What's the largest number you can represent with 3 digits? Nope. It's not 999.
This post is about my fight against "Standardized Testing" in math, and what later became "Common Core." It goes back to 2008 when my daughter was in grade school. I got a call to come to the principal's office. I was surprised, as this was a real first. Like all fathers I suppose, we tend to think of our little girls as angelic and saintlike. In my case, this was the absolute truth.
"Your daughter was being disruptive in class."
It was like an arrow through my heart. I looked over at her. There were tear-streaked marks all down her face. She looked down at her shoes when I shot a glance over at her. And she started sobbing again. The principal continued his monotone diatribe, while I walked over to kneel besides my daughter and hug her.
"Really, Mr. Trice, that's not appropriate..."
I continued to ignore him. "Are you OK?" I asked her. She looked up, nodded her head, and sniffled.
"Tell me what happened" was all I said as I tried not to stare through the principal's skull with my X-ray vision superpower.
"Your daughter tried to correct her math teacher. The teacher explained why she was wrong, and she insisted that she was correct."
I knew she was right and the teacher was wrong. I couldn't wait to hear this one.
"What was the question?" I asked as the principal was about to interject a rebuke to my outburst.
The teacher was also present, and he spoke up. "The question was, what was the largest number that can be represented with 3 digits. I said it was 999, your daughter disagreed."
I remember thinking "Uh-oh. What the heck was she thinking?"
That's when she spoke up, anger in her voice, "Oh yeah? Tell me what 9 raised to the 9th power raised to the 9th power is then??"
Holy crap! She was right! Technically, the problem is not asking for the largest 3-digit number, which is exactly where my mind went upon hearing the question. The question is asking you to represent a number using 3 digits, so exponentiation cannot be ruled out.
I looked over at her and smiled and said "Way to go! You're 100% correct!" And I gave her a high-five. She smiled. Then cried some tears of joys as she laughed. She knew I had her back.
Edit: Please stop posting 9^99 is larger than 9^9^9 in the comments. That's not correct. You are confusing 9^9 with 9 squared.
9^9 = 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 = 387,420,489
9^9^9 = 9^387,420,489 which is way bigger than 9^99.
"Well? What do you say now?" I asked them both as I rose.
"That is not the correct answer," the principal insisted.
"The hell it isn't!" I said.
"We have not covered exponents yet," explained the teacher.
And so it went. For 30 minutes I gave them hell. I asked for a compromise. My daughter was not to be marked wrong, due to the ambiguous nature of the question, and I won't insist that the rest of the class be marked wrong, because they did not learn exponents yet.
"You don't understand," the principal said, "This is a standardized, nationwide test. We don't have the power to change her grade."
I then asked them to factor into account her "real grade" if it was marked correct when it came time for them to compute her report card grade. Again, they declined. That got me angry.
You see, for 5 years straight, my daughter has had the same grade in math: 100%. She scored 100 on every test she ever took. Seriously. She has a unique mind. It was 4 years later that I was called by a math teacher again. This time it was for geometry. The teacher was going over how triangles added up to 180 degrees, always, no matter what. My daughter thought about this for a few minutes as the lesson went on, and she raised her hand. "I know how to make a triangle add up to 270 degrees."
And she did. All she had to do was stare at the globe in the corner of the classroom. When the teacher said it was "impossible" to have a triangle add up to 270 degrees, she corrected him with an incredible example. If you draw a triangle on globe, each angle being 90 degrees, you can connect the north pole to the equator, the equator line can go 90 degrees around the globe perpendicular to the first one, then then north pole can drop a 90 degree line to meet this line at the equator to complete the triangle. Triangles on curves can have more, or less, than 180 degrees, depending on convexity or concavity of the surfaces.
In the second instance the teacher called to congratulate me on raising such a brilliant little girl. Back to the first instance...
My real fight began when I got home. I looked up the formal procedure to request a third party review for a dispute over a national test question. It was laborious. I met with the superintendent of schools, who called the principal, who brought the math teacher to another meeting, this one at the state capital.
Their faces were no longer smug and arrogant when I walked into the room. In fact, I sensed fear. Real fear. They looked white as ghosts.
The tone was civil. The teacher began with a 2 minute prepared speech about how brilliant my daughter is, and then the inevitable conjunction showed up: "...but..."
The superintendent nodded.
"Mr. Trice, the only way I can give your daughter credit for that one answer," (and he really put emphasis on one) "is to go to the national board of education and have everyone who took this test have their answers marked incorrect."
Amazingly, he thought that would make me want to back down.
"OK. Do it."
The three of them were mid-stance, not yet fully risen from their seats, and they froze.
"Beg pardon?" asked the superintendent.
"I said, do it. As in, make it happen. As in, execute that course of action."
They sat back down. The next hour involved them trying to persuade me against it. Finally, they started the concessions. My daughter would be given a score of 100 instead of 99, but the others would not be penalized. After all, this was two months later, etc. etc. etc.
"No. I gave you that option already and it was declined. I want every exam in the country marked incorrect that has 999 as the correct answer."
It took an attorney and another 3 months, but I got the result. My daughter scored the only 100 on the exam that year for her grade, not just in her class, but in the country.
I didn't care what it cost. I didn't care how much effort it took. I didn't care that an entire federal department was given tens of thousands of hours of work in addition to the demands placed on it.
I cared that an individual who had the ability to shape my daughter's future mind made her cry when she was right and he was wrong and he knew it. This could have been handled so much better by the overlords.
Forget about it being my daughter for a second. The truly sad thing is, look how a unique mind was mistreated for being brilliant. How many times does something parallel to this happen in our once great country? How many teachers squelch out the faint cry of genius from some shy personality sitting in the back of a classroom?
My daughter is now a sophomore in college, carrying a 3.82 in Biology with a leaning towards pre-med. I fought hard for her, and continue to do so. I remind her all of the time about a great quote from Samuel Clemens, aka Mark Twain.
"I never let schooling interfere with my education."
Don't let common core stand in the way of your own children's education.