Geometry in early years: sowing seeds for a mathematical definition of squares and rectangles
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In early years schooling it is becoming common to propose activities that involve moving along paths, or programming robots to do so. In order to promote continuity towards the introduction of geometry in primary school, we developed a long-term teaching experiment (with 15 sessions) carried out over 4 months in a first grade classroom in northern Italy. Students were asked to program a robot to move along paths, to pretend to act as robots and to represent the sequence of commands and the resulting paths. In particular, in this teaching experiment, an overarching mathematical aim was to sow the seeds for a mathematical definition of rectangles that includes squares. Within the paradigm of semiotic mediation, we intended to foster the students’ transition from a dynamic perception of paths to seeing paths also as static wholes, boundaries of figures with sets of geometric characteristics. The students’ situated productions were collected and analysed together with the specific actions of the adults involved, aimed at fostering processes of semiotic mediation. In this paper we analyse the development of the situated texts produced by the students in relation to the pivot signs that were the beginnings of an inclusive definition of rectangles.
- ASPHI (2011). PerContare. http://percontare.asphi.it. Accessed 11 Sept 2014.
- Baccaglini-Frank, A., Antonini, S., Robotti, E., & Santi, G. (2014). Juggling reference frames in the microworld Mak-Trace: The case of a student with MLD. In C. Nicol, P. Liljedahl, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36 (Vol. 2, pp. 81–88). Vancouver: PME.Google Scholar
- Baccaglini-Frank, A., & Bartolini Bussi, M. G. (2012). The PerContare Project: Proposed teaching strategies and some developed materials. In F. Dellai, I. C. Mammarella, & A. M. Re (Eds.), International Academy for Research on Learning Disabilities 36th Annual Conference (pp. 194–196). Trento: Erickson.Google Scholar
- Baccaglini-Frank, A., & Scorza, M. (2013). Preventing learning difficulties in early arithmetic: The PerContare Project. In T. Ramiro-Sànchez & M. P. Bermùdez (Eds.), Libro de Actas I Congreso Internacional de Ciencias de la Educatiòn y des Desarrollo (p. 341). Granada: Universidad de Granada.Google Scholar
- Bartolini Bussi, M. G. (2013). Bambini che contano: A long term program for preschool teacher development. In B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds.), Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education (pp. 2088–2097). Ankara: Middle East Technical University.Google Scholar
- Bartolini Bussi, M. G., & Baccaglini-Frank A. (2014, submitted). Using pivot signs to reach an inclusive definition of rectangles and squares. CERME 9.Google Scholar
- Bartolini Bussi, M. G., & Boni, M. (2009). The early construction of mathematical meanings: Learning positional representation of numbers. In O. A. Barbarin & B. H. Wasik (Eds.), Handbook of child development and early education: Research to practice (pp. 455–477). New York: The Guilford Press.Google Scholar
- Bartolini Bussi, M. G., Boni, M., & Ferri, F. (2007). Construction problems in primary school: A case from the geometry of circle. In P. Boero (Ed.), Theorems in school: From history, epistemology and cognition to classroom practice (pp. 219–248). Rotterdam: Sense.Google Scholar
- Bartolini Bussi, M. G., Garuti, R., Martignone, F., & Maschietto, M. (2011). Tasks for teachers in the MMLAB-ER Project. In B. Ubuz (Ed.), Proceedings of the 35th conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 127–130). Ankara: Middle East Technical University.Google Scholar
- Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English, et al. (Eds.), Handbook of international research in mathematics education (2nd ed., pp. 746–783). New York and London: Routledge.Google Scholar
- Bartolini Bussi, M. G., & Martignone, F. (2013). Cultural issues in the communication of research on mathematics education. For the Learning of Mathematics, 33(1), 2–8.Google Scholar
- Bartolini Bussi, M. G., Sun, X., & Ramploud, A. (2013). A dialogue between cultures about task design for primary school. In C. Margolinas (Ed.), Proceedings of ICMI Study 22: Task design in mathematics education (pp. 551–560). Oxford: ICMI.Google Scholar
- Battista, M. T. (2007). The development of geometric and spatial thinking. In Frank K. Lester (Ed.), Second handbook of research of mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (2nd ed.). Charlotte: Information Age.Google Scholar
- Clements, D. H. (2004). Geometric and spatial thinking in early childhood education. In D. H. Clements & J. Sarama (Eds.), Engaging young children in mathematics. Mahwah: Lawrence Erlbaum.Google Scholar
- Duval, R. (2000). Basic issues for research in math ed. Proceedings of 24th PME (Vol. 1, pp. 55–69). Hiroshima, Japan.Google Scholar
- Falcade, R., & Strozzi, P. (2009). Construction and representation of space in 5-year-old children. In O. A. Barbarin & B. H. Wasik (Eds.), Handbook of child development and early education: Research to practice (pp. 499–520). New York: The Guilford Press.Google Scholar
- Kaur, H. (2015). Two aspects of young children’s thinking about different types of dynamic triangles: Prototypicality and inclusion. ZDM Mathematics Education, 47(3) (2014, this issue).Google Scholar
- Koleza, E., & Giannisi, P. (2013). Kindergarten children’s reasoning about basic geometric shapes. In B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds.), Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education (pp. 2118–2129). Ankara: Middle East Technical University.Google Scholar
- Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of children’s reasoning about space and geometry. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space. Mahwah: Lawrence Erlbaum.Google Scholar
- Lin, F. L., & Yang, K. L. (2002). Defining a rectangle under a social and practical setting by two seventh graders. ZDM, 34(1), 17–28.Google Scholar
- LOGO Foundation (2000). A LOGO primer or what’s with the turtles? http://el.media.mit.edu/logo-foundation/logo/turtle.html. Accessed 11 Sept 2014.
- Luria, A. R. (1976). Cognitive development: Its cultural and social foundations. Cambridge: Harvard University Press.Google Scholar
- MIUR (2012). Istruzione. http://hubmiur.pubblica.istruzione.it/web/istruzione/prot7734_12. Accessed 11 Sept 2014.
- Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Mathematics Education Library (Vol. 17). Dordrecht: Kluwer.Google Scholar
- Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.Google Scholar
- Papert, S. (1993). The children’s machine: Rethinking school in the age of the computer. New York: Basic Books.Google Scholar
- Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2015). Early-years teachers’ concept images and concept definitions: Triangles, circles, and cylinders. ZDM Mathematics Education, 47(3) (2014, this issue).Google Scholar