Screens and Exponents

Last night the 7-year-old asked me what 3^7 equals. Seriously??? How does he even know this math language? Did I try to teach him exponents one day, and now I can’t remember? (That might actually be the case…)

Then he says, “Is it 2,187?”

Hmm. This is strange. I check it on my calculator (thank you, ever-present iPhone), and he’s correct. WHAT?!?! I know my kid is sharp. But exponents? Without paper OR a calculator? After staring at him for a few incredulous moments, I ask the 7-year-old, “How did you know that?”

“TedEd, Mom.”

Oh. Right. He is not a math genius. But he is a curious kid with a sponge-like brain. He watches and absorbs. And almost every morning, I am able to get breakfast on the table and lunches made because I plop both kids in front of the computer in the kitchen to watch YouTube episodes of  TedEd. I tend to like the informational ones about space and science, but the 7-year-old LOVES the puzzles. There is a whole collection of them. And the one called The Infinite Hotel Paradox has about 7 seconds of cartoon video where it says and shows that 3^7 is equal to 2,187 (at minute 3:27 if you want to check.)

Okay. So now I’m feeling like it’s not such a bad thing that I rely on that computer in the morning. The kids are absorbing some interesting things. But here’s the part I really enjoyed as a parent and a math teacher…

I showed the 7-year-old how I used the calculator to check the answer. I started with the basic calculator on my iPhone and demonstrated that 3 x 3 x 3 x 3 x 3 x 3 x 3=2,187.

Then I turned my phone horizontally to access the scientific calculator so I could show him how I solve the same problem with exponent notation. But before I even got to that, he went bonkers over the calculator in scientific mode. So many buttons!! We started playing with the square root button. He typed “3” then hit square root. (It’s the one in the second column, middle row.)

I saw a small number show up as the answer (a little bit less than 2). He saw a very large number show up (because he hasn’t learned about decimal points yet.) I didn’t realize this until we typed “4” then square root and got the relatively simple answer of “2.”

“Wow!” he said, “That is so cool! The first one was a really big number. This one is a really small number.”

I suggested he try the same process with 8 and then 9. Then with 15 and 16. Then with 24 and 25. Each time he first thought he saw a big complicated number, then a small simple number. I tried to explain that actually the seemingly complicated number was not so big. It was in fact very close to the same amount as the small number. I pointed out that there was a difference between having commas in a number versus a period in a number. But he didn’t seem to be listening to me or to be caring very much. He was way too interested in experimenting with the calculator. And that was exactly as it should be.

(Mathematically…if your child understands the concept of multiplication, you could explain that exponents are simply multiplying a number by itself over and over again. But the concept of exponents was not really the point of what I noticed happening in this interaction. First, it is amazing what kids absorb and hold on to. I still remember all the Spanish words I learned watching Sesame Street, and even though I never studied Spanish in school, I still remember those particluar words really well. So, don’t beat yourself up about TV or computer time that incorporates learning. Second, let your kids play with math tools. Hand her a calculator. Watch her explore it. Point things out, but mostly sit back and watch. Finally, I feel the need to be really honest. They only spend half their morning YouTube time on TedEd. The other half is spent watching the Pink Panther. I’ll let you know later what they learn from that…)