Alana on self-paced math learning

How are you?

Good, how are you?

I'm well. Um, do you have any tournaments today?

Not today. I know there was one, but we ended up not doing it, um, because I think we'll definitely be busy with tournaments next month and the following months.

Got it. Well, that's good. And then what are you most excited about learning these days?

Well, these days, I think the most— the part I look forward to the most, probably my class in STEM, just because I love what we're doing and I love all the fun we're having just together as a class and learning. I also love my classmates and my teacher.

Wonderful. Tell me what you're doing.

Well, usually we go over some physics on Brilliant. I think that's great because doing it with the class, well, one, it's really engaging and also, and also I just need to learn more in general. And then we do spend a healthy amount of time doing math. Um, on our own and with other people, um, asking, um, our classmates and my teacher for help if needed. What's— what I think is cool about it is that there are a lot of the different students in my class are in different grade levels. So I'm on 7th grade right now. There's a kid in my class who's on 8th grade. There's probably other people in 8th grade, 7th grade, maybe 6th grade. I'm not sure. So it's really fun. I help out a few other people. They help out me. So I think we have a good balance overall.

Wonderful. How far through 7th grade math are you?

I started a bit recently after I transferred from 6th to 7th. I'd say maybe a third of the way or of the textbook, and then I can always linger and then do and then make sure I understand everything.

And are you on Mathspace or Khan Academy?

I'm on Mathspace. I did— I used Khan Academy when I wasn't in STEM. I was just in humanities and I liked it a lot, but I'm just— I'm trying out Mathspace here.

And do you find that you rely on guides or tutors for explanations or peers for explanations, or you usually figure it out on your own? Or use the software? How do you figure things out when you get stuck?

Um, I think most of the time when I get stuck, I use the software, and then if that becomes unhelpful, then I turn to one of my classmates or Erin, my teacher.

Got it. Um, and are there any patterns as to when the software does not do a good job of providing explanations, or No kind of— I'm curious to know how it is to be learning math in a self-paced program like this. So I'm wondering, and, you know, so wondering, is it like 80% of the time the software does it, or are there certain kinds of problems the software is fine, or is it learning new concepts? Can you make any generalizations as to whether, when, and where you need to ask for help beyond the software?

Yeah, I think Most of the times when I ask for help is when I think I'm doing it right, and then I find out I'm doing it wrong. So I ask the software, the AI they call it, for a hint. Usually that hint reverses or changes my view on the problem, and I end up doing it right. There's also a case where I use the hint button a lot of times, and it just doesn't click for me. So that's usually when I have to go to my guide or to my classmates.

And so when you say it doesn't click for you, you mean the explanation they provide doesn't quite make sense to you?

Yeah.

Okay. It's not like the click doesn't work. It's, you know, it could have been— you could have meant that the software didn't work because you clicked on it, didn't work, but you mean it, the explanation didn't make sense, correct?

Yes.

Um, so some things make sense on their own, other things, um, and they call it an AI bot that kind of provides an explanation.

Um, they call it an AI bot, but I think, um, it might, I think it has some components of AI and maybe some hardcoded questions that it pulls from, but either way it's helpful.

Got it. And can you re— if you don't like, if the AI's or the bot's first response is not adequate, can you sometimes ask it additional questions to get better answers?

I can.

And is that usually successful or for some reason there are just certain kinds of things that we need a human to understand?

I think I think a lot of the times when I ask again, gives me maybe an easier hint, but not always an easier hint, maybe just one that's easier to understand.

Got it. Um, no, that makes sense. And then, so I'm very interested in, with, with when learning math, in my experience, some things are just kind of tiny variations on problem you already know how to do, and other things are new concepts. And I would expect you need more explanation when you run into new concepts. Is that accurate?

Yeah, when I run into new concepts, I do need a little more explanation. Sometimes it helps that the new concepts are sort of linked with ones I've done in the past. So it's not always like, whoa, I don't know how to do it. But yeah, I'd say so.

Got it. And then, um, I don't remember 7th grade math curricula well enough to know, but what are some of the new concepts you've had to learn for 7th grade math so far?

Well, I've been working recently with positive and negative integers. I never really did that before, so it's a little confusing, but I think I'm kind of getting the hang of it.

Got it. So had you heard, even heard of negative numbers before, or not at all?

I have.

So I'm very interested to know, because negative, if, if you'd heard of negative numbers, you probably had a vague understanding of them. But then when you're solving problems based on positive and negative integers, what was, can you say what had to click to go to be able to solve the problem successfully?

I think I just had to know what to do in each case. Um, like when you're, I don't know, trying to solve an equation or inequality, you have to know the steps and then also what to do if this number's a negative and that, and when you reverse the sign. So I think you just have to know what to do.

Got it. So would you say, and I want to differentiate conceptual understanding from procedural understanding. So, you know, concept is understanding the idea, procedures are the step-by-step process to get the answer. Would you say you actually mostly understood the concept, but you needed the example of the procedure for how to do it?

Yeah, I think that that is sometimes the case. I think I have a plan in my mind, but I can't visualize it for certain. So I go to an example and then I, um, and then I find a way.

Got it. And, um, cases where, well, first of all, in understanding negative, positive and negative integers, bless you. Um, did you have to go to a human being for help on that or the, the bot totally helped you out on its own?

I think definitely for some cases I had to go for, um, I had to go to my guide and my classmates.

Mm-hmm.

But I think the bot was pretty capable of helping me. Got it.

And would you say when you went to the— bless you— the human beings, was it more for procedural understanding or conceptual understanding?

I'd say both. I think sometimes I was confused as well as confused on what to do. So I think usually it's both.

Got it. No, this is very interesting, but it sounds like it's working to do the self-paced math pretty well for you. Is that accurate?

Yeah, definitely.

Do you have a goal for when you want to complete 7th grade math?

Um, not at this time. I def— I want to go through it. It's more challenging than 6th grade was, so it's taking a little while longer. Um, and that's not bad. It's good, of course. Um, and I'm still taking, taking 6th grade tests. Yeah. So Of course, going into 8th grade would be really beneficial. Um, I'm just not sure if I'll be able to do it by the end of the year. If I do, that's cool.

Did you, did you start with 6th grade math at the beginning of the year this year?

Yes, I did.

Was it difficult for you?

I think at the beginning of the year I did, or at the beginning of the year I think I didn't really understand the software and also the problems itself. And then as time went on, I grew to understand both. Yeah. So getting better at math.

And you, if I understand correctly, you sort of skipped 5th grade. Is that accurate?

Not really. I did 5th grade on Khan Academy.

Okay. Okay. So you had done 5th grade, so you're ready for 6th grade math when you got here. You basically— sounds like you finished it in one semester. Is that accurate?

I think I might have overlapped a little bit. I started— I think I might have just been doing it a little while in the past year. I might have taken some tests, but yes.

Okay, so basically it sounds like at this point, would you say you expect to finish 7th grade math before next September?

I think it's possible, but it is a little harder, and it's taking a little longer. So I think I'm just going to have to see.

Of course. No problem at all. And then are you still working on Harvard CS50?

I am. It's going a little bit slow because I've just had a very busy few weeks. I've been training a lot more, but, um, I am really trying to fit it into my schedule.

And which lesson are you on? You still on Lesson 1?

Yeah.

Okay, got it. Okay, no problem. Again, you've got a big competition. You still hope to be a national champion, I take it?

I'm hoping to do good in the tournaments coming.

Yeah, to do well. Um, well, Yeah, absolutely. Well, wonderful. In which case, it's been really interesting getting into your head regarding learning math, and good to see you as always. Until next time.

Thank you. You're welcome. Bye-bye. See you next time.