Implementation of “Symmetry in Mathematics” (SOI-IT-456)

Abstract

“Symmetry in Mathematics”,  proposed by Ivo Žikić, is an educational pathway that is well-structured for implementation in lower secondary school. I have integrated additional resources from Europeana and conducted an activity involving the use of apps to apply the concept of symmetry in a real-world context. Therefore, the acquisition of mathematical concepts occurred through observation, followed by digital production. I implemented the learning scenario in a first-year class of lower secondary school, consisting of 15 students, 10-11 years old,  including two students with disabilities.

The Learning process

I chose to initiate the activity differently from the original scenario, placing the student at the center of learning by discovering the characteristics of axial symmetry using paper.

During one hour of lesson, we work with sheets of paper, pencils, and rulers. I asked the students to take a sheet of paper, fold it in half, and make a hole in the paper, using the tip of the pencil, so that it pierced both halves of the paper. Subsequently, the students opened the sheet and measured the distance from the axis of symmetry, corresponding to the fold of the paper. In this way, they discovered that the two points, P and P’, were at the same distance from the axis of symmetry and that one and only one symmetric point corresponded to a point, and that the axis of symmetry corresponds to the axis of the segment PP’. 

They repeated the procedure, punching the ends of a segment and the vertices of a triangle, and other geometric figures. I asked questions that allowed the students to understand the characteristics of geometric transformation, such as:

•  Does one point on the plane correspond to only one distinct point? 
• Is the axis of symmetry equidistant from the ends of the segment consisting of a point and its symmetric counterpart?
• Does the shape of geometric figures remain unchanged? 
• Are the lengths of the sides and the angles unchanged?

 Through the collective discussion, the students deduced the characteristics of axial symmetry, without me having to state them explicitly, as in a traditional frontal lesson.

In the subsequent one-hour lesson, I proceeded to show the students the video recommended by the author, the resources on Europeana, and the review video.

During my implementation, I decided to incorporate multidisciplinary activities involving the topic of Geography by utilizing resources from Europeana. The students spent one hour in class searching on Europeana for flags from different countries, and they had to choose one that almost included one axis of symmetry. They then drew the flags in their notebooks, identified the axes of symmetry, and added the link to the image.

I decided to utilize the concept of symmetry as an opportunity to foster their creativity. During a one-hour lesson, I tasked my students with designing and creating a digital flag for our school, incorporating geometric figures that include at least one axis of symmetry. This allowed them to apply the concepts they had studied to real-world situations, demonstrating the acquisition of new skills. The flags designed by the students were then shared with the class, and they collectively identified any axes of symmetry and errors present.

Outcomes

As a teacher, the outcomes of the lesson included the successful integration of Geography with Digital Skills. By leveraging resources from Europeana, students were able to explore various images, particularly flags, which served as a foundation for understanding symmetry and its application in design. This interdisciplinary approach not only deepened students’ understanding of both subjects but also encouraged them to think critically and creatively. Furthermore, the lesson fostered collaborative learning as students shared their findings and collaborated on flag design projects.

In the lesson, the students had the opportunity to explore Geography and Digital Skills through engaging activities. They used resources from Europeana to discover different flags from around the world, which not only helped them understand symmetry but also broadened their geographical knowledge. Through hands-on flag design projects, they applied what they learned about symmetry and digital tools to create our own school flag. Working together, they shared ideas, provided feedback, and learned from each other, which enhanced their teamwork skills. Overall, the lesson provided them with a fun and interactive way to learn while developing important skills for the future.

Link to the learning scenario implemented: Symmetry in Mathematics (EN-CUR-208) – Teaching With Europeana (eun.org)

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CC0 1.0: the featured image used to illustrate this article has been found on Europeana and has been provided by the Tartu Art Museum.