# Implementation of “Symmetry in Mathematics” (SoI-UA-523)

Author: Natalia Grushko, Mathematics and Computer Science Teacher in a Secondary School

School/Organization: Zalishchyky State Gimnasia

This educational scenario greatly appealed to me. The topic in mathematics covered therein is the same as mine. The scenario was closely tied to pure mathematics. Therefore, I decided to expand and complement it into a STEM project. Here, I integrated ecology, biology, programming, and engineering.

The project “Unveiling European Art with a Green Perspective” is an innovative way to combine education in mathematics, computer science, ecology, and engineering with the study of European cultural heritage through the lens of symmetry. Students explore the fundamental concepts of symmetry, rotation, and transformations through various tasks and practical exercises. They also investigate symmetry in nature, analyzing symmetrical forms in plants, animals, and natural landscapes. In computer science classes, students created programs using Python to generate symmetrical patterns. They applied mathematical concepts to create various ornaments. Students explored the relationship between symmetry and ecology, analyzing how symmetrical patterns exist in nature and how this affects the ecological balance. Through the study of Europeana, students deepened their knowledge of various aspects of European cultural heritage, including its art and architecture. Students used their knowledge of symmetry, mathematics, and ecology to design engineering structures such as solar panels or wind turbines with the aim of minimizing their impact on the environment.

To successfully implement my task, I recalled materials from the “Digital Education with Cultural Heritage 2023” course from the European School Academy. The age group I chose was 14-15 years old. There were 28 students in the class. The project lasted for 5 lessons, each lasting 45 minutes.

The first lesson was mathematics, held in the classroom. Students summarized the main concepts from the topic “Geometric Transformations.” Namely: the concept of geometric transformation, displacement (movement), and its properties, equality of figures, parallel translation, symmetry with respect to a point and a line, rotation, composition of displacements, homothety and its properties, similarity transformation, and its properties. Similarity of figures, areas of similar figures. The application of similarity transformations and homothety to problem-solving. Inversion. Application of inversion to problem-solving.

The second lesson was combined – biology, ecology, computer science, mathematics. Using digital platforms and tools, students processed material related to symmetry in nature, worked in groups and individually, and developed digital materials. During the research, students made conclusions about the importance of symmetry in nature for maintaining a balanced ecology.

The third lesson was an art lesson. Students worked with materials from the Europeana website. They familiarized themselves with the collection of European art on the Europeana platform. They developed analytical and creative skills through the study of works of art. They enriched their understanding of the diversity and beauty of European cultural heritage.

The fourth lesson was computer science. Creating symmetrical patterns using Python and GeoGebra. Students learned the basic concepts of symmetry and their use in programming. They developed programming and mathematical modeling skills by creating symmetrical patterns.

The engineering lesson: Development of engineering structures for renewable energy sources. Students learned the basic principles of designing engineering structures for renewable energy sources. They familiarized themselves with solar panel and wind turbine technologies. They developed design and creative skills by creating engineering structures to minimize environmental impact. They used the principles of symmetry obtained from European cultural heritage and mathematics to improve the design and functionality of engineering structures.

Art, mathematics, technology, engineering, biology, and computer science were all involved in the project. Students learned about the physical principles of engineering construction, studied the history of engineering art, deepened their knowledge of ecology and mathematics. They worked with software such as Tinkercad to design and create their own structures, Geogebra to help with complex mathematical calculations and develop prototypes to better understand design decisions. And all this was done using Europeana resources.

Resources Used: Europeana

Online educational material:

## Abstract/Introduction

The implementation involved the adaptation of a learning scenario titled “Exploring European Art with a Green Perspective” into a comprehensive STEM project. The learning scenario was originally focused on mathematics and art, exploring European cultural heritage through symmetry. However, it was expanded to incorporate elements of ecology, biology, programming, and engineering.

The implementation context included a diverse range of subjects such as mathematics, art, biology, informatics, and engineering. The project aimed to engage students aged 14-15 years old in a holistic exploration of European cultural heritage and STEM concepts. The educational settings varied, including traditional classroom sessions for mathematics and art, digital platforms for programming, and hands-on activities for engineering. The group size consisted of 28 students, allowing for collaborative learning and individual exploration.

Throughout the implementation, students delved into various aspects of symmetry, mathematical modeling, ecological balance, and engineering design. They utilized digital tools such as Europeana, Python, Geogebra, and Tinkercad to deepen their understanding and create innovative projects. The interdisciplinary approach fostered critical thinking, creativity, and problem-solving skills among the students, preparing them for future challenges in both academic and real-world contexts.

## Main text

### Implementation Context

Project Task

Students were tasked with developing engineering designs for renewable energy sources such as solar panels or wind turbines, aimed at minimizing their impact on the environment. They utilized their knowledge from mathematics, engineering, informatics, and ecology to create optimal designs that are both effective and environmentally friendly. Students incorporated principles of symmetry, derived from the study of European cultural heritage and mathematics, to enhance the design and functionality of their engineering constructions.

Key Competencies

Critical Thinking: Students learned to analyze information, evaluate alternatives, and make informed decisions regarding the development and use of renewable energy sources.

Problem Solving: Project participants developed skills in seeking and implementing innovative solutions to reduce negative impacts on the environment.

Creativity and Innovation: They generated original ideas and worked on implementing them into practical solutions, fostering innovative thinking.

Communication Skills: Students learned to effectively communicate, exchange ideas, and collaborate as a team to achieve common goals.

Self-regulation: They developed the ability to plan their work, monitor task execution processes, and evaluate their achievements.

Sociocultural Competence: Project participants expanded their cultural and intercultural experience by interacting with classmates and utilizing materials from European cultural heritage.

Environmental Awareness: They developed awareness of environmental issues and learned to make responsible decisions to preserve the environment.

### The narrative (Learning process/Stages of implementation)

Project Structure First Stage – Mathematics

Materials:

Annex 1

In the math class, students focus on studying transformations and symmetry. After the introductory explanation of the lesson topic and review of previous knowledge, the teacher conducts a summary of the material. Students gain an understanding of basic concepts such as transformations, symmetry, and rotation, and review examples of their application. Then they move on to the practical part of the lesson, where the construction of symmetric figures and patterns is applied in various exercises. The use of the GeoGebra program allows students to explore transformations and symmetry through interactive tools. At the end of the lesson, a summary takes place, during which students summarize the knowledge gained and draw conclusions about the practical application of the material.

Second stage

Annex 2

In the biology and ecology class, students focus on studying the relationship between symmetry in nature and ecology. After the introductory explanation of the topic and its significance, students are engaged in creating digital materials that illustrate various natural objects with symmetric structures. They explore symmetric forms in plants, animals, and natural landscapes, reproducing them in digital format. While creating digital materials, students gather information about the impact of symmetry in nature on ecological balance. They learn how symmetric patterns contribute to the development and preservation of ecosystems and biodiversity. Students use various digital tools and platforms such as presentations, videos, interactive websites, or illustrations to showcase the gathered information. This not only allows them to deepen their understanding of the topic but also to share the acquired knowledge with others. At the end of the lesson, students present their digital materials and discuss their findings regarding the importance of symmetry in nature and its impact on ecological balance. This process contributes not only to learning but also to the development of students’ ecological awareness and their readiness to address environmental issues.

Third stage

Materials

Annex 3

Lesson plan includes an introductory word, during which the lesson topic and the importance of studying European cultural heritage through Europeana resources are explained. Then, students familiarize themselves with various artworks on the platform and explore their symmetry and other

characteristics. After that, students move on to the exploration of engineering designs for energy sources. They study different types of mills, windmills, and solar panels, analyzing their structure, working principle, and environmental impact. Subsequently, students choose one piece of art where symmetry is traced and which interests them the most, and create their own interpretation through creativity. The lesson concludes with a summary and discussion of students’ impressions, as well as assigning homework for further research on European cultural heritage and engineering designs for energy sources.

Fourth stage

Annex 4

Computer Science Lesson: Creating Symmetric Patterns using Python The aim of this lesson is to learn the basic concepts of symmetry and their application in programming, introduce students to the Python programming language, and develop their programming skills and mathematical modeling through creating symmetric patterns. The lesson begins with an introductory word, explaining the lesson topic and the importance of studying symmetry in computer science. Then, an overview of the Python programming language is conducted, where students receive a brief introduction to the syntax and basic functions of the language, as well as an explanation of how Python can be used to create symmetric patterns. After that, students receive a practical task with Python, where they need to write a program to generate symmetric patterns. They use the concepts of symmetry learned to create various ornaments, explore different ways of reflecting symmetry, and experiment with creating their own geometric objects.

The lesson concludes with a summary, summarizing what was learned in the lesson, and discussing students’ impressions of working with Python. Then, homework is given to create symmetric patterns using Python and further improve them.

Fifth stage

Materials

Annex 5

Students work with the resource https://ua.mozaweb.com , which provides a visual demonstration of the operation of mills, wind turbines, and solar panels.

In the engineering lesson on the development of engineering designs for renewable energy sources, students familiarize themselves with the basic principles of developing such designs and the technologies of solar panels and wind turbines. During the practical task, they use the Tinkercad environment to create 3D models optimized to minimize environmental impact. Additionally, students use the principles of symmetry, acquired from European cultural heritage and mathematics, to improve the design and functionality of their projects. Summative testing and

assessment help students check and improve their designs considering the principles of ecological efficiency and symmetry.

Roles of the student and teacher at different stages of the project:

Preparation: Teacher: Defining the project topic, forming work groups, providing information sources, conducting introductory training, providing methodological assistance in setting project goals and tasks. Student: Discussing and choosing the project topic, interacting with the work group, researching and collecting information, setting project goals and tasks.

Execution: Teacher: Monitoring and supporting student progress, providing feedback, organizing consultations, assisting in resolving technical or methodological issues. Student: Completing project tasks, collaborating in work groups, researching, creating project products, receiving feedback from the teacher, self-assessment, and peer assessment.

Presentation and evaluation: Teacher: Organizing presentations, planning the evaluation process, assessing project results, providing feedback, determining the success of project execution. Student: Presenting project results, answering questions, accepting criticism.

Learning outcomes (What did you achieve?) Achievements:

Increased Knowledge of European Heritage: Students expanded their knowledge of European cultural heritage, familiarized themselves with artworks, studied various materials, and explored architectural solutions.

STEM Skills Development: The project facilitated the development of students’ skills in applying scientific, technical, engineering, and mathematical approaches to creating models and developing designs.

Practical Experience in Designing: Students had the opportunity to create digital models, apply theoretical knowledge of biology, mathematics, and engineering solutions in their design development.

Creativity and Presentation Skills: The project allowed students to develop their creativity, the ability to present their ideas in digital resources, presentations, and other formats, fostering the development of communication and public speaking skills.

Consideration of Future Career and Identity: Through project execution, students had the opportunity to feel part of nature, contemplate their future career paths, and personal values from an ecological perspective. They reflected on their identity, considering the importance of natural resources and their connection to cultural heritage.

Environmental Awareness and Engineering Solutions: The project enabled students to immerse themselves in the creation of engineering solutions that contribute to environmental preservation. They explored the impact of renewable energy sources on nature and the future of our planet, while developing their technical and scientific abilities.

Integration of European Heritage and Environmental Responsibility: While working with European heritage materials, students not only learned about their national and cultural identity but also understood how it relates to environmental responsibility and the preservation of our shared planet.

Application of STEM Approach: The STEM approach pushed students towards developing innovative thinking and scientific-technical skills. They saw themselves as part of a larger environmental movement capable of making positive changes in the world.

This comprehensive approach to education helped students not only expand their knowledge and skills but also understand their place in the world as active citizens responsible for the future of the planet and their own self-determination.

### Outcomes for the educator

Students had the opportunity to showcase their creativity and develop construction and engineering skills by designing their own renewable energy projects.

The project contributes to students’ awareness of the importance of using renewable energy sources and minimizing environmental impact.

Students utilize knowledge from various subject areas such as mathematics, computer science, engineering, and ecology to solve real-world problems.

They have the chance to work in teams, exchange ideas, and collaboratively solve tasks, fostering the development of communication skills and teamwork.

The “Ecological Engineering Constructions” project plays a key role in developing environmental awareness among students as it focuses on creating and applying technologies that contribute to environmental conservation. Project participants study the principles of renewable energy sources and their impact on nature, as well as develop practical solutions to reduce negative impacts on ecosystems. This project provides students with the opportunity to understand the importance of sustainable development and make informed environmental decisions in the future.

The primary work of students at project stages involves self-directed learning, creative approaches, critical thinking, teamwork communication, skills development with various information sources, problem-solving, material and resource management, as well as presenting project results. During the project work, students interact with each other, learn problem-solving, creative approaches, information analysis and evaluation, critical thinking, communication skills, and teamwork skills.

The teacher may assist students in resolving conflicts, implementing group interaction strategies, fostering students’ creativity, and independence.

Students’ project work includes studying the theoretical basis, making models, and developing 3D models in software environments, fostering students’ creativity, technical, communicative, and presentation skills. The teacher’s work includes providing guidance, assisting in team organization, supporting creative approaches, fostering additional knowledge and skills development for students.

#### Annex 5

Images from the implementation

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

Do you want to discover more stories of implementation? Click here.

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

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