Cutting Edge > Courses > Mineralogy > Teaching Activities > A Fun and Effective Exercise for Understanding Lattices and Space Groups

A Fun and Effective Exercise for Understanding Lattices and Space Groups

Dexter Perkins
,
University of North Dakota
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This activity was selected for the On the Cutting Edge Exemplary Teaching Collection

Resources in this top level collection a) must have scored Exemplary or Very Good in all five review categories, and must also rate as “Exemplary” in at least three of the five categories. The five categories included in the peer review process are

  • Scientific Accuracy
  • Alignment of Learning Goals, Activities, and Assessments
  • Pedagogic Effectiveness
  • Robustness (usability and dependability of all components)
  • Completeness of the ActivitySheet web page

For more information about the peer review process itself, please see http://serc.carleton.edu/NAGTWorkshops/review.html.



This page first made public: May 9, 2008

Summary

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.

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.

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.

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Other Materials

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 sym

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