Using Projects

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Assigning the Project

Some issues to consider related to projects:

Group work or individual effort? We assign some of our projects as a group project and others are meant to be individual endeavors. This choice may influence some of the answer to the other questions listed below.

How much credit do the students receive? What part of the grade should come from these projects? Should it count as much as an exam? Less? More?

Will the material covered on the project still be part of the exam? This will depend on the type of project. Can a project be given in place of an exam?

Getting students started We have used different techniques to get students started. We can let students do prelimina work in class. We can have students turn in a project proposal so we can give some feedback. We can have students turn in some roughdrafts before they move to the final stages of their work. It 's also possible to turn the project into a portfolio so that they could keep working on their project.

Grading Rubrics We often have a (sometimes vague) grading rubric in mind when we asssign the project. Do we hand out - or otherwise make available - this rubric to our students?

Grading Issues

Grading art vs grading mathematics How do you grade a tessellation? Can we really penalize students for a lack of artistic ability in a math class?

Grading Rubrics As mentioned above, we have developed grading rubrics to help us assign partial credit:escherwiki:Tessellation Art Project Grading Rubric Developed by Bryan Clair. If the paper is the main focus of the project we need to use another grading rubric (not online at this point)

One of our colleagues has used a grading method for homework, where students can re-submit their work to receive higher grades is they can improve their work. We have never tried this with the projects.

The grading in the courses is something we still at times experimant with:

Clair 2008: Homework: 20%; Attendance and in-class work: 20%; Projects: two @15% each; Exams: three @10% each

Bart 2007: One exam – 20%; Tessellation Project – 10%; Basilica Cathedral Fieldtrip - 10%; Flatland and the fourth dimension project - 7%; Saint Louis Museum Fieldtrip - 8%; Homework and in-class work – 20%; Final – 25%

Bart 2004: Two exams – 20% each; One Project – 10%; Homework, and in-class work – 20%; Final – 5% for paper about math and art, and 25% for the in-class final

Some Examples

We do not always give the same assignments every semester and the particular of the assignment may also differ from instructor to instructor. Below are some example of projects we have asssigned in the past. There have been other projects but the projects below are those that have been used most often.

The Tessellation Project with a focus on experimentation

The write-up of this project can be found here: escherwiki:Tessellation Art Project. The objective of this project is to have the students explore the different techniques we developed in class to make tessellations. Creating tessellations based on respectively translations, rotations and reflections and experimenting with combination techniques is a great way to check if they really understood the concepts.

The students are expected to create 10-12 tessellations with varying techniques. They pick out their favorite tessellation and create a nice finished product. This involves inking and coloring the tessellation and making the tessellation on quality paper and of a sufficiently large size.

They are also asked to write a short paper (up to 2 pages) explaining what the symemtry group for their tessellation is and how they constructed it.

The Tessellation Project with a focus on the written report

In this alternative version of the tessellation project we ask the students to create one interesting tessellation. It needs to have more than just translational symmetries. The students are also asked to write a 10-15 page paper explaining the thoery of tessellations. They should use their tessellation as the running example of the concepts throughout the paper, and they have to identify what the wallpaper group for their tessellation is.

The Non-Euclidean Geometry Project

After we cover spherical and hyperbolic geometry we sometimes assign a project escherwiki:Non-Euclidean Geometry Project We usually leave the choice of geometry the students wish to explore up to them. The way we have it set up now, the project consists of two parts: a project and a paper.

For spherical geometry the suggestions include:

Make a spherical tessellation.
Take one of Escher's spherical Tessellations and modify it.
Write a poem/short story involving Spherical Geometry.

For hyperbolic geometry the suggestions include:

Make an interesting hyperbolic tessellation (more intricate than basic triangles).
Take a simple hyperbolic tessellation and turn it into an Escher like tessellation by decorating it.
Take one of Escher's hyperbolic tessellations and modify it.
Write a poem or short story involving Hyperbolic geometry.

In the (short) paper they should write about either sperical or hyperbolic geometry. They can get a lot of the information across by comparing and contrasting the geometry to Euclidean geometry.

The 4-D Project

We have in the past assigned a project after reading Flatland. escherwiki:Flatland and the Fourth Dimension. This project checks both if they really read Flatland and if they understand the 4th dimension.

Year-end General Art Project

In the past we have assigned a project near the end of the semester. This is a general art poject. Students are asked to create an artwork. This can mean pretty much anything: painting, sculpture, music, short story...

The art should incorporate mathematics. This can mean pretty much anything. This course has covered: