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. ReflectionRotation

Molecular Symmetry Are these molecules symmetric? How can we help students visualize the symmetry?

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 methane vitamin C

Molecules Rotate In Space water methane vitamin C

Molecular Symmetry Online

Symmetry Toolkit

Learning Basic Symmetry Finding symmetry elements of a molecule requires students to: 1. Understand the 3D structure of a 2D drawing 2. Understand the effect of rotation, reflection, inversion 3. Find symmetry operations 4. Define the symmetry elements geometrically

Molecular Symmetry Online A Website for teaching and learning molecular symmetry Design Principles: 3D Interactive Visualization Open Content - any molecule can be studied Modularity - can be used at various content levels Applicability - drill and practice, testing, presentations

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

Typical Problem Ammonia Hypothetical structure with 180º rotation axis Is there an axis around which we can rotate the molecule by 180  and obtain an identical structure? If not, how would a structure with such an axis look like?

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!