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What we covered:
– The dangers of accumulating learning debt: the gap between what you can do and what you need to be able to do.
– If you miss building up your foundational skills in school or sports, you can get by for a while. You develop some compensatory strategies, like favoring your forehand over your backhand, or using ChatGPT to write all your school essays.
– But learning debt is like any other kind of debt: it accrues interest and eventually comes due. Over time, the workarounds become more complex. The cognitive load increases. You start avoiding situations that expose the gap, and this is where you hit your ceiling. You can’t pursue an engineering degree if you can’t do algebra. You can’t be competitive in tennis if you can’t hit with your backhand.
– Learning debt often begins because of a lack of oversight by adults. Parents, teachers, and even coaches sometimes think they’re being nice not telling you that you need to work on your weaker side, or you need to stop using a calculator on your math problems. It feels like nagging, and it can create conflict between adults and learners. So they let it slide.
– But this failure to hold the line early on inhibits students’ future potential. And when it occurs across many students across many schools, it degrades the whole educational system – leading to the current situation in which many students are totally unprepared for the rigors of college.

0:00 - Introduction
2:04 - Course phases: instruction, final review, final exam, remediation if needed
5:25 - Generating full-length SAT exams for our prep course
6:53 - Loosening up the gravity throttle for high-performing students
14:59 - Aptitude is measured by accuracy rate
18:07 - Accuracy correlates first with aptitude, second with conscientiousness
21:35 - Assessment vs. non-assessment accuracies
23:43 - Propagating accuracy through the knowledge graph
24:27 - Hidden skill gaps force bad compensations
25:27 - Sports make skill deficits and bad compensations obvious
33:38 - The Math Academy system holds you accountable for every skill
34:18 - Completing the square: a common skill deficit with temporary workarounds
36:15 - Reliance on Desmos undermines students’ ability to graph functions
37:38 - You need to know your multiplication facts for factoring
38:13 - Foundational deficits are usually caused by lack of adult oversight
38:52 - Shoring up foundations is effortful but has huge ROI
40:40 - Filling in missing foundations makes kids so much more confident
41:12 - Missing foundations stall learning and drive cheating
42:12 - Faking competence backfires downstream
45:33 - The truth hurts but is the kindest thing in the long run
46:26 - Learning debt eventually comes due, with students paying the biggest price
47:12 - Kicking the can down the road in education
49:46 - The cost of a broken education system

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The raw transcript is provided below. Please understand that there may be typos.

Justin Skycak (00:00) Welcome to the Math Academy podcast. I’m Justin Skycak, Chief Quant and Director of Analytics at Math Academy. And I’m here with our founder, Jason Roberts, to talk about the dangers of accumulating learning debt, the gap between what you can do and what you need to be able to do. If you miss building up your foundational skills in school or in sports, you can get by for a while. You can develop some compensatory strategies, like favoring your forehand over your backhand.

or even using chat GPT to write all your essays. But learning debt is like any other kind of debt. It accrues interest and eventually becomes due. Over time, the workarounds become more complex. The cognitive load increases and you start avoiding situations that expose the gap. And this is where you hit your ceiling. You can’t pursue an engineering degree if you can’t do algebra. You can’t be competitive in tennis if you can’t hit with your backhand.

Learning debt often begins because of a lack of oversight by adults. Parents, teachers, and sometimes even coaches think they’re being nice by not telling you that you need to work on your weaker side, or you need to stop using the calculator on all your math problems. It feels like nagging, and it can create conflict between adults and learners. And so they let it slide. But this failure to hold the line early on inhibits students’ future potential.

And when it occurs across many students, across many schools, it degrades the whole educational system, leading to the current situation in which many students are totally unprepared for the rigors of college. That’s the main idea. Now, let’s get into the details.

Jason Roberts (01:45) All right, so let’s just talk a little bit about a couple of things you’re working on, Kate, that might be interesting for people, might not. ⁓ So what’s sort of top of your list right now?

Justin Skycak (01:59) ⁓ so handful of things are, ⁓ we got to kind of integrate, ⁓ course phases into, into the backend and front end phases being like, well, there’s the instruction phase where you’re doing like your, lessons and reviews and everything you’re going through the course. But if you’re taking a final exam, which is something that we’re, we’re, we’re starting to integrate into the system more.

then you have a review period, a pure review period before the final exam. ⁓ And then you take the final. And then if you get below, say, like 90 % on it, you’re going to do, ⁓ you’re going to, after you do your remediation based on the things that you missed, you’re going to take the final again. So there’s, of course, like right now the way that it goes is like,

hit 100 % of the course, that means you’ve completed all the lessons in the course and now you’re just kind of sitting there.

Jason Roberts (03:01) undefined

situation where you’re going to work for some period of time and get a final exam and it’s unclear how long how long that’s going to be. Yeah, right. it three weeks? What is it? Which I emails from teachers who have because like we don’t really have the final exams turned on for normal students yet, which we need to.

Justin Skycak (03:17) Yeah, I don’t think we even have that in the UI yet, right? You can’t like request a final exam or anything.

Jason Roberts (03:23) Yeah, because I felt like without the ability to control it a little bit and have more visibility into what’s going on, it was just going to create a lot of problems, even though we really need to get that totally finished up because it is an important thing, but especially for schools. Schools are like, well, we need to, they really want a final exam. Then we’ll have to have someone to go and create a final exam based on our stuff. That’s just like a lot of unnecessary work. But, ⁓

But I do have situation where they’re like, well, so-and-so finished their geometry course and has been working, seemed like the last few days, like how much longer do they have to go to the final? I mean, we have the data. I have to like go and do a database query and go out. looks like 170 XP. So I don’t know, four or five days or something. You know what I mean? It’s like, so we got to, we have to, well, you and I talked about was like, we need to say,

Justin Skycak (04:10) And it’s a reasonable question too.

Jason Roberts (04:23) When you’re 100 % of the done lessons, maybe you’re 97 % through the course, we have this sort of, we kind of figured out the heuristic to kind of make it seem reasonable. So they’re progressing through the reviews closer to 99 % to take a final exam, you know, that kind of.

Justin Skycak (04:39) Yeah, yeah, exactly. Yep. so, ⁓ so the thing that I’m working on now is, is, is, is basically like, I mean, previously we just had this concept of like, heck a hundred percent means you completed the course, right? But now there’s really like, well, that means what that used to mean now means you completed the instruction phase of the course. There’s like, there’s gradations of what it means to complete a course now. And now, so I kind of got to go back to all those areas where that’s included in the logic.

and kind of separate that out. ⁓ That’s not too bad, but it’s just a thing. ⁓ I mean, it’s just a handful of other things that are on my list for the next few days are some updates to the SAT prep course exam selection. mean, our exam selection is pretty solid now. ⁓ We generate these.

Jason Roberts (05:10) Right.

Justin Skycak (05:38) synthetic practice exams based on questions that we have in the system. And they’re meant to kind of emulate a sort of SAT style exam. And so that way, based on your performance, we can get like an actual score estimate, how well you’re gonna do on the real thing. ⁓ so we, yeah, we’ve got a pretty solid V1 of it, but there’s some opportunity to make it better, to diversify the question selection a little bit more.

Um, generally the exams are going pretty well, but we, um, I think Alex pointed out in, in, one of the recent exams for, for, for one of the students, there was one, there were two questions that are a little bit closer to each other than you would actually see on a real SAT exam. Yeah, a little too similar. They weren’t from the same topic, they were kind of from the same module. And so we really need to kind of spread, spread that out.

Jason Roberts (06:32) be tested. Yeah. You have two questions on absolute value equations or something. It’s like, we kind of covered that. Like we should do something else. Yeah. Right.

Justin Skycak (06:42) So that’s another. ⁓

Let’s see. Oh yeah. And then there’s the, uh, in the gravity feature. got to loosen that up a little bit for the high performing students. like we, how, how, how much do we allow you to build?

Jason Roberts (07:06) along a single learning path.

Justin Skycak (07:10) Yeah, in a single day or so.

Jason Roberts (07:13) depends on A and C depends on B and D depends on C, like how far on the path can you go in a single day? Now, the thing of it is that your memories consolidate when you’re sleeping. And until you’re sleeping, when you just kind of learn something that day, it’s not in your long-term memory. mean, they consolidate, they consolidate to long-term memory. So if it’s therefore not in your long-term memory and it’s just sort of in short-term memory, then it’s taking up spots in your working memory.

which makes it hard to think through the topics or the ideas in topic B or topic C because this topic’s in A and B are kind of, so if you’re in topic C and you did A and B in the same day, then the skills and stuff is sort of more in your shorter term memory. It’s not really a long term memory, which means like you said, your working memory slots, working memory, the short term memory, and there’s long term memory. if when,

when new information moved to long-term memory, that it does not take slots in your working memory. And everybody has like a very limited number of working of slots in the memory. And I think it brings between like four and seven for most people. you know, and then this sort of correlated to like IQ aptitudes. So really, really brilliant people can keep more things in their head at one time. And ⁓ that’s a really nice advantage for them. But so the idea being that you want

And what distributed practice based repetition does is it really does a better job of consolidating this long-term, moving new information to longer-term memory and consolidating it in your long-term memory so it doesn’t fade. But anyway, the idea being about the throttling is that if you’re doing, if you allow them to do three or four copies in a single day and you’re like, well, if they have enough working memory, they’re high enough aptitude, then maybe they can

the skills that they kind of learned in A and B and C earlier in the day, they have slots available and their working memory. They can still do D. A lot more people be like, I can’t remember. How does this work? You need to slated to get those long term members to solidify over two or three days. So that doesn’t take up working memory. So their working memory is entirely available for.

the new skills in topic D and the intermediate results of the problem, things like that, right? Does that…

Justin Skycak (09:43) You to reduce the cognitive load by allowing it to consolidate more. And in particular, this, this is problematic in skill hierarchies because when you are climbing the skill hierarchy, you’re often pulling, you’re pulling context from the lower topics as well. If those are not consolidated, then you’re, it’s, eating up, it’s going to be eating up more of your working memory capacity, more likely to put you in a state of cognitive overload. Whereas it’s, it’s, it’s safer.

to do like a breadth, like if you spread things out, you’re not building a ton on the same path in a single day. means if you, instead of doing like five topics that stack on top of each other and getting that whole tower of cognitive load, if you spread that out horizontally along the graph, like each topic is really, like its prerequisites are much better consolidated.

in your memory, so it’s a much lower. ⁓

Jason Roberts (10:43) So your entire working memory is available for the and the intermediate results. Everything came before. It’s long term and you know it. It’s free.

Justin Skycak (10:47) Yeah, for that one.

Yeah. Yeah.

Yeah. Yep. So we’re going to just based on a student’s, mean, a good proxy for for how well as a student able to stomach more of this kind of cognitive load is just how well are they doing on the system in general? What’s their accuracy? What’s the pass rate? All that sort of stuff.

Jason Roberts (11:13) a little

bit of work, yeah, because if, ⁓ here’s a couple failure modes. Failure number one is the obvious one. Parents says, okay, my student is in algebra and they need to know how to solve systems of linear equations with substitution because they’re gonna have a test on it on Friday and it’s Wednesday. And the students behind is maybe they didn’t do so well on some stuff, maybe they didn’t do some homework they were supposed to do, maybe they were out sick, whatever, so they’re behind.

And they’re like, well, and some parents are using the system.

in kind of as sort of like a secondary or learning system along with what’s going on in class. Although I think typically it’d be better to have learn ahead in the system so you don’t have to constantly match stuff up. That’s a whole nother thing quick discussion. But say you’re in that situation and you’re like, OK, well, there are nine topics behind. And so then they you’re in the moms like, OK, well, you got to get through all this stuff.

You know, you didn’t do well on the last test. got to get another, you know, whatever. And so the kid, I’m going to set the gravity and the kids like, it’s like bang, bang, bang. There’s no throttle on it. And they do like, you know, they do.

Justin Skycak (12:30) nine

in one day they’re struggling and there’s so much information that they don’t even do well.

Jason Roberts (12:35) They probably just start failing in the third or fourth one. Repeatedly, and mom is like, why is it going on? They’ve just got negative XP and they fail because the kid’s like, I don’t know, can’t do this. And so then you put in, and that was what I was imagining when I first brought up the idea of a throttle. When we first built it and you first built the gravity, I was like, think we need to throttle it. And you’re like, what do you mean? And I go, well, here’s what’s going to happen. You’re like, that’s a point. And then so you built it in and then it’s like, okay, well then you got the parent is like, well, my

They can only do like one a day. My kid is, you know, high aptitude gift, whatever, and they, can do more. think this feels a little restrictive. Like they can, this is not a problem. So it’s like, what you want to do is have the system calibrate to the students. What we perceive to be their sort of working aptitude, as far as we can tell within this context. It’s like, okay, well, just like if were a tutor and your parent would say, well,

we need X, Y, and Z to happen that here would be like, mm, yeah, we can do that. Or I don’t know. we’re going to, you know, they would be calibrating based on your student that you’re that are working with. like I every different kids are capable of different things. And you want to just be realistic about what how fast certain students can absorb information and master it without the whole thing melting down and be turning into a disaster. You know, and and if.

The biggest problem of course is when…

We talk about people aren’t doing what they’re supposed to be doing. There’s no feedback. People get way behind and they’re trying to make up for stuff in some really short period of time. And there’s only so much you can make up in a short period of time, you know, both things just failing.

Justin Skycak (14:19) Yeah, exactly. So yeah, we have a throttle currently, but it’s aggressive. kind of like built for like, it’s good. Or sorry, it’s aggressive in the sense that it’s very

Jason Roberts (14:30) It’s

a conservative view of what a student is capable of doing.

Justin Skycak (14:35) Yeah, yeah, yeah, it’s quick to throttle. And so I need to loosen that up for some of students who are really doing like more than that. Like the performance is more than just like, okay, that’s decent. Students who are just like, wow, they’re just knocking it out of the park. Like you can let them go further, give them more rope on that sort of thing.

Jason Roberts (14:59) Okay,

so one thing someone might ask a parent in particular might say, how do you measure aptitude? I mean, this obviously is indirectly, we’re not giving them an IQ test or anything.

Justin Skycak (15:12) Yeah.

mean, so the one I remember back the first time when we started thinking about this, we kind of take this into account in various places in the system. It’s not just this gravity. It’s also built into space repetition. ⁓ It’s also built into like what kind of quizzes to give. It’s part of the glove fit on a student.

And really, mean, the number one metric on it turns out to be just what is the student’s accuracy on the system? ⁓ That’s even more, even better, that reflects more of the signal than even their pass rate or anything. Because you can pass a lesson and get like 90 % of it, right? Versus pass a lesson and get like 100 % of it, right?

And there’s a difference between that. ⁓ And I remember back when we were first kind of starting to build this into the system, we were wondering like, what should we, how do we measure this? And I just looked at like accuracy and I got our accuracy for basically ⁓ all the students in my classes, in the math academy classes, in the Pasadena program. And it was just, it lined up so perfectly.

with the kind of like, you know, if I just as a tutor, like

Jason Roberts (16:44) I’m going to have a sense. I know. I can tell you’re pretty, yeah.

Justin Skycak (16:47) You know, there’s the kid who’s just like, all right, that kid is like, the whiz kid. he, yeah, he or she is just really like, I can give them challenge problems and stuff and that sort of thing. And then they, yeah, of course they show up as at the top of the accuracy list. They’re not, they don’t need like three or four repetitions.

on each question per knowledge point, like they pretty much one shot it. And we just give them a two question. We give a second one just to be really sure that they didn’t just get the first one right by chance. ⁓ But yeah, they’re learning right is incredibly fast. They’re getting stuff right. And then, ⁓ yeah, on the other hand, the students who would like struggle more

conceptually or just need more repetitions to get stuff really locked into their memory. Also the students who are more forgetful of stuff. I mean, that shows up in their accuracy because of all these factors, they’re less likely to get a question right. the really interesting part, which was nice to see in the data, is that there are students who

don’t have like astronomically high accuracy, maybe their accuracy is like 80%, which is like, that’s solid. That’s good. Like if you start, and this is also when you’re first learning the material and stuff, like that’s a good accuracy. But you can have students like that who pass like 99 % of their tasks. And what that indicates is that like they’re more of like a,

more of an average like on an aptitude level, but in terms of like diligence, conscientiousness, doing what they’re supposed to, aligning themselves with the learning process, like they’re really good. And you can also have students who are like have a like high, like the 80 % accuracy, but their pass rate on tasks is maybe like 85 % or 90%. Like sometimes those students like,

It’s not bad, but sometimes ⁓ these are kind of like more like the, the more of the knucklehead smart kids who are kind of like, they’re really fast on the things that come easy to them. And a lot comes easy to them. But then once they struggle, they just kind of like, they rage quit or just like fall off the wheels, like for whatever reason.

Jason Roberts (19:34) Yeah, the latter reminds me of my son and the former rising of my youngest daughter.

Justin Skycak (19:40) It’s like one of those quadrant memes. Yeah. It’s like aptitude and like conscience. ⁓

Jason Roberts (19:45) Yeah.

So Colby was not super high in conscientiousness, but high in aptitude and working memory. Whereas my youngest was higher in, uh, mean, you know, high aptitude, but not, not that high, not as high as my son, but much higher in our conscientiousness. Right. You know, and, it was, so she would, she had really high.

And she had pretty good accuracy too, pretty high pass rate, but that’s the same kind of thing where, but there’s a difference between, then you have the kids who have both, right? And they’re not as common obviously, because both are high consciousness and high aptitude are both independent, they’re pretty orthogonal, as you’re saying, right? ⁓

Justin Skycak (20:34) more orthogonal than you would expect.

Jason Roberts (20:36) Yes. And then when they’re together, you’re like, wow. You know what mean? That’s the thing. So anyway, so you’re just trying to measure, but…

So accuracy, high accuracy will measure, know, if really high accuracy means both are true, right? If they have good but not, ⁓ you know, good or really good accuracy, but not amazing, like, then you have some combination of those two, but not to full extent or whatever. And so you’re like, okay, so

Right, okay, so if you have high accuracy rate, does it give more emphasis, more weight to quiz accuracy as opposed to lesson or review accuracy to those? Because those are different animals, right?

Justin Skycak (21:33) Yeah. Yeah. It, ⁓ it, so the accuracy metric, we, we actually split that out into two accuracies that we’re keeping track of. There’s their assessment accuracy and there’s non assessment accuracy. yeah. so that, that then, mean, assessment accuracy is, is always going to be lower, but non assessment accuracy. Cause you’re under timed conditions. It’s a much like you don’t have reference material. It’s a, it’s a harder situation. And so what we do.

Jason Roberts (21:45) Got it.

Justin Skycak (22:01) in terms of what accuracy do we use is we measure those separately and then average them together. If you were to ⁓ just measure a flat out accuracy from all their answers, students are submitting fewer quiz answers than lesson answers and stuff. ⁓ So you would get overwhelmed by the non-assessment accuracy. ⁓

Jason Roberts (22:19) Yes.

I feel like, it really shows you where the rubber meets the road. Can you do this question on time conditions in the context? You don’t have any context is like if there’s seven, 10, 12 other questions, you have 15 minutes go. How well can you do now? If it could is getting high accuracy on that, then they’re really absorbing the material well. And that’s really what we use to calibrate whether they’re like, because if they’re not learning it well, that’s when we give them reviews and everything they missed. And that kind of really

kind of slow things down because if it’s fine, if they’re doing well on, you know, lessons and reviews, but if they can’t do the quizzes, it’s like, you know, okay, you’re probably a very conscientious student. You’re using notes and all these kinds of things to help you get through this. And that’s good. But, you know, we don’t want to overweight that to mean to think that you’re a genius and can move at some, you know, hyper speed pace. Well, let’s treat you as you are, which is a good student who’s

does high consciousness and let’s let’s move at the pace that is the right fit for you. The quizzes really are and miss we have the midterms and finals as we have those one and are really also will play a big role in helping to calibrate that.

Justin Skycak (23:42) Yeah, yeah, exactly. I should also say that our accuracy metrics, in addition to like having an aggregate or like a general across the all topics accuracy metric, we also measure student accuracy ⁓ on every topic individually and have that kind of propagate through the graph to get an accuracy estimate. you can, sometimes it happens that like you have a student who’s like, maybe they’re like, generally they’re like one of the really

bright kids in the class, but for whatever reason, there’s this one, this one thing that they are struggling with a little bit. And they’re more like an average student in that category. You’ve got to slow it down a little bit.

Jason Roberts (24:20) Yeah

⁓

Justin Skycak (24:25) You

should you you have a couple examples, right?

Jason Roberts (24:28) cohort of Proto Math Academy students, super bright kid, really fast, really good. And boy, he sucked at graph, like two dimensional graph this line, like interpret this graph, he’d be like, and then he almost developed like a, a, like a fear of it or something. And

Justin Skycak (24:45) And

he’s used to everything coming like really easy, right? And it’s like, this is one thing that it does not. And so he doesn’t like it. So he was just like, I want to do it, which means he gets worse at it because he’s trying to avoid it.

Jason Roberts (24:56) Yeah, I mean, it was just just it was just so. That was so weird, man, I don’t don’t I that was the one example. Maybe you can remember something else I’ve talked about, but that was the most like glaring example of someone whose aptitude and performance on on any number of mathematical skills was just really great. And there’s just one thing he was just like, dude, I mean,

It’s like a sports man. Like I was never going to left handed layout. People are like, dude, why are you, what’s wrong with your left hand? It’s like you come up with these compensatory skills for something that, you know, what else happening to, I mean, this is maybe a little out of scope, but you, you do the, yeah, you do these compensatory things to say, okay, like in sports, that is kind of a thing. Like, you know, in like soccer or basketball, like, oh, he can’t go left.

Right. And I remember, I remember this interview, so funny with Kobe Bryant talking about this one player who just owned him in practice for a long time, I realized after a couple of weeks that the guy couldn’t go left. Yeah, that was funny. He’s like, yeah, but he just owned me. And then I realized, oh, the guy can go left, you know, and then he can overcome it. And that happens. You have these people who they compensate it and they kind of hide the fact that they can’t do it because they can do some other things so well that distract you. It’s like, oh, wait a minute, you know.

Justin Skycak (26:09) Get going.

Yeah, I have two reactions. The first one is very brief, but just one of your dogs, Maisie, like she can’t go backwards, right?

Jason Roberts (26:36) She struggles

to back up.

Justin Skycak (26:45) It’s like she looks like she’s stuck, then she looks very annoyed and she like very slowly kind of like…

Jason Roberts (26:52) She has to kind of turn around. She’ll

wedge herself between the ottoman and the cow. She’ll like see her legs up and then she gets in and she’s like, you have to be like, all right, amazing. Move them ottomans so you can walk around. It’s like,

Justin Skycak (27:04) Yeah, it sounds ridiculous, but I’ve, ⁓ yeah, I remember when back when I was staying with, with you and Sandy over the pandemic, like I’d see it in front of me and I would have to move the ottoman sometimes cause you just look at me like, aren’t you going to do something about this?

Jason Roberts (27:18) In

possible situation, clearly.

Justin Skycak (27:22) The second thing is just kind of it’s kind of interesting. Yeah, sometimes you can accumulate these defects in foundational skills that you don’t realize are there until you kind of force yourself to confront them head on. So just like your left handed layup, it’s kind of like, well, in a game, maybe you…

Jason Roberts (27:43) left hand to lay out in a game of my life just for the to be fully accountable there never

Justin Skycak (27:46) Yeah.

And so you probably like realize like, like during a game, you probably go for the right handed layups because you know your left handed layups not good, Yeah.

Jason Roberts (27:58) So, okay,

I had a crutch, we talked about previous show, my crutch is my speed, so I could use my speed or quickness to go, and I could just go right around people. But then they start realizing, okay, Jason’s fast and he’s gonna go right, so what am I gonna do? I’m gonna cheat right, I’m gonna close that off and make him go left. That would be the smart move. So what I learned is I would do behind the back.

layup. would do I could do a left hand left. I would do I would go right and then I’d go to buy right hand up but I would go around them left get my body in between them with a behind the back. And so that I became known and any gem that I play with it like Jason’s behind so people go as bad it looks badass. Right guy doing behind the back layup even when you see a pro to that’s cool. But I did it because I couldn’t do a left in an end it is just really kind of a weekend it was just a crutch it was just a because I could do a left hand layup.

Justin Skycak (28:43) Yeah.

Jason Roberts (28:56) It was ridiculous. Yeah, mean, we just think like, like Jason, like, just do it, learn how to, it’d be easier to learn how to find the back thing. But I just.

Justin Skycak (29:11) You jump through all these hoops, these compensatory hoops. And sometimes, yeah, they can look cool. They can attract attention and everything. But it does kind of place ⁓ some limits on your ability.

Jason Roberts (29:24) I would have been a better player had I solved the left-hand layup problem early. ⁓

Justin Skycak (29:30) Yeah. Often

like you may not even know about these issues that these defects and the foundations that you have. ⁓ Like, so something that happened to me, I played hockey for all the way from elementary school through high school. And so I got to be like a pretty good skater. And recently I started ⁓ doing kind of going to public skates with my wife. ⁓

And, and I got kind of bored of just skating around in hockey skates the whole time. So was like, okay, I’m going to do some figure skating skill training and see if I can do like spins and stuff, which like, it sounded, it sounded pretty fun. ⁓ and so I I’ve been doing that for, for a while, but, ⁓ the first time I stepped out there with figure skates and started trying to like do these spins on like one leg and stuff. I realized that there were lots of. ⁓

just compensatory movements that I would do while I’m skating normally. Like there’s certain ways where it’s like maybe like a certain type of stop with my left leg in a certain position or like I had much, my balance was very, I found it much, much, much easier to balance on my right leg than my left leg. I’d be able to like, I could do like a spin move like really quickly on my.

right leg and then the left leg like wouldn’t even get like halfway there. Like what the hell is happening? What’s going on? And like, just, it’s stuff that like, I never realized previously. It didn’t, it wasn’t obvious. It wasn’t clear from watching me skate. Nobody ever said anything from that. It never hindered me in a game, but once you get into a situation that’s, that’s, that’s really isolating these skills and holding them accountable, ⁓ you, start to notice some, weaknesses in there.

Jason Roberts (31:22) Yeah, it’s interesting. ⁓ You know, like, for instance, my basketball career, like if somebody had said, like, I didn’t have a good enough outside jump shot, which is I talked to previous show, but that’s why I didn’t make it at the college level. You got to have a three point shot if you’re under, you know, 6’3 or something, right? Nowadays, you really should and everyone should. But I didn’t.

Left-handed layup. I don’t think it was the kind of thing that I wouldn’t really notice because I could have had a compensation for it, but you don’t really, it’s really hard to have a compensation for a lack of a jump shot. I mean, you can be ridiculously good at driving to the hole, but it’s just much harder to overcome that. And so what would have been ideal in my situation would have been like a coach coming to me and say, okay, Jason, here’s what you do well. Here’s what you do. Okay. Here’s what you’re, here’s your real holes. There’s some real weaknesses. You don’t have a good jump shot.

You don’t have a left-handed layup. You don’t do this defensively, whatever. They come up with these things and we are going to work on those. You are going to put in real time working on those because it’s gonna, and it’s gonna take time. It’s not gonna be fun, but it’s gonna open up your game. It’s gonna open up your potential because guess what? When you can shoot a jump shot, they have to come outside and guard you. can’t back away and make up for your, you know, cause if you’re fast, people just back up. They’re like, I’m not gonna get close to you cause you’ll just go around me. So.

make you come into me and then I have time to adjust and whatever, but, and get help from other people. But if you have an outside jump shot, I can come out and guard you. And if I come on guard you and then you used to be to go around me, right? Now it’s now you’re really dangerous. And now, okay, well, I’m going to guard you in a way I’m going to guard you. If you have a jump shot and you’re fast, but you can only go right. Then I’m going to come out and guard you. And I’m going to shape my shape. I’m going to go to left. I’m going to make you.

I’m going to be up on you tight. And if you go around me, go to left, but you’re not really going to go. You’re not really do anything because you can’t even do a left hand layup. Problem solved. We’ve solved the Jason problem. Now we can play with new people and they don’t know your game. You get away with all this stuff because nobody really knows. If somebody really knows you’re like, that’s an easy solution. Yeah. Right. If a good coach is just wants to shut down and that’s what they do in the pros and layers, they kind of analyze the other team, find their weaknesses and their tendencies and shut down what they want to do. So and that’s what we try and do in math is like

We’re not going to let you, the math Academy system will not allow the student to progress until they’ve mastered the material and you got to have a jump shot and you got to be to go dribble left and dribble right and take left-hand layups and right-hand layups. You you got to do everything. You know, you don’t get the cheat and make up, you know, bullshit compensations to fake your way through. It’s like, oh, you can’t do graphs. So you’re just really good at algebra. And you kind of come up with some solution when anyone who’s remotely competent at this stuff could just look at the graph and to tell you that’s where the thing.

That’s where the, you know, the singularity is.

Justin Skycak (34:14) Yeah, it doesn’t

work because we’re holding every individual skill accountable. You know, probably the concrete example that comes to my mind of a compensatory skill in math, and I would see this all the time back when I was tutoring, ⁓ would be students who never really learned how to complete the square. ⁓

And they struggle with it when it comes back in calculus, when you’re doing some integrals that require completing the square. And in particular, in inverse trig function integrals, ⁓ the square is like, yeah, yeah, yeah. So it’s one of the techniques you learn in algebra. it’s just kind of like, you quickly move on to just using the quadratic formula after it. ⁓

Jason Roberts (34:49) And so the complete. Yeah.

I

can stick in minus b plus minus, you know, whatever.

Justin Skycak (35:07) Yeah, yeah, exactly. And so anytime students are asked to solve an equation by completing the square or whatever, do something with completing the square, oftentimes the problems are structured in a way so that it ultimately just amounts to solving a quadratic equation or finding the roots of a quadratic function. And the kids are always just like, I don’t like completing the square. I’m just going to do quadratic formula. And then they use that all the time. And then- ⁓

Jason Roberts (35:36) I’m just gonna drive to the hole, right?

Justin Skycak (35:39) Yeah, exactly. But then in calculus, it comes to using completing the square in calculus, this is not a thing that you can use the quadratic formula for. You are restructuring an expression so that you can actually integrate it. You’re not solving the equation. And so there’s no way to do it other than to complete the square. And then that causes a lot of pain and struggle.

Jason Roberts (36:04) And they fight again because they don’t want to have to do. don’t remember this. It’s algebra, the stupid thing. Yeah. It seems unfair. It gets so funny.

Justin Skycak (36:14) I mean, okay. One, one more concrete example is when classes allow students to just use Desmos to graph everything and students don’t actually like know what the graphs of different functions look like, or just, they don’t know this in their head. Their, their compensatory strategy for everything is just like, plug it into Desmos, jig the parameters a bit until the graph looks like it, like the desired and, and, and,

And that’s kind of their strategy. But then they’re missing out on like, they don’t actually understand geometrically what these transformations do. They have figured out how to use the resource provided to them to obtain the answer of what is the effect of the geometric transformation. But they don’t actually know this in their head what the geometric transformation is. All they know is how to find it. But when you’re talking about like ⁓ more advanced

reasoning about graphs and stuff that pull that in as a component skill, it becomes ⁓ kind of another one of those problems where you can’t really do it on the, you need to be able to do this on the fly in your head really quickly as part of a compound thinking move. Or maybe sometimes you need to invert it. just like the, when you like,

Why do you have to learn your multiplication facts? Well, for instance, when you’re factoring a quadratic equation, you need to be able to invert that process. And if all you need, all you know is how to like perform multiplication by repeatedly adding a thing, you can’t easily invert. Like given the result of a multiplication, what are the factors that went into it? You don’t know it, so you can’t invert it. So it just, you, you’ll lose the sort of mental, it’s, it’s no longer a tool in, in, your brain.

Jason Roberts (38:07) And it’s so, it’s just, again, it’s that like…

The development of compensations is often a lack of oversight from the adults, parents or teachers, and a lack of willingness to do the work to overcome that weakness. They’re just like, ⁓ I just let them use Desmos. I just let them use a calculator. ⁓ I don’t really give them tests because it’s hard. you know, it’s kind ⁓ of a laziness, pain avoidance from the adults, you know?

In helping kids, you know, I don’t know, the kids, whether in college and doing real analysis or their third grade learning, their multiplication tables, you know, learning is, is, is, is effortful. You know, it doesn’t have to be painful, but it’s effortful and it takes some time. And sometimes it’s not always what you wanted to do. Like I didn’t want to work on my jump shot. Nobody made me work on my jump shot. So guess what? I never got a good enough three point jump shot. therefore my college career college basketball career ended before it started.

That’s the result. That’s how it ends. you know, you can say, well, you know, I was never good at graphs. And so I, my son, have him do the thing and he’s just, you know, it’s like, okay, but you’re, they’re going to pay for it later. And so you might as well do the hard work now do it earlier. And it, like I said, it opens up your game. Now you can do all this stuff and

And then, and otherwise you start prematurely shutting down for future avenues of growth, future opportunities. It just shuts it down. You don’t learn math. Well, guess what? Science has shut off to technology. A lot of technology jobs are going to be shut off. Sometimes you can fake your way through and just kind of, but it’s not great.

Justin Skycak (39:59) Even

if you do, you’re not going to like, there’s a limit on how successful you can be.

Jason Roberts (40:04) Exactly. you really it’s really about, know, and so I think that’s one thing that’s great about the Math Academy system is it just doesn’t it’s not a human. It doesn’t get bored. Right. As Captain America would say, I can do this all day. You know, that can be like, can do this all day. Like we’re going to work on your jump shot until you’ve got a killer jump shot. And trust me, when you have that killer jump shot, you’re going to thank me. Trust me when you’re normal equation tables.

you’re gonna thank me. You may not thank me now, but you’ll be like, thank God I can do this.

Justin Skycak (40:40) And we hear about this all the time from, from parents who have seen their kid grow so confident by filling in their foundational skills, right? Like it’s like this level of confidence in their mathematical ability that they never even expected or thought was possible to have. It’s like, where did that come from? Why is my kid, my kid is actually like confident feeling good, crushing their math class. It’s like, well, they, they just filled in their

fundamental skills are actually prepared for it now.

Jason Roberts (41:11) So much because that’s the biggest drag on him is this is as missing those missing foundational skills. It’s the drag we’ve talked about that for that. It’s the drag. It’s what keeps you from making forward progress. You accumulate too many missing foundational skills and all progress pretty much stops. And then you have to resort to faking, cheating, getting all kind of extra help, trying to make up for a really lagging grade with extra credit and other stuff to try. You know what mean? It’s this kind of

You know, it’s not.

Justin Skycak (41:42) Because bad enough, you get forced into a situation where you have to perform compensatory activities in order to just keep up with the class or whatever expectations are being placed on you. And as a result, it’s like you’re not progressing forward at all. You’re just, you’re, you’re, you’re cheating your way. The gap is growing even bigger. You’re getting more solidified into your position. You’re actually going backwards because you’re not actually doing these problems the right way. So you’re not actually.

practicing the component skills, you’re forgetting a lot of what you did learn. And now, and now you got admitted to college and you show up and you don’t know your middle school math and you’re placed in a remedial math class. you’ve got pretty much no, like pretty much nobody in the history of this class has gone on to complete an engineering degree.

Jason Roberts (42:31) I

mean, the idea that you don’t know middle school math and you can is a utter fantasy. mean, I don’t know if they’re going to be in a situation where they have to give out fake degrees. What are you going to do? I mean, they missing years and years of math unless they use something like Math Academy, in which case use Math Academy because they’re not going to have the manpower to tutor all these kids individually and have them overcome years of math in a single year just so they can do

calculus and linear algebra and multi-verbal calculus. mean, they’re so far behind. And then, and they’re only in college for four years. And so you got to get all that done. And then you have to have years of, of skill training and your engineering classes, which, you know, you have to have, or you have to know basic, you know, first year physics and, or chemistry and stuff to do anything. And it’s just.

So that’s my words that you let people running around out there who have a degree in civil engineering or mechanical engineering, you actually don’t, are completely incompetent. They don’t know anything. And then that can create a disaster. That’s bad, really bad for society. Cause you can have all these people who, well, I mean, if you have engineering companies or people who are hiring engineers who’s…

hiring, ⁓ criteria so weak that people can fake their way through, or you’re just like the nephew of somebody and you get in and then you cause real damage because if somebody trusts your calculations or results, and then you can really gum up the processes or create things that just break or hurt people or whatever. Or you have a bunch of kids who graduate with these sort of fake degrees and

because they couldn’t do the harder classes. They kind of made these fake easier versions of these classes that allowed them to compensate for all the fact they didn’t really understand a lot of stuff. But then they can’t pass the hiring criteria of these places. So they have all this debt, all student debt and no ability to really get a job in their field that would allow them to pay for it. Because like, okay, so if you go out and you get 60, 70, 80, $100,000 in debt going to…

get an engineering degree and then you’re just like, you’re not going to get hired as an engineer and you’re going to get hired as a barista or something. like, well, you you can make, mean, I guess you can, you can live as a barista or work at a restaurant or any number of jobs that are not high, high skilled, but that’s gonna be hard to carry around a load of $700,000 student debt. Those jobs don’t allow you to live at any kind of reasonable rate and pay that kind of debt off. It’s absolutely crushing. So the whole thing is a disaster.

created by adults thinking that they were being nice, which all they were doing is allowing people to lie and fake and cheat or people negotiate or lobby or whatever. Any kind of compensation to overcome the fact that people aren’t doing the work and learning the material, learning the core skills that they need to do whatever it is they want to do. It’s just…

Justin Skycak (45:33) Yeah. Yeah. It’s like the situation basically turns into you, you’re too afraid to tell kids that they’re not on track for their goals. ⁓ and so you just keep telling them that everything’s fine. Yeah. And the, and the parents, well, you just keep saying everything’s fine. Everything’s fine. Everything’s fine. ⁓ if you had told them early, then at least they could have rectified the situation. They there’s time to fix this.

and kind of change the future trajectory. you keep the smokes screwing up long enough and it just gets to a point where it’s kind of locked in.

Jason Roberts (46:15) It’s an unsolvable problem like we talk about the bad, the teacher who tries to be nice from day one, they create an unsolvable problem for the year.

Justin Skycak (46:23) And somebody is going to, can’t solve the problem. so whatever happens, somebody’s going to get screwed by it, whether it’s the, the kid or, or society or like the employers and like, whatever, like somebody there, there’s a, there’s a cost.

Jason Roberts (46:40) Someone’s

going to the checks going to come due and it’s probably going to be the student is going to pay the biggest price because at the end of the day, employers and stuff, people need stuff done. And there’s only so many sort of fake positions or whatever that people that can be created in society where people are doing nothing or nothing real because they can’t do these things. But, know, I was just thinking like

⁓ Yeah, it’s, it’s, it’s thing is that like the rot can start early and start in elementary middle school. It’s like, we don’t teach multiplication tables. And because they don’t have multiplication, you know, we, kids are struggling with algebra. So we have, like, it’s very watered down algebra and we let them use Desmos and calculators and stuff. they, they can’t actually graph things and they can’t actually solve things. And so then they, don’t really, all this stuff’s weeks, they can’t really do calculus. And then, and then what happens is like, so you these, these

high school courses and they, if you get a D or if you had an F, you fail algebra one, you know what your class taking next year? Geometry. Yeah. And it’s not just Pasadena. That’s like the norm. You, you’re in a public school, you fail a class, you’re going to the next one. And so then the rot goes all the way up and then you get kids at, you know, really elite public universities and private school, private universities. I don’t think it’s restricted to public.

Where these kids who, like we said at Harvard, I mean, that is just absolutely an embarrassment. It’s a humiliation that that.

Justin Skycak (48:19) It’s really unfair to kids who were more prepared.

Jason Roberts (48:24) Did it work? Yeah. I mean, that’s infuriating for unfair. It’s ridiculous. And it’s just a sham. But the rot goes all the way up. And so you just got to nip this stuff in the bud. And it’s like, you got to hold standards early. You got to fix component core skills early. You can’t allow students to progress up the ladder and carry along all of these weaknesses and then come up with all kind of ways to put up smoke screens and

and hide it by not giving standardized tests and giving inflated grades and glowing recommendations and whatever nonsense you’re doing. ⁓ It’s just, the truth always comes out, right? And I some people feel like, well, fake it long enough. I got my degree and I got my high paying job. At least I made it. like, yeah, I doubt it. I doubt it.

Justin Skycak (49:19) You know, you think right now was that just like, it’s like, yeah, that’s what you think right now. But, ⁓ the, that’s what the person thinks right now, but these things change. Eventually you get yourself in a new situation and you didn’t. Yeah. The bill comes through just like the kid who, cheats through a few math problems. They think they got their hack. They think it’s all solved and then bam, bam, you’re smacked in the face by life.

Jason Roberts (49:46) That’s right. Right. So do the hard work early, fix the problems early, and then everything is much, much, much easier later. If you just, if you’re lazy, you procrastinate, I don’t want to deal with it. I don’t want to solve these problems. Well, you know, and, and, and, and oftentimes, ⁓ mean, kids are kids. They’re always going to be kids. They’re always going to find ways to try and get away with that. Do extra homework or not, if they can. I mean, there are some who want to do homework.

Most of them are just finding ways to do less of it. It’s the adults. These are adults. These are adults created this problem. You know, it’s no one person’s It’s not the teacher’s fault. It’s not the school administrators. It’s not the school board. It’s not the parents. It’s not the politicians. It’s everybody. We all created this together. You know, and sometimes, you know, you just have to look at system and say, okay, this thing is broken. There’s rot. And we got to

dig out the rot and we got to start fixing these things. And so that we have a a healthy educational system. So students are able to be successful and learn things that they want to learn and be able to do things they want to do and become the kind of people live the lives they want to lead. And ⁓ that starts, it starts early and you got to, you know, stay on it a whole, whole career.

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