Lina Fonseca
Abstract
Mathematics and reasoning are strongly related. Every child must have the opportunity to reason mathematically, to deepen its mathematical comprehension. To do so children need a daily mathematics diet linked to mathematical reasoning. To understand what kind of reasoning children use, how they justify their options, what difficulties they reveal, a qualitative case study was designed with 2nd grade students. The main results point out that young child reveal emerging deductive reasoning, empirical and analytic proof schemes to support their own resolution options and some difficulties in organizing their work, but they reveal to be persistent to look for solutions.
Keywords
Early years, justification, mathematics, proof schemes, reasoning.
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References
Baroody, A. J. (1993). Problem solving, reasoning and communicating, K-8: helping children think mathematically. New York: Macmillian.
Bragg,L. , Loong, E., Widjaja, W., Vale, C. & Herbert, S. (2015). Promoting reasoning through the magic V task. Australian Primary Mathematics Classroom, 20 (2), 10-14.
Darmstadter, H. (2013). Why do human reason? A pragmatist supplement to an argumentative theory. Thinking & Reasoning, 19(3-4), 472-487.
English, L. (2004). Mathematical and analogical reasoning in early childhood. In L. English (Ed.), Mathematical and analogical reasoning of young learners, (pp. 1-22). London: Routledge.
Esteves, V. (2013). Raciocínio Matemático de alunos do 2.º ano de escolaridade. Relatório Final de Prática de Ensino Supervisionada do Mestrado em Educação Pré-Escolar e Ensino do Primeiro Ciclo do Ensino Básico. Viana do Castelo: Escola Superior de Educação. http://repositorio.ipvc.pt/handle/20.500.11960/1849
Fonseca, L. (2004). Formação inicial de professores de Matemática: A demonstração em geometria. Coleção Teses. Lisboa: APM.
Goldenberg, E. P., Cuoco, A. & Mark, J. (1998). A role for geometry in general education. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp.3-42). London: Lawrence Erlbaun Associates Ltd. Publishers.
Goswami, U. (1992). Analogical reasoning in children. London: Erlbaun Associates Ltd. Publishers.Harel, G. & Sowder, L. (1998). Student’s proof schemes: results from exploratory studies. CBMS, Issues in Mathematics Education, 7, 234-283.
Harel, G. & Sowder, L. (2007). Toward Comprehensive Perspectives on the Learning and Teaching of Proof. In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning, (pp.805-842). Reston: NCTM.
Herbert, S., Vale, C., Bragg, L., Loong, E. & Widjaja, W. (2015). A framework for primary teachers’ perceptions of mathematical reasoning. International Journal of Educational Research, 74, 26-37.
Kilpatrick, J., Swafford, J. & Findell, B. (2001). Adding it up: Helping Children Learn Mathematics. Washington: National Academy Press.
Mason, J., Burton, L. & Stacey, K. (1982). Thinking mathematically. London: Pearson.
Ministério da Educação (ME) (2007). Programa de Matemática do Ensino Básico. Lisboa: Direção Geral de Educação.
Ministério da Educação e Ciência (MEC) (2013). Programa de Matemática do Ensino Básico. Lisboa: Direção Geral de Educação.
NCTM (2000). Principles and standards for school mathematics. Reston: NCTM.
NCTM (2014). Principles to action. Ensuring Mathematical Success for All. Reston: NCTM.
Oliveira Martins et al. (ME), (2017). Perfil dos alunos à saída da escolaridade obrigatória. Lisboa: Ministério da Educação/ Direção Geral de Educação.
Plaxco, D.B. (2011). Relationship between student’s proof schemes and definitions. Master of Science in Mathematics. Virginia: Polytechnic Institute and State University.
Pólya, G. (1945). How to solve it. Princeton: University Press.
Russel, S. (1999). Mathematical reasoning in the elementary grades. In L. Stiff & F. Curcio (Eds.), Developing Mathematical Reasoning in grades K-12, (pp. 37-44). Reston: NCTM.
Schultz-Ferrel, K., Hammond, B. & Robles, J. (2007). Introduction to reasoning and proof (Grades Prek-2). Portsmouth: Heinemann.
Sternberg, R. (1999). The nature of mathematical reasoning. In L. English (Ed.), Mathematical and analogical reasoning of young learners, (pp. 1-22). London: Routledge.
Stylianou, D., Chae, N. & Blanton, M. (2006). Students proof schemes: a closer look at what characterizes students proof conceptions. In S. Alatorre, J. L. Cortina, M. Sáiz, and A. Méndez (Eds). Proceedings of the 28th annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (Vol.2, pp. 54-60). Mérida, México: Universidad Pedagógica Nacional.
Sumpter, L. & Hedefalk, M. (2015). Preschool children’s collective mathematical reasoning during free outdoor play. The Journal of Mathematical Behaviour, 39, 1-10.
Categories: 2018, Articles - JETEN, Mathematics Education
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