Isabel Vale, Ana Barbosa
The rapid evolution of today’s world requires that all students have access to an education that values creativity, critical thinking and problem solving. It means motivating students to use multiple strategies when solving a problem, including the visual ones as an important support in solving all kinds of problems, including those in which the visual component is not evident. So, teachers should include practices that lead students to think visually and develop this ability through experiences that require such way of thinking. In this context, we discuss the advantages of using visual strategies when solving problems with multiple approaches, illustrating those ideas with some examples.
Problem solving, problem solving strategies, visualization, creativity, thinking styles.
Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241.
Boaler, J., Chen, L., Williams, C. & Cordero, M. (2016). Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning. Journal of Applied & Computacional Mathematics, 5(5),1000325. doi: 10.4172/2168-9679.1000325
Barbosa, A., & Vale, I. (2015). Visualization in pattern generalization: Potential and Challenges. Journal of the European Teacher Education Network, 10, 57-70.
Clements, D. & Battista, M. (1992). Geometry and spacial reasoning. In D. Grouws (Ed.),. Handbook of research on mathematics teaching and learning. (pp. 420-464). New York: Macmillan Publishing Company.
Eisenberg, T., & Dreyfus, T. (1991). On visual versus analytical thinking in mathematics. In L. Burton & C. Hoyles (Eds.), Proceedings of the 10th International Conference of the International Group for the Psychology of Mathematics Education (pp. 153-158). London, United Kingdom.
Fischbein, H. (2002). Intuition in science and mathematics: An educational approach. New York, NY: Kluwer Academic Publishers.
Fujita, T. & Jones, K. (2002), The Bridge between Practical and Deductive Geometry: developing the “geometrical eye”. In A. D. Cockburn and E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol 2, pp.384-391). UEA, UK.
Giaquinto, M. (2007). Visual thinking in mathematics: An epistemological study. Oxford, UK: Oxford University Press.
Haylock, D. (1997). Recognizing mathematical creativity in schoolchildren. International Reviews on Mathematical Education, Essence of Mathematics, 29(3), 68–74.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.
Liljedahl, P. (2004). The AHA! Experience: Mathematical contexts, pedagogical implications. Unpublished doctoral dissertation, Simon Fraser University, Burnaby, British Columbia, Canada
Lowrie, T. & Clements, MA (2001). Visual and nonvisual processes in Grade 6 students’ mathematical problem solving. Journal of Research in Childhood Education, 16(1), 71-97.
NCTM (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM.
Presmeg, N. (1986). Visualization in high school mathematics. For the Learning of Mathematics, 6(3), 42-46.
Presmeg, N. (2014). Creative advantages of visual solutions to some non-routine mathematical problems. In S. Carreira, N. Amado, K. Jones & H. Jacinto, (Eds.), Proceedings of the Problem@Web International Conference: Technology, Creativity and Affect in mathematical problem solving (pp. 156-167). Faro, Portugal: Universidade do Algarve.
Rivera, F. (2011). Toward a Visually-Oriented School Mathematics Curriculum: Research, Theory, Practice, and Issues. Dordrecht, Netherlands: Springer.
Sinclair, N., Bussi, M., Villiers, M. , Jones, K. , Kortenkamp , U., Leung, A. & Owens, K. (2017). Geometry Education, Including the Use of New Technologies: A Survey of Recent Research. In G. Kaiser (ed.), Proceedings of the 13th International Congress on Mathematical Education, ICME-13 Monographs, DOI 10.1007/978-3-319-62597-3_18
Stein, M. & Smith, M. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3(4), 268-275.
Vale, I. (2017). Resolução de problemas um tema em continua discussão : vantagens das resoluções visuais. In L. Onuchic, L. L. Júnior & M. Pironel (Orgs.) Perspectivas para Resolução de Problemas (pp. 131-162). Brasil: Editora Livraria da Física.
Vale, I., Pimentel, T. & Barbosa, A. (2015). Ensinar matemática com resolução de problemas. Quadrante, XXIV (2),39-60.
Vale, I. & Pimentel, T. (2016). Resolver problemas – criando soluções, vendo. Rematec, 11(21), 8-23. http://www-rematec.net.br/índex.php/rematec/article/view/57
Vale, I., Pimentel, T. & Barbosa, A. (in press). Chapter # The power of seeing in problem solving and creativity: an issue under discussion. In S. Carreira, N. Amado & K. Jones (Eds), Broadening the scope of research on mathematical problem solving: A focus on technology, creativity and affect. Springer.
Zimmermann, W., & Cunningham, S. (1991). Visualization in teaching and learning Mathematics. Washington, DC: Mathematical Association of America.