Geometry and optical illusions

Author: Daniela Leone

Methodology and tools

This is a remote learning activity, developed in March 2020 with 1st-grade students of IC21 Bologna lower secondary school.

The tools used are GSuite for Education, GeoGebra and Go-Lab resources. The activity is based on Inquiry-based Learning methodology.

Students had a little experience with GSuite, Go-Lab and GeoGebra but no experience of learning from home. To be able to communicate we used GSuite tools (email, tutorials on Google Classroom, Google Meet calls).

The Go-Lab Inquiry Learning Space used for the activity is a translated version of the French ILS “Changer de perspective” created by Valentin Roussel.

Activity

Thanks to the author, the ILS was useful to guide students in discovering basic geometry in a playful way: it aroused their curiosity about the features that add special effects to images. The questions helped students to reflect and recognize the main properties of parallel and perpendicular lines, angles, areas, by manipulating dynamic figures. The images included in the ILS were inspiring for students.

At the end of the translated version made for the IC21 school, I added an extra task for my students: they were asked to make and share their own images containing optical illusions or special effects, using the GeoGebra Geometry App. 

Gallery

During the online meetings with students, formative assessment was given by discussing the images seen in the Go-Lab ILS, comparing different students explanations, and by sharing the images created by students who challenged each other to explain them. A quiz was also created with questions about the geometrical properties of figures created by students.

All images created by students were collected in a gallery and published on the GeoGebra website. They can be found here.

Evaluation

This activity helps students to learn by doing: not all the images they created fully respect geometrical properties as parallel and perpendicular lines, but they can be improved in a further phase when they will get more experience with GeoGebra. The initial goal was engaging students in trying to apply their own ideas and motivate them to learn how to improve their creations.

Alongside the curriculum content of basic geometry, the activity encourages students developing their digital skills and experiencing the process of designing and creating digital contents. The same activity can be implemented at school, with a shorter time needed.

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