Geometry found in art

By Anne Marie Burdick

As I walked around the Museum of Geometric and MADI Art of Dallas it was more than evident that geometry can be found in artwork. Even if a first time visitor of the museum did not know what MADI art was, they could make a good guess based on the museum’s name. MADI Art is the study of movement, abstraction, dimension, and invention. MADI art consists of colorful shapes that are three-dimensional and two-dimensional. For example, the photo to the left is a colorful three-dimensional piece of artwork made out of wood. The artwork in this museum comes from around the world and consists of sculptures, wooden canvases, paintings, and quilts. Geometry does not need to be left in the school classroom; places like the Museum of Geometric and MADI Art confirm geometry can be found in a variety of locations and provide teachers with different ways to integrate art into their geometry curriculum.

Based on my own research prior to my visit to the museum, I found out that geometry and art were key components of many civilizations. For example, in Southern Africa women used to create quilts, murals, and pottery with geometric designs on them. These pieces of artwork demonstrated symmetry, tessellations, and transformations, all of which are geometry-based concepts. A literary resource for students is the book Women, Art and Geometry in Southern Africa by Paulus Gerdes. This book is a great resource for students to see a historical point of view and how math and geometry are used outside of school.

An activity that teachers could have their students complete in the classroom is It’s Friezing in Here: Tessellations through Art, Architecture, and Cultural Artifacts by, Lynda Colgan. This activity has students create their own four-cell tile. Students are given the opportunity to practice translation, reflection, glide reflection, and tessellations. This activity also allows students to learn why certain culture’s artwork uses particular shapes and designs based on their beliefs.

A second and more interactive activity that the teacher could complete is to have his or her class take a field trip to the Museum of Geometric and MADI Art. At this museum they offer workshops for students. Each workshop is designed and based off of age appropriate curriculum and instruction. Students would be able to create their own pieces of artwork using shapes, color, and space. Not only would students have the opportunity to create their own pieces of artwork, but they will also have the opportunity to tour the museum. This field trip could spark a new interest for a student and could inspire his or her future career.

By integrating art and geometry, students will get the opportunity to see the importance of a core subject. When teachers link math with other subjects they are allowing students to find areas of math they can relate to. The Museum of Geometric and MADI Art proves that geometry is used outside of the classroom. By giving students these resources, we are setting them up to be the next enthusiasts of mathematics, and more specifically geometry. 

Geometry and Art

By Megan Hancock

Imagine you are a student in a high school Geometry class.  Which scenario sounds more appealing?

1. Your teacher gives notes about different geometric concepts and sometimes shows examples of how to use these concepts outside of the classroom. 
2. You go on a field trip to a geometric art museum and learn about different geometric concepts through studying art.

Most students would choose scenario 2. As teachers, we want our students to see the importance of their high school mathematics courses.  By stepping out of the classroom, students experience the richness of mathematics in the real world, and this allows them to begin to understand the value of mathematics.   

I recently visited The Museum of Geometric and MADI Art in Dallas.  MADI stands for movement, abstraction, dimension, and invention. This museum is filled with bright colored art that is made solely out of geometric shapes.  Much of the artwork in this museum spills off the traditional canvas.  Artwork comes from around the world, and students can also display their own geometric art.  

 

In high school Geometry, students learn about geometric transformations, tessellations, and three-dimensional shapes.  All of these topics are present in most of the artwork found in this museum.  The museum offers workshops and classes for students of all ages to learn about the relationship between geometry and art.  They can create their own three-dimensional artwork inspired by the artwork in the museum.   By incorporating artwork in a Geometry class, I believe students will have a deeper understanding of geometric concepts.  

For centuries, different cultures have been integrating different aspects of Geometry into their artwork.  This artwork could consist of quilts, designs on clothing, sculptures, paintings, or photography.  In the American colonies, women used quilting as a social gathering.  They would use these quits as their artistic expression.  African American women were even able to purchase their freedom from slavery with their beautiful, handmade quilts (Zaslavsky, 1996, p. 145).  Shapes, symmetry, rotation, measurement, tessellations, and reflections are all geometric concepts that are present in quilts.   

When studying tessellations in high school Geometry, students can discover which shapes will tessellate and which will not. The National Council of Teachers of Mathematics (NCTM) created the lesson, “What’s Regular About Tessellations?”, that guides students through the discovery of why certain shapes will not tessellate.  This lesson is geared towards a middle school mathematics classroom, but it could easily be tweaked to fit in a geometry course.  After students understand what makes shapes tessellate, they can create their own pieces of artwork using tessellations.  If the students have already visited The Museum of Geometric and MADI Art, they can use the artwork to inspire their own pieces. 

 Students can also use tangrams in a high school Geometry classroom.  Students probably played with tangrams when they were little, so they would be familiar with them.  Tangrams are interesting because the area will always be the same, but the perimeter will change depending on what shape is created.  Students might assume that the area and perimeter will always be the same if the same shapes are being utilized, but they can discover this is not the case.  A larger unit or lesson could be created around this concept in a high school classrooms, and tangrams could be one of the tools that is provided.  

Retrieved from http://www.teacherwebshelf.com

By incorporating art in a high school geometry classroom, students are able to understand how the concepts they learn in class are used outside of the classroom.  Students who are interested in art but not mathematics are given an opportunity to use their talents when creating their own pieces of art. As a math teacher, I am always on the lookout for examples of mathematics in the real world.  High school students struggle to see how mathematics relates to their lives outside of the classroom, so by taking students to museums such as The Museum of Geometric and MADI Art, they are able to make connections between mathematics and art.   

Blasjo, V. (2009).  Two applications of art to geometry.  The Montana Mathematics Enthusiast, 6(3), 297 – 304. 

Zaslavsky, C. (1996).  Multicultural math classroom: Bringing in the world.  Portsmouth, N.H.: Heinemann.  

Geometry in the Dallas Skyline

By Anne Marie Burdick

Photo 1

As I gazed out at the Dallas skyline, I saw a variety of different shapes among the structures. Right before my eyes I was experiencing how geometry was used in everyday life. These geometric structures are what house the thousands of workers that commute into the city everyday to help make the city flourish. People drive daily under a giant parabola that supports the Margaret Hunt Hill Bridge; people eat in a giant sphere that sits above the city; and people sit in giant rectangular prism office buildings. I am now imagining myself sitting in an actual geometry class where my classmates and I dread math and we eagerly anticipate the bell ringing. There is a worksheet in front of me with different 3D shapes and I am not actively engaged. Which above scenario would you rather experience?

Photo 2

If Dallas educators took the time to have students simply look out their windows, they would have the opportunity to see how geometry has created the city they live in. If the skyline is not in site there are thousands of photos on the internet and I guarantee there are plenty of other structures right in the backyard that demonstrate how geometry is used in architecture.  After students have had the opportunity to connect and relate to what they are learning, they will hopefully be more motivated and excited to learn. Here are the stops I made during my tour of Dallas's buildings. I first started out at the American Airlines Center because of the huge arc on the front of the building. I used this structure in my third photo. I then moved to downtown and went to the Renaissance Tower because I liked how the building's windows had symmetric patterns on them. This building is my second photo. I then went to Reunion Tower which is a giant sphere above ground. This structure is in my first photo. Then I stopped by the glass Pyramid on Fairmont. Lastly, I went to Fountain Place. All of these structures were different geometric shapes that could be used in geometry. They all had very unique features and it was easy to see the geometry used in the architecture.

Photo 3

Here is an example of how Dallas geometry teachers could implement architecture and geometry into the classroom. I am going to use the American Airlines Center in this example and connect this structure to an activity that I found online that measures archways. This activity was published in The Mathematics Teacher Journal provided by the National Council of Teachers of Mathematics.  “An Archway Formula” on page 324 is an activity that allows students to discover how to find the radius of the circular archway if they are given the height from the base to the top of the arch and the width of the doorway. Students are able to find their answers by applying the Pythagorean theorem. They could take this activity even further and calculate the radius of an archway in their very own homes!

Retrieved from:
 http://www.jstor.org.proxy.libraries.smu.edu
/stable/pdf/10.5951/mathteacher.108.5.0324.pdf
?acceptTC=true&jpdConfirm=true

Another place where you can find geometry in architecture is at the Guilin Garden in Shanghai. This link gives a mini-lesson where students have to look at different wall panels from the garden and answer questions that go along with it. The questions ask about geometric concepts such as tessellation, symmetry, rotational symmetry, and polygons.

By incorporating real world applications into learning, teachers are giving students reasons for why they should believe math is valuable. Students will be able to walk around in their cities and appreciate the math behind the buildings that tower over them. By incorporating architecture with geometry students are getting concrete examples of where they can use the new content they are learning.

Reader Reflections

The Mathematics Teacher, Vol. 108, No. 5 (December 2014/January 2015), pp. 324-327

Front Matter

The Mathematics Teacher, Vol. 106, No. 7 (March 2013), pp. 481-483

Blog 3 & 4 Prompts - Geometry

Your audience for both of these blogs is a teacher of your grade level who uses traditional instructional approaches to teach geometry concepts. Your blog should discuss how by integrating geometry with a real world topic (CSI, nature, art, astronomy, architecture), learning geometry can be made more engaging, and students can gain a deeper understanding of geometric principles. You want to encourage these teachers to think outside the box and make new connections.

If you need more structure, you can follow this format (but you don't have to!):

Begin by framing your argument for the blog and letting the reader know what your central purpose is and what they can expect to learn from reading your blog. You can also put in a bit of personal experience here if relevant.

Next, give an overview of what you experienced on your field day, with relevant pictures, and how it relates to teaching geometry at your grade level. Provide hyperlinks to the website of any field sites you visited.

Next, discuss some of the background research you did for your PowerPoint presentation that your reader might be interested in, to get some more ideas about how geometry might be integrated with your topic area. Provide links to the resources you gathered.

Finally, give 2 short examples of classroom activities for your grade level that integrate your topic area with geometry. If they are not original activities designed by you, provide the reader with links where they can find those activities and more like them.

Close by reiterating your main argument, and repeating your central purpose in a memorable and convincing way.

RME 2015 Research-to-Practice Conference

By Megan Hancock

Imagine a freshly baked chocolate cake. Now imagine the individual ingredients before they were mixed together and baked.  Would you rather eat a freshly baked cake or the individual ingredients? Most people would prefer to eat the freshly baked cake!  Without the TEKS Mathematical Process Standards, mathematics instruction is just like the individual ingredients for the cake.  The individual activities can stand alone, but when the activities are integrated with the process standards, mathematics becomes much more rich and enjoyable.  The TEKS mathematical process standards can be difficult to implement, but the presenters at the fourth annual Research-to-Practice Conference hosted by the Research in Mathematics Education (RME) Department at Southern Methodist University (SMU) provided attendees with examples and resources to facilitate their implementation.  

The TEKS Mathematical Process Standards describe ways that students should be interacting with mathematics. When the process standards are integrated with mathematics instruction, students are able to problem solve, discuss their mathematical thinking, apply mathematics to real world concepts, and analyze mathematical relationships.  I connected the process standards to a high school mathematics lesson that I displayed during the poster presentation.  “Double Stuffed” was an activity geared towards the first unit in an AP Statistics. I found the lesson on Statistics Education Web (STEW) and modified it to incorporate the TEKS Mathematical Process Standards.  Students are presented with the task of determining whether double stuffed Oreos really do have double the stuffing of single stuffed Oreos.  This was an open ended task, so students were welcome to use whatever methods they saw fit to answer this question.  Students used multiple representations to communicate their mathematical thinking and multiple strategies to solve this problem.   This lesson could also be used throughout the entire year to weave other statistical knowledge and skills together around one task.  

Teachers often struggle with ways to create authentic mathematics tasks that integrate the process standards, but there are many resources available to teachers to help incorporate the standards.  NextLesson provides teachers with real-world problem solving activities that are personalized to students’ interests.  Each activity has multiple different versions so students are able to learn the same concepts while working on a problem that interests them.  Spark 101 Mathematics provides 10-minute video case studies related to science, technology, engineering, or mathematics.  These videos provide teachers with the beginning to a lesson that incorporates real world mathematical topics.

Each presenter at the RME Research-to-Practice conference discussed different mathematics activities that effectively implemented the process standards.  Dr. Candace Walkington, an assistant professor at SMU, discussed personalizing students’ mathematical tasks.  According to Walkington, Sherman, and Howell (2014), “personalized learning can help students meet the Common Core Standards by allowing them to reason abstractly while contextualizing and decontextualizing mathematical ideas and to model situations with mathematics and by providing support for making sense of problems and persevering.” This statement also holds true for the TEKS Mathematical Process Standards.  Personalization goes hand-in-hand with the process standards.  Students will better interact with mathematics if they feel it has an importance in their lives.  

The TEKS Mathematical Process Standards turn mathematics instruction from independent activities to rich, real world activities.  Attending mathematical conferences allows teachers to learn about current research, best practices, and helpful resources.  Teachers are also able to converse with other teachers from different schools and districts to learn what works best in their classes.  The RME 2015 Research-to-Practice Conference did just that.  When standards change, teachers often struggle with adopting new practices to best implement the new standards.  The discussions at the RME Conference provided teachers with ideas for implementation of the TEKS Mathematical Process Standards. 

According to Cherrstrom (2012), “graduate students and professionals who attend conferences have the potential to enjoy and benefit from making a variety of connections” (p. 148).  Attending mathematical conferences allows teachers to learn about current research, best practices, and helpful resources.  Teachers are also able to converse with other teachers from different schools and districts to learn what works best in their classes.  The RME 2015 Research-to-Practice Conference did just that.  When standards change, teachers often struggle with adopting new practices to best implement the new standards.  The discussions at the RME Conference provided teachers with ideas for implementation of the TEKS Mathematical Process Standards.

Walkington, C., Sherman, M., & Howell, E. (2014).  Personalized learning in algebra. The Mathematics Teacher, 108(4), p. 272-279.