Learner Description:

The classroom will consist of twenty students from the Shooting Stars Team and the All Stars Team at MacArthur Middle School.

Overview:

What will be taught?

In this combination mathematics and art elective, students will learn about various tessellation shapes by using computer software. Students will research tessellation artists' and see how they design their work.

How will it be taught?

The first part of exploration includes working with the internet. Each student will look up on the "curriculum links" site to explore all the web sites on the tessellation's page. The students determined that they needed to write down all the words that the student feels would be a method or type of tessellation.

After the internet research for a few days, in the computer lab, a class discussion occurred. There were many math concepts that were listed on the board from the students' research; some topics were related to a tessellation and some topics discovered were not all related to tessellation methods. The students then tried categorizing the similar words into groups and came up with a main topic for each cluster of words. Then the students worked on what the true methods of a tessellation were once the clusters were named.

 This math/art activity will be introduced through student discovery from tessellation samples and software. After the exploration of the computer students will create a list of tessellation types they think are accurate examples of a tessellation. The KWL strategy will guide the process. Examples of tessellation pieces will be given, along with over head examples of tessellation art samples, and the students will have to discover which type of tessellation each piece is according to the list they created from exploration. 

What will the students do and learn?

Students will become familiar with tessellation design through exploration and research. Once students learn the steps of how to create a tessellation, they will have to put that information into use. Students came up with many will design/art projects to create, such as: (2-D and 3-D), such as tessellation kaleidoscopes, key chains, Powerpoint presentations, web sites, and using other unique products. 

Rationale:

Why would you teach this unit?

The purpose of the unit is to create an elective that will incorporate math and art all into one. Most students do not realize that math is related to careers and outside real world applications. This class will allow students to experience the application of a tessellation (mathematics) with real hands-on creations, along with designing their own tessellation by using technology programs and internet sites.

Why would this qualify as an engaged learning unit?

Responsible for learning

Strategic

Energized by learning

Authentic

Challenging

Multidisciplinary

Performance-based

Generative

Seamless and ongoing

Equitable

Interactive

Generative

Collaborative

Knowledge-building

Empathetic

Heterogeneous

Facilitative

Guide

Co-Learner

Explorer

Cognitive Apprentice

Teacher

Producer

Why is technology an important component of this unit?

Technology is a key component in this elective. The internet sites allow the students' to see different a tessellation and tessellation art demonstrated step-by-step. This process will benefit all students, but especially the students that have visual trouble making a tessellation. Tessellation sites emphasize the importance of why a tessellation repeats its pattern (looking like a puzzle fitting together) by using angles and geometry.

Another program that will help students' visualize tessellation's is called Tessellmania. In this program the student choices a shape and the program tessellates the shape; the student will see how the tessellation tessellates. Once the program tessellates the shape, the students choose to design the shape using painting, patterns, and other gadgets available.

Also, Powerpoint and web sites can help other students from the community and other schools in the district to see what a tessellation is all about. Using Powerpoint will allow classes, a fifth grade class that is working on a tessellation unit, to come and view the presentations.

Why is this project authentic/meaningful, and challenging for students?

This elective is challenging and meaningful to students because it extends math concepts into real world application. Escher is an example of how tessellation and art go hand-in-hand. This allows the students to see that creating a tessellation are authentic because of the real world application. For the students to get involved in authenticating this elective, they invited the fifth grade class over to see the display of works that the students' created along with presenting their tessellation presentations and displayed their tessellation projects in the art show. These pieces were judged, but unfortunately no one won an award.

Tessellation's are seen all over, in art galleries and in buildings and mostly in math. A challenging factor in this elective deals with the students' creating a tessellation from different shapes and turning the tessellation into a piece of art work. The students' need to take all the information taught about a tessellation and create their own creation, which could be a quilt, painting/decorating an old piece of furniture, puzzle, 2-D and 3-D projects or others.

Goals: Content, Cognitive and Social:

What new attributes do you expect students to gain?

I expect students to gain knowledge about why the tessellation tessellates according to ninety degree angles, create their own tessellation art piece (2-D and 3-D), and create one tessellation of each type (reflection, glide-reflection, rotation, translation, and symmetrical). 

This knowledge was gained to my surprise by what the students did know in the beginning of the class. The concept of a tessellation is difficult to grasp as to why the shape tessellates. The students came up with the idea that ninety degree angles were in each shape that tessellated. This student discovery allowed the tessellation pieces created to become something that they could understand, by the knowledge gained through class discussion and the research on the internet.

Student Assessment: Enables student and teacher to measure student's attainment of goals.

What are my scoring characteristics? What is the important outcome of this unit?

The most important outcome of this elective is to have students understand the meaning behind the works of a tessellation. Each student should be able to look at a tessellation and determine what shape this art form is steaming from, what angles are in it, what vertices are being used, and what tessellation type is being expressed.

What will indicate that students are novices, practitioners, or experts?

Students gain understanding and knowledge at different levels and at different paces. The student that is a novice will replicate a tessellation once and not explore more. For instance, if the tessellation is a rotation type the student will cut out a piece from the math shape (square, triangle, hexagon, rectangle, and others) and rotate it around a ninety degree vertex once. The novice may experience some bumps in the road and will get frustrated and tend to quite. 

The practitioner would create a rotating tessellation, but repeat the steps to obtain a rotating tessellation until the solution is correct. This type of student will understand the concept, but try to replicate this rotating tessellation until it is perfected; they may use different math shapes and will create those rotating a tessellation to perfection.

The expert not only will create a rotating tessellation but extend that knowledge further. The student will create rotating a tessellation using different types of math shapes. Each math shape will be used, and the student will cut out more than one piece of the tessellation and rotate that piece around a ninety degree vertex (around many vertices). This will lead into and start of how to form these tessellation pieces into some type of animal or piece of art work. The student will make a connection to create a rotating tessellation and will want to excel at this step by turning it into a creature or using different types of papers to decorate their tessellation piece.

How will I measure and communicate student progress on the goals?

This process is an on-going throughout each project. The students work individually to produce their tessellation types and in pairs to compare a tessellation or checking with their partner for accuracy of the piece.

The student does a self check of their tessellation to see if it is an actual, authentic tessellation and then they are ready for a conference with me. I conference with the students to make sure they are on the right track and have performed the correct procedures to create the tessellation types.

 How can the students be involved in establishing goals and criteria for the assessment?

I ask the students where we can go from here, how can we make other projects except for 2-Dementional? What are the next steps in creating more interesting projects using a tessellation? They come up with ideas of 3-D projects, using different types of paper products such as: sran wrap, tin foil, wrapping paper, tissue paper, chairs, boxes, planters, quilts, skateboards, and others.

Once this is established and the students have a few tessellation types mastered or at least recognized, then they move into creating their own way of evaluating themselves. The students came up with a system of grading. I stood at the board and had the students give me attributes that would qualify for a terrific tessellation. Once these ideas were down on the white board, including all the necessary and unnecessary information. The students successfully created the rubric by the knowledge that they have built with researching, exploring, learning and creating different types of a tessellation. The students' felt relieved that they had ownership in the final process of their grade. Each student graded a peer's tessellation project and the grades came out accurate. 

Once the students completed this process, they moved onto bigger and better things. They decided to use Hyperstudio, Powerpoint, and create a web site of a tessellation. My students were engaged and excited to present their Hyperstudio and Powerpoint projects to the fifth grade class.

 How will the assessments be implemented to ensure that they are generative?

These assessments will be ongoing throughout all of the projects for each tessellation type completed. Each student will have an equitable task according to their individual needs. Whatever stage the student is at, novice, practitioner, or expert, the student will gain knowledge and understanding at their level; it depends on what cognitive level they have attained and are willing to achieve in order for a successful tessellation project.  

Authenticating the students' works was done through inviting the fifth graders into the class to see the tessellation Power Point and Hyperstudio presentations. Students displayed their a tessellation in a showcase in the hallway at MacArthur Middle School.

The technology allowed the students to run with their ideas and teach or speak about a tessellation to a younger audience. When the presentations were in the beginning stages, each group of students needed to determine what characteristics were important to explain to an audience. Most students were familiar with the concepts, but had to be prepared for questions from the non-familiar students.

How will the students demonstrate their knowledge and skills?

The students will create a tessellation for each type of tessellation, glide, glide-reflection, rotation, translation, and symmetrical. One 2-D project would consist of using different types of colored paper to create their tessellation to look like a puzzle, others include a 2-D project using more specific papers, designing a tessellation kaleidoscope and tessellation key chain. The culminating activity would be decorating a 3-D object using a tessellation and turning the piece into a tessellation art example. The application of this last tessellation type would incorporate all of the types of a tessellation learned and explored.

A students will provide the next level of synthesizing and creating a higher quality piece of a tessellation. The students will have the knowledge to build on making a presentation or a web site for others to view.

Resources:

What resources will you need to do this unit?

All materials needed: scissors, colored papers, tissue paper, tin foils, markers, colored pencils, 3-D objects, mirrors, computer lab, and I-Books. 

How will the room(s) be arranged?

I arranged my room to have two people for each table for individual tessellation projects. For class discussion and exploration, I put together four tables and we sit around the edges. This works out well for the students to see the examples and feel comfortable to volunteer and this will be less intimidating for the novices. 

The last set-up would include using the overhead to demonstrate some tessellation types for the students to identify. During this set-up each student would be seated at a table, with two per table.

Where will equipment and materials be located to promote maximum use?

I have a drawer with all materials available in the front of the room as well as, each student is responsible for providing their own glue, scissors, pencils, and tape.

How will students with special needs be helped?

The students may sit around my tables and this will be easy access for wheel chairs.

For the special education student, some modifications will be applied and their process of a tessellation type may only go to the novice step. Repetition for these students will help them see what the tessellation is doing and what the student is suppose to create. I would pair up another student that is an expert to aid the novice in providing information that may be helpful in successfully completing the project.

Evaluation:

What was effective?

The most effective piece of this elective was allowing the students to explore and creating a master list on the board about what they thought each tessellation type would be. This allowed the student to find out their own conclusions and take understanding to perform many tessellation types.

In the beginning, the first day, I displayed various a tessellation and asked the students what the definition of a tessellation was by looking at these designs. This worked well for the students to create their own definition and understanding. 

Toward the end of the elective, the students understood the concepts and were able to create technology presentations and web site. In this arrangement, some pros were helping the novices for information that was correct. I didn't have to do anything and if felt strange. Mostly the students were engaged in their choice, and the result of that came with knowledge and understanding of a tessellation.

What wasn't effective?

This elective had twenty-two students with two teachers teaching the class. I feel for the one-on-one attention and learning of this concept, it was hard to do activities with such a large class. If I were to offer this elective next quarter or next year, I would prefer to teach this elective myself with less students.

What will I do differently next time?

I would probably have students begin with their choice of projects instead of telling them what to do, but that is part of the learning process that I went through with the TIP program.