogdan, R., & Biklen, S. (1994). Investigação qualitativa em educação. Porto, Portugal: Porto Editora. Bolívar, A., Domingo, J., & Fernández, M. (2001). La investigación biográfico-narrativa en educación: Enfoque y metodología. Madrid, Espanha: La Muralla. Chamoso, J., & Rawson, W. (2001). En la búsqueda de lo importante en el aula de matemáticas. SUMA, 36, 33-41. Martins, C., Maia, E., Menino, H., Rocha, I., & Pires, M. V. (2002). O trabalho investigativo nas aprendizagens iniciais da matemática. Em J. P. Ponte, C. Costa, A. Rosendo, E. Maia, N. Figueiredo & A. Dionísio (Orgs.), Atividades de investigação na aprendizagem da matemática e na formação de professores (pp. 59-81). Coimbra, Portugal: SEM, Sociedade Portuguesa de Ciências da Educação. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM. Pires, M. V. (2011). Tarefas de investigação na sala de aula de matemática: Práticas de uma professora de matemática. Quadrante, XX(1), 31-53. Ponte, J. P., Ferreira, C., Brunheira, L., Oliveira, H., & Varandas, J. M. (1998). Investigating mathematical investigations. In P. Abrantes, J. Porfirio & M. Baía (Eds.), Les interactions dans la classe de mathématiques: Proceedings of the CIEAEM 49 (pp. 3-14). Setúbal, Portugal: ESE de Setúbal.
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