Over the last few weeks, the headlines have been dominated by new developments in Artificial Intelligence (AI), especially from Google's Gemini and ChatGPT 4o from OpenAI . The announcements have come alongside the release of the book Brave New Words by Sal Khan, the founder of Khan Academy. In partnership with OpenAI, Khan has created one of the most sophisticated AI-for-education models ever produced, called Khanmigo. For this edition of our Blog, we’re exploring MathTrack Institute’s perspectives on how AI and Artificial General Intelligence (AGI) technology will transform learning – and why that’s a very good thing. We provide a unique perspective on how this will impact teachers, parents, and students in mathematics education in the future. This 3-minute video with Sal Khan and his son Imran Khan will help you start to understand the magnitude of these advancements:
As someone who has curated and built a lot of technology, I can quickly tell you this is a very carefully created and regimented technology “demo.” However, it more than serves its purpose. Almost everyone I have talked to about this video has a single shared reaction: WOW. Can you imagine what it would be like to have access to a personalized tutor knowledgeable in every subject matter area, who is available to talk with and chat with whenever you need it? With this technology, you and everyone else can learn anything. Sounds great, doesn’t it? However, you might be wondering if it’s necessary. So, let’s take a step back and examine why personalized learning and high-quality learning interventions are so important and how this burgeoning technology is a promising answer to a long-studied problem.
BLOOM’S 2-SIGMA PROBLEM REVEALS THE PROMISE (AND PROHIBITIVE EXPENSE) OF TUTORING INSTRUCTION
In 1984, researcher and professor Dr. Benjamin Bloom released a paper based on his work at the University of Chicago and Northwestern University and a pair of dissertations from recent graduate students (Anania, 1982; Burke, 1984). This research compared student learning outcomes from conventional, mastery learning, and tutoring conditions. Quickly defined, Conventional Instruction (CI) denotes students learning a subject matter in a class with 30 other students and periodically given assessments to track grades and progress. Mastery Learning (ML), similar to conventional learning, includes adding feedback to the assessment and time allotted for corrective instruction. Tutoring Instruction (TI) is defined as students learning the subject matter with a good tutor (in groups of up to 3 students), where the assessments are held constant, and the corrective feedback is similar to the mastery learning approach. One caveat is that corrective feedback is not used as frequently in this model because questions and errors are addressed in the learning process before the assessment.
The most striking part about this series of research studies was that it was replicated in several settings, which is unusual for education-related research. Also, the difference in final achievement between the three conditions was statistically stunning. Here is a quick summary in graph form of the achievement outcomes by the type of learning environment provided.
As you can see, the average tutored student outperformed 98% of the students from the conventional control class. Thus, Bloom and colleagues had identified and defined the 2-sigma (2 standard deviations above the mean) problem. TI was much more effective than trained ML interventions, certainly much more effective than CI. How could education systems, Bloom and colleagues pondered, make it affordable for everyone to have access to a tutor for all subjects as the direct means for learning all subject matters?
TUTORING INSTRUCTION COSTS 10X MORE THAN EVEN THE BIGGEST SCHOOL BUDGETS
According to data from the 2022 Annual Survey of School System Finances released by the U.S. Census Bureau, public school spending per student went up to $15,347, from $14,358 in fiscal year (FY) 2021 – the largest fiscal year-to-year increase since 2008. This is an average, as States spend significantly different amounts per student. For example, New York spent $29,873 per student, while other states, like Utah, spent $9,552 per student—more than a 3x difference in spending and budget. To deliver personalized education and instruction for every student would likely cost 10x more than even the largest budgets. With an annual cost in aggregate already close to $1 trillion, a 10x increase would bankrupt even the wealthiest countries.
Bloom and colleagues reported that the 2-sigma problem included profound findings that most students could reach a high level of learning regardless of socioeconomic status or background. As Bloom stated then and continues to be discussed today, human learning capacity is relatively the same. Read that carefully: Everyone is born with a similar capacity for learning all subject matters. There are talents, of course, but the capacity is the same at birth. So, how can we research and create systems that allow everyone to reach their potential at a cost society can bear? Shouldn’t that be the goal of advancing human societies?
BACK TO THE FUTURE WITH ARTIFICIAL INTELLIGENCE
Bloom's research showed that educator training increases student outcomes by 1-1.5 standard deviations, even in large group settings. This means a highly trained educator matters and can profoundly impact student learning. We at MathTrack Institute have communicated this powerful idea to our stakeholders since our inception. Bloom’s important findings and subsequent research from others in the field focused on developing high-quality teacher training that yields practical methods (something the average teacher can learn quickly) at no higher cost for deployment. This kind of instruction is not consistently delivered within the traditional Higher Education credentialing system. Therefore, our University System does not produce enough highly trained educators to satisfy even baseline demand. If the system could produce high-quality teachers at scale and a lower cost, it would be an educational innovation of the greatest magnitude ever recorded. That was a widely circulated promise before artificial intelligence through large language models (LLM) had even emerged. Now, something even more profound may be possible at an almost inconceivable speed.
There is a lot to notice in the short video with Sal Khan and his son working collaboratively with the generative AI Khanmigo. For example, when the video starts, Khan sets the parameters for good teaching with his well-designed prompt. Khan starts by asking Khanmigo to help tutor his son through the task by asking questions and nudging him in the right direction (Socratic dialogue), but not by answering the task (discovery learning). This may seem simple, but his prompts are informed by decades of work where Khan and colleagues at Khan Academy attempted to supply on-demand videos and adaptive learning as a solution to worldwide equitable access to learning. Then, Khanmigo followed some good pedagogical practices to talk Imran through the task. This pedagogical approach is as good as many veteran mathematics teachers could do. On a magnitude scale, it is better than most could do at any time, on demand, whenever a student needs it. Not even the greatest human educators are on-demand 24/7 (nor should they be!).
AS EDUCATION EVOLVES, TEACHERS PLAY AN EVEN MORE VITAL, HANDS-ON ROLE IN THE CLASSROOM
Above, I hinted at the profound speed of change that is coming. I believe this change will guarantee that teachers are relevant and remain the most important element in a classroom with students. Over the last 40 years, we have paved the way for personalized curriculum. If you have ever read the book The Diamond Age by Neal Stephenson, we are getting closer to Nell’s copy of Young Lady’s Illustrated Primer. The Primer is an artificially intelligent book that adapts to Nell’s needs and interests, providing her with education and guidance, ultimately helping her navigate the complexities of her world and think for herself. We already have tools, like adaptive learning curriculum and on-demand video, that are incomplete without the companion. Khan himself admits this shortcoming in his new book. Generative AI, like Khanmigo, can now bridge that gap.
Wait, I thought you said teachers were vital? Indeed, they are even more so with the availability of an AI companion. The purpose of mathematics is not to create human calculators. We have great calculators that never make mistakes on our phones. A well-trained adult who can understand and model the intellectual habits of mind and the purposes for scientific creativity of mathematics now becomes even more essential. The good news is this skill set can be trained and developed with adults at a fraction of the cost of a traditional higher education approach. The better news is that apprenticeship-based degrees for training teachers while they work and are paid full-time is a fast-growing trend in the US and beyond. This means that the emerging trend in AI, coupled with teacher training where they learn to curate the use of the AI companion for students while modeling mathematical creativity and habits of mind, can achieve the monumental human impact Bloom dreamed of in his 1984 article.
AI IS A POWERFUL, TIME-SAVING TOOL FOR ENHANCING TEACHING CAPABILITIES
One of the most time-intensive teaching requirements is planning lesson plans and ensuring that all principles and standards are covered. OpenAI’s ChatGPT-4o can produce a syllabus spanning an entire academic year, scope, and sequence for teaching Algebra I, subdivided into units with standards-aligned topics, in 10 seconds. Here is the prompt that I used to output this request.
The output was incredible: ten units, complete with the number of days to cover the topics and the activities that could be accomplished during those days with students. The planning and logistical hurdles of classroom teaching and detailing a logical sequence of topics are now generative—on demand. What does this mean for traditional textbooks and curriculum? Well, that might require a separate post to unpack.
Personalized learning on specific topics does not need to replicate the human approach to tutoring. It can be driven by our human creativity to be so much more. For example, if students are learning about fractions with their AI companion, they can use the software's mimic capability to inform a conversation about fractions. I used the following prompt to ask ChatGPT-4o to talk to me as an ancient Egyptian mathematician and help me understand how they would write fractions.
Here is the response:
What if you were a pre-algebra or algebra student learning about the Cartesian plane? Instead of learning about this as the x/y axis, with guidance, you could chat with the inventor Rene Descartes about it.
Descartes, or the simulation of Descartes, further explains the motivations and reasons for developing the Cartesian plane and how it led to advancements in several fields of human inquiry and scientific discovery—instantly giving context and reasons for learning this topic. Mathematics isn’t about being able to do stuff. It's about understanding the motivations behind why things were created. All of that is now possible with AI, as long as we have the human teacher to curate the journey.
THE HUMAN GUIDE MODELS, NURTURES AND INTERACTS IN REAL LIFE
So, I mentioned that the human in the classroom will become even more important. As we evolve with these tools even further, the notion becomes even more antiquated that all content knowledge for mathematics must be carried around in a textbook or someone’s head (not scalable). If I want to learn about Einstein’s theories, I can chat with him about it. I may even someday be able to chat about it with an AI model Einstein in virtual reality (5 years or less!). Why do I need a professor lecturing me in a 6 month-long, expensive course on his works? There is no longer a middleman of cost to access high-quality content—no barriers and no multibillion-dollar entities that gatekeep access.
The skills of a human educator are in process, classroom management, modeling creativity, and intellectual habits of mind and scientific behavior through their interactions with their students. They can also curate interactions with AI companions by creatively utilizing their capabilities, something that can be trained. It may take a teacher of today several decades to understand the depth and breadth of mathematical study, even for just the K-12 curriculum. But, this curator approach to teaching mathematics can happen much more quickly. Students do not learn intellectual behavior by memorizing the top ten mathematical habits of the mind. This is learned through human modeling, behavior, and activity, which will be gained over time as students evolve through phases of age-appropriate maturity and interact with healthy adults. The AI companion will be able to track this, remember a student’s journey, and report their work, behavior, and changes in that behavior to the teacher. This is true for informing parents about their children's progress as well. Imagine when you get home, you can ask your child's AI companion what really happened at school today!
That vital human role as curator is a skillset that can be learned, trained, and developed quickly, establishing a higher probability of healthy adults in every classroom, community, and country. We have already been doing that at MathTrack Institute, where people with no background in mathematics have trained on our GROWTH framework, and their students are performing at the same level as those taught by 10-year teaching veterans. Those outcomes were achieved by teachers before the full maturity of generative AI we have today.
This training doesn’t cost four years of your life and $120K in tuition. You can do it while working full-time as an apprentice and, in half the time, for a tenth of the cost. You can now get a bachelor’s degree in Applied Mathematics and a teaching license without debt. We will be embedding the use of AI into our teacher training soon, as a means to help shape their understanding of how to model their use in their professional classrooms. These adults will learn how to curate these tools effectively, successfully setting the parameters for their use in the way that Sal Khan did in his short “demo” with his son. For the first time, we can equitably scale the proven best education framework to kids of all backgrounds, anywhere, anytime, at a cost that won't break state and federal budgets. The work of the human educator, as a curator of these tools and model of creativity and intellectual behavior for the student, will level the playing field in a way that has never been possible. My team and I work for that future.
