Ones, Tens, Hundreds, Problems?
My niece is in grade 1, and she is adept at adding single digits. With little hesitation she can do her basic addition. She even showed me that she could do things like add 100 + 100. I thought this was really neat so I asked her some questions.
Me: What’s 1+1?
Niece: That’s easy it’s two.
Me: What’s 100+100?
Niece: It’s 200 duh!
Me: What’s 1000 + 1000?
Niece: 2,000 these are easy!
Me: What’s 10 + 10?
Niece: … I don’t know.
She has not learned place value, and therefore her ability to reason this was not developed. I tried to walk her through it. I got her to draw dots, but miscounting the dots led to incorrect answers. I tried having her write out the answers to see a pattern.
1 + 1 = 2
10 + 10 = ?
100 + 100 = 200
1000 + 1000 = 2000
She found the process confusing. I did not know what to do. I’ve never taught math to someone this young. This was just some fun we were having, and then I felt that her confusion might result in a math phobia that would predominate the rest of her life (I may be a bit overdramatic, but I was worried). We decided to take a break from math for the moment, and worry about that problem later, but I find myself still thinking (months past) about that moment.
Language and Thought
I remember in my intro to psychology class where we talked about what came first the ability to think or the ability to talk. Can we share thought or elaborate our thought without language? How does language affect our ability to think? Can we even think without language? Are we limited in thought by the language that we are given?
My niece gave a curious example for me to ponder upon. She was able to reason, with ease, how to add hundreds and thousands together, even though she has little understanding of place value. My hypothesis is that she can do this because the language of hundreds and thousands still uses our single digit counting; she is simply counting a unit that happens to be named hundred. One plus one equals two, one apple plus one apple equals two apples, one hundred plus one hundred equals two hundred. For my niece hundred was just another quantity that we can add together. Ten, however, did not have the single digit number in front of it. We do not call ten one-ten, or twenty two-ten, and she was thus unable to reason it in any way. Why is that? Why do the tens have this magical new way of naming numbers? Every other number that does not require a ten type number, uses single digits (i.e. 1,000,000 - one million; 100,000 - one-hundred thousand; 1,000,000,000 - one billion). Is this a fault in our language of mathematics, or just another hurdle that we must overcome? Is this language deficiency making our sense of place value more difficult to grasp?
I don’t know, but it’s interesting to ponder...