Anthony J. Campbell

AI, 2-Sigma & The Future Of Education: Aristotle For An Army Of Alexanders

Anthony J. Campbell
AI, 2-Sigma & The Future Of Education: Aristotle For An Army Of Alexanders

“Free education is abundant, all over the Internet. It's the desire to learn that's scarce.”
Naval Ravikant (@Naval)

Recently, I ran into something called ‘Bloom's 2-Sigma Problem'. Benjamin Bloom, an educational psychologist, found that an average student could perform two standard deviations better than others when given one-on-one tutoring. In plain English, this means that any student could perform better than 98% of their peers, when given sufficient personal attention!

What interested me most about these findings is that, given enough personal attention, nearly every kid could be a prodigy of sorts. In addition to having a personal instructor, every student progressed along the learning track using a mastery-based learning approach. In a nutshell, students need to demonstrate a certain level of mastery (i.e. scoring 90% on a test) in prerequisite knowledge before moving on to more advanced material. In doing so, understanding is guaranteed and no student lags behind. On paper, it appears to be the ideal solution to an increasingly out-of-touch education system. This begs the question why this hasn't been acted upon?


The short answer is economics. The somewhat-longer answer is that no major or minor country has adopted an educational approach incorporating Bloom's findings because of the fact that it is cost-prohibitive. One-to-one tutoring is simply too costly for society to bear on a large scale, something echoed by Bloom himself. Nowadays, teachers get paid less and less and many a school district has been forced to resort to cost-saving measures.

According to the National Center for Education Statistics, the average American Middle School has 595 students with the average class size being 26.8 students for every teacher. In effect, such a middle school would have:


595 / 26.8 = 22.2 ≈ 22 Teachers


That makes 22 teachers delivering instruction. That number doesn't account for administrative workers, librarians, school nurses, P.E. teachers, etc. The exact number differs from one source to the next, but consensus seems to be that most Middle School teachers make approximately $49,000 per year, before taxes. Which makes:


$49,000 * 22 = $1,078,000 in salaries, per year, per middle school


If we were to incorporate Bloom's one-on-one teaching at even one middle school, all of a sudden the costs would skyrocket. As you might already guess, costs will be 26 times as high:


595 * $49,000 = $29,155,000 in salaries, per year, per middle school


That's quite the number, huh? Even if we were to decide that we would allot teachers to groups of four students, thereby cutting the cost by 75%, we'd still end up with the eye-watering total of nearly $7.5 million solely for teacher salaries! For some reason, I don't see Flint, Michigan incorporating this anytime soon.


”What is thy bidding, my Master?”

Even some back-of-the-napkin math is quite clear: it's impossible for all but the very wealthy to hire personal tutors. That only accounts for one half of Bloom's findings, though. What about Mastery-based progression? During my research I couldn't find a single school that incorporates master-based progression in their curriculum! Not in Finland or Scandinavia - with their much-vaunted educational system -, and most certainly not in the United States.

Once again, it comes down to economics and practicality. Normally, a teacher has his or her hands quite full with keeping a class of 26 hormone-fueled teenagers under control as it is. With a standardized curriculum, that is. Now, what do you think would happen if a teacher had to keep track of where each student is in the curriculum? Potentially, that means 26 students at different levels, struggling with different concepts, all vying for the attention of one underpaid middle school teacher.

A different type of mastery…

A different type of mastery…

While there is no ‘correct’ way to incorporate mastery-based learning, there are some common aspects across the board. Any curriculum, whether you're teaching arithmetic or quantum physics, can be divided into small bite-sized chunks. Every chunk has defined student outcomes (i.e. “A student knows Newton's Three Laws”), information to transfer via lectures or text, and some form of testing or exercises to solidify the knowledge and ascertain if it's sunken in. Normally, we call these chunks ‘Lessons’. Fancy, I know.

Lambda School is of the few institutions I know of that actually incorporates mastery-based progression and takes Bloom's findings into account. It might sound a little preachy to always be talking about Lambda School, but it's the truth! Every week, students learn new skills and information and get tested on them five times a week. On Mondays through Thursdays, it's relatively simple assignments. On Fridays, all student have to pass a three-hour practical test to move on to next week's instruction. If you fail the Friday-test, you have the entire weekend to revise, consult with your instructors and Project Managers, and retry the assignment. If you fail again, you redo the past week.

The great thing with Lambda's incorporation is that students don't have to ‘catch up’ with the rest of the class once they've fallen behind. This makes perfect sense when you think about it. Failing a test means that the previous material hasn't settled in just yet. It's the height of foolishness to then require that student to both fill in the gaps of their knowledge, as well as finishing the normally-scheduled lessons for that day.

So, Lambda takes a different approach. Whenever you ‘fail’ a week's lessons, you restart those weeks classes with whomever else might be at a similar point in the curriculum as you are. Over the course of a 45-week program, some (if not most) people will fall behind a week here and there. In effect, you get a bunch of smaller classes, each on their own week. The trailblazers and laggards might be separated by a good fifteen weeks. That's fine, though. As long as the results, graduation and full comprehension, are the same. Over the long-term, this might result in Lambda and other schools stop ‘batching’ their students and having them start all at once. Perhaps a new cohort could start every single week, allowing people to seamlessly move from cohort to cohort, and from week to week.


The Hungarian Kingmaker

Just to give you an example of what's possible when one-on-one tutoring and mastery-based progression come together, I'd like to introduce you to László Polgár. Lászlo is a Hungarian chess teacher and educational psychologist who came to prominence thanks to his three daughters. At their birth, Lászlo decided to bring his theories on learning into practice. You see, Lászlo was convinced that genius is “… a learned trait”, one that was brought about by sufficient passion for the subject and plenty of dedicated work.

He also postulated that this was possible as long as their education started before their third birthday and they began to specialize by age six. In 1992, Polgár told the Washington Post: "A genius is not born but is educated and trained….When a child is born healthy, it is a potential genius.”

In preparation, Lászlo studied the biographies of 400 great intellectuals, from Socrates to Einstein. One of his main principles to promote mastery was to make the topic exciting and maintaining the child's enthusiasm. He also tried to achieve a pedagogical situation where a sense of achievement dominated. He tried to do this by maintaining a success-to-failure learning rate of ten-to-one. This was done to eliminate failure, anxiety, and shyness, which would only block the child in his opinion. finally, it was of the utmost importance that the child would have clear goals he/she could autonomously strive for every single day. (So you don't get burnt-out prodigies who don't know what to do with their lives.)

The results of the ‘experiment’ are quite revealing. Lászlo is the father of the famous "Polgár sisters": Susan, Sofia and Judit, all three of whom are outstanding chess players. Sofia ended up becoming the number six female player in the world. All because she started early and worked very, very hard.

Wait, what about the other two sisters, Judit and Susan? Well, they would end up becoming the best and second-best female chess players in human history, respectively. Talk about a high-achieving family! Surely, Lászlo himself must've been a world-class chess player as well right, to account for the genetic talent?

Nope. Lászlo was only a mediocre chess player who had to study tirelessly to teach his daughters. Nor was their mother any good at chess. It's very difficult to attribute the enormous success of these women to something as ephemeral and vulgar as ‘talent’. "My father believes that innate talent is nothing, that [success] is 99 percent hard work," Susan says. "I agree with him."


An Aristotle For An Army Of Alexanders

Like it does in so many other industries, Artificial Intelligence holds massive promise to revolutionise education. We've all seen the 2014 movie ‘Her’, right? The one where Joaquin Phoenix falls in love with an AI, voiced by Scarlett Johansson? In it, an Operating System is capable of flawlessly responding to human speech; doing tasks for us, helping us with our works, and even having a conversation. Firmly in the realm of science-fiction, right? According to some scientists, it might be closer than that.

What if we were able to create such an artificial assistant? A program that people - even children - can talk to and help them throughout their day. What would the ramifications be for learning and education?

Aristotle, one of the giants of Western philosophy, tutored Alexander the Great in 343 BC. At the time, one only as wealthy and powerful as the king of Macedon had the wealth and influence to get such tutors for his son. While the exact lessons imparted by Aristotle on a young Alexander aren't clear, it's been used as the ur-example of what great tutors can bring about. Now, what if we could replicate Aristotle? What if he could live on every tablet and phone on planet Earth?

With advances in Artificial Intelligence, every single student on Earth can have full-time personal one-on-one tutoring by the world’s greatest expert in the field. Imagine being taught physics by Einstein or Stephen Hawking and astrology by Neil Degrasse Tyson. Not just that, but them being able to empathise with you and adjust their teaching-style to your personality. It'd be the most nurturing, not to mention effective, teacher you've ever had.

We'd have an Aristotle for an army of Alexanders.

It's been theorised that for every Einstein and Oppenheimer born in relative wealth, a dozen or more spend their entire lives in poverty. With neither access to education or advancement. What if we could take this away? What if the Polgár sisters are no longer an anomaly? What if every child could be a prodigy by our standards?

Where would humanity go? What incredible advances in the arts and sciences would it precipitate? What good could we do?

In regards to having an artificially-intelligent tutor and mentor, I believe it's not so much a question of ‘if’, but rather ‘when’ and ‘by whom’. Who will be the first to bring true artificial intelligence to the masses?

P.S. If you want to read up on Bloom’s 2 Sigma Problem. You can find some more info here and here. Read the original paper here. In addition, if you wish to learn more about Lászlo Polgár, I'd recommend Geoff Colvin's ‘Talent is Overrated’