First-grade students’ strategies for 2D/3D transformations
DOI:
https://doi.org/10.34019/1982-1247.2020.v14.27595Keywords:
Spatial structuring, Connection 2D/3D, Mental rotation, Primary gradesAbstract
In this paper, we aim to understand which relationships between components, compounds and the whole do 1st grade students use to transform two-dimensional representations into three-dimensional constructions. We focus our analysis on the strategies used by two students during a task involving the dynamic relationship between 2D and 3D. Data were collected during the first set of tasks from the cycle 1 of an ongoing design-based research. Results show that students can establish relationships between the components, squares, and the whole, the box, using mental movements to transform two-dimensional constructions into three-dimensional constructions. Collective discussions seem to contribute to a collaborative construction of mathematical knowledge and to the shift from representations using physical models to mental models.
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References
Battista, M. (2007). The development of geometric and spatial thinking. In F. Lester (Ed), Second handbook of research on mathematics teaching and learning (pp. 843–909). Reston, VA: NCTM.
Battista, M. T. (2008). Development of the shape makers’ geometry microworld. In G. W. Blume, M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Cases and perspectives (vol. 2, pp. 131–56). Charlotte: Information Age.
Battista, M.T. & Clements, D. (1996). Students’ understanding of three-dimensional rectangular arrays of cubes. Journal for Research in Mathematics Education, 27(3) 258–292.
Bruce, C.D. & Hawes, Z. (2015). The role of 2D and 3D mental rotation in mathematics for young children: what is it? Why does it matter? And what can we do about it? ZDM, 47(3), 331–343. doi: 10.1007/s11858-014-0637-4
Gravemeijer, K., & Cobb, P. (2006). Design research from the learning design perspective. In T. Plomp, & N. Nieveen (Edits.), Educational design research (pp. 72–113). Enschede, The Netherlands: Netherlands Institute for Curriculum Development (SLO).
Hallowell, D.A., Okamoto, Y., Romo, L.F., & La Joy, J. R. (2015). First-graders’ spatial-mathematical reasoning about plane and solid shapes and their representations. ZDM, 47(3), 363–375. doi: 10.1007/s11858-015-0664-9
Johnston-Wilder, S. & Mason, J. (Eds.). (2005) Developing Thinking in Geometry. London: The Open University.
National Council of Teachers of Mathematics (2007). Princípios e normas para a matemática escolar (2.ª ed.). Lisboa: Associação de Professores de Matemática (Obra original em inglês publicada em 2000).
Okamoto, Y, Kotsopoulos, D., McGarvey, L. & Hallowell, D. (2015). The development of spatial reasoning in young children. In Davis, B. (Ed.) Spatial reasoning in the early years: Principles, assertions, and speculations (pp. 15–28). New York: Routledge.
Venkat, H., Askew, M, Watson, A. & Mason, J. (2019). Architecture of mathematical structure, For the Learning of Mathematics, 39(1), 13–17.
Battista, M. (2007). The development of geometric and spatial thinking. In F. Lester (Ed), Second handbook of research on mathematics teaching and learning (pp. 843–909). Reston, VA: NCTM.
Battista, M. T. (2008). Development of the shape makers’ geometry microworld. In G. W. Blume, M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Cases and perspectives (vol. 2, pp. 131–56). Charlotte: Information Age.
Battista, M.T. & Clements, D. (1996). Students’ understanding of three-dimensional rectangular arrays of cubes. Journal for Research in Mathematics Education, 27(3) 258–292.
Bruce, C.D. & Hawes, Z. (2015). The role of 2D and 3D mental rotation in mathematics for young children: what is it? Why does it matter? And what can we do about it? ZDM, 47(3), 331–343. doi: 10.1007/s11858-014-0637-4
Gravemeijer, K., & Cobb, P. (2006). Design research from the learning design perspective. In T. Plomp, & N. Nieveen (Edits.), Educational design research (pp. 72–113). Enschede, The Netherlands: Netherlands Institute for Curriculum Development (SLO).
Hallowell, D.A., Okamoto, Y., Romo, L.F., & La Joy, J. R. (2015). First-graders’ spatial-mathematical reasoning about plane and solid shapes and their representations. ZDM, 47(3), 363–375. doi: 10.1007/s11858-015-0664-9
Johnston-Wilder, S. & Mason, J. (Eds.). (2005) Developing Thinking in Geometry. London: The Open University.
National Council of Teachers of Mathematics (2007). Princípios e normas para a matemática escolar (2.ª ed.). Lisboa: Associação de Professores de Matemática (Obra original em inglês publicada em 2000).
Okamoto, Y, Kotsopoulos, D., McGarvey, L. & Hallowell, D. (2015). The development of spatial reasoning in young children. In Davis, B. (Ed.) Spatial reasoning in the early years: Principles, assertions, and speculations (pp. 15–28). New York: Routledge.
Venkat, H., Askew, M, Watson, A. & Mason, J. (2019). Architecture of mathematical structure, For the Learning of Mathematics, 39(1), 13–17.
Battista, M. T. (2008). Development of the shape makers’ geometry microworld. In G. W. Blume, M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Cases and perspectives (vol. 2, pp. 131–56). Charlotte: Information Age.
Battista, M.T. & Clements, D. (1996). Students’ understanding of three-dimensional rectangular arrays of cubes. Journal for Research in Mathematics Education, 27(3) 258–292.
Bruce, C.D. & Hawes, Z. (2015). The role of 2D and 3D mental rotation in mathematics for young children: what is it? Why does it matter? And what can we do about it? ZDM, 47(3), 331–343. doi: 10.1007/s11858-014-0637-4
Gravemeijer, K., & Cobb, P. (2006). Design research from the learning design perspective. In T. Plomp, & N. Nieveen (Edits.), Educational design research (pp. 72–113). Enschede, The Netherlands: Netherlands Institute for Curriculum Development (SLO).
Hallowell, D.A., Okamoto, Y., Romo, L.F., & La Joy, J. R. (2015). First-graders’ spatial-mathematical reasoning about plane and solid shapes and their representations. ZDM, 47(3), 363–375. doi: 10.1007/s11858-015-0664-9
Johnston-Wilder, S. & Mason, J. (Eds.). (2005) Developing Thinking in Geometry. London: The Open University.
National Council of Teachers of Mathematics (2007). Princípios e normas para a matemática escolar (2.ª ed.). Lisboa: Associação de Professores de Matemática (Obra original em inglês publicada em 2000).
Okamoto, Y, Kotsopoulos, D., McGarvey, L. & Hallowell, D. (2015). The development of spatial reasoning in young children. In Davis, B. (Ed.) Spatial reasoning in the early years: Principles, assertions, and speculations (pp. 15–28). New York: Routledge.
Venkat, H., Askew, M, Watson, A. & Mason, J. (2019). Architecture of mathematical structure, For the Learning of Mathematics, 39(1), 13–17.
Battista, M. (2007). The development of geometric and spatial thinking. In F. Lester (Ed), Second handbook of research on mathematics teaching and learning (pp. 843–909). Reston, VA: NCTM.
Battista, M. T. (2008). Development of the shape makers’ geometry microworld. In G. W. Blume, M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Cases and perspectives (vol. 2, pp. 131–56). Charlotte: Information Age.
Battista, M.T. & Clements, D. (1996). Students’ understanding of three-dimensional rectangular arrays of cubes. Journal for Research in Mathematics Education, 27(3) 258–292.
Bruce, C.D. & Hawes, Z. (2015). The role of 2D and 3D mental rotation in mathematics for young children: what is it? Why does it matter? And what can we do about it? ZDM, 47(3), 331–343. doi: 10.1007/s11858-014-0637-4
Gravemeijer, K., & Cobb, P. (2006). Design research from the learning design perspective. In T. Plomp, & N. Nieveen (Edits.), Educational design research (pp. 72–113). Enschede, The Netherlands: Netherlands Institute for Curriculum Development (SLO).
Hallowell, D.A., Okamoto, Y., Romo, L.F., & La Joy, J. R. (2015). First-graders’ spatial-mathematical reasoning about plane and solid shapes and their representations. ZDM, 47(3), 363–375. doi: 10.1007/s11858-015-0664-9
Johnston-Wilder, S. & Mason, J. (Eds.). (2005) Developing Thinking in Geometry. London: The Open University.
National Council of Teachers of Mathematics (2007). Princípios e normas para a matemática escolar (2.ª ed.). Lisboa: Associação de Professores de Matemática (Obra original em inglês publicada em 2000).
Okamoto, Y, Kotsopoulos, D., McGarvey, L. & Hallowell, D. (2015). The development of spatial reasoning in young children. In Davis, B. (Ed.) Spatial reasoning in the early years: Principles, assertions, and speculations (pp. 15–28). New York: Routledge.
Venkat, H., Askew, M, Watson, A. & Mason, J. (2019). Architecture of mathematical structure, For the Learning of Mathematics, 39(1), 13–17.
Published
2020-08-30
Issue
Section
Artigos
