Tuesday, August 16, 2016

Tinkering for Teaching Geometry Proofs

   We begin preparation for Geometry Proofs long before the unit officially starts: in our Algebra class. Justifying steps while solving equations with an appropriate property,  helps build the idea of "every step has a legitimate reason to be done, and is done with purpose".
   In the first weeks of Geometry class we zero in on definitions and the use of their structure ("if..., then..."). This helps identifying "the cause and effect" for following actions, and, essentially, for statements and reasons we will be using in proofs.
   Every lesson, for weeks before the Proofs Unit, I pepper my students with short jeopardy-style questions: " "Segment bisector" implies.....", ""Midpoint" implies...". Every day we use ProofBits, like the ones on the photo below to help students see regularity and structure used in the process. The same questions 
are also given in the form of symbols or/and diagrams. This allows students to appreciate the structure of definitions, their importance and meaningfulness of symbols and diagrams in geometry.
  These little daily recall exercises ease student's transition to formal proofs. I personally find the process of writing them beautiful and mentally satisfying, and I hope my kids see the beauty and satisfaction in it, once the stress of trying to remember steps is gone.
This photo "gives it all out": I've been using my "proof-bits" for quite a while, and my magnets started to loose color and shape. It was definitely the time for an update! Thank goodness for a long summer vacation: I learned how to use my gadgets, and made a new set.
It is now bigger and more unified, which means it will be easier for students to see/recognize and work with the bits. It is also a full collection of vocab, postulates and theorem one would need in class.  To make it more functional, I laminated them (matte finish) and glued them o to a magnet sheet. This is very easily done, since the template is made to fit the 8.5"x5.5" sticky address labels. The size of each Bit is about 8"x2", so they are very easy to see from any point in the classroom. 

You may see the preview of the ProofBits HERE.