Paragraph proofs

photo credit: http://aardvarkmath.blogspot.com

Being an unexpected math teacher, I learned to teach Geometry from the textbook. This meant subjecting students to the horror that is 2 column proofs. For those of you who blocked proofs from your high school memory, a proof is a logical argument that explains why something is true. This year we only write paragraph proofs, and I will never go back. Yes, my population is nearly half current or reclassified English Language Learners. Yes, a disturbing number of my students come to me scoring basic or below on state tests in mathematics. Yes, I have a fair share of mainstreamed special education students in the mix as well. So, why does it work?

Language is the most powerful tool we give out students. Being able to express yourself is empowering and fulfilling. So much of mathematics is mystical and inaccessible to students. A labyrinth of patterns and algorithms, memorizations of tricks and processes to get the one right answer.  Student lose interest in mathematics not because they don't want to know, but because they tire of not having the language to know what to ask or how to ask it. The mathematics classroom rarely honors what students know if the knowledge is partial. Paragraph proofs help change that. Mathematicians write paragraph proofs. If we want to empower our students to be successful in math, we need to empower them with the language skills that enable them to be successful mathematicians.

I always cringe working with two column proofs because so much is dependent on putting the correct pieces in the correct place. This approach requires the student to have a clear vision of the solution and a precise articulation of that vision. My students live in a math fog perpetuated by years of mediocre mathematics instruction. It is unfair for me to ask them to perform a high level task they haven't been prepared for. Paragraph proofs allow them to tell me what they know. It says "hey, it's ok you don't remember the theorem. It's great you remembered what the theorem tells us, and you deserve credit for that understanding". Here are the biggest changes I have seen in my classroom as a result of teaching paragraph proofs:

1). Hardly any students leave a problem blank.
2). Students are more willing to collaborate in groups to practice writing.
3). Students are more reflective on their work and even REVISE to improve arguments.
4). Students come up with crazy creative ways of thinking about the problem outside of the axiom model.

Most of all, students LIKE proofs. For the first time, many of these students feel comfortable writing about math. Yes, they still complain, because writing about math is hard, but they are open to the process because paragraph proofs give them a voice in the math classroom. This is the first year students have told me they enjoy writing proofs. Nothing in the world of geometry could make me happier! Now to figure out how to transition to proofs in google docs ;)