Processos de raciocínio espacial na representação de figuras 3D por alunos do 1.º ano do ensino básico

Joana Conceição; Margarida Rodrigues

doi:10.48489/quadrante.23007

Authors

Joana Conceição Instituto de Educação, Universidade de Lisboa, Portugal https://orcid.org/0000-0002-4295-0368
Margarida Rodrigues Escola Superior de Educação, Instituto Politécnico de Lisboa | UIDEF, Instituto de Educação, Universidade de Lisboa, Portugal https://orcid.org/0000-0003-4658-6281

DOI:

https://doi.org/10.48489/quadrante.23007

Keywords:

spatial reasoning, spatial structuring, representations, collective discussions

Abstract

In this paper, our aim is to analyze in what way does 1^st graders’ drawings of 3D shapes promote their spatial reasoning as well as their spatial structuring. For that, we analyze the drawings from seven students during two tasks, as well as, their communication, during collective discussions, concerning those resolutions, in the classroom. Data was collected during cycle 1 of a design-based research. Results show that students draw their constructions by segmenting them into different parts, and use different types of drawings to show the relationships among those parts, like slated squares, in the case of local structuring, or drawing smaller squares inside larger squares or using numeric codes to represent different layers, in the case of global structuring. Also, in local structuring, in some cases, students’ drawings show miscounting or lack of coordination between perpendicular parts. Spatial structuring seems to be anchored in spatial reasoning processes, related to understanding and transforming, that allow establishing relationships between 3D shapes and their plane representations, like relating, rearranging, sectioning, dimension shifting and locating. By letting students use different ways of communicating, we gain a better understanding of students’ ideas and, at the same time, allow them to deepen their spatial structuring.

References

Battista, M. T. (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., & Clements, D. H. (1996). Students’ understanding of three-dimensional rectangular arrays of cubes. Journal for Research in Mathematics Education, 27(3), 258–292.

Blanco, T., Godino, J., Sequeiros, P., & Mantecón, J. M. (2019). Skill levels on visualization and spatial reasoning in pre-service primary teachers. Universal Journal of Educational Research, 7(12). 2647–2661. https://doi.org/10.13189/ujer.2019.071212

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 Mathematics Education, 47(3), 331–343. https://doi.org/10.1007/s11858-014-0637-4

Clements, D. H., Sarama, J., Swaminathan, S., Weber, D., & Trawick-Smith, J. (2018). Teaching and learning Geometry: Early foundations. Quadrante, 27(2), 7–31.

Davis, B., Okamoto, Y., & Whiteley, W. (2015). Spatializing school mathematics. In B. Davis (Ed.) Spatial reasoning in the early years: Principles, assertions, and speculations (pp. 139–150). New York: Routledge.

Gravemeijer, K., & Cobb, P. (2006). Design research from the learning design perspective. In T. Plomp & N. Nieveen (Eds.), Educational design research (pp. 72–113). Enschede, The Netherlands: Netherlands Institute for Curriculum Development (SLO).

Gutiérrez, A. (1996). Children’s ability for using different plane representations of space figures. In A. R. Batturo (Ed.), New directions in geometry education (pp. 33-42). Brisbane, Australia: Centre for Mathematics and Science Education, Q.U.T.

Gutiérrez, A. (1998). Las representaciones planas de cuerpos 3-dimensionales en la enseñanza de la geometría espacial. Revista EMA, 3(3), 193-220.

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 Mathematics Education, 47(3), 363–375. https://doi.org/10.1007/s11858-015-0664-9

Mulligan, J. (2015). Looking within and beyond the geometry curriculum: Connecting spatial reasoning to mathematics learning. ZDM Mathematics Education, 47(3), 511–517. https://doi.org/10.1007/s11858-015-0696-1

Nunes, M. J., & Rodrigues, M. (2018). Compondo e desenhando formas tridimensionais: Um contributo para a caracterização do raciocínio espacial de crianças de 5 anos. Quadrante, 27(2), 63–88.

Panorkou, N., & Pratt, D. (2009). Mapping experience of dimension. In M. Tzekaki, M. Kaldrimidou & H. Sakonidis (Eds.), Proceedings of the 33th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 281-288). Thessaloniki, Greece: PME.

Radford, L., & Barwell, R. (2016). Language in mathematics education research. In A. Gutiérrez, G. C. Leder, & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education (pp. 275–313). Rotterdam: Sense Publishers.

Sack, J., & van Niekerk, R. (2009). Developing the spatial operational capacity of young children using wooden cubes and dynamic simulation software. In T. Craine & R. Rubinstein (Eds.), Understanding geometry for a changing world: Seventy-first yearbook (pp. 141-154). Reston: NCTM.

Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press.

Sinclair, N., Moss, J., Hawes, Z., & Stephenson, C. (2018). Learning through and from drawing in Early Years Geometry. In K. Mix & M. T. Battista (Eds.), Visualizing mathematics: The role of spatial reasoning in mathematical thought (pp. 229-252). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-98767-5_11

Thom, J. S., & McGarvey, L. M. (2015). The act and artifact of drawing(s): Observing geometric thinking with, in, and through children’s drawings. ZDM Mathematics Education, 47(3), 465–481.

Van den Heuvel-Panhuizen, M., & Buys, K. (2008). Young children learn measurement and geometry: A learning-teaching trajectory with intermediate attainment targets for the lower grades in primary school. Rotterdam: Sense Publishers.