Conrad Wolfram on Computational Thinking and Revolutionizing Math Education

On this episode of the Getting Smart Podcast, Tom Vander Ark talks to Conrad Wolfram, CEO of Wolfram Research and author of The Math(s) Fix, to discuss the evolving role of computational thinking in education. They explore how the surge in computational power and AI can transform math education by moving away from manual calculations and focusing on real-world problem-solving.

Conrad Wolfram shares insights on the necessity of integrating computational tools into the curriculum, emphasizing that modern education should prepare students for complex problem-solving using AI and natural language interfaces. They also discuss the challenges and opportunities in updating math education to reflect these advancements, aiming to equip students with skills relevant to today’s tech-driven world.

Transcript

• Introduction
• The Evolution of Human-Computer Interaction
• The Role of Natural Language in AI
• Revolutionizing Math Education
• Future of Computational Thinking in Education

Introduction

Tom Vander Ark: We’re talking about computation and computational thinking today. I’m Tom Vander Ark. You’re listening to the Getting Smart podcast, and we’re joined today by a repeat guest, Conrad Wolfram, the CEO of Wolfram Research and the author of The Math(s) Fix. Conrad, it’s great to see you again.

Conrad Wolfram: Yeah, very nice to be back.

Tom Vander Ark: We ran into each other in the hallway at South By and vowed for a reunion to discuss what’s right and wrong with math education in the world. You and I have shared careers in the information age, where the nature of computational power available to human beings dramatically increased and transformed the way we live and work. It didn’t, however, transform the math expectations that we have for young people. We continue to torture young people with hand calculation. 

The Evolution of Human-Computer Interaction

We’re going to talk about that, but since we recorded our last podcast and since you published The Math(s) Fix four years ago, the world has changed. The computer age ended, and I would argue we started a new age of human-computer interaction where we are interacting with reasoning and creation engines with a new level of power and sophistication. And we’re doing it primarily through natural language. The user interface for human-computer interaction is changing. I’d love your take on this frontier and what’s happened. Have we really shifted to natural language, and is natural language an adequate interface for the sort of complex problem-solving that you at Wolfram have been world leaders in for the last 30 years? Where are we? What’s happening?

Conrad Wolfram: Yeah, it’s a really, really interesting question. I agree with you. I’m talking AI age. So, you know, I don’t know where we are exactly, but it’s a new industrial revolution, probably the fastest moving in human history. And it’s very quintessentially human in the sense that industrial revolutions were about brawn rather than brain. This one’s clearly in the latter category. And so that feels very personal in a sense. In terms of the interface, I mean, my observation is twofold.

The Role of Natural Language in AI

 I think we have had a natural language interface before in a way, but in slightly different ways. Search was something where we started using natural language again much more than we had before. The back end of that was much less sophisticated, and we were changing our language, so it wasn’t very natural. Back in 2009, we launched Wolfram Alpha, and the idea there was to get computations done using pretty much natural language. Now, I think what we’ve got is a far more natural interface to something that feels more humanistic but has all sorts of problems associated with that, some of which may get ironed out.

One observation I would make is that I think through history, we’ve often got new interface types. Or they become prevalent, like what was called WYSIWYG (What You See is What You Get) with windowing and so forth. I think typically they’ve added to previous interfaces more than got rid of them. For example, we still type, and I think we will still at some level type syntactic code even though we have windowing, because the windowing stuff works very well in a set of cases and expands how we can interact with the technology. But I don’t think it’s the whole story in every case. So I think there are two or three things to disentangle or to slice differently. I think our interface, whether it’s natural language or very abstract, will continue to include both. Abstract representation to get precision and to turn a lot of different effects into the same representation will remain crucial. It allows us to make decisions, solve problems, and make progress. The interface to that may be linguistic to set things up, but there are many things we’ll do linguistically now that we would have had to be very deliberate about before. Then there’s also the back end of how the linguistics work. One thing I’ve said about Wolfram Alpha versus LLMs like ChatGPT is that if they were humans, LLMs are sort of at one end of the spectrum. They interact nicely with humans and have a very nice form of words. It isn’t necessarily accurate. Wolfram Alpha is more at the aspergic end of the spectrum. We are fact-based, very definite, and accurate. We’re not always the best at communication. Actually, it’s been very exciting to see how those two have been put together to sort of make the best of both worlds. A bit like a police drama.

Tom Vander Ark: So you’re definitely a believer that when it comes to attacking problems, a mix of these models is best. What does that mean for the interface? Can we rely increasingly on natural language, or should we continue to use abstract languages like the language of math and the language of Python and Java? Will we continue to use those languages, and how and when are they going to be useful?

Conrad Wolfram: So I suppose my belief is the following: At some level of complexity in describing computational ideas, you need an abstract representation. So yes, I think we need computer languages. But computer science and the like, which have been about humans writing by hand, will dissipate. Different forms of AI, including Wolfram Alpha and LLMs, will write code which we may explicitly see or may not see, but we may sometimes by hand have to edit that code. In advanced cases, we may want to do something with it. We may want to understand it. It may be cleaner for us to look at the code to understand it and work with it than to speak in English. You can discuss lots of problems in English and get various advantages from discussing them using math notation. You get precision and the fact that a biological effect, a physics effect, and several other effects end up representing the same abstraction, giving you tremendous power. You can use the same process of getting to an answer for that abstraction. So the idea that we can just speak with imprecise human language and replace all the abstraction developed over hundreds of years is inaccurate. We have a much wider use and convenience of natural language, but sometimes we will need explicit abstraction in fewer cases. They’ll build on each other. We have our own Wolfram language, which is a high-level language with 6500 or so built-in functions, vastly more than Python. Once people learn the vocabulary, their interaction speed is much better than with Python. It represents their thought processes more directly because they have more words to represent what they’re saying. With human languages, a large vocabulary lets you directly get to a meaning. LLMs can handle that vocabulary easily. We get very short, effective Wolfram Language code from LLMs, providing very nice abstractions for humans to use.

Tom Vander Ark: There’s an interesting parallel around content knowledge in domains and industry verticals. When search became popular 15 years ago, there was the idea that we don’t need to learn content anymore because you can just Google anything. With a language interface, our task shifts to editing and curating creation. That content knowledge, as well as the knowledge of abstract language and creating quality prompts and editing for better answers, requires both content knowledge and abstract language knowledge. Content experts are making better use of the tools. Do you agree?

Conrad Wolfram: Yeah, this is very much what I’ve said and continue to say in different domains. When you’ve got new technology, new machinery, what’s the human role? The human role that succeeds is to zoom up a level. Instead of pulling levers at the ground level, you’re defining the envelope of change. When you drive a car, you’re not changing the fuel mixture. The car figures that out. You’re commanding the car to accelerate, brake, or go from A to B. We’re becoming more like the CEO of the process rather than the ground-level expert, but being a CEO is difficult for several reasons. I describe this in The Math(s) Fix. Think about Steve Jobs or Elon Musk. They’ve got a zoom-up, zoom-down issue. They look at the big strategic picture, like the future of handheld communicators with touchscreens, while also obsessing over the radius of a corner to make it feel right. It’s getting the big picture to head in the right direction and zooming into details to get precision and the right answer. That’s very hard to do. Very successful people like Jobs and Musk didn’t always get it right. Humans need to improve at this, and it becomes harder with more automation.

Revolutionizing Math Education

Tom Vander Ark: So let’s maybe summarize where we are, particularly in regard to education. At a time where a powerful set of tools is available to learners in high school as well as university, allowing them to take on far more complicated problems than a young person could have done five or ten years ago and actually deliver value to their community. Is that fair?

Conrad Wolfram: Yes, it is. The learning they need and the contribution they make change quite a bit. It’s easy to see this, especially with math. Math is one of the world’s most successful problem-solving systems. And machines now do the hardest part. For hundreds of years, math was great, but the limitation was turning the abstract question into the abstract answer by hand. We developed clever systems for minimizing calculating. A friend of Alan Turing, who was one of my math teachers, said math is the art of avoiding calculation. And he was right. But in the last few decades, calculating has become incredibly cheap, and we can calculate pretty much anything we want. The question is what to calculate and how to set up problems to effectively use math systems. We must not get fooled by results because the more complicated the problem, the harder it is to verify. These are the crucial steps now. The exciting part in education is that many students get turned off by math when it becomes very abstract, often around late primary

 school. Now we can give them hard problems that seem relevant to their lives but that previously didn’t seem linked to math because they couldn’t use it to get a better answer. Now they can. They need to know a much wider range of toolsets, understand when to deploy them, and recognize when things go wrong. For example, consider the Tour de France bike race. Let’s look at all the parameters and try to understand the factors like air resistance, angle to the wind, and rolling resistance of the bike. These are hard, messy problems, but they can be tackled by 12-to-15-year-olds. This real experience, or at least some educational version of it, is much closer to real applications than what we’re doing now. It pushes problem-solving skills into areas that are both more exciting to students and more relevant to their lives.

Tom Vander Ark: So I think you’ve highlighted two problems with our current math education. One is that we give students problems rather than inviting them to find and frame them. Problem finding and opportunity recognition are more important than ever. Second, we spend a significant portion of time teaching them how to solve given problems using hand calculation. Let’s shelve problem finding for a moment. Why are we still teaching hand calculation? Is there any value to long division and factoring polynomials and multiplying fractions?

Conrad Wolfram: Is there any value to learning the pluperfect subjunctive of “amo” in Latin? Well, there’s some value, but I wouldn’t force everyone to learn it. I think there are better things to do. The overarching problem in most places is that assessments tie down subject changes. Math is critical because of the tech needs, and it’s seen as more accessible through numbers, so trying to change its content faces a massive ecosystem shift. This overarching failure of the incentive framework makes it hard for incentives to align with real-world changes. We need rapid subject evolution matching the real world. Another underlying problem, especially in the U.S., is the difference between the essence of the subject and the mechanics we focus on. For instance, in photography, we might still start with loading film into a camera, though it’s not essential in modern photography.

Tom Vander Ark: People suggest stopping teaching algebra to teach data science, which is a crude approach. You and I support teaching algebraic reasoning and multivariable problem-solving. We’re giving kids problems instead of inviting them to find and frame problems where they identify variables. We’re teaching hand calculation rather than modeling complex systems, teaching the wrong algebra in the wrong way, emphasizing hand calculations. Do you agree?

Conrad Wolfram: I might characterize it differently. The problem is when you say algebra, let’s say equation solving, you’ve got to look into the details. For example, you might want to model an effect to get a better answer. What’s the best tool for that? Is it machine learning, traditional algebraic equation solving, or another tool? We don’t address this at all in schools, which is catastrophic. The equation that best matches the problem, regardless of how horrific it looks, is important because computers can solve it. The curriculum is linked to outdated techniques. The algebra taught is related to techniques from a hundred years ago. These techniques aren’t irrelevant, but we need to use them differently, with more complex versions, without doing them by hand. The data science vs. algebra debate is a false dichotomy.

Tom Vander Ark: This debate has been conflated with the reading wars where explicit phonics aligns with the science of reading. Some are conflating this with teaching mathematics, assuming teaching hand calculations is equally important.

Conrad Wolfram: That’s an important point. That mistake has confused some, including people in the UK government. One key difference is literacy is a function we can all agree is an outcome we need. Writing and composing are essential. The question is how to best achieve literacy. I don’t know all the pluses and minuses of phonics, but it’s a mechanism for that outcome. We can agree on the outcome. The problem with math is we don’t agree on the outcome. Conflating the phonics argument with math reform is false.

Tom Vander Ark: The two objections I hear regarding hand calculation are related to editing the work of a computer and boosting computational thinking. Do you think learning hand calculations helps with either editing or boosting computational thinking?

Conrad Wolfram: There’s some value, but there are better ways to do it with fewer negative consequences. It’s like learning Latin to learn English—useful but not necessarily the best approach. Hand calculations aren’t the right starting point. We have numerous ways to solve problems now thanks to mechanized calculating, so computational thinking needs to focus on understanding how tools operate and setting problems appropriately. One big mistake with current approaches is training people to think in outdated ways. Traditional math is akin to learning to drive a horse and cart instead of a car. It isn’t hitting the skills we need.

Future of Computational Thinking in Education

Tom Vander Ark: I want to be clear for our listeners that we aren’t arguing for less math but for more computation and computational thinking. We want young people engaged in more rigorous problem-solving earlier on significant challenges and contributing sooner. This isn’t less math; it’s more math utilizing computational power and learning earlier. Is that fair?

Conrad Wolfram: More than fair. The intellectual and conceptual are becoming the same as the vocational or practical. Anything procedural will be done by machines. Training people for manual procedures won’t prepare them for useful tasks. For example, science hasn’t become conceptually simpler since the advent of computers; it’s become harder because of more available options through machinery. We need higher-level, more conceptual mathematics, more practical for real problems. Before computers, math wasn’t useful for many real-life applications beyond accounting and bits of physics. It was useless for most biology or social system modeling. Now, thanks to mechanized calculating, math is highly relevant. Stripping out mechanized calculating from education removes its real-world context and utility. Every job with a family wage or better involves mathematics and computational thinking daily. Whether as a biologist, geologist, or lawyer, every job now has a computational foundation. These are critical skills for everyone.

Tom Vander Ark: When you wrote The Math(s) Fix, I hoped it would change the world, leading to new math learning expectations and better assessments. That hasn’t happened much. Teachers are still trapped with dated math expectations. How do we fix this?

Conrad Wolfram: I wish I had the full answer. On the ground in places like the U.S. and UK, not much has changed, but the overall sentiment has shifted more than one might think. Several factors helped, including my book and the AI revolution. When we released Wolfram Alpha in 2009, educators were excited about integral calculation, something we’d been doing for 20 years. AI and LLMs have pushed the idea that all subjects might be wrong, leading to a push for changing content rather than just teaching methods. The last 30 years have seen a mismatch between real-world math and school teaching. We better not replicate this mistake for AI.

Tom Vander Ark: I couldn’t agree more. At the recent air show, many apps were automating bad instruction, including hand calculations in math. These well-intentioned efforts are trapped in bad policies linked to outdated expectations.

Conrad Wolfram: There are various ways to address this. One way I’ve tried is working with countries interested in adopting early. We’ve had a few successes. Sadly, I wish a U.S. state would step up.

Tom Vander Ark: What about Singapore? Historically respected their math education. Any chance a smaller country could flip?

Conrad Wolfram: Singapore isn’t as revolutionary in content as we might think. They teach the sensible end of traditional math and do it well within their culture. They have pedagogical sophistication but aren’t revolutionary in content.

Tom Vander Ark: What about the apprenticeship pathways in Germany, Switzerland, and Scandinavia? Do you see them incorporating more relevant math expectations?

Conrad Wolfram: Not yet in those countries, but vocational directions are incredibly powerful. Questioning universities and traditional college paths opens exciting possibilities. There are new universities and different tracks where traditional methods aren’t bought into. One major driver in many countries is college admission. Colleges often note top students can’t do much useful when they arrive and require retraining. This could influence schools to change. There’s progress, but top-down pressure is needed.

Tom Vander Ark: This all became very real for me recently. My granddaughter came home from a school concert and said, “Papa, learning long division in school seems so dumb. What do you think about that?”

Conrad Wolfram: She’s off on a good track.

Tom Vander Ark: It put me on the spot. And I think many kids and teachers are in this same position, stuck between outdated school gateways and college requirements. We have work to do.

Conrad Wolfram: We do. In some ways, assessments are becoming devalued, which opens possibilities. Other currencies could emerge, offering options.

Tom Vander Ark: Many states are adopting a new portrait of a graduate. In some cases, they’re creating new diploma pathways, and I think that’s going to be the key opening: to create new diploma pathways that are linked to high-wage, high-demand employment. I think we’ll be able to create a fast pathway that values computational thinking and assesses it in new and better ways. I’m hoping that once a handful of those openings are created, we’ll be able to flip the system.

Conrad Wolfram: Yeah. One thing just to add that I think, as you say, AI for pedagogy rather than changing the subject is quite prevalent. But I would say our early experiments with computer-based math content are quite exciting in terms of having AIs help to teach, tutor, and assess more open-ended computational thinking and math. I was a bit skeptical of how well this would work, but it turns out that the framework we’ve built for helping teachers to understand how to teach this is actually very helpful for getting AIs to help teach it. I’m actually rather positive because one of the impediments we’ve had, among the other ones we’ve talked about, is how to roll this out with the current teaching workforce. Well, I think there is some great assistance to that now coming down the track. I think AIs will help directly, you know, correctly deployed for that purpose.

Tom Vander Ark: Conrad, we so value your advocacy, not to mention the sort of computational power that your family has brought to the world. I want to urge everybody to pick up a copy of The Math(s) Fix if you haven’t read it already. And for a quick fix, check out ComputerBasedMath.org. Is that still a good resource?

Conrad Wolfram: That’s still a good resource. I’ve got some blog posts people might enjoy on conradwolfram.com as well.

Tom Vander Ark: We will include a few links to those. Thank you. We’ll include a link to our friends at South Fayette Schools, just outside of Pittsburgh, which is another great example of a U.S. school district that has a beautiful computational thinking framework K through 12 that they developed with Carnegie Mellon. So around the edges, we’re seeing people rethink computation in large part because of your work and your advocacy. So thanks for being with us, Conrad.

Conrad Wolfram: Thanks. It’s great to talk again, Tom.

Tom Vander Ark: Thanks to our producer, Mason Pasha, and the whole Getting Smart team for making this possible. Until next week, keep learning, keep leading, and keep advocating for computational thinking. See you next week.

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Conrad Wolfram

Conrad Wolfram is strategic director and European cofounder/CEO of Wolfram Research, founder of computerbasedmath.org and author of “The Math(s) Fix”.

Over the last 30 years he has been a key part of the technology transformation that has brought maths, computation and data science to the forefront of today’s world and moved us towards the 4th industrial revolution. Conrad regularly appears in the media, speaking about subjects ranging from the computational future and artificial intelligence to 21st-century education.

Links:

• Watch the Full Conversation
• Conrad Wolfram Website
• Conrad Wolfram Bio
• Language Matters, and What Matters Has Changed by Conrad Wolfram
• Conrad Wolfram on Computational Thinking
• The Math(s) Fix Review by Rachelle Dene Poth
• South Fayette Computational Thinking
• Digital Promise – Computational Thinking
• US Math Wars by Conrad Wolfram