Inbal Tuvi-Arad
Department of Natural Sciences, and The Chais Research
Center for the Integration of Technology in Education, The
Open University of Israel
Learning with Visualizations

Symmetry Is All Around Us
 In life
 In Art
 In Chemistry

Introducing Symmetry
 Are these objects symmetric?
 How do we know that?

A Short Definition
 Symmetry is defined in terms of elements and operations.
 Element – an axis, a plane, a point.
 Operation – rotation, reflection, inversion.
 An operation is symmetric if the resulting object is identical to the original one.

How Do We Know?
 We rotate or reflect the object in our mind.
Rotation Reflection

Molecular Symmetry
 Are these molecules symmetric?
 How can we help students visualize the symmetry?
O H H O
H
H
O water
H
C
H
H methane
H
H O
O
O vitamin C
O H

Visualization Of Hidden Parts
 Present molecules in 3D
 Allow students to rotate structures on screen
 Present symmetry elements on screen
 Allow students to draw their own elements

Molecules Are 3D Objects water vitamin C methane

Molecules Rotate In Space water methane vitamin C

Molecular Symmetry Online
Molecular Symmetry Online

Symmetry Toolkit http://telem.openu.ac.il/symmetry

Students ’ Quotes
 “Before I couldn’t see anything. Now I do.”
 “I no longer need to imagine the structure in my mind.”
 “I can see the symmetry element in my mind, but I’d rather use the toolkit to draw it and check if I’m right.”

Molecules Are Dynamic
 How much symmetry is lost due to vibration?
 How can we visualize it?

Continuous Symmetry
Perfect symmetry is rare:
 Molecules are dynamic entities
 Both physical conditions and chemical environments creates structural distortions
 Minor substitutions creates major changes in the symmetry of a molecule

Continuous Symmetry
 The Continuous Symmetry Measure determines the distance of a given structure from perfect symmetry.
 It can be used to compare between various distorted structures.
 Symmetry becomes a continuous property of matter.

Visualization Of Hidden Parts
 Present molecules in 3D
 Allow students to rotate the structure
 Calculate symmetry measures in the background
 Present original and resulting molecules interactively

CoSyM Website http://telem.openu.ac.il/symmetry/csm

Typical Problem
 Is there an axis around which we can rotate the molecule by 180
 and obtain an identical structure?
 If not, how would a
Ammonia

Teachers ’ Quotes
 " When I teach about molecular structure I describe only rigid structures, I never imagined how molecules move."
 "I felt a big difference… the visualization opened my eyes."
 "Now I am going to look at molecules in a different way. There is no sharp distinction between symmetry and no symmetry - there are a lot of levels in the middle."

Summary
 Online Symmetry tools help students visualize the hidden process of solving problems.
 Visualization of molecular symmetry, and continuous symmetry contribute to deeper understanding of molecular structure.
 Website tools can be used at various content levels and for various teaching and learning purposes.
 Exposing teachers to advanced scientific content can improve the way they teach more basic topics.

With Appreciation To:
 Colleagues:
 Dr. Paul Gorsky – The Open University of Israel
 Dr. Ron Blonder – The Weizmann Institute of Science
 Molecular Symmetry Online Team:
 Dov Garmise, Vered Tooby-Fishberg, Zeev Perl
 CoSyM website Team:
 Open University team: Dr. Dina Yogev-Einot, Dov Garmise,
Uri Shefi, Roy Sharoni, Itai Har-Even, Nadav Peer, Zeev
Perl
 Hebrew University team: Prof. David Avnir, Dr. Mark
Pinsky, Dr. Alexander Sterkin, Shadi Laham, Chaim Dryzon

Thank You!