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Episode Summary:

Ever wondered why traditional math education might be holding back our true potential to understand and use mathematics effectively?

Conrad Wolfram, strategic director of Wolfram Research and a prominent advocate for transforming math education, joins Jon and Kyle in this episode to explore revolutionary approaches to teaching math. With a fascinating journey from a math and physics enthusiast to a leader in computation software, Conrad sheds light on how our current education system may not be equipping students for the real-world challenges that await them in a technology-driven environment.

Resources:

• US Math Wars: What I Know & What I Don’t [Conrad Wolfram]

Attention District Math Leaders:

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What about opportunities for those who are eager and willing to elevate their practice, but do not have the support? 

Book a call with our District Improvement Program Team to learn how we can not only help you craft, refine and implement your district math learning goals, but also provide all of the professional learning supports your educators need to grow at the speed of their learning. 

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Episode Summary:

Conrad’s Mathematical Journey and Notation

Jon, Kyle, and Conrad had a discussion about Conrad’s background and interest in mathematics. Conrad, the strategic director of Wolfram Research, shared his journey from being a math and physics enthusiast in school to working on building computation software. He also reflected on his struggles with understanding a particular math problem when he was in boarding school, which later led to his interest in improving math notation. The team also discussed the nuances of mathematical language, with Conrad explaining the differences between ‘y equals 3’, ‘y double equals 3’, and ‘y triple equals 3’.

Conrad’s Struggles With Probabilities and Misdiagnosis

Conrad shared his struggles with understanding the differences between conditional and unconditional probabilities, reflecting on how his confusion may have been due to a lack of confidence and intrinsic interest in math. His experiences also brought to light the issue of misdiagnosis in education. Kyle and Jon showed empathy towards Conrad’s past experiences, recognizing the difficulties that many students might face in math, particularly due to a lack of understanding or interest. Conrad’s story also highlighted the importance of perseverance and revisiting concepts to overcome confusion.

Misconceptions in Mathematics and Fraction Addition

Kyle, Jon, and Conrad had a discussion about the common misconceptions and misunderstandings surrounding mathematical concepts. Jon shared an anecdote about a student who had difficulty with math due to a single instance of failure, which led to a negative self-perception. Conrad emphasized the importance of starting with the student’s perspective to better understand their issues. They also discussed the concept of adding fractions, which Conrad admitted was not something he had ever done in his life. This led to a discussion on the practicality of teaching precise fraction addition in schools.

Reevaluating Math Education in the Digital Age

Conrad explained that knowledge of higher times tables was historically important due to their relevance in old monetary systems based on base 12. However, he questioned the continued emphasis on memorizing multiplication facts in modern education when technology can easily handle such computations. Jon and Kyle shared their transitions from teaching math procedurally to focusing more on conceptual understanding and the reasons behind mathematical operations. Conrad noted his realization that much of what is traditionally taught could be better accomplished by computers, suggesting a need to shift focus in math education to areas where human thinking is more valuable.

Reimagining Math Education With Computers

Kyle, Jon, and Conrad discussed the future of math education, with a focus on the role of computers and the need for a more conceptual, process-based approach. Conrad proposed a shift towards a computational curriculum, emphasizing the importance of teaching humans how to use machines to optimize their decision-making. The group also debated the balance between teaching fundamental concepts and challenging students with more advanced material, with Conrad arguing that the current system is off-balance. They agreed that math should be used as a tool to solve problems rather than an end in itself, and highlighted the importance of teaching a wide range of algorithms and tool sets. The discussion also touched on the need for a debugging process in aiding students, and the possibility of incorrectly defining problems.

The Limitations of Relying on Numbers Alone

Jon, Conrad, and Kyle discussed the limitations of relying solely on numbers in decision-making processes. Conrad highlighted the need for a more nuanced approach, referencing historical decisions that were made based on a broader understanding of situations rather than precise figures. He further explained the issue of underestimating the linkage between risks, illustrating with examples such as the 1980s Lloyd’s insurance crisis and the 2008 banking crash. Kyle related this to investments, pointing out that people often focus on interest rates without considering volatility or standard deviation. Conrad agreed, suggesting that distributions should be used judiciously to avoid discarding most of the data.

Discussing Toolset Limitations in Education

Conrad, JON, and Kyle discussed the limitations of a narrow toolset in modern problem-solving and its implications for education. They highlighted the importance of understanding the process and the role of tools in problem-solving, and criticized the current education system for not keeping up with the demands of a more automated world. Conrad emphasized the need for students to gain experience in handling mathematical problems, including those that cause the computer to produce incorrect results, and suggested that calculus and machine learning should be taught at earlier stages. The team agreed on the importance of a balanced approach, focusing on teaching a 4-step problem-solving process and the use of machine learning in classrooms. They also expressed appreciation for Conrad’s contributions to the education space and his advocacy for understanding and thinking.

FULL TRANSCRIPT

00:00:00:01 – 00:00:21:15
Conrad Wolfram
What we should be doing is rebuilding curriculum on the basis that computers are better than people at calculating. That’s what they do. The question then you need to ask is a hard question, which is what is it the human needs to know to optimize the use of this fantastic human endeavor that we have? I mean, just to put this in context.

00:00:21:15 – 00:01:08:05
Jon Orr
Ever wonder why traditional math education might be holding back our true potential to understand and use mathematics effectively in this digital age, with A.I., with computers, with calculators that are in our pockets? Conrad Wolfram, strategic director of Wolfram Research, prominent advocate for transforming math education, is here. Joins myself and Kyle in this episode to explore revolutionary approaches to teaching math with a fascinating journey from a math and physics enthusiast to a leader in computational software, Conrad sheds light on how our current educational system may not be equipping students for the real world challenges that await them in our environment.

00:01:08:11 – 00:01:39:11
Jon Orr
So stick with us and you’re going to learn Conrad’s unique insights into the common misunderstandings and misconceptions in mathematics and students competence and interest. You’re going to hear about his shifts towards computational thinking and how we can embrace technology in our problem solving capabilities. Also, you’re going to learn an understanding of why a revolution, of what you’re also going to learn and understanding of why a reevaluation of what and how we teach in math class could lead to more effective and meaningful educational outcomes.

00:01:39:11 – 00:01:55:08
Jon Orr
So here we go. Let’s dive in.

00:01:55:10 – 00:01:56:24
Kyle Pearce
Welcome to the Making Math.

00:01:56:24 – 00:02:03:09
Jon Orr
Moments That Matter podcast. I’m Kyle Pearce and I’m Jon Orr we are from that moment. this is.

00:02:03:09 – 00:02:05:01
Kyle Pearce
The only podcast that coaches.

00:02:05:01 – 00:02:27:19
Jon Orr
You through a six step plan to grow your mathematics program, whether it’s at the classroom level or at the district level. And we do that by helping you cultivate in foster your mathematics program like strong, healthy and balanced SRI. So if you master the six parts of an effective mathematics program, the impact that you are going to have on your teachers, your students will grow and reach far and wide.

00:02:27:21 – 00:02:35:23
Kyle Pearce
Every week you’ll get the insight you need to stop feeling overwhelmed, gain back your confidence and get back to enjoying the planning and facilitating of your.

00:02:35:23 – 00:02:36:15
Jon Orr
Mathematics.

00:02:36:15 – 00:02:37:15
Kyle Pearce
Program for the.

00:02:37:15 – 00:02:39:15
Jon Orr
Students or the.

00:02:39:15 – 00:02:42:16
Kyle Pearce
Educators that you serve.

00:02:42:18 – 00:03:01:09
Jon Orr
Hey there, Conrad. Thanks for joining us on the making math Moments that Matter Podcasts. We’re actually really pumped. We’ve been following your work for a long time, so we’re super excited that you’re joining us here today. But before we get into it and start our conversation, how’s it going? And I know that you’ve been traveling a bit, so like, where abouts are you coming from today?

00:03:01:11 – 00:03:18:12
Conrad Wolfram
Thanks for inviting me. It’s it’s good to be here. I am from near Oxford in England, so I’m actually at home and it’s slightly strange because I grew up in Oxford, but I went to university in Cambridge, so if anybody knows me, that’s kind of like went to the enemy and came back to get right.

00:03:18:14 – 00:03:38:09
Kyle Pearce
Now I want you to tell us a little bit about yourself. I have a sneaky suspicion that folks in the audience for this podcast know who Conrad Wolfram is. However, we want to give you an opportunity. Tell us a little bit about your journey in mathematics. I know that could probably be a whole episode in it. Yeah, Yeah.

00:03:38:10 – 00:03:42:16
Kyle Pearce
Tell us a little bit more of what got you to where you are and were super interested.

00:03:42:21 – 00:04:05:07
Conrad Wolfram
Let me start in the middle of work, backwards, forwards. So I like it. My day job is I’ve been strategic director of Wolfram Research for 30 years or so. My brother founded it. He’s my older brother. I’m the upgrades. I’m the new a new improved model business. He saw a need for building computation software and found it in 88 and I was just finishing up my school and then going to college and so forth.

00:04:05:07 – 00:04:27:19
Conrad Wolfram
So I have been working on how to make the computer better, to serve the human, so to speak, so we can get math used, math computation. That’s different times for this. And which, by the way, I would include A.I. and data science as well over the last 30 plus years. So hurricanes, I mean, I was, you know, let’s say I was better at math and I wasn’t French.

00:04:27:21 – 00:04:29:09
Conrad Wolfram
I write languages that’s.

00:04:29:09 – 00:04:30:21
Jon Orr
Like a lot of us.

00:04:30:23 – 00:04:51:19
Conrad Wolfram
So I guess I was probably most interested in physics and science, although I enjoyed math, but I enjoyed math because I could beat some of my friends out, though not all of them. I was a pretty good school, so there were some pretty talented folks there. I remember being with one guy won the Physics Olympiad internationally, for example, so it was pretty stiff competition.

00:04:51:21 – 00:05:24:13
Conrad Wolfram
I had a journey where I was a math physics sciencey kind of person did better in those was great. When I could drop these other subjects, I just didn’t get on with and I went off and I did natural sciences and Math at Cambridge in England. And then went off and worked on building computation software. And then lastly, I was left asking maybe we need to do more for the human is that we’ve built all this stuff that works really well in terms of computing stuff, but let’s take a look at what the human is learning to work in this new zone.

00:05:24:15 – 00:05:44:01
Jon Orr
Cool. It is an interesting story. Now, I think I’m going to dig a little bit here on like that past experience. And I want to know we ask every guest their math moment, but I want you to like, think back when we think about our math moments here on our show, we kind of think like, what is it when we say math class or math class?

00:05:44:04 – 00:06:04:11
Jon Orr
There’s always like this for me when I hear it, even though I you know, I spent 19 years in the classroom when I still hear the term, I immediately and transported back to like when I was young, when I was in school. Yeah. When I like my mike math moment. Like it takes me right back to grade five, like the fifth grade and thinking about multiplication, then I’ve shared that here on the podcast.

00:06:04:11 – 00:06:16:06
Jon Orr
Lots of times. But as soon as I hear it, my brain goes right to it. So when I say math class, like what math moment is sticking with you all this time? Give us a little snapshot of that.

00:06:16:08 – 00:06:32:09
Conrad Wolfram
Yeah, there are a few. I mean, so what I do remember, I was maybe I’m guessing 15, something like that. And I had a homework. I was at boarding school. So, you know, you’re sitting at home. It was pretty hard. I was in the top math set, I think. So it was fairly hard. Tough problems. Anyway, all evening I’m sitting there.

00:06:32:10 – 00:06:54:11
Conrad Wolfram
I couldn’t understand. I just didn’t think I had enough parameters in it to figure out what was going on. And eventually I realized there was a problem. It was that they should. The problem is, in traditional math notation, there are a lot of ambiguities. As I later came to realize, I didn’t realize this and I realized it’s my building mathematical loss problem was that it was like they were defining something.

00:06:54:13 – 00:07:16:20
Conrad Wolfram
They weren’t asking me the question. So I spent all evening trying to figure out, like, I don’t get this. It’s really confusing. And it was what they should have been clear about is that I don’t know what it was, why it’s something B three or whatever it was not, is it three Now? It’s very interesting because in Mathematica we have single equals, which means assignments.

00:07:16:22 – 00:07:37:11
Conrad Wolfram
Like you say, Y equals three. That means you assigning Y the variables. B three. If you say Y equals three, it means you’re testing whether wise three or not. If there’s a triple equals, which is that. So it will double equals because we’re symbolic language, right? It means that if you’re saying is y equals three, there are actually three true spouses for that because this is why it was three.

00:07:37:11 – 00:07:56:05
Conrad Wolfram
Well, no, Y has already been set to be two. So the answer is no false. It’s going to be three, in which case it’s true. Yes. Or it hasn’t been set, in which case it’s undefined. So that’s a third option. So the triple equals goes back to what’s traditional languages, which is you just have to choose values you have true or false.

00:07:56:05 – 00:08:17:00
Conrad Wolfram
So if it’s undefined, it’s false is basically. So anyway, all of that moment, I mean, it’s funny, at the time it was just frustrating and I did actually figure it out before I had to like hand in the homework and I actually got through it, but it was like hours and that stuck in my mind. And then later one of the things very similar to that was conditional probabilities.

00:08:17:04 – 00:08:40:06
Conrad Wolfram
And again, both of these things, I only realized years later that was a confusion, that it wasn’t just me that was confused like conditional probabilities. There are probably is that there were unconditional ones that were conditional, but actually that’s not really true. It’s like every probability is conditionals. Just whether you explicitly state the conditions, know the probability of it being sunny tomorrow depends on the world not imploding.

00:08:40:08 – 00:08:59:23
Conrad Wolfram
Now, the fact is the world not imploding is hopefully a small enough probability conditional that basically we can assume it’s zero. So there were a lot of things recognizing the difference between conditional and unconditional probabilities. And actually that was just it wasn’t. So I think one of the things that I learned or I find interesting is I wasn’t just being dumb.

00:09:00:00 – 00:09:18:02
Conrad Wolfram
Maybe that’s true of other people, too. It was actually a bit confused, so I shouldn’t have doubted myself so much. I suppose that was something I learned from that in a sense. I mean, there were a lot of other things where I got confused for all sorts of reasons because I was confused. Nothing to do with it. But that was a case where I guess it was to do with it.

00:09:18:04 – 00:09:49:11
Kyle Pearce
Yeah, well, it’s an interesting story because you’ve articulated and I think what I’m hearing, not only was it frustrating for you as a child, right. I as an educator as well, think of how many students are having these frustrating moments. And we know that math can be frustrating for many different reasons. But imagine that student who is sort of I don’t know if you were open about it like that, you were openly frustrated and saying to people like, Hey, I’m really struggling with this, or if you just kind of battled that on your own.

00:09:49:11 – 00:10:10:20
Kyle Pearce
And then we look at how the statistics around how many people feel like they are, quote unquote, math people and not math people and so forth. And you start to recognize that we’re playing in a game, this math world where so many people believe it’s like it’s black and white, it’s this or it’s this and there’s nothing else.

00:10:10:20 – 00:10:24:18
Kyle Pearce
But you’ve highlighted that this ambiguity that does exist. Think of how many students and maybe adults along the way have encountered similar challenges, but may not have been able to articulate what was really going on. Like maybe they never recognized.

00:10:24:18 – 00:10:44:08
Conrad Wolfram
Right. What you did see. It’s worse than that, right? Because, I mean, firstly, confidence has a lot to do with it, right? I mean, I was from a fairly academic background. I was at a good school. My teachers were were mostly not all, by the way, but they were mostly and one of my math teachers was a friend of Alan Turing’s computer science lesson.

00:10:44:08 – 00:11:05:13
Conrad Wolfram
So he had been a very clearly he was a clever mathematician, a rather eccentric fellow. I enjoyed it. I mean, not I really enjoyed his math lessons, but I enjoyed them partly because of the things that were nothing to do with math, as he used to say. You’ll find my lessons of more about life, the math of. So I had a good edifice and in the end I could push through it.

00:11:05:19 – 00:11:21:13
Conrad Wolfram
I think a lot of the problem is people don’t have confidence. But there’s another problem which is in a sense, the bigger problem is I had some interest intrinsically in math, quite enjoyed the process of it, but there are a lot of people where they’re being told they have to do this and they don’t have the foggiest idea why.

00:11:21:15 – 00:11:42:06
Conrad Wolfram
I mean, it’s like by the time your, you know, yeah, you can see that in the world, you need to add numbers up. But by the time you’re solving equations, it’s like, why is this necessary? And so then they get stuck. And by the way, is another thing that happens a lot, which, by the way, I hope I may help with, which is that often I think some students get misdiagnosed.

00:11:42:06 – 00:12:15:07
Conrad Wolfram
For what? That’s why the stuck. And in fact, in my book, I talk quite a lot about my daughter had this problem at some point. She’s pretty good at math. She’s a science person and she was in a good school and all the rest of it. And yes, even as a middle class parent and things with myself reasonably good at math and so forth, as an average middle class parent, I think I would have struggled to really help and actually diagnosis and she might just not be able to pursue a science stuff because her math wasn’t up to it, apparently, although in fact it was fine and it was things like that.

00:12:15:09 – 00:12:31:08
Conrad Wolfram
Oh, I don’t know. I can’t remember exactly what it was, but it was like she’d missed the class two years earlier on adding fractions or something. So, you know, the process for adding fractions kept getting wrong. And then they said, well, she wasn’t good at problem solving because of that. I was like, But that’s and in fact, she was exquisitely good at geometric problems.

00:12:31:08 – 00:12:35:01
Conrad Wolfram
Of course, she’s very good at geometry, so she.

00:12:35:01 – 00:12:35:22
Kyle Pearce
Is not good at solving.

00:12:35:22 – 00:12:38:11
Conrad Wolfram
These problems, very good at problem solving.

00:12:38:13 – 00:12:48:15
Jon Orr
So it’s like there is a disconnection between this educator’s understanding of the two different things that are really looking at those, looking at one, and then inferencing that automatically implicates the other. Yeah.

00:12:48:15 – 00:13:05:24
Conrad Wolfram
And what really happens? How often is this happening? Yeah, I mean, it took me probably I don’t know, six or 7 hours. She sent me scans of her homework and I said, okay, I think I understand. I mean, my brain works a similar way to hers. I kind of understand a certain amount about why she might be doing this, where she got stuck and why she’s done it.

00:13:06:00 – 00:13:14:18
Conrad Wolfram
So it didn’t take me very long and then she was fine. I haven’t there’s been no other problem. But if she hadn’t had that help, I’m just not quite sure what would have happened.

00:13:14:20 – 00:13:33:00
Jon Orr
Hmm. Yeah, it’s hard to say what would happen, but I mean, in the reality is probably what would have happened is she would have had that label, Oh, I’m bad at math because I had this adding maybe this trouble with adding this one case. But in general, I’m not so great at problem solving because I was told that this happens all the time.

00:13:33:00 – 00:13:53:10
Jon Orr
Kyle said At the beginning of the episode, we’ve had, you know, 200 something episodes and every time we ask teachers or leaders about their math moment and you wouldn’t believe there are people listening to this episode right now going, I listen to every single episode and they’re all noting these instances where they were told they were bad at math.

00:13:53:10 – 00:14:15:14
Jon Orr
And it has. That’s their math moment. It was like I did this one thing and now I have this deep, I guess not a connection, but a connection to this identity that I’m not a math person and I’m bad at math because of this one instance that I’ve now carried through my whole history of mathematics, because it was related to a computational error that I had a long time ago.

00:14:15:15 – 00:14:33:18
Conrad Wolfram
And I think the mysteriousness of it doesn’t help. I mean, as in if you’re sort of, you know, make a mistake in history or something, it’s kind of like it’s not really mysterious in a sense. One of the problems with math and, you know, I’ve written, as you know about this a lot is the fact that we need to stop what actually the student cares about in their life.

00:14:33:19 – 00:14:53:22
Conrad Wolfram
Now, a few students may actually care about the abstract math in its own right, but not most students and not at the beginning. And so if we start from that, they’re lost and then they can perhaps turn the handle and do things. But then when they can’t understand, when the thing goes wrong, they just they’ve got nothing to fall back on.

00:14:53:22 – 00:15:00:04
Conrad Wolfram
There’s nothing to relate to. It’s kind of like it’s just like you got this wrong and it’s just a mysterious, weird thing.

00:15:00:06 – 00:15:24:23
Kyle Pearce
Yeah. And the part that pops into my mind where you had mentioned, you know, you can only imagine how often this is happening. And I worry that it’s a lot more often than we might even be assuming here, because we talk about content knowledge and how important it is to have a deep conceptual understanding of the mathematics and not just say, knowing at a surface level, say the procedure or the process.

00:15:24:23 – 00:15:50:12
Kyle Pearce
Right? And the reality is, is that there are so many individuals out there that have not essentially gone down that path, may or may not have experienced it themselves in schooling. And yet they’re there trying to essentially diagnose we’re like math doctors, right? You’re there and you’re not only trying to teach the course on math, but you’re also trying to see where things are going wrong.

00:15:50:12 – 00:16:12:15
Kyle Pearce
And it’s like and being able to ask the right questions and being able to imagining your daughter if she’s struggling, if I’m not confident and fractions is a great example, let’s be honest, is how does the average classroom teacher teach adding fractions or working with fractions in general? And it’s typically procedurally because that’s how we had learned it ourselves.

00:16:12:15 – 00:16:26:01
Conrad Wolfram
And here’s the really crazy thing which may offend some of your listeners, but here it is. I have never added, let’s say 7/8 and 5/13 in my life other than in education. I mean, it’s not something I do.

00:16:26:03 – 00:16:26:20
Kyle Pearce
You know.

00:16:26:22 – 00:16:28:01
Jon Orr
I have that in common.

00:16:28:01 – 00:16:28:18
Kyle Pearce
I don’t have that in.

00:16:28:21 – 00:16:30:21
Jon Orr
Common for anyone listening right now to.

00:16:30:22 – 00:16:47:03
Conrad Wolfram
I mean, why are we forcing students to learn? It’s a totally different thing from saying, you know, do you have a rough idea of what three quarters looks like or what a half of three quarters is? Or do you know how you would guess? Similarly, multiply in a half of points, 7/8 of something? I mean, any of those things, right.

00:16:47:03 – 00:16:55:10
Conrad Wolfram
But adding fractions precisely is not something I’ve ever done. And yes, it’s in every curriculum around the world pretty much. I don’t understand why.

00:16:55:12 – 00:17:16:06
Jon Orr
Totally. And I think you nailed the almost absurd ity of it in saying like precisely because we don’t typically do that in our daily lives on that precise like will draw a picture to represent it or will estimate or will predict because we have that mental math capability and we don’t go, I’m going to add those exact numbers up in.

00:17:16:10 – 00:17:18:08
Conrad Wolfram
Order to size up for compute or leave.

00:17:18:08 – 00:17:21:23
Jon Orr
It in like inexact form. You know, it’s like, oh, and now it’s exactly when’s.

00:17:21:23 – 00:17:25:07
Kyle Pearce
The last time your cake was cut in like 11/13?

00:17:25:11 – 00:17:26:05
Conrad Wolfram
Perfect.

00:17:26:07 – 00:17:28:24
Kyle Pearce
You know, I should go try to do that.

00:17:29:01 – 00:17:50:17
Conrad Wolfram
Oh, Liam, it’s funny because my colleague John McClane wrote years ago that was slightly heartless, not most significantly heartless education minister in Britain who got very upset because people weren’t learning by rote. There are 11th and 12th times tables. There was a big question about what they should learn up to ten or up to 12 anyway. It doesn’t really matter how they learn them or not.

00:17:50:17 – 00:18:07:17
Conrad Wolfram
But my colleague pointed out that if he’d done the analysis right, so why is it the 11th and 12th time terms were in there at all? Well, it’s probably to do with old money and weights. So if you look at money that was all based on base 12 basically means you have three and four be able to divide.

00:18:07:21 – 00:18:25:08
Conrad Wolfram
So divisible. That’s why money works that way, I think, a lot. And so it was very important if you were doing everything by hand, that was important to have. But now, in fact, it’s very rare you by hand need to know it doesn’t harm you to know them. So it’s just funny because they hadn’t even done the analysis of why it was it wasn’t a great right.

00:18:25:10 – 00:18:26:07
Kyle Pearce
Just always did it.

00:18:26:12 – 00:18:49:11
Jon Orr
I’m curious if you always believed this about this focus on the importance of knowing the how in the computation versus the why, or was there like a tipping point for you? Like, I think for us, just to give you some background, I think we both taught math very, very traditionally, which is like that very direct route. Here’s exactly how you do it.

00:18:49:11 – 00:19:11:17
Jon Orr
We didn’t start with context. We call them naked problems, like, here’s how you do this, here’s how you do that. We did that for years and we had a point where we started to focus more on, say, understanding the why, the conceptual, the representations along this route and thought this is more important. But we did start because we went through school thinking that mathematics was this computation.

00:19:11:19 – 00:19:40:16
Jon Orr
And I remember, you know, very adamantly telling parents that these ideas of adding fractions with very precise numbers in this way was a really important thing for your son or daughter to know and represent. Do and show me and do a 100 of them. So I’m wondering like, did you always believe this about the way you’ve articulated your view about mathematics, or was there a tipping point like we’ve had where it transitioned into this and you’re like, Oh my God, I can’t believe that I did it.

00:19:40:16 – 00:19:43:17
Jon Orr
Like, I was thinking this this whole time. And now I think this.

00:19:43:19 – 00:19:54:16
Kyle Pearce
Yeah, Like we used to think that knowing all of these things as you were articulating is very important because it’s how we had learned that’s math. Were you like that at any point or did you see it early?

00:19:54:16 – 00:20:15:01
Conrad Wolfram
I think I probably wasn’t. But here’s why. It’s a bit complicated. I mean, the machinery wasn’t there fully, but when I was at school, I mean, this was in the 1980s mostly. So I remember I was the first person to have a graphic calculator, and they had outlawed them from the English A-levels by that point. So I could take my maths A-level with a graphics calculator and my teacher was good at that point.

00:20:15:01 – 00:20:35:02
Conrad Wolfram
He said, Let’s use the technology and go further. So I mean, I was always into, let’s push that. I mean, I am naturally somebody who says I want the machinery to do stuff for me. If it can’t, that’s just my natural thing. But I mean, I think by the time we were building, it really I suppose, crystallized fully for me when WolframAlpha came out in 2009.

00:20:35:04 – 00:20:54:04
Conrad Wolfram
So it was very funny happen that because it was like we producing and the thing we were excited about was that you could type plain English and get an answer out. But what really happened is a lot of teachers said, Oh my God, you couldn’t do integrals and you can do calculus and you can do precise equations solving in Wolfram Alpha.

00:20:54:06 – 00:21:12:04
Conrad Wolfram
And we were going, Well, that’s wonderful, but, you know, I should be able to do that for like 20 years so far in Mathematica. So it’s kind of like it’s good that you’re excited about that now, but that’s kind of old news compared to what we thought was the news. So then it crystallized. I was then I think, gosh, what are we doing in education, really?

00:21:12:06 – 00:21:31:11
Conrad Wolfram
And there was sort of if I look back, there were various moments when it was obvious that I would have sided. So I think I was probably always so. And then I started looking into it and saying, Hang on just a moment. Maybe we can just look at knowing as I do, what’s what’s possible technically, what’s out there, what computers do these days.

00:21:31:11 – 00:21:52:23
Conrad Wolfram
Maybe I can suggest some things are critical. I looked at it more and more and it was like, Oh my gosh, everything seems to be a bit backwards. Certainly when you’re at late primary or early secondary onwards, it seems like we’re doing things that computers do much better. This isn’t the thing we humans need to, but there are actually much harder things we need to be doing, which we’re not doing.

00:21:53:01 – 00:22:15:04
Conrad Wolfram
So to me, I mean, the question I want us is said to be, well, I’ve heard various people who say they get upgraded private school into college students and they give them a problem like, you know, here’s a million data points from an experiment. Go figure out what’s going on. And the students, like didn’t do that, especially the normal distribution.

00:22:15:04 – 00:22:37:14
Conrad Wolfram
But I don’t know what I’m doing here. So they can’t that’s not a problem that been set up for. So I’m thinking to myself, my gosh, But so we’ve gone. So I suppose there have been points of realization. To answer your question, I think I was probably always when I bothered to think about it sided with technology, but there wasn’t that much technology to side with that school.

00:22:37:18 – 00:23:01:06
Kyle Pearce
Well, we can definitely see some similarities in terms of how our thinking has shifted. I think it comes with essentially and I’m speaking about myself, not about you, but for me it’s it was ignorance. You just don’t know what you don’t know at the time. And I was doing what I thought was right at the time and over, you know, over that learning over that experience, you start to recognize, Oh yeah, this is what we should be doing.

00:23:01:06 – 00:23:25:00
Kyle Pearce
And I know you’ve been an advocate for mass reform, and what better person to be an advocate than someone who’s working in this in data science and and working in all of the wonderful tools that you’ve been a part of in building your book. The Math Fix, I know, helps to kind of dig into this. And actually, I believe you wrote a article recently on the math wars.

00:23:25:02 – 00:23:44:02
Kyle Pearce
So I want to dig in there a little bit because we see and don’t worry about offending our audience. You are talking to an audience that I think we’re going to be linking to these resources in the show notes. And our audience are the crew who are with you in this move. So I wonder, can you paint us a little bit of a picture?

00:23:44:04 – 00:23:54:13
Kyle Pearce
What is it that you’re seeing? We’re hearing some of it already. And what are you pushing for in terms of like the direction we should be going, whether it’s in the U.S. or Canada or elsewhere?

00:23:54:15 – 00:24:14:17
Conrad Wolfram
Let me paint the revolutionary picture was where I would like to be. So I would like it the math curriculum. I’m also going to strip the word math out because it’s such a polarizing word this point. But whatever you want to call it, math, computational curriculum, core computation, the mainstream thing that people are learning in their school, which they’re currently learning.

00:24:14:19 – 00:24:36:08
Conrad Wolfram
To my mind, you need to assume computers exist not for the pedagogy, but for the actual computing. I mean, the hint is in the name that computers. What they do is they calculate and compute things. So what we should be doing is rebuilding curriculum on the basis that computers are better than people at calculating. That’s what they do.

00:24:36:10 – 00:24:55:15
Conrad Wolfram
The question that you need to ask is a hard question, which is what is it the human needs to know to optimize the use of this fantastic human endeavor that we have? I mean, just just put it in context to my mind, computation has been probably the best way of making decisions that humans have ever come up with.

00:24:55:20 – 00:25:20:02
Conrad Wolfram
And we have driven so far, whether it’s science or medicine or these elements, it’s all driven by compute. We can discuss it in English or we can put it precisely and we have a whole system by which we compute answers from questions. That’s what the point of it is. And for hundreds of years, the sticking point was that you set the abstract problem up in this process and you tried to get it to the abstract answer.

00:25:20:04 – 00:25:38:11
Conrad Wolfram
And that was the hard thing. That was the really expensive thing. Only humans could do that, and that was what you had put all your effort into. And so you had to simplify the problem down, make the calculating really simple. And then we have machines that have done basically completely turned around, have turned that on its head more than any machine in human history.

00:25:38:11 – 00:25:58:10
Conrad Wolfram
I think it’s turned anything on its heads. And now that stat of the calculating is the cheapest by a long way. We have fantastically powerful machines to do that. And so what’s really tricky is taking a real problem and abstracting it into the system so that the computer can then answer the question and then we go to the answer Do we believe the answer?

00:25:58:11 – 00:26:17:13
Conrad Wolfram
We get runs, we get the right problem. Have we got the actual answer? Question? Are we being fooled in some way, which are very hard things to determine? So we are not exactly. This is the full step process and step one or to define in abstract, still very humanistic things. Maybe our lens and then modern A.I. will help with some of those steps.

00:26:17:13 – 00:26:36:14
Conrad Wolfram
They are. Step three is the calculating which for years we’ve had computers do much better than us. And step four is the interpretation. I mean, you go back around the loop and get a better answer. So in education, what we need to focus on is running that process with modern machinery. And then the question becomes what is it human needs to know?

00:26:36:14 – 00:26:45:16
Conrad Wolfram
When does the human need to about calculate? When do they not? When do they need to know about these other steps and what they need to know? And that’s what I’ve been trying to figure out for over a decade. What would the curriculum look like?

00:26:45:18 – 00:27:07:18
Kyle Pearce
Just what pops into my mind when I hear you say that that is such a logical process to follow in order to help us get to the answers. Now, the answers are probably a little bit harder. The actual answer, the exact curriculum and what that looks like. But ultimately what I’m hearing is something that we’ve been advocating for quite some time.

00:27:07:18 – 00:27:45:18
Kyle Pearce
And I think, you know, Msi2, for example, in the U.S. and some of the research that you’ve seen for decades that are suggesting that we obviously too heavily focus on content curriculum versus a process curriculum or as they call it, the practices in the U.S. in terms of what I think I’m hearing you say, and feel free to elaborate or to dispel this understanding or this thought is that we need to spend more time on giving students and people in general humans the tools so that they can reason and that they can conjecture and that they can do the thinking.

00:27:45:18 – 00:28:07:18
Kyle Pearce
The real problem solving, the thing that your daughter was told that she wasn’t so great at, when in reality it sounds like she actually was very good at that thing and it was more of a content piece, right. Really, it’s more of a focus on the process piece and then what content pieces are important and then I guess at what depth right do we need to go to?

00:28:07:18 – 00:28:17:14
Kyle Pearce
Do we need the 1130 or can we work with adding some more simple fractions where we can visualize them and things make sense in our minds?

00:28:17:16 – 00:28:50:03
Jon Orr
And I think where you’re getting at, Kyle and I think we’re kind of where you were going was like, Where is this cut off? How much should we do? Should everyone be learning all the algebra to get into college or and like how we should be doing getting calculus or other things? Like I think you’re an advocate for saying that we should be learning more about data management, data science to get into college, then say these gatekeeper courses that most people have to take, which may not be appropriate for where they want to go, but it’s currently like a gatekeeper, and I wonder for our audience, because teachers are finicky people in a way, and

00:28:50:03 – 00:29:06:00
Jon Orr
this is where this math wars, I think comes from. Teachers go one side, too. The pendulum or the other. And I think we have a hard time thinking about the middle, you know, like where the middle lies, because I think teachers will swing to one side versus the other. So it’s like, where’s this cut off? How much do we know or should we know?

00:29:06:03 – 00:29:28:20
Conrad Wolfram
Home is the subject By the time you’re like pre college and of school, I think it’s 80% off track in terms of what I would optimize the action. So figure out how you teach it from the actual content of the subject, because there are a lot of things that go along with that. So when you talk about Algebra two and the rest of it, it’s kind of like this is just way off in my view, optimized what we need.

00:29:28:22 – 00:29:51:13
Conrad Wolfram
And so to me what we need is much messier, harder problems to solve, which are something in the world. We had a series of problems and one was, for example, sugar. I mean, this is a hard problem, but why should I ensure my laptop computer right now? That’s very complicated. It’s got to do with how much you know, how important it is to you, how much it matters if it goes wrong, how much the insurance costs, what, etc., etc., etc..

00:29:51:13 – 00:30:09:23
Conrad Wolfram
It’s quite rich and actually quite hard to figure out whether it makes sense. That’s a typical starting problem. I mean, we ended up with Markov chains, which aren’t usually covered until college, but I think an absolute be amenable in school, but not if you’re doing all the calculating. So the problem is what you’ve got to do is strip out.

00:30:10:02 – 00:30:33:07
Conrad Wolfram
And one of the things that humans may think about rigor. So one of the problems in the math wars, as I understand them in the U.S., I mean, they’ve got what’s happened is whether we change the content of math has got confused with a lot of other topics, topics about woke non-work, whether it’s you’re supporting one group of people or another, or whether we’re being you know, we’re trying to get college admissions working one way or another.

00:30:33:07 – 00:30:50:19
Conrad Wolfram
It’s got all enmeshed in this. I’m trying to strip back and say, right, let’s start with what we need, which is the right subject and the right subject is highly conceptual. This is not easy. It’s not like it’s got we’re going to make it easier so people can get into college more easily. Now, that’s not what we need.

00:30:51:00 – 00:31:24:13
Conrad Wolfram
The easy stuff is done by computers. What we need is harder problems, more conceptual understanding, handling messy situations which computers even ideal that are improving do rather badly at. And we need to be in charge of those eyes and computers not beholden to them. And so that’s a very good way of looking at. But I think the thing we really that crystallizes it is if you look in the outside world, either in everyday life or in technical jobs or whatever it is, what are people actually doing with math and how are they doing it?

00:31:24:15 – 00:31:44:13
Conrad Wolfram
And what they’re doing is they’re solving vastly harder problems than we would have solved 50 or 100 years ago. Because they can because they’ve got the calculating machinery and then they’re trying to work out whether math can be used. And sometimes, by the way, and this is a whole separate problem in all democracies, we got a problem because it’s overstated what math can do.

00:31:44:15 – 00:32:03:10
Conrad Wolfram
Can math predict how good mask wearing is always for a pandemic? Well, certain things it can do certain over claims, certain places where we don’t know. It’s very, very complicated. And we also need to build into our societies people understanding that math can’t answer everything in practice. Right.

00:32:03:12 – 00:32:27:23
Kyle Pearce
Well, it’s interesting to what sort of caught me in what you’re describing here and use Mark off chains as an example. But you were saying what popped into my mind when you said that is there’s so many concepts along this journey. Currently, the current journey we have where it’s almost like because we’re so hyper focused on the calculating that everything becomes the calculating, and that’s a massive hurdle, right?

00:32:27:23 – 00:32:52:15
Kyle Pearce
So you start thinking about now we just got to calculate all these things and we’re stuck in this rut and we haven’t even had the opportunity to start thinking about what it is that we’re actually doing because we’re stuck in the mud over here and stress levels are increasing. And so and then what happens? Typically time runs out and then there’s an incomplete understanding and usually an incomplete really ability to calculate for many.

00:32:52:17 – 00:33:21:04
Kyle Pearce
And we sort of when you zoom out a little and or zoom out a lot, you start to look at the entire curriculum and you start to think about how much of that time did we spend to try to call it perfect, that the procedure that we’re trying to put into place so that we could get to the thinking instead of really trying to glossing over the wrong word, but spending significantly less time on, say, the actual calculating.

00:33:21:04 – 00:33:41:07
Kyle Pearce
And, you know, John, put down an example here. Maybe you can speak to it. I’m sure you have some thoughts, but how often does the idea of factoring quadratics come in or different types of polynomials come in and you go, We spend so much time on when you can look at it as a interesting logic problem, right to go, okay, like let’s work on what’s happening.

00:33:41:07 – 00:33:43:11
Kyle Pearce
But why? Like, why are we doing.

00:33:43:11 – 00:34:09:24
Conrad Wolfram
It if you take quadratics? And the interesting case because to me, the idea of equations as a toolset for solving problems is really important and roughly how they work. But actually they aren’t usually quadratics that pop out of the problem, right? There might be cubic so cortex or differential. And I’d like our students to be able to use all of those tools much earlier on and they could do if they weren’t fooling around trying to learn the quadratic formula by heart.

00:34:10:01 – 00:34:16:14
Conrad Wolfram
But if you must. Student Well, right, Well, yes, that’s what I know. That’s especially understanding it. Yeah.

00:34:16:15 – 00:34:18:21
Jon Orr
We don’t say that Kyle.

00:34:18:23 – 00:34:39:13
Conrad Wolfram
Guy, but I mean, one thing you’ll see and we can post is the computer based math dot org slash outcomes. We tried to lay out a system of outcomes that we thought were interesting and one of the things we tried to do in that is separate what I call concepts and tools. So the concept of equations, the concepts of machine learning as a way to solve a problem.

00:34:39:15 – 00:34:56:24
Conrad Wolfram
I want our students to have a much wider range of exposure to these algorithms and to these options of toolsets, but not necessarily have to know how to do it by hand. They need to know where they go wrong. Where does machine learning screw up? Why would you use an algorithmic approach as a formal algorithmic approach? Raw machine learning?

00:34:57:01 – 00:35:04:12
Conrad Wolfram
Those are crucial questions for now. Not let’s pretend to be a computer, which is effectively what we’re asking them to be.

00:35:04:14 – 00:35:27:16
Jon Orr
That’s an interesting thought about what popped into my mind Soon, as you said, it’s almost like how do we help students do debugging, like the debugging of a computer program? Like when you think about it, it’s like, okay, I don’t do the actual computation of the program, but I need to look at the lines of code and go, I know that piece of code does this and it’s supposed to give me that.

00:35:27:18 – 00:35:35:09
Jon Orr
And it didn’t. And now I need to go like, Well, what do I tweak now with the tools I have with the lines of code, with the functions?

00:35:35:09 – 00:35:50:14
Conrad Wolfram
Yeah. So I just find the problem wrong is that I got the wrong answer because I wasn’t actually. I mean, you know, I think we saw this. We just go back to the pandemic. I think in various jurisdictions we saw this. It’s like, what’s the actual problem we’re trying to solve here? Well, we’d like as few people as possible to die or get sick.

00:35:50:14 – 00:36:12:10
Conrad Wolfram
But there’s dying now from COVID. There’s die later from other diseases because the health systems were broke and there’s die a little bit. Let’s not we have economic problems and social problems. So, I mean, it’s a complicated definitional problem that’s very complicated in that case. But don’t just apply math to the I mean, one of the podcasts I want to do some time with my colleague actually is worry about the secondary effects.

00:36:12:12 – 00:36:39:00
Conrad Wolfram
Okay. So one of the sort of little things that I think is wrong in right now is numbers so powerful as persuaders as marketing that you run the thing where you think you’ve got the number and you forget about secondary effects sometimes, which can overwhelm the primary effect because they were harder to quantify. And so I think 50 or 100 years ago when things were, you know, people quantified less, they didn’t jump to the number in exactly the same way in it.

00:36:39:00 – 00:36:57:22
Conrad Wolfram
And so then you, in fact, sometimes got saner decisions because we weren’t looking at the number precise. But that’s a deep societal what should be part of our education in core computational subject. People need to know that so they don’t get fooled, but they do use math and computation to their maximum effects.

00:36:57:24 – 00:37:22:05
Kyle Pearce
What pops into my mind when you say that is like, I think about, for example, investments. People look at like, what’s the best? Everyone rushes to the rate and meanwhile it’s like, is the volatility massive? Where is it? Could be it’s -25% or it could be up 45, you know, or is it consistent, you know, what standard deviation, like all of those things sort of come in and yet nobody’s asking those things.

00:37:22:05 – 00:37:26:09
Kyle Pearce
Right. And it’s like almost worth they don’t want to do the thinking around it or they just been trained.

00:37:26:09 – 00:37:47:24
Conrad Wolfram
No, they just think it happens often with risk. I mean, the question I’ve often asked is why do people underestimate the linkage between risks? So an example case of this. Many years ago, the insurance market in London, Lloyd’s got themselves horribly snarled because they insured rounds in a risk in a circle, basically. And so they thought that the risks were unassociated when they’d actually insured with you.

00:37:47:24 – 00:38:11:23
Conrad Wolfram
And this happened again in 2008 with the banks, basically, that, you know, if you see if you model your risk being independent the chance of bank, you going bust and bank B going bust and bank in the US and the U.K. and if you think those are all independent, you muddle them that way. If you start and a lot of people did assumed a lot of independence, but actually a common sense tells you these things in a modern world, not independence at all.

00:38:12:00 – 00:38:36:09
Conrad Wolfram
So then you have modeled completely the wrong thing basically, and things go wrong from that. And another thing I see, I just well, I’m on the financial examples. I mean, one of the things that happened in the banking crash in 2008 was that a lot of people use normal distributions for modeling were actually long tail risks. I mean, there were many issues that but one of them was that why did they use normal distributions?

00:38:36:09 – 00:39:03:02
Conrad Wolfram
Well, because that was the one distribution that sort of got to at school. Maybe they were lucky and got to a parcel distribution. I mean, I know in mathematical we have like 200 built in, right? But then you have to ask question, why are you using a distribution I mean distributions to is throwing out most of the data initially so that you can work with something that you can compute with, which was very important from is now if you’ve got a million data points, don’t face a distribution to it is the first thing you do because you’re throwing out most the data.

00:39:03:04 – 00:39:25:24
Conrad Wolfram
That’s not what you need to do is number one. So we’re often actually teaching people not only but having a very narrow toolset. We’re then forcing them into thinking only in that toolset, often it’s actually even the wrong toolset for the modern age because of the machinery. And I sometimes compare it to if you do DIY and all you have is a hammer, you’re just given a hammer, right?

00:39:26:01 – 00:39:36:12
Conrad Wolfram
And then very, very late in the process, you’re given a screwdriver as well. So if you give them a hammer, every problem kind of looks like a nail. That’s all you can do. So that’s what you try first for sure.

00:39:36:12 – 00:39:44:08
Kyle Pearce
It is literally me on a job site for sure. Well, you know, it’s all I’ve got. But yeah, point noted for sure. That’s a great analogy.

00:39:44:10 – 00:40:09:03
Jon Orr
Yeah. And I think that there’s so many important things here, and I can’t help but think about our classroom teachers and trying to, like, navigate this complex. What’s important? Where should I put importance When I hear your name, I automatically transports like my Wolfram moment. I get transported back or it’s got to be like 15 years ago. And either I watched a TED talk or something.

00:40:09:03 – 00:40:25:06
Jon Orr
It was one of the Wolfram Brothers had an analogy. It was a while ago about what’s the importance and it was the same conversation. And what I get worry about a little bit and I’m going to share that analogy in just a sec is but I get worried about this like this black box that sometimes we wonder about.

00:40:25:11 – 00:40:43:23
Jon Orr
Where is the importance of like knowing what’s inside the black box and knowing what we need to know outside the black box. And what I mean by that is like your analogy was that, you know, a hundred years ago or even more than a hundred years ago, if you had a car, you know, like if you owned an automobile, there was no one else to help you fix the automobile.

00:40:44:00 – 00:41:04:20
Jon Orr
So you had to know, you know, how to fix it. You know how to change this and you how to do this and start it up and change the engine or fix it. Yeah. See, I don’t even know. But you fast forward to today and you can have a car. I know none of those things because there is a process and there are other tools at your disposal that you can then rely on to have your car fixed when it breaks down.

00:41:04:20 – 00:41:20:07
Jon Orr
But back then, if a car broke down, you had to be the one to know it, to fix it. And then when you fast forward that to or translate that and this is where the talk came in and it was like translate that into mathematics in the classroom. Is that this is that the importance of like, do I need to know how to factor or no when to factor?

00:41:20:08 – 00:41:34:05
Jon Orr
There are tools to help do these things, but where am I? I get worried. And maybe this is where teachers, because those teachers are on like both ends of the spectrum, they swing from one side to the other and they struggle to figure out what the middle is, is if we always kind of think, where do we put the focus?

00:41:34:05 – 00:41:47:18
Jon Orr
If, say, the factoring isn’t that important, does the factoring become the black box where it’s like the thing goes in the black box, I don’t know what happens in there and then it comes out and now I can use it, but do I need to know what’s going on inside the black box?

00:41:47:22 – 00:42:09:19
Conrad Wolfram
This is possibly the main issue of our age right, which is we’re entering the age. And the question is what do we as humans need to know? In fact, it’s happened in all industrial revolutions. It’s just closer to home because it’s all about intelligence rather than, as I say, brain rather than brawn. It’s like in previous industrial revolutions where machines physically did things, but actually it’s the same kind of thing.

00:42:09:19 – 00:42:30:22
Conrad Wolfram
And the nature of progress of human society is that you specialize, you have things that you automate, more, people get more specialized. Some people know about the actual thing, but then it allows you to use it across course. Of course, as you point out, with cars at the time when people fixing cars, there were very few drivers and cars because you couldn’t do that.

00:42:30:24 – 00:42:56:08
Conrad Wolfram
And driving is not the same as automotive engineering. Now that’s separate. So I think it’s very much the same with computation. Computation was a very specialist activity and certainly in any serious way it was for a very small number of people. Most of the world were, and I would argue some and all computation illiterate, and that’s bad and it’s now bad, particularly because we have such power with machines to democratize everyone, right?

00:42:56:08 – 00:43:15:20
Conrad Wolfram
So it’s not necessary. It was necessary because there were only very few people who could be trained up to do this. Now it isn’t. So I think for teachers, I mean, teachers have a very tough time because in my view, they’ve got a curriculum that doesn’t make a lot of sense in many cases, which they got to teach to because they got to get kids past the exams and everything else, a confidence bump amongst other things.

00:43:15:22 – 00:43:33:04
Conrad Wolfram
And yes, often even the teacher really understands that this isn’t quite right. It’s hard to navigate. I mean, I would say a few things that can at least perhaps slightly help. I mean, one of them would be keep in mind that the of mathematics in the end is to make better decisions. I mean, that’s what it’s achieved in life.

00:43:33:06 – 00:43:56:01
Conrad Wolfram
And if we just keep that focus, even if you’re having to dive into things that I think should be a black box, then at least we can keep that sort of we’re trying to solve problems and be precise in solving this problems. In terms of the whole black box issue. In the end, the most important thing is, you know, how to assess whether your black box is operating or not.

00:43:56:01 – 00:44:26:24
Conrad Wolfram
And I talk a lot about flight simulators. If you want to look at how flying has become much safer, on the whole, it’s because what we’ve got pilots to do is not I mean, pilots do end up knowing quite a lot about how the aircraft work, but actually it’s a lot about experience and accelerating in simulators. So what they’re doing is they’re experiencing in a way they wouldn’t have done 50 years ago all sorts of cases, which they’ll hopefully never face as an actual pilot.

00:44:27:01 – 00:44:47:19
Conrad Wolfram
And they have experience of what to do in that case. So that’s what we ought to be doing with math. We ought to be taking problems, getting experience of how to handle systems, including stuff that goes wrong. You know, the computer produces garbage, including why the program crashes, including why the problem was able to find that it was hard to spot that, etc., etc., etc..

00:44:47:21 – 00:45:21:10
Conrad Wolfram
And we should be running those over and over again. That’s what the students need experience in. And in order to do that, as you correctly said earlier, there isn’t infinite time and or infinite ambition or will. So do these things and picking the student is succeeding. So we’ve got to we’ve got to do what’s essential. And so I think that means cutting out a lot of things, but it isn’t really you assume the black box, it’s that you accept that there’s machinery and automation and you then walk out what it is you do around that in order to get confident that you’ve got a good result.

00:45:21:12 – 00:45:45:00
Conrad Wolfram
And actually, just to be clear about that, what we’re doing now with hand calculating curricula is mostly terribly bad for that. And I would argue is in fact one of the reasons why huge catastrophic mistakes get made in real life, because what people are used to doing is checking. They’re working by hand. But the moment you start putting a real big problem in a computer to build a bridge, you can’t check it by hand.

00:45:45:00 – 00:45:55:24
Conrad Wolfram
That’s not the way you can do it. So then you haven’t built up in your education the wherewithal for how do you check things that are far more complicated than you could calculate? And so we’re losing.

00:45:56:01 – 00:46:11:24
Kyle Pearce
What I’m hearing you say. And I don’t know if this might be helpful for some friends listening, but what I’m envisioning in my mind is it’s not an all or nothing as John saying that pendulum, it’s like somewhere in the middle. And it really if you picture the pendulum, it’s like imagine that it’s sort of like somewhere in the middle.

00:46:11:24 – 00:46:37:17
Kyle Pearce
It’s not going all the way to either side, but it’s just kind of hanging out somewhere in the middle. And I’m picturing that, you know, sure, we’re going to have some students maybe do some calculating, but let’s be intentional about the calculating they are doing so that they understand what’s going on in the black box. And then let’s like kind of move back a little bit and then let’s look at some other examples and like see if students can identify is this possible, Where would that factored quadratic?

00:46:37:17 – 00:46:41:15
Kyle Pearce
What would that look like on the graph? I know it’s your curriculum and, you know, let’s.

00:46:41:17 – 00:47:01:05
Conrad Wolfram
Say the beginning, which is to reorder. I mean, again, I’m dicing between things that individual teachers can and can’t do because, I mean, they can’t reorder everything because they under a curriculum that orders things. Right. But if I were to be able wave a magic wand, I would have calculus taught to ten year olds and I would have machine learning the primary schoolchildren.

00:47:01:07 – 00:47:19:24
Conrad Wolfram
And I wouldn’t worry at that stage about the end. So the other thing I think that’s a mistake is I think we should teach what the thing does as a point where they won’t be capable of dealing with the hands part of it. So why do we leave calculus so late? Because you need a lot of algebraic skills to be able to do integrals and things.

00:47:20:01 – 00:47:40:05
Conrad Wolfram
Yeah, but if I take this, I guess I’ve got to now put water everywhere. But I take this class, for example, and I say, Well, how much water will it hold? It’s actually you can go and start discussing this with it. Probably less than that anyway. You can slice it into little disks. And the question is how much volume is each of those disks, etc., etc., etc..

00:47:40:07 – 00:48:03:13
Conrad Wolfram
And you know, when you make it small, small, smaller, what actually happens? Those are skills and understandings that I think are much earlier stage than we give people credit for. And a kind of interesting and the conceptual and important. But don’t get worried about it, maybe that you come back later if you want to actually say, well, okay, when you actually want to calculate that what was happening inside the computer, if indeed that’s important enough.

00:48:03:14 – 00:48:10:16
Conrad Wolfram
And I think I’m sorry, I’m doing a bit of mopping up here as I’m about to see. That’s what I don’t know. I hope you didn’t.

00:48:10:18 – 00:48:12:08
Jon Orr
Kill it all over your keyboard.

00:48:12:10 – 00:48:20:03
Conrad Wolfram
I did. Still a bit on my people, but it’s not even it. So it’s wi fi right now. It’s not anything worse than that. Anyway, you.

00:48:20:03 – 00:48:23:14
Kyle Pearce
Were trying to get the answer to your problem. How much water can it hold?

00:48:23:16 – 00:48:43:07
Conrad Wolfram
Well, yeah, and I only spent a little bit of it, so. So I guess a lot more than I spilled. But and machine learning, you know, to me, the use of machine learning to solve problems is a very early stage. I mean, it’s like how kids learn right now, the details of setting up new neural networks. And that’s highly complicated.

00:48:43:07 – 00:49:01:08
Conrad Wolfram
But don’t get that’s going to be so when we write in curricula, we’ve been taking topics and we’ve been trying to sort of put them at different levels and stages in a sense for a given topic. It’s not like you do all of that at this moment because you kind of come back when you can go inside more where that might be relevant.

00:49:01:10 – 00:49:16:03
Jon Orr
I think we could keep talking about this all day and we want to be respectful of your time, but we are so glad to have you here and chat with us about these huge ideas and how it relates to the classrooms in their classroom teachers and what they have to think about. And it’s kind of big things to think about.

00:49:16:05 – 00:49:25:11
Jon Orr
I’m wondering if there is one big takeaway you want to a classroom math teacher to kind of take away from this conversation. What would that one thing be?

00:49:25:13 – 00:49:48:17
Conrad Wolfram
Eat the four step process that I talk about always in mind and try and help students to figure out where they are in that process and spend as much time as you can in the confines that you’ve got on. They define abstract and interpret steps and zooming out. So like, okay, what’s the problem we’re trying to solve? How are we going to abstract as to what’s the right thing to do, right?

00:49:48:17 – 00:50:08:15
Conrad Wolfram
Let’s run an equation and do that by hand or computer, whatever’s okay at that stage, and then interpret the result to see what it matched. The thing you started with when people talk about, you know, am I suggesting people shouldn’t get the basics, it’s just I’m suggesting different basics. And the basics in my view are that four step process that has driven for hundreds or you could argue thousands of years.

00:50:08:15 – 00:50:27:12
Conrad Wolfram
In essence, the rise of mathematics. And I think if we can get our students really understanding that and feeling it so they sort of instinctively fall back on this when they’re confused or don’t know how to proceed, I think that’ll help a lot. So I that would be one thing I would advocate, I guess.

00:50:27:14 – 00:51:11:19
Kyle Pearce
I love it. I love it. This has been a great conversation. I want to thank you because not only, you know, we have many people in the education space and advocating for set in different ways, but ultimately advocating for understanding, advocating for thinking, and to have someone from your space, from the real world having created so many different tools and continuing to create these tools and having that reiterated from that side of things, from industry, from seeing what’s going on in the world, us, I think that’s a really helpful thing for educators to feel confident because it’s so easy when the messaging that you’re hearing around the math wars, for example, when people are hearing

00:51:11:19 – 00:51:33:09
Kyle Pearce
people’s thoughts and opinions as to what they believe is important, which really comes down to oftentimes beliefs and it’s not necessarily it’s not necessarily based on research, it’s based on the way things happen for them in the way they think things should go. So I want to thank you on behalf of the Mickey moments that matter audience and all those math moment makers out there.

00:51:33:09 – 00:52:02:08
Kyle Pearce
Thank you for taking the time and for all of the amazing tools that you have brought to the world and continue to bring. We will be posting links in the show notes. So I grab the computer, talk forward slash outcomes, and we have the UC Math War article as well as a link to your book as well, the math specs and hopefully will be able to stay in touch with you and potentially dig in a little deeper on a future episode down the road.

00:52:02:10 – 00:52:04:23
Conrad Wolfram
Thanks very much. It was a fun conversation.

00:52:05:00 – 00:52:05:20
Jon Orr
Thanks, Tom.

00:52:05:22 – 00:52:13:14
Kyle Pearce
Take care. Thanks, Conrad. All right. Their math moment makers. Until next time, I’m Kyle Pearce.

00:52:13:14 – 00:52:20:19
Jon Orr
And I’m Jon Orr high fives for us at a high five for you.

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