Triangles abound in our newly released learning module: Classifying Triangles by Systems of Line and/or Angle Properties.
A new school year is well underway for many of us. Classrooms are buzzing with learners, eager to find out the school year has in store for them. And teachers are jumpstarting “norms” for student engagement with and learning in mathematics. Undoubtedly, these norms will shape how students “see” themselves as participants in, contributors to, and successful learners of mathematics.
For me, an important message, or norm I want students to embrace is:
Making sense of mathematics means Creating, Connecting, and Communicating
Too often, students today experience mathematics as a tedious collection knowledge and procedures, and learning as a “get it” or “don’t get it” endeavor. The gap between school mathematics and mathematics as applied and practiced in the real world is often substantial.
On April 8, 1982 while on sabbatical in Washington, Israeli scientist Dan Shechtman observed crystals with five-fold symmetry.
The problem? This was considered impossible.
He was mocked for his discovery and asked to leave his research group. But he stood by his findings despite criticisms, some from none other than Linus Pauling, one of the towering figures of science and the only person to twice receive the Nobel prize unshared; to the day he died, Pauling never accepted Shechtman’s findings.
“The main lesson that I have learned over the years is that a good scientist is a modest and attentive scientist,”
— Dan Shechtman
Both Shechtman and Pauling used Zometool for modeling quasicrystals, as it can be used to model all quasicrystalline shapes.
Paul Hildebrandt says “Marc Pelletier and I glued those balls and painted those struts by hand; quasicrystal researchers were among our very first customers”.
Below, a beautiful x-ray of quasicrystals and some related links:
Wall Street Journal: Chemistry’s Cinderella Story
MSNBC: Vindicated: Ridiculed Israeli scientist wins Nobel
The Official Website of the Nobel Prize: The Nobel Prize in Chemistry 2011 - Dan Shechtman