Implementation of “Symmetry in Mathematics” (Sol-GR-572)
Author: Katerina Spitsa
Organisation: 2nd Experimental Model Kindergarten of Thessaloniki
Abstract
This is a Story of Implementation with the title “From Symmetry to Shapes”. The learning scenario I implemented, was “Symmetry in Mathematics” by Ivo Žikić, which was designed for secondary education. I did all the necessary alterations to implement it in the Early-Childhood Education. The main goal of my learning scenario was to introduce the concept of symmetry to my 16 preschool students in a way that was engaging and developmentally appropriate and make them familiar with 2D and 3D shapes. The learning scenario incorporated storytelling, games, art projects, and technology to help students explore symmetry. Students worked in groups to find symmetrical objects in the classroom, created symmetrical art, and learned about 2D and 3D shapes. The activities fostered creativity, problem-solving skills, teamwork, and spatial reasoning.
Main Text
- The Rationale
My name is Aikaterini Spitsa and I implemented the learning scenario by Ivo Žikić , “Symmetry in Mathematics” , with my 16 students of the 2nd Experimental Model Kindergarten of Thessaloniki, a school in the second most populated city of Greece. Our school, as all experimental schools, is a place of innovation and research in the field of preschool education that focuses on activities that promote students’ self-activity, creativity and critical thinking. The initial scenario’s activities, although it was for secondary education, was altered to be suitable for early-childhood education and was implemented in a way that allowed students to develop their cognitive and social skills and expand their knowledge through interdisciplinary approach. Students were formerly familiar with the use of camera and ICT tools as well as teamwork procedures. The methodology used were exploratory learning, cooperative learning, teaching by problem solving and learning through play. Whereas the teaching strategies we used were: brainstorming, questions and answers, following an online story, working in groups, presenting to the plenary.
2. Introduction to the topic (15min)
The students were introduced to symmetry with a case study. When they entered the classroom in the morning, they saw their pictures on the board cut in half. They immediately started asking and investigating the case. They wanted to find out who did it. Students tried to answer question like: “What do you think happened? How can we solve the problem?”. Students said that a thief came to our school and stole half of their photos and then all together tried to find clues with the use of magnifying glasses.
Students looking for clues. CC BY-NC-ND. Katerina Spitsa
3. Storytelling (30min)
Then I introduced the story “The Witch Symmetry” digitally and project it onto the interactive whiteboard. You will find the story in the following link
The story is about the Witch Symmetry who lives in a castle with symmetrical objects and animals. She has a magic stick called “Axis of Symmetry”. One day she woke up and found that everything in her castle were cut in half and her magic stick was missing. Then, students tried to answer some comprehension questions such as:
-Where does the Symmetry Witch live?
-How do you imagine her castle?
-What does evenly symmetrical mean?
-How did she want her things to be?
-What happened one day in the forest?
-What do you think happened?
-What was happening in the forest?
-What do you think he should do?
-How can we help?
We talked about symmetry and the axis of symmetry with the use of Europeana materials such as:
A video: Intro to Symmetry: All About Symmetry for Kids – FreeSchool (youtube.com)
And the materials provided by the learning scenario I implemented such as:
- (700) Lines of Symmetry *Explained* Math for Kids – YouTube
- Identify line symmetry (practice) | Khan Academy
Then we heard an audio file on the last slide of the fairy tale presentation in which the witch invited us to help her by looking for symmetrical objects in the classroom.
4. Field Study (30min)
We followed the witch’s instructions about finding symmetrical objects in class. Students were divides in groups of four. Each group had to find and photograph symmetrical objects in the classroom. Students used classroom materials, such as pens, plastic straws, ribbons, wooden sticks, to find vertical and horizontal axes of symmetry in flat geometric shapes and objects, tiles, and other objects in the classroom, took pictures of the symmetrical objects they found using tablets and stuck a post-it note on them. In the following picture you can see the materials they used as an axis of symmetry and some of the photos they took.
5. Book Reading (20min)
We also read the book “The magic mirror” by Sofia Madouvalou and used a mirror to create symmetries.
Students use the mirror to create symmetries. CC BY-NC-ND. Katerina Spitsa
6. Practising symmetry through art and games (30min)
After watching the video from the learning scenario I implemented (700) Lines of Symmetry *Explained* Math for Kids – YouTube, and the following video https://youtu.be/q1TQtfNw4JA, we decided to create sour own symmetrical butterflies by folding a piece of A4 paper, drawing half of the page and printing the other half.
Samples of students’ creations. CC BY-NC-ND. Katerina Spitsa
We also created a two-players game with the use of a table, plastic tape and wooden shapes. The first player created something using shapes and the second had to recreate it symmetrically.
The two-players game. CC BY-NC-ND. Katerina Spitsa
7. Pixel Art Symmetry Creations (20min)
Since we had talked about pixels previously, we formed groups and created symmetrical pictures, like a butterfly and a tree, using small colored paper squares on a grid.
Pixel Art Symmetry Creations. CC BY-NC-ND. Katerina Spitsa
8. Symmetry Drawing (30 min)
We, then used the online drawing tool Symmetry Artist (mathsisfun.com) and created our own symmetrical paintings. Have a look at some of our creations.
Students creating symmetries online. CC BY-NC-ND. Katerina Spitsa
We, also, used a piece of graph paper and with the help of a vertical axis of symmetry, students drew symmetrically.
Some of the students’ symmetrical creations. CC BY-NC-ND. Katerina Spitsa
9. From symmetry to 2D shapes
Due to the videos, we watched previously, students identified a lot of 2D shapes that were symmetrical, so we created table games of matching shape halves and creating figures. Then, students formed pairs and with the help of the tablet’s camera, went shape hunting and took photos of different shapes in the classroom. We identified the shapes’ names and characteristics and tried to recreate them using wooden sticks and colored pipe wires.
Searching for 2d shapes and reproducing them. CC BY-NC-ND. Katerina Spitsa
2D Shape Creations. CC BY-NC-ND. Katerina Spitsa
“The castle and the sun” by Paul Klee
We used the painting Castle and Sun, 1928 – Paul Klee – WikiArt.org in order to find the shapes on it, name them and identify their characteristics. We used a lot of art techniques to recreate it, such as stamping on paper with paint and pieces of carton or wooden bricks and collage on paper with colored carton shapes.
Stamping procedure. CC BY-NC-ND. Katerina Spitsa
Stamping creations. CC BY-NC-ND. Katerina Spitsa
Stamping with wooden bricks. CC BY-NC-ND. Katerina Spitsa
10. From 2d Shapes to 3d Shapes
After identifying and practicing with 2D shapes (circle, square, triangle, rectangle), we moved to 3D shapes (sphere, cube, cone, cylinder) which we tried to recognize, match with 2D shapes and find similar objects in our classroom. We also tried to create our own 3D shapes using plasticine and toothpicks.
From 2d to 3d shapes. CC BY-NC-ND. Katerina Spitsa
Creating 3d shapes with toothpicks and clay. CC BY-NC-ND. Katerina Spitsa
Then we recreated Paul Klee’s painting using 3D shapes. Students collaborated in smaller teams and each team chose a different material to revive the painting (legos, wooden bricks, magnets).
Students collaborate in groups recreating Paul Klee’s artwork. CC BY-NC-ND. Katerina Spitsa
The 3D artworks of all the teams. CC BY-NC-ND. Katerina Spitsa
11. 3D Shapes Teachable Machine
With AI application Teachable Machine we created a project that could identify 3D shapes.
Students training the AI tool. CC BY-NC-ND. Katerina Spitsa
Our project with the AI tool. CC BY-NC-ND. Katerina Spitsa
12. Symmetrical Recyclable Buildings
Students continued playing, on daily basis, with 3Dshapes with the use of loose parts and recyclable materials and created symmetrical buildings.
Students building 3d symmetrical constructions . CC BY-NC-ND. Katerina Spitsa
Students building 3D symmetrical constructions 2. CC BY-NC-ND. Katerina Spitsa
13. Outcomes of the learning scenario
Outcomes for the teacher
Implementing activities about shapes and symmetry with the use of Europeana Resources can lead to several benefits for the teacher:
Improved Classroom Management:
- Engaged Students: Fun activities tend to lead to fewer disruptions and a more focused classroom environment.
- Differentiation Opportunities: These activities were adaptable and allowed for differentiation to cater to different learning styles and abilities.
- Formative Assessment: Through observation and interaction during activities, I gained valuable insights into children’s understanding and identify areas that need more focus.
Professional Development:
- Teaching Strategies: I had the chance to explore new and creative ways to present mathematical concepts.
- Collaboration: Group activities foster collaboration among students, which was a valuable teaching tool.
- Positive Reinforcement: Witnessing children’s engagement and learning from these activities was a rewarding experience.
Increased Job Satisfaction:
- Effective Learning: Seeing children grasp new concepts and develop their skills was very satisfying.
- Positive Classroom Environment: Engaged and excited students contribute to a more positive and rewarding classroom atmosphere.
- Creative Expression: These activities allowed me to express creativity in designing and implementing lessons.
Outcomes for students
Implementing activities and Europeana resources about symmetry, 2D shapes, and 3D shapes with groupwork, art, and games in preschoolers can lead to a variety of positive outcomes.
Learning Outcomes
- Shape Recognition and Identification: Students developed the ability to recognize and identify basic 2D shapes (circle, square, triangle, rectangle) and 3D shapes (sphere, cube, cone, cylinder).
- Spatial Reasoning: Through play and exploration, children developed their spatial reasoning skills, which involved understanding the relationships between objects in space.
- Symmetry Awareness: Engaging activities introduced children to the concept of symmetry, to recognize and identify symmetrical shapes according to different axes of symmetry and how shapes can be divided into matching halves.
- Vocabulary Development: Activities introduced and reinforced vocabulary related to shapes (e.g., corner, side, edge, vertex) and spatial concepts (e.g., above, below, beside).
Developmental Outcomes
- Fine Motor Skills: Art projects helped children develop their fine motor skills, which are essential for tasks like writing and drawing.
- Problem-Solving Skills: Games and challenges encourage students to think critically and solve problems as they worked with shapes.
- Social Skills: Group activities promoted collaboration, communication, and teamwork skills.
- Creativity and Imagination: Art projects and open-ended activities allowed children to express their creativity and explore their imagination.
Overall Benefit
- Increased Engagement: By incorporating play, art, and games, learning became more engaging and enjoyable for students.
- Positive Learning Environment: These activities created a positive and stimulating learning environment that fosters curiosity and exploration.
- Foundation for Future Learning: Understanding shapes and spatial concepts forms a strong foundation for future learning in math, science, and other subjects.
Link to the learning scenario implemented: https://teachwitheuropeana.eun.org/learning-scenarios/symmetry-in-mathematics-en-cur-208/
Do you want to discover more stories of implementation? Click here.
CC BY-SA 4.0: the featured image used to illustrate this article has been found on Europeana and has been provided by the Ίδρυμα Εικαστικών Τεχνών & Μουσικής Βασίλη και Μαρίνας Θεοχαράκη.