Week 2: Connecting the Dots

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Billy's 3rd grade class is moving on to multiplication; meanwhile, Billy is still counting basic sums on his fingers. This has obviously been a nightmare for him, and it makes him feel stupid in class when others can answer basic multiplication questions but he can not. Multiplication requires a facility with basic, single-digit sums that Billy currently lacks, so until he is comfortable with addition, multiplication will always be out of reach. 

To help him catch up, I have created some flashcards that we use to repeatedly drill everything from 0 + 1 =1 to 10 + 10 = 20. I am hoping that, as we progress day-by-day, week-by-week, Billy will start to recognize helpful patterns that will aid him in committing these sums to memory.

He's already noticed some patterns involving sums with the number 1, and sums with the number 0. When we first started last week, he would recite the problem, hold up some fingers, and wiggle them awkwardly before coming up with the answer to a simple problem like 1 + 5. Today, I showed  him 1 + 5, and with fingers at bay, he responded almost instantly with "SIX!".

"How did you get that so fast?"

"I dunno."

"What's one plus six?"

"Seven."

"What's one plus nine?"

"Ten."

"What's one plus four?"

"Five."

"What's one plus any number?"

"Uhh......I just count one more number..?"

"Right! Exactly!" 

It was a proud moment for me. Even if he couldn't articulate the pattern, I knew that he was getting a sense for it. It manifests itself as a connection between two neurons uniting two separate regions of the brain guarding what seem to be two seemingly disparate ideas; dots collide, giving off random sparks that, every so often, grow to illuminate the world in a whole new way.

Once he knew it implicitly, we worked on creating an explicit, more formal definition. We call it the "Rule of One", and it states that any number plus one is equal to the next number.