A Fun and Effective Exercise for Understanding Lattices and Space Groups
Dexter Perkins
, University of North Dakota
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This activity is part of the On the Cutting Edge Exemplary Teaching Activities collection
HideSummary
This activity uses figures from Francois Brisse as Esher drawings to teach students about 2-dimensional symmetry, especially involving translation.
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Context
Audience
This activity is designed for an undergraduate required course in mineralogy and is generally for sophomore or junior level students.
Skills and concepts that students must have mastered
Students should have a basic understanding of crystal symmetry, including translational periodicity and space groups.
How the activity is situated in the course
This activity is a stand-alone exercise, but is part of a larger volume of classroom and laboratory activities from "Teaching Mineralogy," a workbook published by the Mineralogical Society of America, Brady, J., Mogk, D. W., and Perkins, D., (editors), 1997,406 pp.
I allow students to spend two class periods on this project and follow with a one hour discussion and wrap-up session.
I allow students to spend two class periods on this project and follow with a one hour discussion and wrap-up session.
Goals
Content/concepts goals for this activity
This activity is designed to help students to understand crystal symmetry in 2- and 3-dimensions using drawings similar to Escher drawings.
Higher order thinking skills goals for this activity
Other skills goals for this activity
This activity should aid in a student's ability to work in groups.
Description of the activity/assignment
This activity uses figures from Francois Brisse as Esher drawings to teach students about 2-dimensional symmetry, especially involving translation.
This exercise is based on discovery learning. Students need little introduction to lattices and space groups. They can figure things out for themselves. For example, they will figure out what a glide plane is, and if you tell them ahead of time it takes away from the learning experience. The last question, which asks them to make their own symmetrical drawings, is difficult but often leads to some spectacular results.
This exercise is based on discovery learning. Students need little introduction to lattices and space groups. They can figure things out for themselves. For example, they will figure out what a glide plane is, and if you tell them ahead of time it takes away from the learning experience. The last question, which asks them to make their own symmetrical drawings, is difficult but often leads to some spectacular results.
Determining whether students have met the goals
Students have met the goals of this activity if they thoroughly and accurately answer the problems embedded within the activity and if they are able to discuss the activity during the wrap-up session.
More information about assessment tools and techniques.Teaching materials and tips
Other Materials
- Assignment description, hand outs, and instructor's notes. (Microsoft Word 18MB Nov12 08)
- Assignment description, hand outs, and instructor's notes. (Acrobat (PDF) 239kB Nov12 08)
Supporting references/URLs
Buseck, P.R., 1996, Escher patterns and crystal defects: Proceedings of the Teaching Mineralogy Workshop, Smith College, June 1996, p. 44-64.
Brisse, F., 1981, La symé
Brisse, F., 1981, La symé