Abstract
In this chapter, we discuss the results of a research project which investigates aspects of students’ cognitions during the process of solving tasks dealing with a Dynamic Geometric Environment with touchscreen (DGEwT). In this chapter, we discuss data from two teaching experiments carried out with Brazilian and Italian high school students dealing with GeoGebraTouch (GT) and a Geometric Constructer (GC) software. With the focus on strategies used by students to solve the proposed tasks, we suggest two domains: Constructive and relational. Furthermore, we suggest the drag-approach as an important form of manipulation to improve geometrical thinking. Finally, we present a selected variety of representative examples of didactic, cognitive, and epistemological implications for learning and researching with the use of DGEwT.
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Notes
- 1.
To see this kind of motion , please download the video: https://youtu.be/qC-G96NssJk
- 2.
In Brazil we are working with prospective mathematics teachers as well as with Sketchometry devices. We decided not to discuss data from their TE in this chapter.
- 3.
In recent analyses we used SCR PRO (Assis 2016) as a strategy to review some details that emerged from the video analysis.
- 4.
The whole video is available on https://www.youtube.com/watch?v=qC-G96NssJk
- 5.
In quadrilateral ABCD, the middle points (E, F, G and H) on each side have been drawn, forming quadrilateral EFGH. What characteristics does EFGH have? What happens if ABCD is a rectangle ? What if it is a square ? What if it is any quadrilateral? Demonstrate.
- 6.
Build a quadrilateral ABCD. On each of its sides build a square external to the quadrilateral with one side coincident to the side of the quadrilateral. Consider the centers of the squares that have been built: R, S, T, U. Consider the quadrilateral RSTU: what can you observe? What commands do you use in order to verify your conjecture? This activity was thought as a task to introduce curiosity among students for the Napoleon Theorem , which was explored on the next assigned task.
- 7.
Inspired by Arzarello et al. (2002).
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Appendices
Appendices
Appendix 1: Timeline of the Varignon Theorem Task (Discussed on TE 2)
Appendix 2: Timeline of the Task Shown in note (a) of Table 5
Appendix 3: List of Icons Elaborated for TE with GeoGebraTouch
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Bairral, M., Arzarello, F., Assis, A. (2017). Domains of Manipulation in Touchscreen Devices and Some Didactic, Cognitive, and Epistemological Implications for Improving Geometric Thinking. In: Aldon, G., Hitt, F., Bazzini, L., Gellert, U. (eds) Mathematics and Technology. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-51380-5_7
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