Proof of Joy

The tutoring period had already started. There were four students in the room who were already busy working collaboratively on exercise problems I have assigned to them.

I was erasing the doodlings Berenice and Leslie did on the dry-erase board during advisory period earlier when Danny came in. He was panting.

"Sir, I do not know how to do proofs, and I want you to help me." There was urgency in his voice.

I handed him the list of exercises we used in class earlier. "Choose any one that you think you could or want to do, and do it on the board."

"Okay."

As Danny copied his chosen problem on the board, he read aloud every word and symbol. He also said out loud what he was thinking about the problem.

"For my first step, I'm gonna write in the first given which is..."

He took a few steps away from the board, knelt on one leg, wrapped his left arm around his chest, and touched his chin with his right hand.

I took a quick check on the four students. Kari had a grin on her face. She had been watching Danny since he came in.

"You always say that it is a good thing to write the last step and just fill in the middle steps afterwards." He mumbled.

"Okay, I think the second step is..." He started writing again.

"Is it right, Mr. Jope?"

"No." I said. But before I had the chance to explain myself, he erased what he just wrote.

"No? Then it must be this... I must be right this time."

"Yes, you are."

He continued on his own while still talking to himself aloud. Occasionally, I made comments on what I was hearing.

"I'm done. Sir, did I do it right?

While I took a moment to review the two-column proof he had written on the board, I could tell he was intently studying my face for any trace of approval.

When I said yes, the young man threw his arms up, his face glowed like the neon orange shirt he was wearing.

"Oh, my God! I can do proofs now!"

I asked him to do two more problems, which he happily solved with minimal errors.

That afternoon, Kari and I had complimentary front row seats to the most entertaining geometric proof presentation we both have ever witnessed!

Daniel's joyful feet and Kari's beguiled face: priceless!