Course:Minicourse MAA 2012

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Many institutions have liberal arts courses in mathematics. Creating a mathematics course that satisfies the math requirement and at the same time shows students how mathematics plays a role in other disciplines is both a challenge and very rewarding. Artwork by artists such as Escher, Picasso and Dali is a very useful tool in the classroom when exploring such topics as symmetry, isometries, non-Euclidean geometry, and many other topics.

The mini-course will start by walking the participant through a number of examples and activities that demonstrate how art is used to motivate mathematical concepts, that demonstrate how to write successful group explorations for the classroom, and discuss different grading rubrics and techniques. The main source of the examples will come from this Escherwiki.

For example, in Euclidean geometry we will look at the topic of symmetry. On our Escherwiki there are seven explorations, which range from very basic exercises that explore the basic concepts to explorations showing applications in real life. The Symmetry of Stars and Polygons Exploration is fairly straightforward and asks students to actively draw and discuss lines of symmetry. The Symmetry, Escher and Architecture Exploration on the other hand was devised to show examples where different forms of symmetry were used to create visually appealing architectural elements. We will discuss these examples, look at how the explorations are written, what the students are expected to do in each case, and we will discuss possible grading rubrics.

The symmetry explorations are important when we move on to Wallpaper Patterns. There are many examples of explorations related to wallpaper groups and tessellations and as in symmetry we will look at some carefully selected examples and discuss what we expect from the students and how student work is graded.

Testing students can take different forms at this point. We have assigned Art projects, done field trips and given more straightforward exams. We will discuss how we would assign relative weight to these assignments: is a project worth as much than an exam for instance? When assigning a project, do we focus on active learning by having students create many different tessellations using different techniques, or do we assign an art project where the majority of the points are earned in a reflective paper? How does one grade a project? Examples of specific assignments with their grading rubrics will be provided to facilitate the discussion.

The rest of the workshop will alternate between discussions of topics of interest to the participants and giving them time to create teaching materials on their own or in groups. Topics will depend on the interest of the participants but will likely range from writing and grading projects, incorporating fieldtrips, to teaching more advanced topics such as non-Euclidean geometry. The following is a tentative outline of activities.

Part A. 1:00-3:00 p.m. Thursday, Salons HI, Marriott Hotel

  • Introductions (ca. 10-15 minutes) – We will have everyone give their name, institution, typical class size, and typical courses taught.
  • Euclidean Geometry (ca. 30 minutes) – We will discuss topics in Euclidean geometry we teach, such as symmetry, isometries, and wallpaper groups. We will looks at examples of these concepts from the art world, and ways to teach these concepts.
  • Creating an exploration (ca. 10 minutes) – How do we create/write an exploration? Look at examples.
  • Adapting and / or creating a tessellation activity (Estimated time 25 minutes) – Participants will either adapt an existing exploration for their own classroom or write their own.
  • Projects, Fieldtrips and Exams (ca. 15 minutes) – We will discuss how to evaluate students. Projects, fieldtrips and straightforward exams can all be used to test student knowledge. We will discuss possible ways to test students, and how many points we might assign.
  • Grading (ca. 20 minutes) – We will discuss possible grading rubrics for assignments.
  • First session wrap-up (ca. 10 minutes) – Ask for topics that people want to see in the second session.

Part B. 1:00-3:00 p.m. Saturday, Salons HI, Marriott Hotel

  • Non-Euclidean Geometry (ca. 30 minutes) – We will discuss how to use works by Escher to help illustrate spherical geometry and hyperbolic geometry, we will look at online applets such as Spherical easel and Non-Euclid, and discuss how to teach these topics to freshmen.
  • Creating an exploration (ca. 20 minutes)– We will spend time creating explorations. The topics will depend on the interests of the participants.
  • Discussion and suggestions for explorations (ca. 30 minutes) - We will share some of the explorations created in small groups and help improve the assignments if needed.
  • Math Appreciation- fractals, 4th dimension, etc (ca. 15 minutes) - A short discussion of additional topics.
  • Wrap up and evaluations - (ca. 20 minutes)