2

Keynote 1: Fixing Human Education for the AI Age

Conrad Wolfram is the strategic director and European co-founder and chief executive officer of Wolfram, a global company that has championed a transformative shift toward computer-based mathematics and a reimagining of the mathematics curriculum to advance computational literacy for all.¹ He cautioned he would be “brutal” in his remarks “to get at the nub of the issues around this empowering era we are in.” Math and computation are driving society forward, but education is not offering solutions, whether in the United States or elsewhere, he said. “We are in a massive new industrial revolution, one that is the most quintessentially human in history,” he stated. “What do we as humans need to do in the future? And therefore, how do we need to be educated?” Math, he said, is at the center of the issue.

ENTERING THE AI AGE

Education has not been bold enough in reacting to the massive changes in the real world, he posited. Ubiquitous computation and massive computing power over the past few decades have led to new ways to make decisions at all levels and have enabled the artificial intelligence (AI) revolution. Entering this new AI age, the big-picture question to answer is what it means to be human and what we need to learn. Perhaps akin to the Industrial Revolution in the 19th century, people feel either encouraged or attacked by machines, but all agree that change is happening very quickly. Bigger questions that need to be asked before zooming into math, computation, and data science include what it is to be human, what we need to learn, what is considered cheating, and how education can adapt effectively and quickly to these changes. Without a framework for fast adaptation, education is failing almost everywhere, he stated.

Wolfram reflected on some of the changes he has seen in the field. In 1988, when his company launched, math and computation were buried in research departments within companies and organizations. Now, those at the board and other senior levels are concerned with AI and data science. Formerly niche issues have moved to “dead center,” which should point to how to educate people, he said. While math was always central to such fields as physics and accounting, high-level computation has led to newly conceived fields, such as data science, social media, and AI, as well as expansion of computation to existing fields, such as biosciences, history and archaeology, sports, agriculture, and marketing and business. This was the picture in 2022. Today’s decisions depend on high-level computation. Moreover, he added, “all subjects are potentially computational, and we have to make sure core education fits with that.” The emergence of large

___________________

¹ For more information, see http://www.wolfram.com

language models (LLMs) in 2023 represents a major new bridge between the computational and human worlds. It will involve many more people and makes much more apparent the need for change.

Education must reflect this changed real world and the kinds of things people need to learn. Incremental changes in curricula will not suffice. To make deep, fundamental change, he urged looking at the “real subject” (content, not just how to deliver it), today’s machinery for learning (not older technology), and human involvement (what thinking entails in the modern age). Often at educational conferences, Wolfram said, the subject (“what we need to learn”) and pedagogy (“how we optimize learning it”) get confused. Particularly when dealing with AI, the primary focus is needed on reformulating the subject now that we have major new machinery, Wolfram said, which in turn will change the pedagogical toolset for delivery.

Math is at the epicenter and emblematic of the challenges facing all subjects in education. “If we haven’t got this straight for math, we’re going to be in real trouble for all the other subjects, even though math itself is extremely important,” he said. Math is at the epicenter because most governments consider it the most important core school subject for the AI age. It is more quantitatively assessable, with more learning hours and students than most subjects. Yet, he said, it is the subject that is more divergent from the real world than any mainstream subject. To be bold, he said, in his view the math community has done a terrible job in adapting to the real world over the last few decades. He recalled that when Wolfram Research launched Mathematica 1.0 in 1988, Steve Jobs, founder of Apple Computer, said it would enable students to focus on the “prose of mathematics without getting lost in the grammar.”² To Wolfram, this situation still exists, as mathematics education gets lost in the mechanics without zooming out to concepts with the modern machinery available.

MAINSTREAM NEEDS FOR THE AI AGE

To Wolfram, the most important mainstream need for the AI age is to make better decisions in life, work, and society. Computation can help with many, although not all, such decisions. He has adopted the terminology of “computational thinking” at the high end of knowledge and “computational literacy” at the low end. Not everyone must be an expert, but everyone needs computational literacy. Today, day-to-day survival depends on how to think computationally and having computational literacy, he

___________________

² Peter H. Lewis 1988. Personal computers: Liberating the prose of math from its grammar. The New York Times, July 19. https://www.nytimes.com/1988/07/19/science/personal-computers-liberating-the-prose-of-math-from-its-grammar.html

reflected. Another mainstream need for the AI age is a modern framework for reasoning. Oxford University offers a PPE, or philosophy, politics, and economics, course; he opined that a “C” for computation should be added because it has become ascendant in working out many things.

To Wolfram, a key crisis in education is the lack of a core computation and computer literacy subject. In his view, 80 percent of precollege mathematics education is off base in terms of content, worldwide. In real-world math, computers do almost all the calculating. Yet, in educational math, people do almost all the calculating. We are educating people in math for a world that is no more, because in the modern world, computers have liberated people from hand calculations.

He offered a four-step computational/math process: (1) define the problem; (2) abstract to a computational form; (3) compute by taking the question in abstract form and finding a solution; and (4) interpret the results, possibly with a need to iterate the process. Schools around the world focus on step 3, which drains time from the other critical steps. He called for education that mostly uses computers for this step so that students spend more time on the other three steps, using “messier problems that match real life.”

Another change since 2023 is that AI can help in some of these other, formerly human-only, steps, although he cautioned against solely relying on machines for these steps. The second step of abstraction used to mean representation by mathematical formulas; now it usually means generating code both to cover a wider range of abstraction, and so that a machine can compute results. Removing the computer from education results in removing almost all modern contexts of mathematics, he said. Although he acknowledged that many mathematicians disagree, Wolfram opined that math was not very useful for working out many things before computers. But the power of computation means there are now “brand new recruits” in bioscience, medicine, and other fields. Teaching math the traditional way with traditional hand calculations means teaching students the wrong algorithms and patterns of thinking. Students are equipped with a computational toolset that does not reflect the real world.

From a cost-benefit analysis of the four steps above, step 3, calculation, used to be very expensive. Thus, a long time was spent in step 2, abstraction, to achieve something clean and neat to minimize calculation. Computation is now extremely inexpensive, so multiple abstractions can be considered with many computations. Another exciting consequence, in his view, is the possibility of reordering the curriculum. For example, he posed, why not teach calculus to 10-year-olds, three-dimensional geometry before two dimensional, or machine learning to elementary students? He shared several example problems that students have performed that reflect new patterns of thinking, empowered by computers.

MISTAKES IN MATHEMATICS EDUCATION

Wolfram offered his list of mistakes in math education. The claims made, including teaching the basics, being trustworthy, and changing through evidence-led innovation, have in fact resulted in a lack of progress. Succeeding in education has meant improving assessment results, which at this point rewards students who do well in multiple-choice, close-ended (easy-to-grade) assessments rather than open assessments. Teaching the mechanics of the past and focusing on how a machine works, rather than how to work the machine, also means education does not prepare students for the real world. He called for innovation-led evidence rather than evidence-led innovation. “To jump to something new, you cannot get formal evidence about what will work up front. You have to come up with the best guess, try it with as low a risk as possible, and then iterate to get the evidence,” he pointed out. Otherwise, change will be only incremental, which is not what this urgent time requires. Not changing is riskier, he added.

A consequence of the lack of change is rejection of many students who could otherwise advance. Rather than look at their ability to solve quadratic equations, for example, focus on imparting a bedrock of good thinking. Another consequence is playing out in the workplace, where increasingly bad decisions are made because people do not understand the role of computation in getting answers. Societal dislocation can also occur, because when people do not understand how decisions are made, they become confused and dissatisfied. Education should include an understanding of overly simplistic real-world computation and evaluation of claims that computation can solve problems that it cannot. The curriculum should include broad outcomes that include experience with current technologies. Students need to know the variety of computational tools at their disposal, similar to workers needing a range of tools for different jobs.

COMPUTATIONAL THINKING AND COMPUTATIONAL LITERACY IN THE AI AGE

It is not straightforward to deliver computational thinking and literacy in the AI age, Wolfram continued. He explained that the Wolfram Language Concept tries to represent everything in computation in one consistent style, encompassing programming language, superset computation representation, and human technical communication language. It offers a high-level abstract way of communication that traditional mathematical notation cannot do at this point.

Drawing on work done in Estonia, Wolfram described the approach taken to develop and deliver a new curriculum including supporting teachers. To figure out the curriculum, the developers worked backward from

real-world problems to the materials needed for students and teachers. Thinking about problem sets helps work out which pieces of math, computing, and data science are needed to impart to students. It involves modern outcomes, open-ended assessments, and a fast, iterative process for developing curricula. AI tutoring and assessment are promising to move forward new approaches and help teachers interact with students at different levels. A multidimensional process brings together different math processes, levels of outcomes, contexts, and grades.

Wolfram shared 11 dimensions of core computational thinking—outcomes that students should be able to master. He noted the outcomes are much broader than exist in most countries, such as communicating and collaborating and feeling confident to tackle new problems, and said he welcomed comments about the dimensions identified.³ Different layers of learning are articulated for different-aged students. As a whole, the outcomes must engender AI-age “thinking” that is based on hybrid human–AI management and intertwines creativity and process.

He and colleagues have been building a computational curriculum “that assumes computers exist.”⁴ They start with a problem that would interest students (e.g., How fast can a bicycle go in a race?), then zoom out to the math needed to solve the problem. Detailed modules are provided for teachers so they have the confidence to teach concepts that may be new to them. In another example, students see if they can spot a cheat.

UNIFYING EDUCATION

Looking at the policy or state level, curricular efforts are very disjointed, Wolfram observed. Book publishers, assessment tools, standards, and other components need to come together because they are intertwined in the modern world. Symbolically representing these different components, as done in Estonia, can be a great advantage. AI tutoring and assessment can be helpful, he said. A mistake is to equate AI with LLMs. AI is an outcome to achieve. LLMs are statistical ways to get to that.

Wolfram presented a detailed proposal for fundamental change to mathematics education in The Math(s) Fix to define the problem, fix it, and navigate the change.⁵ Many of the problems are similar across countries or states, but the pressure points to make change differ. Funding is a major aspect. Large initiatives are needed.

___________________

³ The required outcomes from core computational thinking identified by computerbasedmath.org can be viewed at https://www.computerbasedmath.org/materials/math-education-outcomes.php#detailed-view-in

⁴ The curriculum is available at computerbasedmath.org and computationalthinking.org

⁵ Conrad Wolfram. 2020. The Math(s) Fix. Wolfram Media, Inc.

It is important to address what AI can do and what humans can do, especially moving into an era of successful AI. To begin to answer this question, he noted that AI is good at helping humans practice things. AI and humans may jointly construct arguments in the future, so people need experience in how to interact with machines to do that. However, humans, and not AI, will continue to handle other humans. AI can be used to procedurize things, while humans need to know how to manage AI. Finally, he said, some argue that LLMs supplant the need for abstraction, but abstraction is and will still be powerful to make progress.

“Do not cleanse the reality,” Wolfram stressed. Education often looks for ways to simplify with the belief that a subject will be easier to learn. The reality is a world of messy problems, machinery not working, competition, and complex human emotions. “We want people to get used to that so they have confidence and can apply it when they go outside,” he said.

The job of education is to enrich life. Computational thinking can help. A key process to achieve it is to accelerate experience. For employers, this could mean training nontechnical workers to understand and use computational thinking. Universities should offer a core computational thinking subject, as well as computational courses relevant to other subjects. Policy makers have to fix the stuck ecosystem of education for subject change. It is far easier to get funding for incremental change, for example, a small increase in SAT⁶ scores, than for an alternative subject that will better prepare students with what they need to know. The United States unlocked the ecosystem for commercial start-ups several decades ago. Similarly, unlocking the education ecosystem is now needed. Incentives are not aligned. Iteration is far too slow, and funding is siloed. Understanding the linchpin for system change in a particular place can foster change.

Wolfram concluded that making these changes can result in first-rate human problem solvers, not third-rate human computers, which is what the education system is currently delivering. In every industrial revolution, you need to “work up a level,” he urged. Rather than pretend to be the machine that was just introduced, work up to the next level. Do not compete with what the machine does, but optimize human–computer hybrid decision making. Computational literacy is needed for all, and those countries, states, and organizations that prioritize this will leapfrog their competitors. Closing the divide between computational haves and have-nots will lead to better enfranchisement across society and rebuild trust.

___________________

⁶ Refers to the standardized college admissions test widely used in the United States, originally called the Scholastic Aptitude Test (SAT).

DISCUSSION

Padhu Seshaiyer reflected that the process of define, abstract, compute, and interpret harkens to the philosophy of design thinking, which has five steps, beginning with empathy.⁷ He asked where empathy, which involves understanding the needs of users, fits in with the four steps outlined by Wolfram. Wolfram responded that part of the define step is trying to understand what people think is important. He also stressed that the steps he laid out are not sacrosanct; rather, the concern is that a process exists and people can be educated to go through it.

Deborah Stine noted that an assumption in the policy world is to engage with those with lived experiences. She asked Wolfram whether this type of engagement took place in creating the ideas to change the curricula that he presented, and also wondered if they might be better suited to the college level. Wolfram said his examples come from secondary and primary schools. In terms of applicability to the real world, he said secondary math seems to be further removed from people’s lives than primary math. Input for this should come from the real world, he stressed. Teachers are not in the real world doing math, so they cannot be expected to know what to teach. They know delivery and how to organize pedagogy, not the subject as applied in a fast-moving world, and it is not fair to expect them to know it. Another mistake is to pick mathematicians, not other users of mathematics, to develop the content as they represent only a small fraction of real-world utilization. To exemplify this, he noted that only a small fraction of Mathematica users classify themselves as mathematicians, instead mostly being experts in other technical subject areas. This distribution needs to be reflected when developing modules and teacher training in data science modeling, geometry, information theory, and a foundation category, “architecture of math.”

Zarek Drozda asked about Wolfram’s experience in Estonia in implementing new curricula. Wolfram replied that Estonian teachers have more mathematical training than in many countries, but less computing experience. They requested a very detailed, explicit description of every minute of a lesson when teaching something new to them. Political changes and assessments remain a challenge to mass adoption. He expressed regrets that the new curricula were not better embedded at a policy level. High-stakes assessments that support open-endedness and the types of curricula he has advocated would be a powerful incentive.

Ben Galluzzo shared that, as one piece of evidence to show demand for new approaches, his organization has run open-ended, real-world-based

___________________

⁷ The framework for design thinking is considered to encompass five steps: empathize, define, ideate, prototype, and test.

contests that have grown from 10,000 to 100,000 participants in the last 15 years. Students want these types of challenges, he stated. Elementary school students like challenging problems, he continued, and their teachers are teaching a variety of subjects to them. Twenty-five years into a postdisciplinary world, he asked Wolfram about extending his work across disciplines. Wolfram agreed with the value of teaching subjects in a more cross-disciplinary fashion. However, he opined, math is particularly misaligned; with limited funding and ability to scale, he said math is the place to focus first. He expressed the hope that workshops and other gatherings can pull together different strands of innovative things happening across disciplines.

David Weintrop noted the value of core foundational conceptual pieces in education and asked where they fit in the changes Wolfram believes are necessary. “This is the big question of our age, given there are machines,” Wolfram replied. “What is it we need to learn as humans and what is left to machines? To back up, what is the essence of math and what are the mechanics of the moment in carrying it out?” He called for two quick tests. First, for a given topic, does one practically use it? A second, more difficult test is to determine if seeing something done manually empowers a person’s conceptual understanding. He suggested that international experts come together to agree on math’s core values and desired outcomes. To that end, he invited attendees to participate in the Maths Fix Campaign for Core Computational Curriculum Change.⁸ Wolfram also offered open-source and free resources for educators and for the advancement of K-12 computational thinking education.⁹

___________________

⁸ For more information, see https://www.computerbasedmath.org/take-action/

⁹ For information on Wolfram|Alpha for educators, see https://www.wolframalpha.com/educators; for information on Wolfram Cloud to interact computationally with data from Wolfram|Alpha, see https://www.wolframcloud.com/; for demonstrations and thousands of interactive manipulatives to use in teaching, see https://demonstrations.wolfram.com/; for information on high school statistics, see https://demonstrations.wolfram.com/topic/high-school-statistics

This page intentionally left blank.