Identifying Symmetry in 2-D Drawings

Dexter Perkins

University of North Dakota

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Initial Publication Date: April 2, 2015 | Reviewed: August 4, 2022 (see revision history: 2 events)

Summary

These three activities are problem sets that make students think about symmetry in 2-D. They all involve identifying symmetry from drawings. I purposely omitted jargony words/phrases such as lattice, unit cell, point group, etc. so the students can concentrate only on identifying the symmetry present.

Crystallography | College Lower (13-14), College Upper (15-16)

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Context

Audience

These were developed for an undergraduate mineralogy class.

Skills and concepts that students must have mastered

Students only need a brief introduction to symmetry operators before doing these exercises. In fact, doing these exercises is a good way for them to learn about and comprehend symmetry. In many ways, the less explained beforehand, the more valuable the exercises.

How the activity is situated in the course

I use these as in-class group activities and also to assess student understanding of symmetry. I sometimes take them apart and use individual question on exams or quizzes. They see these exercises as an introduction to symmetry and symmetry operators and operations.

Goals

Content/concepts goals for this activity

The goal is for students to be able to identify symmetry in 2-D drawings. The exercises include lattice symmetry, point symmetry, and space symmetry (except glide planes and screw axes). If they can complete these exercises, they can identify all three -- even though they may not know what a lattice is, or what a point group is, etc.

Higher order thinking skills goals for this activity

Identifying symmetry is a higher order challenge and can be quite difficult for some students. It involves pattern recognition, spatial reasoning and other skills that can only be developed with practice.

Other skills goals for this activity

These exercises have value when done by individual students. However the value is increased by an order of magnitude if, after they do them individually, they redo them in groups of 3 or 4 students. I think the group work is essential.

Description of the activity/assignment

Students only learn to identify symmetry by practice. These activities provide that practice. Besides learning to identify symmetry, these activities will get them thinking about how symmetry operations may combine. After completing these exercises successfully, students will be ready to hear about lattices, about point symmetry and point groups, and about space symmetry and space groups.

Determining whether students have met the goals

One of the three activities is a symmetry quiz -- although it can be used as an in-class activity instead. More important, is to assess student learning during class discussion after they complete these exercises. Good discussion easily reveals whether students have met the learning objectives.

More information about assessment tools and techniques.