Geometry and Art
Based on an
original unit by Barbara Lierly and Elaine Sullivan
Scenario: This is a group project. You and your partners are going to be the instructors for the day. Research, design and then teach a lesson that integrates art and geometry. Think about what you've learned about basic geometric figures, congruence, similarity, polygons, and transformations. Research material from a variety of online web resources. Utilize these as a starting point to expand on previously learned geometric concepts. Include the historical background and significance of the art form. Plan a hands on, creative art project that demonstrates the art form. Make your lesson fun, relevant and/or unusual. Devise a lesson for your classmates to create works of art. You will be making new connections between math and art utilizing a hands on approach.
Choose one of the following topics:
The Task:
1. Decide who you would like to work with. Groups should have 4 members. Examine the topics by visiting the various links and see what items might interest you. Place your top three topic choices on a piece of paper in numerical order and give your list to the teacher. The topics will be assigned on a first come first served basis.
2. When you get into your groups, decide which role you would like to take. See the roles below. Share ideas and brainstorm to see who would be the best person for each job.
3. Read the description of your role. With your team members, look at the websites for your topic and think about the questions from your role's perspective.
4. Many of the websites will have lessons and instructions pertaining to your subject. As a group discuss what kind of art lesson you could create. Design the art lesson.
5. Remember, the overriding goal is to relate geometric principles to your art project using proper vocabulary terms related to math. The project is based on a core understanding of the geometry involved. You may want to consult your textbook or some of the other geometry books in class to help in making the connections.
6. Look at the Design Principles for help in creating your art lesson for the class.
7. Design a presentation for the class to teach the art lesson. Make sure the lesson includes all the items described in the task. Each member of your team should have a speaking and/or teaching part in the presentation.
8. Use the student template. Write a lesson plan outline and submit on the Monday prior to your presentation.
9. With your group decide how to present the material required in the task. You may include examples of an artists' work in your presentation. You may teach the entire class or you may divide the class into groups for your art lesson.
Master Imagineer
All throughout history, artists have interpreted innovations in mathematics, science and technology in visual terms. Your role will be to apply geometric principles to a creative artwork. Your job is making the theoretical mathematics into an object of beauty for the rest of the world to see. Keep notes on what worked and what did not work, so you can share these tips when we look at the finished product. Think about the following questions as you proceed and refer to the principles of design. These will give you art vocabulary terminology to describe your work for the artist's statement. And by all means, use your imagination!
1. How can you construct basic shapes like squares, triangles and polygons using art materials?
2. What art materials did you use?
3. How can geometric principles be used to create larger patterns?
4. How can geometry inspire your own original work of art?
5. Can you write an "artist's statement" which relates the geometry to one or more of the principles of design in your work?
6. What expressive qualities, feelings or moods does the artwork display?
Creative Engineer
You are a vital member of the group full of knowledge and skills. You will provide the framework and direction with the facts and figures to quantify your directions. Keep the group grounded in logic and knowledge of geometry so they will investigate the reasoning behind the art objects. You will make us understand how the mathematics functions before the form is created. Groundwork questions are given for you to ponder as the project is being developed.
1. How are geometric principles related to artwork?
2. Which geometric principles are being utilized? Example: Perpendicularity, Parallelism, Similarity, Congruence, or Symmetry.
3. What are the interrelationships between the figures?
4. Why is the vocabulary of geometry important when describing this art? Example: Axis, Rotation, Translation, Arc, Plane?
5. Explain what new math you have learned from your investigations.
Time Traveler
Your task as historian is to look as far back as the Egyptians or Euclid if necessary for inspiration. Did you know that the Egyptians build the pyramids by using a sophisticated system of coordinate geometry? Use your research of the past to enhance our understanding of some of the artwork that was produced on a miniature or monumental scale. Now research your subject and find out why geometry and art are so important to the cultures which produced them. Give us the historical perspective on the artists and mathematicians who have a geometric vision and structure to their work. You are not limited to the past, however. Well into the future artwork will be made using mathematics. Maybe you want to focus on the rationale behind modern, post-modern or post-post modern work. Your group can decide where to travel, but give the context of your insights. Minimalist artwork can be stark, geometric and exciting, too! Think about some of these questions as you proceed.
1. Who were the creators of this mathematics and art?
2. How does the culture of the time affect the development of the geometry and art?
3. What was the significance of deduction and proof in the geometric principles behind the art form?
4. Can we examine the use of this art form today?
5. How can you find examples to show to the class?
Assembly Manager
Now you can quote the words of American inventor Thomas Alva Edison: "Genius is one percent inspiration and ninety-nine percent perspiration." While the gathering, sifting and categorizing is going on, touch base with the others and start to make a package to present to the students in the class. The organization is important, because you want to make an impact that we will all remember. Diversify and make it visual and fun! We want to be educated, informed and intrigued by your work. This is a forum for great display, so go ahead and make us pay attention to your work and let us enjoy the process, too. Think about how you can do these things and answer these questions as well.
1. Can you develop a lesson plan examining the spatial relationships of geometric figures by drawing, transforming or explaining the artwork using geometric principles such as postulates, theorems or proofs?
2. How can you relate the lesson to prior learning in the classroom?
3. Does your lesson include creative elements so students can make an art project on their own using steps clearly outlined?
4. Can you create a rubric so creativity will be encouraged?
5. Are you presenting the proper citations to the class so they may visit websites or access the printed material, photos, or videos if they choose to pursue another project?
Student Rubric
|
CRITERION
|
1
|
2
|
3
|
SCORE
|
| Was the lesson interesting/entertaining? |
The lesson was boring | The lesson was somewhat interesting | I really enjoyed this presentation | |
| Did the group seem organized? |
The group didn't seem to know what they were doing | Most of the time the group was organized | This group really had their lesson well planned | |
| Were the
visual aids/handouts useful? |
There were no visual aids | Some of them were helpful, some were confusing | They were all very helpful and really added to the lesson | |
| Was the art project easy to follow/learn? |
I got completely lost during the art lesson | I got a little lost during the art lesson, but mostly it was well done | The art lesson was very easy to follow and complete | |
| TOTAL SCORE FOR LESSON: |
GROUP GRADING RUBRIC
|
CRITERION
|
1
|
2
|
3
|
SCORE
|
| Were tasks completed on a timely basis? | Rarely completed or handed materials in on time | Almost always completed/handed in material on time | All tasks were completed on time | |
| Was the group organized? Did they have a plan? |
Team had little direction; seemed disorganized | Team was organized most of the time | Team was very well organized | |
| Was the group self-sufficient? | Team needed continual guidance during prep period | Team needed assistance on occasion during the prep period | Team operated almost completely on their own | |
| Did all of the group members Participate? | Only one member participated | Almost all members helped present the lesson | All members participated fully in the presentation | |
| Was the lesson complete? | None of the 3 sub-topics were covered sufficiently | Almost all sub-topics were covered | A very thorough, complete coverage of the sub-topics | |
| Were effective VISUAL AIDS used? | No visual aids used to enhance presentation | More visual aids could have improved the lesson | Visual aids were very well used during the presentation | |
| Was the lesson well-presented? | Both the lesson and the art project were hard to follow | Either the lesson or the art project were hard to follow | The lesson and the art project were easy to follow and well taught | |
| TOTAL SCORE |
TEACHER RUBRIC: Individual Grading
|
CRITERIA
|
1
|
2
|
3
|
SCORE
|
|
On task in the lab
& in the classroom |
Frequently reminded to get back to work | Reminded to focus on work occasionally | Always focused and on task | |
|
Participation within the group |
Frequently let other members do the bulk of the work | On occasion, did not share work load | Participated during entire preparation process | |
|
Attitude
|
Whined and complained most of the time | Complained when group ran into difficulties | Positive attitude during entire prep period | |
|
Attendance/Tardiness
|
Often late, or missed more than one class | Always on time, missed no more then one class | Perfect attendance | |
|
Organization within the
group during prep period |
Rarely came prepared for class/lab session | Usually came prepared for class/lab sessions | Always came prepared for class/lab sessions | |
|
TOTAL SCORE FOR
PREP PERIOD |