Using Dynamic Geometry Software to Develop Powerful Thinking in K-5

My research will improve mathematics teaching and learning at the primary school by identifying more effective ways of allowing young children to develop sophisticated mathematical ideas while drawing on their powerful visual and kinaesthetic capacities.

Teachers at several schools around the province of British Columbia, as well as in Ontario and other parts of the world, are using materials developed in this research project as a basis for their own lesson planning.

Visit: Dynamic Geometry for Teaching – Developing Powerful Thinking

Principal Investigator: Dr. Nathalie Sinclair
Funding Agency: SSHRC

Addtional Team Members:
Shiva Gol Tabaghi
Harpreet Kaur
Eileen Bennison (David Roy School)

What's Proposed

Two decades ago, a new type of computer software was introduced, one that offered a radically new way of representing mathematical objects. Dynamic Geometry Environments (DGEs) enable the creation of dynamic representations—hitherto static objects such as triangles, points, and numbers can now move continuously on the computer screen; these objects can grow, change, and morph over time. Based on the testimonies of some of the great mathematicians of the past, imagining dynamic mathematical objects is central to coming to know about them and being able to work with them in problem-solving contexts. The static media of the past were not conducive to making such personal, dynamic images shareable with others. DGEs change all that.

Much research on the use of DGEs has focused on geometry learning at the secondary level. Given the limited amount of formal geometry taught prior to secondary school, and biases against the use of technology by young children, there has been very little research on the potential of DGEs in the primary school classroom. However, researchers are becoming increasingly concerned about the lost opportunities of current primary school curricula, a loss that is particularly troublesome given the enormous informal geometric ideas young children bring to formal schooling. Moreover, with the increased use of technology in elementary school classrooms as well as both the growing awareness of the importance of geometry, the time is ripe to study the role DGEs could play in improving student mathematics learning in the primary school. The basic tools of DGEs are more than appropriate for the primary school geometry curriculum. In fact, based on the strongly visual, kineasthetic and empirical nature of young children's interactions with the world and the importance of developing flexible geometric imagery at an early age, they are most appropriate for learners of this age, who often develop narrow conceptions of shapes through interaction with static representations.

How This Project is Carried Out

The proposed research has three main foci. The first is to compare the learning trajectories of children's geometric thinking across age groups in the context of Dynamic Geometry Environment (DGE) use. This component of the proposed research will not only serve to identify the affordances of DGEs, it will contribute to the general understanding of how digital technologies change the way learners (and the way mathematics itself) changes. The second focus is on the long-term effect of DGE use on children's thinking and problem solving. We currently have limited understanding of how dynamic visual representations can affect children's strategies and imageries in various areas of the mathematics curriculum. The third focus is on the classroom interactions involving DGE use engaging the teacher, the students and the tasks. The goal is to develop teaching episodes involving suitably designed DGE-based tasks that will enable a better understanding of how teacher and student discourses in the classroom can promote more sophisticated mathematical thinking.

Where to Learn More

Review some of the materials used in this project.

The following publications describe some of the initial research results involving the use of DGEs with young learners:

  • Sinclair, N. and Moss, J. (2012). The more it changes, the more it becomes the same: The development of the routine of shape identification in dynamic geometry environments. International Journal of Education Research.
  • Sinclair, N. and Crespo, S. (2006). Learning mathematics with dynamic computer environments. Teaching Children Mathematics 12(9), 436-444.
  • Sinclair, N. and Kaur, H. (2011). Young children’s understanding of reflection symmetry in a dynamic geometry environment. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, Ankara, Turkey.
  • Sinclair, N., Moss, J. and Jones, K. (2010). Developing geometric discourse using DGS in K-3. Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, Belo Horizonte, Brazil: PME.
  • Sinclair, N. & Jackiw, N. (2007). Dynamic Geometry Activity Design for Elementary School Mathematics. Proceedings of the Seventeenth ICMI Study Conference “Technology Revisited,” Hanoi, Vietnam.