In this informal Socratic tutoring session, educator Michael Strong engages six‑year‑old Alana in a conversational assessment of her addition skills. The dialogue begins with casual talk about Alana’s recent trip to Las Vegas to support a teammate, then moves into a series of addition problems ranging from simple doubles (10 + 10, 20 + 20) to slightly larger numbers (100 + 100, 500 + 500) and mixed sums (10 + 11, 5 + 6, 6 + 7). Michael uses probing questions to uncover Alana’s reasoning, encouraging her to articulate how she arrives at answers—whether by counting on fingers, mental calculation, or the “one‑more” heuristic (recognizing that adding a number that is one greater yields a result one greater than the known sum). Alana demonstrates growing competence, correctly answering many problems and reflecting on her strategies, while also expressing occasional uncertainty. Michael reinforces the value of both concrete manipulatives (fingers, paper) and mental holding of numbers, praising progress and encouraging continued practice. The session blends instructional scaffolding with supportive rapport, highlighting Alana’s developmental trajectory in basic arithmetic.
Chapters
Hear you.
You can't?
Oh, now I can, now I can. How are you?
Good, how are you?
I'm well. What's been going on these days? Have you been going?
Yeah, going to Vegas and, um, Vegas. Yeah, I went to Vegas last week.
Wow, what did you do in Vegas?
We mostly went there to cheer on for my teammate from my gym. She was at a Tough Enough fight.
Got it, got it. And how did they do?
She did actually pretty good. She just lost.
That's okay, that's completely okay. Um, and How has school been going?
It's been going good.
What you doing in school these days?
Well, I'm mostly doing math, writing in our journals, and playing games in math groups and reading groups.
Marvelous. In math, are you doing addition and subtraction, or have you gotten to multiplication?
Mm, I'm mostly going on adding and subtracting.
What's the biggest numbers you can add together?
I don't really know.
Can you add 10 plus 10?
Yes.
What's that?
20.
All right! You know, a year ago I asked you about something like that and you were not able to do it, so you've definitely learned more math.
Thanks.
How about 20 plus 20?
20 plus 20?
Mm-hmm.
40.
Excellent, you got it. How about 50 plus 50?
50 plus 50?
Mm-hmm.
100.
You really got it. Um, how about 100 plus 100?
200, or I don't know.
Yep, that's exactly right. How about 500 plus 500? 10,000?
No, it's 1,000. Oh, okay.
But you're getting the pattern, you definitely have the pattern. I thought there would be a place where you were not yet familiar, but it sounds like you're getting it. How about more complicated lower numbers? How about something like 11 11?
Uh, I don't really know actually.
Okay. How about 10 plus 11?
Uh, 29. I mean 21.
21, that's exactly right. So if 10 plus 11 is 21, then 11 plus 11— can you figure out what 11 plus 11 is if you know what 10 plus 11 is?
Okay, 11 4 is 31? I don't know.
Okay, so let's go slowly. That's okay, you're doing great. So I want to back up. So you knew what 10 10 was, that was 20, right?
Yeah.
Then you figured out what 10 plus 11 was. What did you say that was?
That was 21.
Yep. So now I'm asking about 11 plus 11, right?
Yeah.
So if 10 plus 11 is 21, um, and we're still adding 11, but instead of adding 10 plus 11, we're adding 11 plus 11. 11 is 10 plus 1, right?
Yeah.
So if 10 plus 1 is— 10 plus 11 is 21, and 11 plus 11 is just like that except now we have a 10— I mean, an 11 rather than 10. How much bigger do you think 11 plus 11 is going to be as compared to 10 plus 11?
Okay, 11. 22.
Go, Alana! What I really like about that is you were reasoning through it. You were figuring it out. Do you know how you figured it out?
Yes, I just counted on my fingers without looking.
I see. Okay, that works. That totally works. So let's, let's, some other numbers. Presumably you know 5 5, right?
Yeah.
What's that?
10.
Okay. Can you do that without your fingers?
Yes.
Okay. How about 6 6? Can you do that without your fingers?
Uh, I don't know actually.
Okay, um, with your fingers, what is 6 6?
Okay, actually I can get them. I can't really get them in order.
So you're not sure what 6 6 is?
I'm not surely true.
Okay, that's okay. So 5 5 is 10, correct?
Yes.
So suppose we add, instead of 5 5, we say 5 6. What do you think that should be?
Okay, 5 6 might be 11.
That's exactly right. And did you figure that out using your fingers or using your Head, brain, or both?
Uh, my brain.
You did. How did you figure out that 5 plus 6 would be 11 if 5 plus 5 is 10?
It's because if 5 is 5 and 6 is adding 1 more, I figured out it would be 11.
That's exactly right. So what one of the tricks I'm trying to help you figure out is the adding 1 more thing. Because if you can figure out you just add one more, then it's pretty easy to get the answer, right? You think you could use the— as long as we're just making one number, one of the two numbers, one bigger, then the answer should be just one bigger. Does that sound right?
Yes.
So 5 5 is 10, but 5 6 is 11 because it's one bigger. One of the two numbers is one bigger.
Right? Yes.
So now I'm going to go from 5 6 11 to 6 6. Which should it be?
Okay. 6 6? 12.
Yes, that's exactly right. And did you figure that one out using your fingers or your brain or both?
Uh, probably both.
Okay, but do you see how that's another example of one more? 5 plus 6 is 11, and 6 plus 6, one of the two numbers is one more. We went from 11 to 12, right?
Yes.
Um, how about I give you another one more? How about what is 6 plus 7?
6 plus 7. 7, 2, 3, 13.
That's right. And did you figure that one out using your brain or your fingers or both?
Uh, probably both.
Okay, did you see that's another one more? That 6 6 is 12 1 is 13.
Yes.
So part of this is one of the tricky things about doing the one more thing is you have to hold the numbers in your brain. Is it hard to hold numbers in your brain?
Not too hard, but sometimes I get a little mixed up.
Yeah, that's why sometimes fingers can help or writing on paper. Do you like to do math when you write it down on paper?
Yes, I do.
Because what that does is sometimes we all get confused when we hold numbers in our brains. And sometimes it's a little bit hard to figure out, but if you put it on paper, it's easier. And I would say it's useful to be able to hold numbers in your brain when you can. Do you think it's— you can get better at holding numbers in your brain?
I think I can get better.
No, I bet as you get older, you'll get much better at it. Um, and then sometimes we all forget too, but it's, it's I like to think about, does it seem weird to say we hold numbers in our brain?
Uh, not too weird.
Okay, so yeah, 10 plus 10 is, I mean, is 20. I'm gonna go back and then 10 plus 10 is 20, and 10 plus 11 is what?
10 plus 11, 21.
There you go. And how about 11 plus 11?
11 plus 11, maybe 22? I forget.
And you sort of said it. What did you say?
I said 22, but I didn't.
No, that's exactly right. Did you— were you kind of holding numbers in your brain when you figured that out?
Kind of, but I forgot that one, so I just said what that I thought it was.
Okay, okay. Well, I don't want to spend too much time, but I thought it'd be interesting to think about math and to think about how you can use your fingers and you can use your brain. And when you use your brain, you've got to hold numbers in your brain, which is sometimes hard. Would you say so?
Yeah, sometimes it's hard.
But I bet you'll get better and better and better at holding numbers in your brain, and then you can then you can add them together in your brain without your fingers. Does that seem useful?
Yes.
Okay, well, I'm so glad you went to Las Vegas to support your friend, and I hope you have a wonderful day and a wonderful week. Okay?
