Tessellations
Motivation
The “hook” to draw students into this assignment will be a subtitled video of an interview with M.C. Escher followed by a slide show of his tessellations.
The “hook” to draw students into this assignment will be a subtitled video of an interview with M.C. Escher followed by a slide show of his tessellations.
Instructional Objectives
After looking at and analyzing a variety of mathematically based/derived artwork and learning about several artists who used mathematical principles to create art, students will work in small groups to create an artwork based upon a mathematical principle or formula.
Product— Students will make sketches first and will be challenged to think about how they will select a medium/media and use art elements such as line, shape and/or pattern to make an artwork derived from or based upon what they have learned in mathematics.
Key Concept—Students will demonstrate their understanding of how a mathematical principle can generate art.
New York State Learning Standards for the Arts
Standard Three—Responding to and Analyzing Works of Art
Students will view tessellations from a variety of sources including Islamic mosaics, honeycomb and quilts. They will analyze and discuss the tessellations of M.C. Escher.
Students will analyze and discuss The Lightening Field and sculptures created by Walter de Maria and compare his work to the work of Chuck Close.
Students will view, analyze and discuss tensegrity sculptures created by Kenneth Snelson. They will see how artists used mathematical principles to generate art that is playful and thought provoking.
Indicators
This will be evident from class discussion, when students express an understanding of the history and use of the concept of tessellations and of M.C. Escher’s creative exploitation of geometry.
This will be evident from class discussion, when students compare Walter de Maria’s Lightening Field to his Bed of Nails and discuss his use of intervals and the grid. It will be further evident when students can compare the apparently dissimilar work of Walter de Maria and Chuck Close, expressing a realization that both artists used the grid to create their work.
It will be evident when students comment on Kenneth Snelson’s tension-based sculptures and experiment with the concept of tansegrity.
Standard Four—Understanding the Cultural Contribution of the Arts
Students will see how artists have made mathematical concepts concrete so that we can not only understand the concepts, we can interact with them, enjoy them, and we are challenged to make discoveries of our own. Students will see that artists are creative thinkers who challenge us all to experience things in new ways. Numerous examples will inspire students to use mathematics to derive a sculpture or two-dimensional artwork.
Standard One—Creating, Performing and Participating in the Arts
Students will work in small groups of four to brainstorm and then to create a work of art based upon a mathematical principle.
Indicators
This will be evident when students brainstorm on task and sketch to communicate and work out solutions. It will be further evident when students work together to generate an artwork from a mathematical principle or concept.
Standard Two—Knowing and Using Art Materials and Resources
Students will work together to identify and select appropriate materials to realize their idea.
Indicators
This will be evident when students select a medium/media that can make an abstract idea concrete. The successful projects will use knowledge of art supplies gained over the course of the school year and may also employ everyday items in unexpected ways.
During a critique, students will explain the mathematical principle or formula that governed their creation and how they employed their knowledge of “tools” available to visual artists to make an abstract concept visual and concrete.
Materials
This lesson will take place later in the school year and requires students to select media appropriate to their chosen subject. The following materials will be available: glue; watercolors and watercolor paper; pencils; erasers; sketch paper; cardboard; rulers; protractors; string; hole punches; and scissors. The lesson also requires a projector to show a PowerPoint presentation and Internet access with the ability to project.
Strategies
Lecture/presentations, giving students examples, use of media, class discussion, using higher level thinking skills, hands-on activity, and displaying and critiquing student work
Developmental Procedures
Activity:
Students will watch a very short video of an interview with M.C. Escher.
Key Questions:
Were you surprised to learn about M.C. Escher as a student? Why or Why not?
Activities:
Students will see a PowerPoint selection of tessellations from a wide variety of sources, both historical and contemporary. They will then see the tessellations of M.C. Escher.
Activities:
Students will view works by Walter de Maria, including The Lightening Field and Bed of Nails. Then, students will view a selection of portraits by artist Chuck Close.
After looking at and analyzing a variety of mathematically based/derived artwork and learning about several artists who used mathematical principles to create art, students will work in small groups to create an artwork based upon a mathematical principle or formula.
Product— Students will make sketches first and will be challenged to think about how they will select a medium/media and use art elements such as line, shape and/or pattern to make an artwork derived from or based upon what they have learned in mathematics.
Key Concept—Students will demonstrate their understanding of how a mathematical principle can generate art.
New York State Learning Standards for the Arts
Standard Three—Responding to and Analyzing Works of Art
Students will view tessellations from a variety of sources including Islamic mosaics, honeycomb and quilts. They will analyze and discuss the tessellations of M.C. Escher.
Students will analyze and discuss The Lightening Field and sculptures created by Walter de Maria and compare his work to the work of Chuck Close.
Students will view, analyze and discuss tensegrity sculptures created by Kenneth Snelson. They will see how artists used mathematical principles to generate art that is playful and thought provoking.
Indicators
This will be evident from class discussion, when students express an understanding of the history and use of the concept of tessellations and of M.C. Escher’s creative exploitation of geometry.
This will be evident from class discussion, when students compare Walter de Maria’s Lightening Field to his Bed of Nails and discuss his use of intervals and the grid. It will be further evident when students can compare the apparently dissimilar work of Walter de Maria and Chuck Close, expressing a realization that both artists used the grid to create their work.
It will be evident when students comment on Kenneth Snelson’s tension-based sculptures and experiment with the concept of tansegrity.
Standard Four—Understanding the Cultural Contribution of the Arts
Students will see how artists have made mathematical concepts concrete so that we can not only understand the concepts, we can interact with them, enjoy them, and we are challenged to make discoveries of our own. Students will see that artists are creative thinkers who challenge us all to experience things in new ways. Numerous examples will inspire students to use mathematics to derive a sculpture or two-dimensional artwork.
Standard One—Creating, Performing and Participating in the Arts
Students will work in small groups of four to brainstorm and then to create a work of art based upon a mathematical principle.
Indicators
This will be evident when students brainstorm on task and sketch to communicate and work out solutions. It will be further evident when students work together to generate an artwork from a mathematical principle or concept.
Standard Two—Knowing and Using Art Materials and Resources
Students will work together to identify and select appropriate materials to realize their idea.
Indicators
This will be evident when students select a medium/media that can make an abstract idea concrete. The successful projects will use knowledge of art supplies gained over the course of the school year and may also employ everyday items in unexpected ways.
During a critique, students will explain the mathematical principle or formula that governed their creation and how they employed their knowledge of “tools” available to visual artists to make an abstract concept visual and concrete.
Materials
This lesson will take place later in the school year and requires students to select media appropriate to their chosen subject. The following materials will be available: glue; watercolors and watercolor paper; pencils; erasers; sketch paper; cardboard; rulers; protractors; string; hole punches; and scissors. The lesson also requires a projector to show a PowerPoint presentation and Internet access with the ability to project.
Strategies
Lecture/presentations, giving students examples, use of media, class discussion, using higher level thinking skills, hands-on activity, and displaying and critiquing student work
Developmental Procedures
Activity:
Students will watch a very short video of an interview with M.C. Escher.
Key Questions:
Were you surprised to learn about M.C. Escher as a student? Why or Why not?
Activities:
Students will see a PowerPoint selection of tessellations from a wide variety of sources, both historical and contemporary. They will then see the tessellations of M.C. Escher.
Activities:
Students will view works by Walter de Maria, including The Lightening Field and Bed of Nails. Then, students will view a selection of portraits by artist Chuck Close.
The grid
Key Questions:
Compare the work of Walter de Maria that we just saw to the portraits by Chuck Close. What do these artworks share in common?
If an artwork is generated by a mathematical principle, that is if it is a product of a prescribed method, does that diminish its meaning?
Activity:
Students will view sculptures by the sculptor Kenneth Snelson. They will see how he used tension and the triangle to create seemingly impossible forms in space.
Compare the work of Walter de Maria that we just saw to the portraits by Chuck Close. What do these artworks share in common?
If an artwork is generated by a mathematical principle, that is if it is a product of a prescribed method, does that diminish its meaning?
Activity:
Students will view sculptures by the sculptor Kenneth Snelson. They will see how he used tension and the triangle to create seemingly impossible forms in space.
Floating Compression/Tansegrity
Key Question:
Do you see how Kenneth Snelson discovered a mathematical principle and then pushed it as far as he could?
Would you say the same of all the artists whose work we saw today?
Activity:
I will tell students: "All of the artists we have seen became fascinated with a mathematical principle and 'ran with it.' I want you to work in small groups (I will assign the groups.) and identify a mathematical principle that you could use to generate art.
Activities:
As the artworks progress, students will walk around the room and see the work of their peers. We will discuss successful aspects of the projects.
When the projects have been completed, we will critique each one. At that time, students will explain how their piece derived from a mathematical concept. Each group will explain its choice of medium/media.
Assessment:
References, Resources and Further Interest:
http://www.diaart.org/sites/page/56/1375
http://www.nytimes.com/2013/07/27/arts/design/walter-de-maria-artist-on-grand-scale-dies-at-77.html?pagewanted=all&_r=0
http://www.mathacademy.com/pr/minitext/escher/
http://www.mcescher.com/
http://gallery.bridgesmathart.org/
http://www.sciencenews.org/view/generic/id/40017/description/When_art_and_math_collide
http://www.youtube.com/watch?v=212XC1zfxXY (how to make a tessellation)
http://www.kennethsnelson.net/icons/struc.htm
http://www.georgehart.com/virtual-polyhedra/straw-tensegrity.html
Do you see how Kenneth Snelson discovered a mathematical principle and then pushed it as far as he could?
Would you say the same of all the artists whose work we saw today?
Activity:
I will tell students: "All of the artists we have seen became fascinated with a mathematical principle and 'ran with it.' I want you to work in small groups (I will assign the groups.) and identify a mathematical principle that you could use to generate art.
Activities:
As the artworks progress, students will walk around the room and see the work of their peers. We will discuss successful aspects of the projects.
When the projects have been completed, we will critique each one. At that time, students will explain how their piece derived from a mathematical concept. Each group will explain its choice of medium/media.
Assessment:
- Students will identify a mathematical concept that can be expressed visually and can generate a two or three-dimensional work of art.
- Students will select a medium or media to make the mathematical concept concrete.
- Students will create a two-dimensional or three-dimensional artwork based upon a mathematical principle or formula.
- Students will explain how their artwork derived from a mathematical principle.
References, Resources and Further Interest:
http://www.diaart.org/sites/page/56/1375
http://www.nytimes.com/2013/07/27/arts/design/walter-de-maria-artist-on-grand-scale-dies-at-77.html?pagewanted=all&_r=0
http://www.mathacademy.com/pr/minitext/escher/
http://www.mcescher.com/
http://gallery.bridgesmathart.org/
http://www.sciencenews.org/view/generic/id/40017/description/When_art_and_math_collide
http://www.youtube.com/watch?v=212XC1zfxXY (how to make a tessellation)
http://www.kennethsnelson.net/icons/struc.htm
http://www.georgehart.com/virtual-polyhedra/straw-tensegrity.html
Click below to read a letter written by Kenneth Snelson. The letter could initiate a discussion and/or project about intellectual property. How and why do we protect ideas? What is the difference between a patent and copyrights?