Michael Strong asks six-year-old Alana what thinking means and how she solves math problems. She describes thinking as using her brain to consider details, then works through addition, subtraction, and clock faces while Michael prompts her to explain her reasoning.
How are you?
I'm well. Are you in the car driving somewhere?
I'm not driving actually, I'm in parking.
You know, as soon as I said driving, I realized you were probably not the person driving and I should have said riding in a car.
So I'm actually at the beach.
Oh, marvelous, marvelous. So I've been thinking about Thinking. And what does it mean to you to think about things?
To me, thinking about things means like using your brain to think about like details of that thing.
Got it. Do you ever think about things when you're in conversation with your parents?
Sometimes when they told me like questions or maybe just places or that kind of stuff.
What kinds of questions do they ask you?
Sometimes I ask them like math questions. I have to think for the answers for that. And that, that's the kind of questions.
You ask them math questions or they ask you math questions?
They ask me math questions.
I see. And then you have to think through math questions?
Yeah, I have to think of the answer to those questions.
Do they give you easy questions or hard ones or both?
Uh, sometimes both.
What's a hard math question you could answer?
A hard math question is like the lows, like 25 plus 25 or something.
What is 25 plus 25?
I would have to think.
Go ahead, go ahead. I want to see how you think it through.
I would say probably 50 or something.
How did you get 50?
Because 2 2 4, so 20 20 is 40, plus 2 fives more is 50.
That's excellent. That's exactly right. Do you do problems like that in school, or you do not do problems like that in school?
Sometimes.
What's the hardest problem you do in school?
Um, for me, I would probably say, um, that time would be probably the hardest.
What would be?
Time.
And tell me what's hard about time.
Like you have to figure out two hands at different places sometimes.
I see, so like a picture of the clock and a picture of the clock at one time, the picture of clock at another time?
Yeah.
I see, um, I can see where that's hard. Are you doing, um, subtraction at school or just addition?
Sometimes subtraction.
So do you know what 50 minus 49 is?
50 minus 49? No, but I'll have to think about it.
You want to think it? You want to see if you can figure it out?
Wait, what was the question?
50 minus 49.
I'm just gonna guess because I probably— it would probably be this, 39.
You mean 50 minus 49 would be 39. Um, okay, how did you get that?
Um, because so Well, I think I got the wrong answer actually. Can I think about it one more time?
Please, please go ahead.
Yeah, actually 39.
And so tell me how you got 39.
Because, um, so 5 plus 4 is Wait, actually, I need to think that through one more time.
Take your time, take your time.
I'm gonna guess on this one for the, um, answer. I'm just guessing that— I'm just gonna guess 10 because when I did this with my hands and I I did this with 4, I got 1, and it's like 49, so it might be 9.
Okay, I like how you're thinking things through. One way to think about this is if you count numbers. So, could we start counting from say 40? So what's the number after 40?
After 40?
Yep.
51.
You go directly from 40 to 51?
No, 50, sir.
You go from 40 to 50?
Yes, from 40 to 50.
41 and 42 and 43 and 44.
All right, so let's go 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50.
Okay, so when you did it that way, 49 and 50 were right next to each other, weren't they?
Yep.
So if, if 50 is the very next number after 49, could 49 be 10 less than 50?
Maybe.
If— how much? 49 plus what equals 50?
Excuse me?
49 plus what equals 50?
Basically 1.
There you go. So if 49 plus 1 equals 50, what do you think 50 minus 49 is?
1.
That's right. Does that seem strange?
Yeah, but I know that when you subtract, you get almost the same answer as the opposite question.
Well, exactly. So addition and subtraction are opposite operations. That's why 49 1 50, or 50 1 49. Or 50 minus 49 equals 1. Does that make sense? Okay, well, um, can you think of any other kinds of questions your parents ask you that get you to think?
Sometimes addition, sometimes subtraction. So maybe my mom asked me, like, in the— sometimes in like the thousands or hundreds plates, like 2,000 plus 3,000 or something like that.
And you can add those?
Mm-hmm.
What's 2,000 plus 3,000?
What's 2,000 plus 3,000?
Yep.
5,000.
Excellent. Go, Alana! Um, I'm gonna let you go and then talk to your dad for a few minutes, okay?
Okay.
Okay, bye-bye. Bye.
