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What we covered:
– In elementary school, there's often an intense focus on conceptual understanding, but not enough time spent building real fluency with core skills. And this has left many kids without automaticity on basic things like multiplication facts. Math is extremely hierarchical, and when students don't have the basic facts at their fingertips, they quickly run into bottlenecks as the material gets more complex.
– Sure, drills can be made more fun, but the bottom line is that they have to get done. In high school and college, most of the class time is spent copying notes from the board -- and these notes are often copied by the instructor from a textbook or from other source material. This game of telephone through transcribing is just a performative activity. It's theater. It's passive and it does next to nothing for learning and retention.
– In upper level college math courses especially, students may only receive short weekly problem sets, which really aren't enough to build mastery, even if the problems are really hard, because students just spend most of their time flailing around.
– The bottom line is that students need reps: lots of them, building up scaffolding to the highest, hardest levels that they're expected to reach. High school assignments tend to be better in that regard, but students frequently don't receive timely feedback, and often their work isn't even graded for accuracy. That feedback loop is so critical: without it, students won't know what they're doing wrong or how to improve.
– So rather than just pattern matching to how math has traditionally been taught, what actually makes training effective? There's a few core principles:
1) Maximize the amount of time spent actively learning, interleaving minimum effective doses of explicit guided instruction active practice.
2) Make sure students are consistently working at the edge of their abilities: not bored, but not overwhelmed.
3) Provide frequent, timely feedback so students can adjust and improve.
These principles should be applied to math education and training environments everywhere.

0:00 - Introduction
3:13 - Professors often wing pedagogy
5:37 - Too much class time is spent transcribing notes
7:41 - College problem sets are too short
12:53 - A lot of homework isn’t even graded for accuracy
18:22 - Copying notes in class is performative productivity
22:29 - Alex taught math courses at University College London
25:35 - Teaching is often an annoying obligation for research professors
30:03 - The bar for teaching is on the floor
32:34 - Even football practices often waste players’ time
34:20 - Most training is inefficient because people pattern match to the status quo
34:57 - First principles for effective training
37:13 - Too many models can paralyze and become a crutch for kids
39:24 - Kids can get stuck using training wheels in math forever
42:05 - Non-standard methods are often distracting and inefficient
46:18 - Designing 6th-8th grade courses to align with school curricula
52:30 - Conceptual understanding without ability is useless
55:17 - Skills practice can and should be gamified

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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, and our Director of Curriculum, Alex Smith,

to discuss common failure modes in teaching math from grade school through university.

In elementary school, there’s often an intense focus on conceptual understanding, but not enough time spent building real fluency with core skills. And this has left many kids without automaticity on basic things like multiplication facts. Math is extremely hierarchical, and when students don’t have the basic facts at their fingertips, they quickly run into bottlenecks as the material gets more complex.

I mean, sure, drills can be made more fun, but the bottom line is that they have to get done.

In high school and college, most of the class time is spent copying notes from the board. And these notes are often copied by the instructor from a textbook or from other source material.

This game of telephone through transcribing is just a performative activity. It’s theater.

It’s passive and it does next to nothing for learning and retention.

And in upper level college math courses especially, students may only receive short weekly problem sets, which really aren’t enough to build mastery,

even if the problems are really hard

because students just spend most of their time flailing around.

The bottom line is students need reps, lots of them building up,

Scaffolding them

to the highest, hardest levels

that they’re expected to reach.

Now, high school assignments tend to be better in that regard,

But students frequently don’t receive timely feedback, and often

Their work isn’t even graded for accuracy.

That feedback loop is so critical. And without it, students won’t know what they’re doing wrong or how to improve.

So rather than just pattern matching to how math has traditionally been taught, what actually makes training effective? Well, there’s a few core principles.

One, maximize the amount of time spent actively learning.

Interleave minimum effective doses

of explicit guided instruction active practice.

Two, make sure students are consistently working at the edge of their abilities, not bored, but not overwhelmed.

And three, provide frequent, timely feedback so students can adjust and improve.

In this episode, we’ll dig into these principles and talk about how they should be applied to math education and training environments everywhere.

Jason Roberts (02:15) What do we got? What’s next on the docket?

Justin Skycak (02:15) Yeah.

okay, I guess another question that we could talk about is, you know, what are some of the most common errors in teaching, you know, besides teaching differential equations in an abstract algebra course? What are, okay, I know that experience was straight out of Alice in Wonderland, and I don’t know that that’s a common instance, but just wanted to.

Alex Smith (02:28) Yeah.

Justin Skycak (02:39) give a bit of flavor to just how bad that can get. But yeah, what are, like, I guess, what about in your guys own, you know, educations? Like, what do you ever encounter just like things that you look back on and you’re just like, my gosh, that was so poorly done. That was so poorly taught. I mean.

I know you guys have, what’s, what is, what is at the top of this list for you guys? I mean, maybe Jason, do you want to start with your like 20 page, 40 page? I don’t, I can’t even remember some packet of abstract algebra definitions the first day or.

Jason Roberts (03:00) Almost all of that.

Yeah,

I remember. So this was like the first week of honors abstract algebra at University Chicago. And this is a well-loved teacher. He’s a really nice guy. And he’s long since passed away. he, I remember getting this packet. didn’t have, I don’t think we had a textbook. use our textbook was Hungerford, which was a, it was the yellow graduate texts.

mathematics. This was a graduate text that we’re using as an introductory abstract algebra undergraduate in the abstract algebra course. mean, granted it was honors, but I mean, still. And so that was just like an indents. It was like crazy to read from. And then he handed us this packet of theorems. It was like, yeah, 30 or 40 pages and you know,

operations and closure and know, it’s homomorphisms and isomorphisms. mean, like all in like the first week, right? Like what’s a, what is it everything from what is a group and set and you know, you know, whatever closed under operations and a billion groups and I mean, it just was, and I’m just looking at this and like, it was all like, you know, proofs.

It was theorems and proofs and definitions. That’s all it was. And it was front and back, 40 pages. And I’m just like, what the hell? And I called a buddy of mine in who was a year ahead and he was really advanced mathematically and he was just laughing at it. He’s like, this is terrible. I’m like, the God’s, what is this? He’s like, ah, you know, I don’t know. And yeah, it was just a nightmare.

You know, and I mean, there is like, there’s so many failure modes. I mean, that’s the kind of failure mode you have in elite university and you get an honors class and then the professors are like, I can do whatever I want. Right. These kids are really bright. They’re really prepared. I can just, we’re just going to go. And there was no thought about it. They really have the preparation. Am I really giving enough time to build some foundational elements that we can then, you know, develop and

Yeah, so that was just terrible. you know, it’s like, know, this universe, there are problems at the university level and the problems at the sort of K through 12 level. So and of course, they’re different from elementary, middle school and high school. So you could just probably look at four different levels now. At the at the university level, just as we’re talking university, it’s like, you know, forget like the extreme cases like what your instance, what you described.

and with differential equations and abstract algebra course or what I’m describing is you go, sit in a lecture hall and professors up there talks and it’s typically three days a week and then you have problem sets and you have like a weekly problem set and then you go and so you’re just taking notes and so then you have you just problem set and typically the problem sets

depending on the kind of university, they can be really, really challenging when you got to kind of work with two or three other people or if you’re reached out, it’s going to be, it’s going to be a long road to ho, a road to ho. And then, and then, you know, maybe you show up at the TA session on Thursday night at eight o’clock and there’s an hour and everybody’s like, ⁓ that was problem three. What the hell? the guy’s like, ⁓ you know, you might want to think about this. And that sort of may or may not be very helpful, but you’re kind of grasping for anything. And

I just found it extremely inefficient, right? mean, you know, it’s like, first of all, the professor is typically just writing problems, you know, at lower level, maybe the calculus level, they’re just doing some problems. Typically they’re doing like theorems and proofs and things. They’re all the book anyway. So why am I even coming here? I this is, this is like, I’m writing out what’s the proof that’s in the book. You don’t even talk about the motivation for it really. It’s like, how, why was this proof written this way? How do you think?

this, the mathematician came up with it. How do they attack this? Where did this come from? None of that. It’s like, we’re just going to jump to the final concise thing. And I just was, I always thought it was a waste of time. And me having ADHD and stuff, I was just anguished. I just had a hard time going to math class because I just couldn’t sit there and watch it. Why am I here? It’s so boring. You know, I might as well just go library and work on my problem set, you know? So I’m taking out notes that are just replications of what’s in the book.

Justin Skycak (07:32) Yeah, and you’re not actually learning from transcribing notes. That’s not actually retrieving information from your brain. You’re not.

Jason Roberts (07:33) So that’s terrible.

Just a moment.

Yeah,

total waste of time. And then of course, the problem sets you do once a week, inevitably, so you push it off until maybe one to two days. Now, the really, really good students might start the night off, and I learned that later in my career. was like, I should probably not wait. It’s due on, you know, problem sets are due on Friday. I better not wait until Thursday night. I should probably start at least on Wednesday morning or something. And the really good students start the week before, you know, and give themselves plenty of time.

But yeah, just thought, I just thought, but the problem is that you have one problem set a week, right? So you’re really compacting all that into a short period of time where you should be doing it every day and you be getting feedback on everything you’re doing, right? And then when you turn the problem set in, especially if they were proofs, you would get it back for like two weeks. Maybe a week if you’re lucky, if at all. And you might get a…

Justin Skycak (08:30) If at all, yeah. If it even gets graded, maybe

Jason Roberts (08:36) If it’s grayed in, it might be like, no.

Justin Skycak (08:36) you get it back. You get it back and maybe they just do a spot check on 20 % of the problems. Just see if you did it, if you completed it or something. get a plus for doing it.

Jason Roberts (08:48) I used to grade for vector

analysis. Okay. And I actually did, here’s what I did. I did a good job. I graded every problem, but you know, they had a massive number of problems and these problem sets, they were like 10 pages front and back. The kids written, right. was students, right. So these are like sophomore, yeah. Sophomores and typically like physics and econ majors. And, but it was like a true vector analysis course. And, ⁓

So within the first week or two, I figure out who the top three students were. And if they all three matched and they got the right answer, I’d be like, as long as I just kind of give it a cursory look at like the way they got to it, all seemed right. I’m like, all right, I’m just gonna say it’s the right answer. But I would do that. then I would, if all three of them didn’t agree, I would look and say, two agree and one didn’t agree? And I’d give it a little more of a look. If that guy got it wrong, these two got it right.

And then, but if they all forgot to read, then I’d work it out myself. And occasionally I’d have to do three, three of the 40 problems myself or something, you know, but then it was, but that’s kind of how, but I graded everything, you know, and it took a while. mean, it was the greater problem set. I mean, it was, I used to check IDs at the gym because I was, I was a varsity athlete. So I had work study. So I had like 20 hours checking IDs at the gym and I would do Friday nights at this one gym that like nobody came to. It was like the old gym.

And so I just sit there grading my grading math paper. So I was kind of making money as a math grader and also checking ideas. So I got my pizza money, right? And but yeah, but I actually did it. But it’s a lot of work. But I remember a lot of grad school or a lot of my math courses were, you know, like points at topology and functional analysis and things like that. I mean, I don’t even remember getting anything back. what it was like a week or two later and it was just kind of like a check or check or.

Alex Smith (10:19) Hehe.

Jason Roberts (10:40) you you didn’t check this case or just really minimal feedback with the grad student or the PhD student usually is a PhD student or who was grading these things at that level of the upper division level and they really didn’t care.

Justin Skycak (10:52) Yep. Yep. there’s, mean, and so this is, this is assuming that like, kind of, uh, I mean, in the, best situation, a student actually like wants to, like, is trying to get feedback from the, from the grader and wants to like see and understand that feedback and take it on board for the, like, a lot of students just don’t care at all. Right. They just want to pass the class. Right. So it’s like, well, like if it comes back like a couple of weeks later, guess what? Like it’s not getting read.

Jason Roberts (10:54) That’s that.

Justin Skycak (11:22) And ⁓ also it’s like, well, even as hard as you described it is to legitimately check over all of everybody’s problems, even using heuristics about like comparing like top students in the class, their solutions and stuff. It’s like, well, if a student wants to kind of bamboozle a TA, a grader, it’s not that hard to do, right? Because you can kind of…

If you start off the problem right and end it right and then just some kind of like miracle occurs in the middle, some expression just kind of, there’s one step buried like, yeah, your five started to look like eights, your X starts to look like Ys and like somewhere in the middle, some X transformed into a Y, some theta became a zero and like, hey, it came out to the right expression that matches up with the output.

Jason Roberts (11:56) You know, like, know, they work, a little messy, it’s a little hard to follow.

Justin Skycak (12:16) Like, you can make a TA’s life hell, like just looking for that. And guess what? They’re not going to be checking for that. They’re like, you can, you can kind of get away with, with, um, with bullshitting your homework to some extent. And, and, and then, I mean, probably show up on the, on the exam that you don’t know what you’re doing, but, um, but it’s like the learning, the learning setup is often bad enough when there’s a student who legitimately wants to engage with it.

And when there’s a student who was just trying to do the minimum amount of work to pass the class, it’s like, it just gets way, way, way worse. So it’s so important to, to, you know, lock all this stuff down.

Jason Roberts (12:49) Yeah.

Well, you know, if you go down to the high school level, like they don’t even grade most homework anymore.

Justin Skycak (12:59) Yeah,

I remember back when I was living in Pasadena and your daughter had a ⁓ physics assignment, right? And ⁓ she was asking, yeah.

Jason Roberts (13:08) She was doing the AP Physics C mechanics or something, but

she was doing it as a freshman, which was really tough, I think. And I was like, I was worried because I knew who the teacher was. And I was like, he doesn’t do a very good job. He doesn’t. And I was like, could you? And you know, you’re much more of a physics guy than me. And I asked you you would sit down with her and you to kind of help her with some homework or help her just kind of see where she’s at. And you’re like,

Justin Skycak (13:13) Right. Yeah.

Jason Roberts (13:37) Like she’s just writing them and somebody’s case is kind of nonsense. And she’s like, you’re looking at graded stuff, like the grading stuff, they were just giving a check. believe that she would just write down stuff that was totally wrong and they were just checking on.

Justin Skycak (13:47) Yeah, it was just whether or not she uploaded the assignment into Canvas. Not whether it’s correct or not, just whether it was uploaded. yeah, there was a lot. ⁓ I mean, it kind of got to the point where the class had moved on to doing one step or two steps beyond the most basic introductory stuff. yeah, there’s a lot that she hadn’t properly learned because it wasn’t

The stuff wasn’t being checked. wasn’t, you know, so yeah.

Jason Roberts (14:16) And so we had hire

a tutor. were working for a little bit, then I had to hire, we hired, you know, we had multiple tutors she was working with to try and get her through that course. Um, that was rough. And, um, you know, it was just terrible teaching. mean, you know, when I was in high school, probably like middle school too, yeah, middle school, you know, when you’re like middle school and high school, you’d have your homework and then you would pass it to person next to you. Right. Each person would move it over and then they would go.

Question number one, the answer is negative seven. Question number two is X squared minus three. You’re like wrong and you’re like, did I get that wrong? And the person’s like marking it wrong. You’re like, that’s a three. I’m really talking about it’s a three and it’s a two, you got it wrong. can’t, you know. You’re having that kind of stuff. but you know, so you would get it back and you’d be like, you got, you know, 16 out of 20. You know, and you see the ones you got wrong and you know, and then the teacher would say, you know, the number you.

Justin Skycak (14:47) Trade and grade, yeah.

Alex Smith (14:54) Thanks.

Justin Skycak (14:57) Yeah.

Jason Roberts (15:12) how many, you know, they kind of look at the ones students tend to miss more and would kind of go over some of those. So least there was a certain level of accountability, a certain level of feedback. Now it wasn’t perfect, right? Because first of all, it ate up 10, 15 minutes of class time and to, you know, if you 20 problems or homework or whatever it is, the teacher’s not gonna go over all of them. People miss different problems. you know, and just going over them doesn’t mean the students are actually doing them. They’re just watching the teacher talk about it. So.

That was better. It was a hell of a lot better because in high school level, each had homework every night. You’re in algebra one or calculus or anything in between. Every night you had whatever, 10, 15, 20 problems to do. It would take you 30 to 40 minutes, 30 to 45 minutes, maybe an hour in the worst case. But you’re doing this every night, five, six nights a week, right? Sunday night. You’d watch Sunday, have dinner, watch the Sunday night show at seven o’clock.

been on home for like four hours, right? And a little grindy, but you did it. And that was at least decent, way better than college. You have one problem set a week and there’s no accountability and very little feedback.

Justin Skycak (16:20) And these problems

that you’re doing are kind of at the most abstracted level often. Like you’re not explicitly getting reps on your lower level stepping stones to build up to these things.

Jason Roberts (16:31) I know

this early on because I had been teaching myself calculus when I was a freshman at the behest of a professor as my advisor and mentor as a physicist. And he said, you need to start teaching calculus. That’s a whole other story. And so I was spending more time thinking about learning what it takes to understand something even as a ninth, tenth grader.

Whereas most kids are just like, they just listen and do homework. I’m just thinking, I was like, why, we should be reviewing and every, I was like, if I was teaching this class, every quiz, I would have a weekly quiz and test every, call it three to four weeks. And at least half that material would be stuff, could be anything from the beginning, of course.

And I would surprise them with stuff from the first week or the third week. they would never, so they’d always have to be continuously reviewing stuff because it’s like, never know what you get. Because then you get to the final exam and now you’re spending like three or four days going over all this, tests and quizzes from, and trying to relearn this stuff as opposed to just having kept it fresh. So they never ever did that. And I was like, this is so obviously the way to do it. It’s just dumb that they don’t do this. But I don’t know, that was at the high school level.

We didn’t do projects, we didn’t have class discussions, we didn’t have challenge problems. There was none of that stuff because it was just straightforward, kind of vanilla stuff. again, at least there was accountability and there was regular homework every night. You could sit there and listen to the teacher talk and take notes for an hour, which was super boring and super inefficient. Most of these math teachers were not the most fascinating, entertaining people in the world. So you’re just like, ugh.

Justin Skycak (18:16) Yeah.

Jason Roberts (18:17) you

know, you’re like sleeping at your desk like this, you know, or head down or kind of, you know.

Justin Skycak (18:20) Yeah. So often it’s just

these like, the teacher has made some notes based on the textbook before class. Now they’re transcribing those notes onto the chalkboard during class. And then the students are transcribing the chalkboard into their notebook. It’s like this game of like telephone. gets like, it’s just the information from the textbook is being replicated in various ways. And we’re all just going to pretend that this is learning, that this is

work that’s being done, just to, I guess, stay busy. like, you know, if somebody walks in the class, it’s like, well, I guess like teachers writing on the board, students are writing in their notebooks, learning must be happening. But it’s like, it’s not at all even close to optimizing retention. And yeah.

Jason Roberts (19:05) So what could be most efficient?

You know, what’s interesting is like the high school I went, the, it was a K through 12, was private school, it called Padea. And it was, it kind of like if Brown University was a high school. And I was started by a bunch of, you know,

Harvard students from the 70s, came down, a bunch of hippies, and they started this school. And so was very kind of progressive, it was very, it called teachers by the first name, and there was no home room, and there was no cafeteria, there was no dress code, and so was very kind of cool in that way. so a lot of it was a very, considered one of the top-notch schools around of that, especially the kind of progressive design. And…

The, I mean, it was actually profiled as part of a story by Michael Lewis. He did a story, was on an MPR like 15 years ago, it’s about this guy who became a famous or really well-known, I think he’s an economist at maybe Yale or Harvard. And he was talking about how he was at this, you know, really crappy public school and this teacher took an interest in him. He was like an immigrant from…

I don’t know, Serbia or Croatia or something like that during that war. then she took initiative and she said, you need to be at a better school of this and got him into Padaja. And you talk about Padaja, was this amazing school, it’s beautiful buildings and stuff. In a lot of ways it was, right? But then even still, the math was, it was still probably better in a lot of places, but it was still just spent an hour in the homework. There was nothing particularly interesting, you know, there was no automated view, it was in mastery base and none of these things.

Right.

Justin Skycak (20:47) You just got to do it in a nice classroom,

nice settings around you. Students are generally behaving well and respectfully. Yeah.

Jason Roberts (20:54) Oh yeah, mean everybody’s,

you know, I mean it was, it was kind of progressive. whatever, somebody played, everybody was dressed as kind of a, you know, you’re hippies and you’re punks and you’re whatever, but the parents were professors at Emory University, they worked in the CDC and stuff. So it was things like that. I mean, so, you know, a lot of, everybody went to good, really good schools and a lot of people went to elite schools and that kind of stuff, right? But it still the, even in a situation like.

That was, and then I go to University of So one of the top five math programs in the country ranked anywhere from typically second or third to 10th at the worst in the country. Math cost has basically sucked in a lot of ways. And I was like, why is this? Like, why is it suck? Why is it suck? Why is the suck so bad? Why is it?

And in lot of our places, it’s going to be worse. The professors, no material even worth it. They’re not as, I don’t know, but it’s just amazing how poor this has done. So we won’t have to worry about middle school and stuff. That’s whole different discussion. Alex, you taught university courses.

So when you were going in and teaching these courses, I mean, I know there’s a certain like format and a certain like expectation, they expect you to do things a certain way and you’re not free to do anything you want. I mean, how did you think about it? Were you, you know, you’re like, hey, I gotta focus on my research, man. Like nobody cares about the teaching, do the best I can, but it’s like, I’m not getting a grant based on my teaching recommendation, I a grant based on my conference papers and things.

Alex Smith (22:29) Well, I mean, when I got the opportunity to teach at UCL, I taught a course in asymptotic analysis and boundary layer theory, is like a fourth, like a master’s degree course, is, it was very closely related to the kind of area where my research was. And I was just super excited to be given this opportunity. So I took it really, really seriously. And so I ended up

I, which to me was just the natural thing to do. Okay. I’m teaching a course. need to basically write up in latex with diagrams, the full nine yards, all the, everything I’m going to teach for this. so prior to teaching the course, I think about in the two months leading up to the course, I wrote this huge document, which is basically the course I’m going to teach. and just at the time, like just handing out kind of like, no, handing out typed notes, complete with like,

kickass diagrams was completely it was it just wasn’t the done thing. The done thing was exactly what you guys are talking about, which is to go up on the board, which is basically transcribing from book of written notes. And I just didn’t I just didn’t want to do that. I just wanted to give give the the chapter we’re going to be discussing this week and I’ll go up on the board and I’ll go through it and we’ll have a discussion about what’s what the stuff is all about, you know, obviously you go through derivations, which are in the thing because you want to set things you want to point out along the way but

I definitely wanted it to be more interactive than your typical session. the students were super appreciative of the fact that I actually went through this huge amount of effort to actually type up these very, very comprehensive notes and everything else. It’s like, wow, we’ve actually got some really proper material that we can study with here. yeah, so I mean.

Yeah, so most of my, I was lucky because I did my undergraduate in Manchester and a lot of the, ⁓ I think they took the teaching side of it a lot more seriously in Manchester, like they, a lot of the lectures, especially at the master’s degree, because I did my master’s degree there too. A lot of the master’s degree notes were actually, were just beautiful. I had this one professor called Anatoly Rubin, who’s like a quite well-known fluid dynamicist. I was just in awe of just how insanely beautiful he was able to write this math and teach it. I mean,

A lot of it was kind of just transcribing from the notes, but the fact he actually went to this effort to create these beautiful documents for us to learn. was like, wow, this is a breath of fresh air. You know, so I was very much inspired by, by that. but, ⁓ but yeah, so certainly at UCL where I went, the, quality of the teaching didn’t seem to be particularly good.

Jason Roberts (25:00) Well,

know, people who don’t know, UCL is University College London, and that’s usually ranked as one of the top universities in the UK, right?

Alex Smith (25:08) in the world in fact but a lot of the time that is for what they’ve achieved in their research and things like that but yeah I mean like I said yeah

Jason Roberts (25:09) Yeah, right.

As is the case with all these universities,

Harvard, MIT, Caltech, Stanford, Chicago, whatever, UCL, I mean, it’s not ranked because they have an amazing course, it’s ranked because of the research that these professors output, right? I mean, that’s the real number they’re looking at.

Alex Smith (25:30) Yeah.

Yeah, I think a lot of the time it’s like, you know, sort of teaching a class is like the thorn in the side. So, got to teach that class is distracting for my research. And I suppose to a certain degree, I can understand it. But, ⁓ but when I, when I was given that opportunity to teach, I really wanted to do a really great job. And, and I, there was another course in numerical analysis, which I taught, I did the same thing again, it went down really well with the students. ⁓ so yeah, just, just putting that, that really solid effort into teaching. felt that they, they, was really

It came across very well, it very much appreciated, but it wasn’t the norm at all.

Jason Roberts (26:06) You know, it’s, yeah, that’s really, it’s really, did they, when you were given the course, the head of the math department, whoever head of undergraduate instruction or graduate instruction, they say, hey, Alex, here’s, we have like a seminar on how to teach, you know, here’s our book on how to teach a class.

Justin Skycak (26:06) yet.

Jason Roberts (26:27) Nobody taught you any, nobody said, this is how it’s done at UCLA. Here’s how we teach a first class. You need to assess based on this. Here’s how you prepare your lectures. Here’s how you run a teaching, office hours, any of that stuff.

Alex Smith (26:39) No, no, like that. You kind of had to sort of learn on the job, I suppose, very much. ⁓

Justin Skycak (26:42) So it takes,

you really have to go in being wanting to work hard to make this class a good experience for the students. Cause there’s nobody forcing you to do that, right? This all has to be very self initiated. You just have to be very.

just that kind of person, driven person. And most people are without accountability measures in place. Yeah. Most people are not going to do that. So yeah.

Jason Roberts (27:01) driven.

Alex Smith (27:10) Yeah, I mean, they were, I think you these in lot of universities, like sort of like, students at the end of the course are asked to rank certain things. And I remember there was one, I did pretty well on those rankings. But I remember there was one lecturer in particular who scored so badly in one particular class. But he was like, he was brilliant in his research. was like, oh well, he’s, guess he’s not a great teacher. you know, I guess, you know, but guess who’s

Justin Skycak (27:16) Yeah.

Alex Smith (27:38) teaching that class next year, the same guys, you know, and there was no like, okay, let’s, you know, no mentoring, I don’t think, okay, well, this hasn’t gone well. Let’s, you know, take you under our wing. Let’s see what, we can improve these classes. Like none of that really, it was just, you know, it’s just not really.

Jason Roberts (27:53) crazy.

You know, speaking of the effectiveness of classes, I was talking to my son Colby, who is a senior in college. She’s double majoring in math, computer science, and he’s part of a four plus one. So he’s doing his graduate undergrad degree together because he was advanced enough in math and stuff that he start. He started like basically

halfway through his sophomore year or for junior year. So he’s able to do this compacted undergrad graduate thing. So anyways, he’s his graduate degree in computer science. And so he’s taking, I was just talking to him on the last weekend about it and he asked, so how’s the machine learning course you’re taking? Cause this is like his graduate level machine learning. And he’s like, yeah, it’s, you know, it’s like, it’s all review, you know, I mean, and I’m like, review from what? And he’s like, well, review from Justin’s course.

Alex Smith (28:44) We’re gonna…

Jason Roberts (28:44) Giving the stuff you did in 10th and 11th grade, 12th grade with Justin is the stuff you’re doing at the graduate degree. He’s like, yeah, I basically learned nothing and almost nothing. He’s learned nothing in machine learning. And he’s learned in, you know, since your course. And he’s learned only a few things, computer science and like operating systems and sort of the system stuff that you didn’t do, like C and memory management stuff. But, you know, in terms of data structures and algorithms and

You know, things like he, he, all that stuff’s review. I mean, he was telling me about the machine learning. He’s like, I said, are you using, uh, he goes, yeah, you know, it’s like, they’re doing some neural net stuff. And he’s like, yeah, we’re just using PI. You know, I see that I’m just using PI torch and this. I’m like, didn’t you have, didn’t you have like, didn’t you have a library? You built your own neural net library. He’s like, yeah, but I have to deal with like another couple of people and they’re not going to understand, you know, they don’t understand neural nets at that level. So I have to use something that’s really.

basic like PyTorch that does most of it for you. And this is graduate level stuff. Anyway, I thought it was really cool. It says a lot about the course that you taught, the Urisco course, the 10th through 12th grade was just ridiculous in terms of what you gave those guys. was incredible. He’s just still making a living off it. He’s still like, where’s your review?

Justin Skycak (29:44) Yeah.

It’s great to hear it’s

made that much of a difference, but yeah, it’s just, well, the, mean, kind of the point that we’ve been hitting on is like the bar for like the status quo of instruction, whether it’s college or high school, whatever, it’s basically on the floor. So if you, if you make an effort to like actually, you know, write up your, your, your, classes, create reference material, you’re already doing better than, than a lot of instructors out there.

If you take that to the next level, make it a super comprehensive course, and also have these broad coverage quizzes that are forcing your students to keep bringing back and reviewing the stuff that you’ve taught them previously. And you’re forcing them to do things from scratch instead of just importing their own libraries. Like, I can do import neural net from.

Whatever torch or psychic learn whatever neural net dot run on data. Wow. I don’t know. Well, that’s not, not, if you like actually force them to build this stuff on their own and you scaffold them up to that. It’s like, there’s yeah, just the bar is on the floor. You just, there’s so much more student potential on the table that just doesn’t get realized. so the

And so this, this Eurisco course, was, this, was not like a full day experience for, for years. This was, this was like a, this was one course, just that there was one course in the school day for, for a couple of years. and, and this is, this was the amount of learning that we were able to pack into it. Why, why is this such an outlier? Why can’t every course be like this? and by the way, and I, I, and I did this like manually without.

I guess was not in the math academy system. I was working my ass off to create all this stuff, to optimize everything. And they came into that course because they had all their math prerequisites in place having done that on math academy system. But it’s like, you know, if we can just get this all just standardized in one reproducible system, every student can just come through, take the course, you know, not just have reference material, but have it being like,

the instruction and the problem solving given to them and minimum effective doses interleaved throughout broad coverage, quizzes, everything. You can just do that in like every course. just totally transforms the learning experience for everybody. Yeah.

Jason Roberts (32:15) Yeah. It’s like actually care, actually really care about the outcomes, care what you’re doing, make things efficient, make them effective. It’s like the commonality that, you know, I mean, think that a lot of, I think some people care, they just don’t know, right? They don’t know how to do it. People just do things how they’re done, right? It’s like I would go watching my son’s football practice and I would see all these kids in their pads standing around most of the time.

Justin Skycak (32:22) Yeah.

Jason Roberts (32:43) And they had like five or six coaches. got the head coach, assistant coach, the defensive coordinator, offensive line coach, skills coach, all these coaches. So you plenty of ways to break them up and groups, have them doing stuff. But still they spent most of their time working. And then if they had the first, they had the starting offense, starting defense practicing, they’d have the second string or third string. They’re all just standing around watching the whole time.

Why don’t you have them playing against each other? First string versus second string, second string versus second you know, just looking back and forth, you know, they should be doing something all time. They’re not perfect.

Justin Skycak (33:13) Nobody should be idle.

There’s no reason for anybody to be idle. Yeah. It’s just a waste.

Jason Roberts (33:20) Just long enough to catch your breath.

Get a sip of water, catch your breath. All right, let’s go. Like, let’s work on stuff. If you’re the skills people, you’re a quarterback, you’re running back or receiver, we’re working on that stuff. Anyway, I was just like, wow. I wanted to go, was like, why do feel like, because I’m frustrated because I’m sitting there watching my son just stand there and stand there and stand there and stand there. like, I can’t even watch this crap. I’d have to pick him up within a practice, it’d be so annoying. I’m like, this is terrible.

Justin Skycak (33:48) It’s like,

well, no wonder football practice takes like three hours or whatever, right? Like those run ridiculously long. And it’s like, there’s just so much empty space. You just compress this two hours. Yeah.

Jason Roberts (33:57) another would be two hours and there’s like 15

minutes or 20 minutes of really good stuff. The rest of the stuff was standing around. It was like just dumb. But I mean, I would say, so was it just, it wasn’t just about math classes, you know, it was just like football practice, you know, or whatever. I mean, and I watched at the high school level too, when he was playing high school football, was the same thing. But yeah, I mean, I don’t know. I just don’t think people think that much about it.

Justin Skycak (34:02) Yeah.

Jason Roberts (34:25) And they just kind of people sort of pattern matchable. This is how I did it. And this is how I think about it. And you’re not thinking, okay, I want to maximize outcome. So I’m going to do everything I possibly can. So if I have receivers and only the big receivers, I want them practicing routes and practicing catching the ball and practicing creating separation, whatever it is, practice that over and build on it. Like let’s just get these receivers doing this. Do out routes, just do it. And routes is just, you know, running after the ball running, you know, whatever. I mean, just like, just

drill instead of just standing around watching like what are we waiting on? mean,

Justin Skycak (34:57) Yeah, you have to come

at it like a first principles problem of you. want to every single student or athlete or whatever, every single trainee needs to be working on the one specific thing that is going to make them better as fast as possible. Every single moment of the time. If you, if you try to pattern match to like existing education structures, how classes are run, how sports practices are run, and you just look around, chances are like 99 times out of a hundred, you’re going to be looking at some kind of setup that just sucks.

Nobody is upskilling very quickly, if at all. Just stand it around. Maybe they’re transcribing notes. You really have to, it’s so weird that just the field of education in this current state is like, really have to be a contrarian, almost. And start from this principle that nobody else wants to start with if you want to actually build something that works.

Jason Roberts (35:50) Yeah, like a first order heuristic is are people actively doing something or not? If they’re sitting in a chair, listening or watching, you know, anything more than the minority of the time, that’s bad. If they’re sitting around watching a practice, just listening to a coach, that is low efficiency. They need to be doing things and then getting feedback on those things.

The second order and second is like, when they are doing this thing, are they doing stuff at the right level with the right kind of feedback? Or they’re being asked to do something that’s beyond them or that’s too far below them, then it’s probably not a very efficient use of their time. And are they getting good feedback or is somebody just kind of yelling at them just in general or somebody saying, okay, here’s what I want you to your foot in here and then I you to shift your weight. Or when you write the proof, got to, you whatever the thing is, are getting accurate, timely feedback. You get those things, but it’s just amazing.

So anytime you see anybody, and it’s kind of funny, they’ll show like in movies and they’ll be like, at end of movie, they make it to the university and they’re at this elite university or something and they’re listening and they’re all just sitting there lecture hall listening to someone talk. Some kind of vaguely charismatic professor talk and we’re like, that is the Shangri-La. They have reached the pinnacle of education. And you’re just like, it’s dumb. This is not really learning. It’s very inefficient, but.

Justin Skycak (37:08) anything else you guys wanted to cover that comes to mind. Alex, you got some.

Alex Smith (37:13) Yeah, was just one just on the subject of failure modes ⁓ in education. wanted to sort of like one that one thing that’s is extremely popular, like, particularly middle school level is like this, failure modes that come about with the concrete represented, representational abstract approach to teaching arithmetic. So for anybody that’s not aware, it’s CPA concrete

Justin Skycak (37:17) Yeah, yeah, yeah.

Alex Smith (37:38) abstract or concrete representation of abstract sometimes it’s called and the idea is to sort of build an understanding of abstract topics and abstract in this case might be you know it’s just anything which is not given like a sort of pictorial representation or physical representation so adding fractions but with no pictures or diagrams or anything and it typically follows that order so you do concrete first which basically means you know kids kind of get you know models of pizzas and they learn to add fractions that way like physical models

And then once they’re done with that, and then move on to ⁓ pictorial, is just add fractures, but using pictures of things that look a bit like pieces. And then they move on to actually adding fractions without any representations at all. And for the most part, this is actually quite a good model for teaching elementary arithmetic, fractions and decimals and things like that.

But there are some sort of failure modes associated with this kind of approach, which I think educators do need to be aware of. The first thing is that ultimately you want to get kids to the abstract approach. You want kids adding fractions by writing down the numbers, giving a common denominator and adding the fractions. You don’t want it to be anchored or stuck on adding fractions using pictures. So

What that means is as you’re transitioning a student through this concrete pictorial abstract model, you need to move them on as quick as possible. Once they got the concrete approach, they need to be moved on to the pictorial approach as soon as they got it. And once they got the pictorial thing, you need to be moving them onto the abstract and then almost like not look back. It’s like, they understand what’s going on here. They then need to of like grinding and, remember grinding is probably not the best word, but developing those

those fundamental skills that are to be used later on. Because if they’re stuck on things like adding fractions with using pictures or diagrams, although it is meant to be a scaffold, it ends up becoming like a crutch. you, yes. We’re moving on.

Jason Roberts (39:33) You want to burn the ships. Burn the ships. Like, okay, we’re moving on. We’re not using

training wheels on the bike. You can ride it now. We’re training wheels.

Justin Skycak (39:41) Thanks

Alex Smith (39:43) Exactly. but that’s something I think can happen in like a classroom environment is kids can get anchored or they get stuck on an approach when they’re ready to move forward. And if these kids like it, it’s like, you for example, my son Dominic, loves counting with beads and things. He’d sit there counting beads all day if it was down to him. So, no, okay, you got counting in tens with beads. Now we’re going to do counting in tens without beads, without pictures, without anything. So you have to kind of move him on as soon as he’s ready.

not when he thinks he’s ready or when he thinks it’s comfortable. So as you feel he’s ready, he needs to move on and almost not look back. And there are times as well where I mean, it’s usually done in exactly that order. So concrete pictorial abstract, but there are times when actually don’t necessarily want to do it in that order. The classic example is that fraction division. in the, lot of people think that

You need to be able to use some sort of pictorial manipulation to figure out what is fraction division, one fraction divided by another fraction, and draw lots of pictures to kind of explain what it is. Before you get onto what you actually do in practice, flip the second number and then multiply. So that is a particular example where you might actually want to do the abstract representation first before you then go back and do the concrete one. So I think that’s something which happens quite often.

Like, yeah, you’re using these pictorial representations when they’re not really needed or using them too early. Another one, one of reasons why actually my own son, was a bit disappointed in his math curriculum at his previous school was that you don’t want to over, we are teaching this basic arithmetic. You want to limit the amount of models that are actually being introduced.

So for example, the curriculum, I think it was called white rose math is that every single new problem was like a different type of model that was being used. And it was really, really kind of like throwing him out, throwing a lot of the kids actually, because again, it’s just cognitive load. The context is changing with every single problem. It’s like, no, pick five models, number lines, fraction models, a couple of others, stick to those and teach all of arithmetic just using those four or five and everything else just.

throw it out with the garbage, you know. So yeah, so that I think is a failure mode. So overuse, of introducing too many models, not moving them on quickly enough. yeah, not moving them on quickly enough and yeah, having them anchored into a situation where they’re using it as a crutch, like a pictorial representation as a crutch.

Justin Skycak (42:05) Yeah, you know, talking about all these models and alternative framings, you know, it reminds me of, you know, back when I was tutoring at my hometown Mathnasium, I met so many kids who loved using the lattice method for multiplication. The one where you would like draw the box and like the diagonals and stuff, film the numbers. It takes forever to do because you got

draw this whole thing, it’s a lot less efficient. But they love this thing because they they learned it in school, right? And as kind of like an alternative strategy. And then they would realize that like, oh,

Wow, get to, as, part of practicing this alternative strategy, I get to draw a cool thing. And not only is that fun to like draw it, but, but also like, I don’t have to be doing math during this time. This is just a drawing break and I can make it really pretty and focus on drawing the diagonals and the teacher is not going to get on my case because I’m doing math. So I’m just going to take, take my sweet time with this, do this. know, sometimes they wouldn’t even draw it.

that carefully or just take their sweet time just kind of sitting there but still draw the grid sloppy and like get a mess up along the way. anyway, so they would always want to use like this, this lattice method for multiplication because it kind of allowed them to bypass the real skill development. And so, so what would end up happening is

they would eventually get frustrated that their homework is taking forever, right? They got like five multiplication problems and somehow this has taken them like an hour to do because they’re using this inefficient method. And so naturally, like, I’m like, well, why don’t you just like, okay, just stop using the lattice method. Just go back, use the standard method. Like, do you want to get done with your homework or not? And so they’d often resist this. so it took me a few…

some time to realize that the reason that they were resisting it was often because they had forgotten how the standard method even worked, because they had been doing the lattice methods for so long, they weren’t practicing the standard method. And so they had basically stranded themselves on this island of lattice method, unable to get back to the standard method that’s going to carry them over into the future. It’s kind of like the teacher introduced this method thinking like, oh, this would be a fun break.

from the typical standard multiplication method, little vacation, little enjoyable vacation. And they don’t realize that a lot of kids are just gonna wanna stay on that vacation forever. Like they don’t wanna come back. And eventually it’s gonna just create lots and lots of friction. when kids are choosing what methods they wanna use, they’re not exactly aligned with the whole.

you know, what’s best for them in the future, what’s going to ease the talent development process, is, what can be used into the future, what scales, what the size of the numbers, what, you know, all that sort of stuff. don’t, they don’t, number one, they don’t care about that. And number two, they don’t know because they’re students, right? So that they can’t see the whole, the road ahead of them. So they’re just going to latch onto whatever method they like.

best as though it’s the flavor of ice cream. Like I like blue. I like chocolate. I like lattice method. I like the one where you draw the stuff. I like the one where you make the tally mark. Like, yeah.

Alex Smith (45:27) Exactly. That’s the great thing about having a system like ours, like Math Academy, to teach this kind of stuff. like we can force the kids to move on and not look back as much as we like. It’s like, okay, the mastery learning procedure in this case is okay, yes, you learn to multiply using some, you might use some sort of grid methods or something like that. But once you’ve demonstrated mastery of that…

We’re going to force you to move on and you’re not going to go back unless we detect that some sort of like fundamental kind of conceptual understanding, which you might want to move them back. But yeah, but as a teacher in a classroom, you almost certainly need to be quite stringent in the, okay, you’ve got this now, we have to move on. that’s the last you’re going to be seeing the lattice method.

Justin Skycak (46:15) You’re ready, kid. Let’s go. Let’s go. Move on.

Jason Roberts (46:18) I actually have a couple of questions for you, Alex. The first is, you’re in the process of creating our sixth through eighth grade courses. So we have a pre-algebra course that bridges fifth grade to algebra one. But there are actual sixth, seventh, and eighth grade courses that basically cover material and pre-algebra, kind of spreads it out. There are some more topics in there, and there are certain standards that we need to hit for certain school districts that want to use various standards.

aligned curriculum as opposed to ours, which is a little bit compressed and it’s a little bit maybe accelerated for students who need more time. And Alex, you said that when you were in the process of doing it, and I just want to hear your thoughts on what is different about it. And also you said you were going to make some adjustments to the fifth and maybe the fourth grade course. By creating the sixth or eighth, you were kind of taking a second look at

what was happening in the fifth grade material to prepare for this. We would keep targets through anything that might be interesting about that.

Alex Smith (47:18) Yeah. so yeah, so as you said, our kind of, so at the moment, our curriculum goes from fourth grade, then to fifth grade and then onto pre algebra and then from pre algebra, then then goes on to algebra one. So pre algebra is like about 200 topics. It’s kind of like, so it’s kind of like sixth to eighth grade kind of compressed into, into a single, into a single course. so

Jason Roberts (47:37) Which

sounds crazy, but the reality is there’s a lot of repetition in those three years. There’s a lot of just redoing the stuff. So it’s not as crazy as it sounds. It’s just, that’s the nature of it. It’s not a lot of progress made in those years.

Justin Skycak (47:46) Kids are not doing much, it’s very compressible.

Alex Smith (47:49) Yeah.

Yeah. I mean, I mean, for example, one of the of the sixth grade standards is to use like the distributive law, you know, a times brackets B plus C equals AB plus AC, you know, that kind of thing. But the sixth grade standards actually, actually say, you know, this is to be done with positive rational numbers only. So there’s not even any negative number arithmetic in there at all. And so we have to sort of write a curriculum for that particular course that covers that standard. And then almost like kind of

You’ll then kind of do the same thing again at eighth grade, but once you’ve kind of mastered all the negative number arithmetic. Now actually, this is actually beneficial, I think, for students that do need a little bit of a slower to go at a little bit of slower pace. I actually think this is a great thing, as a matter of fact. that’s gonna be crucial difference between the two paths. There’s gonna be more scaffolding of that kind of type.

And that simplified geometry problems. What else? There’s a number of adjustments, adjustments like.

Jason Roberts (48:46) There’s something to do with like percentage changes or something like, I saw some email about updated to additional topics on percentage, working with percentages or something.

Alex Smith (48:57) Oh, that was more of a just a just an improvement to our existing curriculum. We have some topics on percentage change, but it turned out it needs to be really kind of expanded out. You know, if you’re compressed into one topic, be like what we’re talking about earlier, like, you know, we one topic on percentage change was really what you needed for properly scaffolded thing, which you certainly would need at that at that level would be one topic on percentage increase one topic on percentage decrease one topic on percentage change on percentage. Given the percentage change, figure out the original value.

stuff like that, applying percentages. So we recently did quite a big broadening of improvement of all that stuff, which is going to be needed for the seventh grade course. So anyway, the original plan for Math Academy was to have the fifth grade, have the fast track, fifth grade to pre-algebra. That’s how we designed the course.

So what happened is that some of the material from sixth grade ended up going into the fifth grade course. The way the standard, the common core standards work is that you can teach stuff before the standard grade. So for example, a decimal division is like a sixth grade standard. Now you can introduce that fifth grade if you want to, because that’s only going to work for certain types of students. what we’re going to do once the sixth and eighth grade courses are

We’re going to do some reconfiguring of the some slight reconfiguring of the fifth grade core just to show a complete one-to-one mapping between our courses and the standards So you won’t be like well hang on second what why they’re doing decimal division in fifth grade. So well, they won’t be anymore So that would be at the grade level that’s That is usually taught out or the standards suggest you teach at so the fast track option will still be there But we’ll also have the the the more regular tracks 6 7th grade

for the students that want it, which I think, I mean, just looking at my own son, I think he probably would prefer, well, certainly the way things are going at the moment, probably be a more scaffolded approach would work for him. But some kids just want to go as fast as possible. you know.

Jason Roberts (50:58) Yeah,

yeah, yeah. Well, of course he’s younger too, so might as well, there’s no weird little rush, you know.

Alex Smith (51:02) Exactly, There’s

no rush at all. I he’s got quite a long time to finish out our middle school path, so yeah.

Jason Roberts (51:10) This is the other thing I want to ask you about. okay. And so just, the, the, the six through eighth vertebrae launch, we’re going to release all three of those courses together. That’s the plan. said really, because it’s kind of a parallel path of the pre-algebra. And so that’s your, we’re shooting to have that sometime in March. Is that what you’re thinking?

Alex Smith (51:28) Yeah, I think, I think end of March is no. Well, now it’s beginning of March. Yes, end of March, I think we’ll be close to being ready. Yeah.

Jason Roberts (51:37) That’s great. That’d be great to have these finally done. So then we’ll have the entire curriculum top to bottom, mapped to two standards and all that’s great. The other thing I want to ask you about, because you’re talking about like models and things. I remember, it must have been a couple of years ago, you volunteered to teach multiplication tables, know, the math facts to your son’s

kindergarten class or something like, or I don’t know, it was older group. No, you were just volunteering at the school. So it was older kids, it must have like third grade. But was at school, it was at the public school that Dominic was at. And it was kind of an interesting experience for you, right? I mean, it was surprising in some ways. Do you remember, was there anything about it that strikes you that’s worth talking about?

Alex Smith (52:30) One thing I found was interesting, there’s a lot of emphasis on kind of like conceptual understanding in math. And that’s where at this level, all these different, like this whole myriad of models and frameworks and things like that comes from. We want to build understanding of math. So let’s do 10 different models that explain what multiplication is. And one thing that struck me is that all the, cause I was given a group, in the UK,

in year four, which is the equivalent of third grade, they have to do a times tables assessment like a quite, quite a time. It’s like 25 multiplication problems all have to be answered within five seconds is weighted towards the more difficult times tables at six, seven, eight, six, seven, eight, 12, that kind of thing. So I was preparing kids that were struggling with this for this particular assessment. And one thing that struck me is that

They all knew what multiplication was. got it. you ask, okay, four times 10, they got it. was just repeated addition. So I’m like, why on earth would anyone spend so much time spending, drilling these kids on like supposed conceptual understanding, using all these pictures and diagrams and models and things you can pick up and this and that, when they already know what it is. What these kids need is to, to, is basically.

drilling on their multiplication facts. you can make it fun. We play games. There was a great one called a times table snap where you would go, you you sort of, put all the numbers on the table and there’s three or four kids and you’ll say like three sevens and snap. Whoever gets it wins the car. get a point. You can make it really, really fun. But it was really about, okay, making sure they understand the root, the times tables, you know, from start to finish and then mixing that. And once they’ve got that foundational knowledge, making,

trying to get them to a point where they can recall them efficiently, but in a fun kind of way. And it worked really well. These kids really did come along very, very quickly just because we just need to memorize these times tables. You know what multiplication is. Now we just need to memorize them. That’s ⁓ how it has to be done.

Jason Roberts (54:32) Well, I know every time there was a pretty broad range in terms of the ability of the students to memorize these things too. I you were sort of surprised that there were some students who really, really struggled to just hold the facts in their head, just keep forgetting them, right? I remember you were just a little surprised by that, if I recall.

Alex Smith (54:50) Yeah, I mean, I mean, there is there is definitely a spread in terms of students abilities to be able to retain these facts. I mean, that’s that’s that’s for sure. But again, I think just that highly targeted practice was what was needed for these kids just just just that remediation small group do something fun, make sure that you do some do some rudimentary work in the beginning, like actually getting to write down the four times table. So right.

Now we’ve got that, let’s play a game. Time table snap or whatever it is we had. And then just make it fun and make sure it make it competitive. Not one kid who’s just like, you know, just, you know, just destroying it because he just knows his time. So it was better than everybody else. Yeah, it was, was, was, was an interesting, interesting experience. ⁓

Jason Roberts (55:35) You know, it’s kind

of interesting. It reminds me of in games, to make these games work with kids because kids who get, kids can get kind of emotional. They get really excited, but they can get a little too emotional about it sometimes and they can easily end in tears. I mean, even like I had fourth and fifth grade as a tear. I’m like, were you really crying about this guy? We were first. They’re like, take it easy. Um, cause I would make everything in game too. And, um, but you almost, there was this, uh, you know, the, the,

Justin Skycak (55:54) Mm-hmm.

Jason Roberts (56:04) It’s a board game called Settlers of Catan. I know you guys are familiar with it. I actually not played it because I’m not really a board game guy. know a lot. I’ve know of it. I’ve read some articles about it. I remember reading a Wired article about these German games like Settlers of Catan that were way better than say Monopoly or something because they balanced the game plays much better. One thing they would do is they would, if further ahead you got, the harder would get for you. And then further behind, so if you were behind, it would be a little easier for you to catch up. So it kept things competitive.

Justin Skycak (56:07) Yeah, I’m familiar with that.

Jason Roberts (56:34) Right? So it’s like, you have to create these games and say, okay, that, okay, if somebody is really fast, you know, because we’re just playing a game, it’s just a game. Right? But like, if one kid’s going to run away with it, the other kids give up. They’re like, well, you know, would have to have, know, Claire is just going to win. I’m like, you know, the kids only want to try. They quit. So you’re like, okay. So you have to, you know, sometimes you have to think about just construct these games like Settlers of Catan, which is like, okay, as you get ahead, you have to

You only get to do 12s, you know, or like two digits, or else the one digit. So it’s harder to like, and so they can, you’re like, I never remember 12 times 11. And so he’s backed out even though you’re going seven times three or whatever, but it’s just a game. anyway.

Justin Skycak (57:16) And ultimately

that’s what the kid who’s ahead needs to be practicing as well, right? Like if they’re really solid on their single digits, it’s like why have them repeatedly practice that? It’s for everybody’s good, including your own good, to make you work on harder stuff.

Jason Roberts (57:31) Well, in golf, have something called a handicap, right? So it’s like, you know, if you’re playing as somebody who says I have five handicapped, I mean, they get five, they hit five strokes over par. They’re really good. And somebody who’s like a 25. Well, they can play together because you’re really just playing, you’re using a handicap. So it’s like, how, how can you beat your handicap? You know, your last tower mini scores, five scores is what your handicap is. Your average is 25 over. Can you get a 23? Can you beat it? Are you, you know, cause if

If you get a over par, so you shoot a 95 and they shoot an 80, so the eight over par, you win. So it’s like, can play against my dad when I’m 12 years old or something, or 13 years old, and we’re playing, we’re using our handicaps to make a fun for both of us. It’s not always easy, it’s easy to do that. mean, things like chess, like, okay, you start with your pieces, then remove some of your pieces from the board.

You you with your bishops and your rooks and stuff and now we’re, now we can play against each other. Otherwise it’s just not fun, right? And for game, for younger kids in particular, I mean, it’s never fun for anyone to play someone who’s a lot better than them, you know, more than like watch like, okay, well, I got destroyed. I mean, I think was kind of cool to play with someone who’s that good, but it’s kind of not really very fun, but it can make you competitive. It’s like, okay, I actually have a shot, right? I actually have a shot here. And if someone is way better, it’s like totally boring for them. They’re just like.

But if they have to fight, then it’s fun for everybody. Because that really, in the end of the day, you’re competing against yourself. And you want them to thinking about that. It’s really about you getting against yourself and you improving. So that’s really cool. Well, so we should probably wrap up. It’s been over two hours. We’ve got a good, solid. Put some points on the board to continue with sports analogies that never seem to come to an end.

Justin Skycak (59:11) Yep, absolutely.

Well, I I guess one of those things like we can stop with the sports analogies once math education is just taught in a way that’s in accordance with the obvious principles from sports, right? I mean, we don’t, the day that people actually teach prerequisites properly before moving on to the next content, like we can, we don’t have to rail on like the, on that sort of failure mode.

Jason Roberts (59:24) I’m not sure if you can hear me.

Justin Skycak (59:37) The only reason that we need to keep revisiting these things is because these obvious things just do not get, the bar is on the floor. Like we talking about earlier, the bar for instruction is on the floor. Once the bar moves up, we don’t have to talk about these things, but it’s like until then, well, yeah, we’re just gonna be talking about this into eternity unless we do something about it to raise this bar up.

Jason Roberts (59:54) They figured it out.

That’s That’s right. All right. That’s a wrap. We’re out.

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