NCTM Process Standards: Reasoning and Proof 

Instructional programs from prekindergarten through grade 12 should enable all students to— 

Recognize reasoning and proof as fundamental aspects of mathematics
Make and investigate mathematical conjectures
Develop and evaluate mathematical arguments and proofs
Select and use various types of reasoning and methods of proof
When students are introduced to proof, they prove things that are obvious.
Prove that:  -1*x=-x.
"Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth."
                                                                        -Benjamin Peirce
Introduce students to something 
new
engaging
intuitive

Start with something intuitive & fun
Push students to explain their thinking
Build formal structures separate from introducing new content
Puzzles
Logic
Q.E.D.
Proof is Powerful
An Example:
Try something different.
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But...
Breedeen Murray
breedeen.murray@gmail.com

The Space Between The Numbers
http://betweenthenumbers.wordpress.com/

@btwnthenumbers


“A proof, that is, a mathematical argument, is [like] a work of fiction, a poem. Its goal is to satisfy. A beautiful proof should explain, and it should explain clearly, deeply, and elegantly… 

“There is nothing charming about what passes for proof in geometry class. Students are presented a rigid and dogmatic format in which their so-called “proofs” are to be conducted— a format as unnecessary and inappropriate as insisting that children who wish to plant a garden refer to their flowers by genus and species.”

                            --Paul Lockhart A Mathematician’s Lament

Okay, One More...