Implementation of « Mondrian and Math lessons » (SOI-HR-467)

juin 4, 2024

3927

Introduction

As a mathematics teacher in a primary and lower secondary school, I believe that integrating art into mathematics education offers a multidimensional approach fostering creativity, critical thinking, and mathematical understanding. When using art as a pedagogical tool in teaching mathematical concepts through visual representations, the pupils are engaged in hands-on activities, stimulating spatial awareness and problem-solving skills.

In sixth grade as part of the curriculum of mathematics in Croatia, deeper learning about quadrilaterals serves as a foundation of spatial mathematics for several reasons.

Quadrilaterals are fundamental geometric shapes and studying them introduces pupils to foundational mathematical concepts such as sides, angles, vertices, and properties of shapes. This helps them develop spatial awareness and an understanding of how shapes relate to each other in two-dimensional space. It also serves as a building block for advanced mathematics because understanding quadrilaterals provides a solid basis for grasping more complex geometric concepts, such as polygons, symmetry, and transformations. Furthermore, this is crucial in various real-world applications, such as architecture, engineering, and design.

In the Croatian curriculum, the study of geometry, including quadrilaterals, is typically integrated into mathematics education at the lower secondary level. Students are expected to learn about the properties of different quadrilaterals, including squares, rectangles, parallelograms, rhombuses, and trapezoids. They also learn how to classify and identify these shapes based on their properties, such as side lengths, angles, and symmetry.

Using art, specifically the works of Piet Mondrian, can make learning about quadrilaterals enjoyable and productive by providing a visual and creative approach to understanding geometric concepts. With this in mind, I decided to implement the scenario Mondrian and Math lessons (LS-RS-344) by Natalija Budinski.

Summary

Mondrian’s artwork often features geometric shapes, including quadrilaterals, arranged in visually appealing compositions. By studying Mondrian’s art, students can see real-world examples of quadrilaterals and observe how they are organized within a space.

Incorporating art into mathematics education can capture children’s’ interest and imagination, making the learning process more engaging and enjoyable. Mondrian’s bold use of colors and shapes can inspire students to explore geometric concepts with enthusiasm.

When designing hands-on activities inspired by Mondrian’s art, such as creating geometric collages or paintings using quadrilaterals as building blocks, pupils are to manipulate shapes, explore spatial relationships, and apply their understanding of quadrilaterals in a creative context.

This important interdisciplinary connection between mathematics and visual arts engages pupils in an exciting and visual manner. Pupils can explore how mathematical principles, such as symmetry and proportion, are reflected in Mondrian’s compositions, fostering a deeper understanding of both subjects.

Overall, integrating art, particularly the works of Mondrian, into the study of quadrilaterals not only makes learning more enjoyable but also enhances the understanding of geometric concepts and their applications in the real world.

Figure 1: Pupils discussing the connection of mathematics and art

Objectives

The original learning scenario served as an inspiration to devise a lesson plan for my sixth-grade pupils, connecting art and the topic of quadrilaterals.

The objectives I envisaged for my pupils were:

To introduce the life and work of Piet Mondrian.
To understand basic geometric shapes and colors through Mondrian’s artworks.
To apply Mondrian’s stylistic elements in mathematical contexts.
To develop creativity and aesthetic sensitivity through combining geometry and colours.

Figure 2: Pupils viewing a presentation on Mondrian’s life and work

First activity

The lesson began with a short presentation on the life of Piet Mondrian. The children were asked to research his life and work on the Europeana website and to use other sites to write down five sentences that really stood out to them.

We then watched two videos, as suggested in the original lesson plan, to deepen our knowledge and then continued our discussion on the link between mathematics and art.

The pupils were given handouts of some of Mondrian’s famous works of art and instructed to work in pairs to write answers to the following questions:

What geometric shapes are present in Mondrian’s works?

The application of which primary colours does Mondrian use?
Is there a balance, symmetry, and rhythm to his compositions?

A short class discussion ensued in which the pupils read their answers. This prepared them for the following activities which were connected to mathematics. By demonstrating how Mondrian’s geometric shapes can be used in mathematical contexts, I hoped to deepen their learning and understanding of quadrilaterals.

Second activity

In groups of four I handed out worksheets with problems involving the area and perimeter of rectangles and squares.

Mondrian’s geometric shapes can serve as an excellent visual tool for understanding and applying math concepts such as area, perimeter, and aspect ratio of rectangles and squares.

Area and extent of a rectangle:

– Using Mondrian’s style, I drew several rectangles of different sizes on the blackboard and asked the pupils to calculate the area and perimeter of each rectangle.

Area and extent of a square:

– I explained that a square is a specific type of rectangle in which all sides are of equal length.

– Using Mondrian’s style again, I showed several squares of different sizes and asked the pupils to calculate the area and perimeter of each square.

Figure 4: Calculating the area and perimeter of quadrilaterals

Calculating aspect ratio:

– With further examples, I explained that the aspect ratio of a rectangle or square represents how many times one side is longer than the other.

– Using examples of Mondrian’s rectangles and squares, I asked the pupils to calculate the aspect ratios for each shape shown.

Through these activities, the children were able to visually understand the concepts of area, perimeter, and aspect ratio of rectangles and squares using Mondrian’s geometric shapes. In addition, these activities encourage creative thinking and connected mathematics with art, which further strengthened their understanding and motivation to learn.

Figure 5: Detailed instruction of the task ahead

Third activity

The next activity involved more calculations of the ratio of rectangle and square side lengths.

The pupils were divided into groups, each group receiving printouts of Mondrian inspired grids, scissors, glue, and a set of colored papers. Their task was to create their own Mondrian-style composition using rectangles and primary colors.

Each group presented their creations and we all discussed how they applied Mondrian’s principles in their works.

Following this creative task, we revisited the concept of fractions and proportions and discussed the importance of fractions and proportions in art and design. Using selected Mondrian artwork I asked the pupils to find fractions within the compositions (e.g., how is the canvas divided; how many shapes are repeated and how many times?).

Fourth activity

Having delved deeper in our discussion of the proportions of different shapes and colours used by Mondrian, the pupils were asked to create their own Mondrian-inspired compositions.

They were instructed to identify and label fractions within their compositions (e.g., 1/4 of the canvas is blue) and encouraged to experiment with proportions by varying the sizes and placements of shapes and colours. They thoroughly enjoyed the chance to express their creativity and self-expression while incorporating fractions and proportions into their art. I invited the pupils to share their artworks with the class.

Those that wished to share their work were encouraged to do us with an explanation of how they incorporated fractions and proportions into their compositions. A class discussion on the relationship between mathematics and art, focusing on the use of fractions and proportions in both disciplines was a great end to the activity.

Assessment

Worksheet: Exploring fractions and proportions through Mondrian’s compositions.

The pupils were given a handout and asked the following:

Answer the following questions based on your understanding of the lesson about fractions, proportions, and Piet Mondrian’s compositions.

1. Define what a fraction is and provide an example.
b. Explain why understanding proportions is important in both mathematics and art.
2. a. Describe the geometric shapes commonly used by Piet Mondrian in his artworks.
b. How does Mondrian utilize fractions within his compositions?
3. a. Imagine you’re creating a Mondrian-inspired artwork. How would you divide the canvas into equal parts using fractions?
b. If you have a canvas divided into four equal sections, how would you allocate the colours red, blue, yellow, and white to represent proportions.
4. a. With your artwork, label the fractions of the canvas occupied by each colour.
b. Explain the thought process behind your composition. How did you use fractions and proportions to achieve balance and harmony?
5. a. Write down one thing you learned about fractions and proportions from studying Piet Mondrian’s compositions.
b. How do you think understanding fractions and proportions can help you in other areas of your life besides art and mathematics?
6. Optional extra question: Imagine if Mondrian decided to add a new colour to his compositions. How would you use fractions and proportions to incorporate this new colour while maintaining balance in the artwork?

Figure 9: Last three questions of the assessment worksheet

This worksheet is designed to assess pupils’ understanding of fractions, proportions, and their application in art through the study of Piet Mondrian’s compositions.

Outcomes:

By applying this learning scenario, the pupils were able to connect their mathematical knowledge in a new and exciting way.

Outcomes for pupils:

Understand the life and work of Piet Mondrian and recognize his influence on art and design.
Identify basic geometric shapes and primary colours in Mondrian’s works.
Apply geometric concepts (rectangles, squares) to solve mathematical problems.
Develop creativity through creating their own Mondrian-style composition using geometric shapes and primary colours.
Demonstrate the ability to present and communicate their ideas within a group.
Connect art and mathematics and understand how geometric concepts can be applied in creating artistic works.
Understand the concept of fractions and proportions and their relevance in art and mathematics.
Analyze Piet Mondrian’s compositions to identify fractions and proportions.
Apply mathematical concepts creatively to create Mondrian-inspired artworks.
Enhance critical thinking and problem-solving skills through artistic expression.

As an educator this activity enabled me to further my skills on several levels.

It helped me guide my pupils in understanding and applying fractions and proportions in real-world contexts and enabled me to facilitate discussions on art to develop pupils’ visual analysis skills.

Conclusion

Fostering creativity amongst my pupils in order to integrate mathematical concepts into artistic projects while at the same time offering support and feedback to promote their learning and artistic growth was a rewarding experience. Artistic activities encourage exploration, making abstract mathematical concepts tangible and relatable. By merging mathematics and art as I did with this lesson plan, I can create a holistic learning environment, nurturing pupils’ appreciation for both disciplines while enhancing their mathematical proficiency. For all of these reasons, applying the resources available on the Europeana website I can connect my mathematics lessons with other subjects in a unique, multi-disciplinary approach.