Background:  The first semester of Geometry focuses on formal two-column and paragraph proofs.  Students tend to struggle understanding the importance and value of doing proofs in a Geometry class.  They aren’t able to answer the question, ‘Why Proofs?’ or make the connection between the logic and deduction required to complete a proof.  This semester, I want students to explore and engage with different types and styles of proofs and to read more about how the mathematics world values proofs, even Einstein!  Also, to see that proofs aren’t just a ‘math thing’, but scientists, historians and others use them to persuade their audience!

Authenticity Lens:  The Framework that I’m choosing for authentic instruction is Authenticity to the Discipline.  This feels relevant for my course since I’m asking students to ‘play the whole game’ at the junior level.  I’m asking students to think and act like mathematicians and critical thinkers when I ask them to complete a proof.  This area of authenticity that I’ve chosen to focus on is exciting since students never seem to understand the value in what they’re doing, or the creativity that’s involved, or that they’re completing a rigorous task that most high school Geometry teachers don’t bother teaching.   It’s really exciting, but I feel I ‘miss the mark’ in getting students to feel that excitement since they don’t understand the ‘why’ or ‘how’ behind proofs.

POP:  How might we allow students to develop their own proof style?

To start the conversation, Nora and I are having students read articles that articulate the excitement and joy behind proofs that will help them understand ‘why proofs’ and to ultimately, develop their own proof style.  Please find the articles here and here.