Making AI better at math tutoring
blog.khanacademy.org
blog.khanacademy.org
I failed in university at math. Why? Because the tutors had not the time to help me. My level of math was not the same as the other students as i was not in the math part of a gymnasium.
I struggled and wasted a lot of time and energy to even find good explanations.
And when i had a math group, one girl was super nice but knew so muchmore than i did because of her math in gym. Professors asumed so much knowledge and no one cared to try to help people.
Best help were people from india on youtube with bad english.
And the most ridiculous part: Every year around the globe people teach this level of university math to probably millions of students. We should have the perfect free educational platform which teaches everyone perfectly already because so many tutors and professors lecture on the same topics over and over and over again. Our educational system is a joke.
THEN SAID A teacher, Speak to us of Teaching.
And he said:
No man can reveal to you aught but that which already lies half asleep in the dawning of your knowledge.
The teacher who walks in the shadow of the temple, among his followers, gives not of his wisdom but rather of his faith and his lovingness.
If he is indeed wise he does not bid you enter the house of his wisdom, but rather leads you to the threshold of your own mind.
The astronomer may speak to you of his understanding of space, but he cannot give you his understanding.
The musician may sing to you of the rhythm which is in all space, but he cannot give you the ear which arrests the rhythm nor the voice that echoes it.
And he who is versed in the science of numbers can tell of the regions of weight and measure, but he cannot conduct you thither.
For the vision of one man lends not its wings to another man.
And even as each one of you stands alone in God’s knowledge, so must each one of you be alone in his knowledge of God and in his understanding of the earth.
That's called "zone of proximal development" in pedagogy.
However, "that which already lies half asleep in the dawning of your knowledge" is often a consequence of things that were revealed to you previously.
When you learn, you could probably make any specific step alone, but you cannot make all the steps alone.
The nice thing about learning, the more you do it, the easier it becomes.
In germany you have the concept of specialization and you can choose different areas.
The syllabus had all the methods we had to know, and I learned them all through youtube on a channel called NumericalMethodsGuy. I stopped attending class and just went to labs (which were really just matlab assignments in numerical methods) and turned in assignments, and wrote exams. I got an A.
Key takeaways:
* Mathematics is hard. Much harder than most other subjects (except physics which is mostly hard because of all the math involved).
* University is not like primary/secondary school. It is a place where you need to learn how to take responsibility for your own learning. Ideally, you learn how to become an adult.
Every one of my classmates began their degrees from a different place. They excelled in some areas and struggled in others. Many dropped out. This led me to believe that most secondary schools do not fully prepare their students to study mathematics. Having said that, those of us who did make it weren't exactly geniuses. Just people who got used to it.
"Young man, in mathematics you don't understand things. You just get used to them." -- John von Neumann
I've been tutoring high school students in math (and other subjects) for 8 years now. One thing I'd like to add is that I can tell who will succeed at mathematics and who will struggle just by watching them work from across the room.
The students who succeed are the ones who can sit there and focus for hours at a time. The ones who struggle do so because they can't focus for more than five minutes and then start socializing. I think one of the biggest issues for people studying math is that they either can't focus (due to ADHD) or they have math anxiety which fills them with dread any time they try to study. This dread can be so overwhelming that they will do anything they can to avoid it, so they stop studying and do something else.
When I was studying math I was spending upwards of 40 hours per week working on homework. Although this is normal for anyone with a full-time job, it's an unfathomable amount of time to be studying math for those who struggle. This is really what it takes though. An unrelenting drive to figure things out.
It really was the savior of me. I can focus for hours when I get into something, but its the friction of starting up that I found other people really helped with. There are formal names for it, like "body doubling", but I didnt know of that, I just knew it was critical to work together with others to get stuff done, which as the above correctly writes, absolutely must be done.
I learned complex math concepts before the university like math i needed for 3d graphics without issues.
If we as a society think its okay to have such an entry barrier, i disagree and therefore really like having an AI tutor.
Understanding things in math is definitely possible, and whoever says otherwise probably sucks as a teacher. Yes, it is possible to just say a lot of random stuff, and the best students succeed to figure it out anyway. But if you take care to actually explain how it works, the proportion of successful students increases dramatically.
Many people who have (unsuccessfully) attempted to apply AI to education have focused too much on the "explanation" part and not enough on scaffolding, navigating, and managing the entire learning process. It’s easy to go on a wild goose chase building an explanation AI.
You fall in love with the idea of AI having conversational dialogue with students, and then you get lost in the weeds of complexity. You solve just enough of the problem to produce a cool demo, yet you're still hopelessly far away from self-service learning in real life.
I don't think conversational dialogue is even necessary.
What we do at mathacademy.com is hard-code explanations and break them up into bite-size pieces that are served at just the right moment. And we close the feedback loop by having students solve problems, which they need to do anyway. (The student's "response" is whether they got the problem correct.)
Sure, hard-coding explanations feels tedious, takes a lot of work, and isn't "sexy" like an AI that generates responses from scratch – but at least it's not a pipe dream. It's a practical solution that lets us move on to other components of the AI that are just as important.
What are those other components? A handful off the top of my head:
* After a minimum effective dose of explanation, the AI needs to switch over to active problem-solving. Students should begin with simple cases and then climb up the ladder of difficulty, covering all cases that they could reasonably be expected to solve on a future assessment.
* Assessments should be frequent and broad in coverage, and students should be assigned personalized remedial reviews based on what they answered incorrectly.
* Students should progress through the curriculum in a personalized mastery-based manner, only being presented with new topics when they have (as individuals, not just as a group) demonstrated mastery of the prerequisite material.
* After a student has learned a topic, they should periodically review it using spaced repetition, a systematic way of reviewing previously-learned material to retain it indefinitely into the future.
* If a student ever struggles, the system should not lower the bar for success on the learning task (e.g., by giving away hints). Rather, it should strengthen a student’s area of weakness so that they can clear the bar fully and independently on their next attempt.
You just need to practice. For hours and hours and hours.
The teacher's job is to help guide you to what you might want to study next. The teacher cannot replace individual practice time.
Reminds me of Ben Orlin's "law of the broken futon": a single missing part can, over time, warp an entire futon and render it unusable.
https://horizonsaftermath.blogspot.com/2016/02/the-law-of-br...
Classroom activities that are enjoyable, collaborative, and non-repetitive (such as group discussions) can sometimes be useful for increasing student motivation and softening the discomfort associated with deliberate practice. However, these activities are only supplements, not substitutes, for deliberate practice. Unlike deliberate practice, they do not directly move the needle on student performance – rather, they "grease the wheels" and reduce psychological friction during the process of deliberate practice.
The need for practice notwithstanding, suspect both practice and narrative/conversational exposition are needed. I’ve worked with students who become very good at applied procedural problem solving through practice but who can only get just so far because they lack foundational constructs to guide them. More time in discussion with an expert could potentially fill in those gaps. An expert who understands the material well enough to adapt it to the learner in front of them.
Those gaps were left by the removal, and lack of coverage towards critical thinking and reasoning which normally preceded these classes.
You don't see these issues in cohorts that have received classical education focused on first-principles.
Coverage of Descartes rules of Method; and a priori deduction are mandatory. The trouble these students are having is primarily because they've been taught by rote(authority and dynamics based in Marxism), instead of by rational first principles. Its infected most publicly funded education.
In all fairness, I don't think more time with an 'expert' would fill those gaps, I've personally observed several contradictions where the supposed expert fails to perform as a result of incentives.
Most teachers at that level aren't actually experts. They have their lesson plans, but the moment a problem comes up outside of that (such as when the salt the earth/burning bridges strategy is used between Algebra->Geometry->Trigonometry courses), they'll just enforce a struggle session making the student suffer so unimaginably that they succumb and believe that they simply are not good at math.
The student as a result of that torture (yes it is that) gets PTSD which few ever recover from.
The structure is by systemic design since math is used to gatekeep all hard science and technology. If you can't understand Math, you won't be able to follow any of the subsequent lessons that use it as the primary tool to impart knowledge (eschewing intuitive or deductive understandings or relationships as was previously done pre-1970s).
Or, as a result of objectives? If the ‘expert’ in this regard knows the material well enough, then the objective and constraints seem relevant. When you are referring to an expert, what is the context? An expert teacher for a class maintains different skill set from an expert tutor.
One on one time with an expert tutor does help tremendously, but realistic goals have to be determined. I made my way through undergrad and grad school as a private tutor for math from elementary school to math majors. The student’s objective, time scale, and current state determine how thorough a tutor can be.
>The trouble these students are having is primarily because they've been taught by rote(authority and dynamics based in Marxism), instead of by rational first principles. It’s infected most publicly funded education.
Yes, but the Marxism aside makes little sense here. Crudely quantifying education outcomes into metrics and making the teachers responsible to said metrics is a primary reason for rote learning (i.e., teaching to the test). The ideas which inspire this type of metricizing come from Taylorism and Fordism, both of which are American schools of thought.
That's flat out untrue. I speak from experience of teaching math all the way from grade school to teaching undergrads and grad students to teaching adults.
I can take a failing student who is completely confused and get them on track in a few hours over a few weeks. 1-on-1 discussions are not just really important, they're astronomically more effective than anything else.
Making math engaging is the number one thing that matters. Being an engaging teacher matters. Adapting to a specific student and their needs matters. Someone can practice something they hate for 10 hours and get nowhere. Someone else can practice something they love for 10 minutes and make amazing progress. You remember things that are engaging, you hardly remember anything about things that are boring.
This is what all of these AI tools get wrong. Even if they understood the problem domain and could explain it --- which they cannot.
I've had this experience with adults switching jobs into programming too. So many avoided STEM because they hated math. After like two hours together they not only got math, they started to enjoy it. Happens all the time.
> You just need to practice. For hours and hours and hours.
This is probably the worst brain damage that Gladwell and others have done with the whole nonsense of 10,000 hours of practice.
No. No amount of poor quality practice where you're hitting your head against the wall will be productive.
You need to learn how to practice math. Practice is worth it after you've gained some mathematical sophistication and some understanding of the problem domain. Most people need peers or a teacher or a tutor to help get them unstuck and point you in the right direction.
> The teacher cannot replace individual practice time.
No amount of practice for 99% of people can replace a tutor. Yes, people with mathematical aptitude don't need one; I didn't. But most people need to have some guidance and then they can practice.
I can't imagine how nice it would have been not to have to hide out of fear that I was having problems figuring out calculus on my own.
Simply being shown it once on a whiteboard or in a book isn’t working for the majority of humans.
Then yes. Practice, practice
You’re already seeing oversupply of educated folks in India and China. Graduate students working as baristas in USA, etc. Sadly inevitable.
In any case it’s good to have the resources I suppose.
I’m also fundamentally skeptical of these stats around math struggling. What percentage of kids who would be very likely to use Khan Academy are struggling with math? And what percentage who are not would even use khan academy to begin with?
Most of the problems with students doing poorly are sadly societal - not to say that this isn’t useful, though.
It teaches you how to think and how to learn which is valuable no matter what.
Most people are still employed if they focus on history or literature. They just might not be making a lot of money or working in history or literature, though some do. Plenty of people in highly "employable" degrees also find themselves unemployed for a long time once they graduate.
The reality is that getting a college degree, regardless of the major, increases your chances of employment afterwards and potential lifelong earnings enormously over only a HS degree.
But as you implied, most of the worst trends in higher-ed, a real corruption of its original intentions and values, have come from a obsession with the idea that higher-ed is solely about employee training.
As to my own experience: I am, according to most standardized tests, very apt at quantitative reasoning, but I never progressed far in math in school. Why? because I was placed on the standard track in math in a public school with a bunch of students who didn't care, and teachers who didn't have time to care, and to be honest, the attitude rubbed off. I once got in trouble because I programmed a python script to do my problem sets when I was 13 because it was faster than doing it by hand for me. In retrospect, that form of "cheating" was a sign that my teachers should have picked up on.
Quite simply, I never had access to a good math instructor throughout my schooling.
Now, decades later, I am intensely interested in a lot of subjects that require a background in math that I don't have, and I am becoming interested in Math for Math's sake. I have been using open access textbooks, and an AI assistant of my own creation to help me learn.
I disagree with this assessment. You don’t need everyone to have a phd. There’s education and there’s Education. With respect to the article, sure it’s great if everyone is good at math, but not everyone needs a math PhD. Additionally there are diminishing returns on the time spent learning more and more math vs. other things.
In any case there have already been tons of math resources available for a while now.
A better example would be chemistry. Should everyone be spending time learning chemistry, why or why not?
Intellectual obesity is a thing - simply knowing more things isn’t inherently useful.
> In any case there have already been tons of math resources available for a while now.
That's great if you have the ability to learn everything from a static resource, and have the time to wait for asynchronous guidance. But what if you just sort of get it, but there is no one that can explain the parts you don't get? I've been to places where the educational standards are low enough that making change from a payment was an impossible task without a calculator. A keen student in that particular village has no one they can easily ask about math when they hit a sticking point.
> Intellectual obesity is a thing - simply knowing more things isn’t inherently useful.
I don't disagree for extreme cases, but creating more resources for people to learn has an incredible payoff, and is almost certainly morally right. Erring on the side of overeducated rarely turns out poorly at the societal, or personal level. Across the world, more highly educated societies tend to be better off across most QOL metrics. I'm well aware that there are anecdotal counterexamples of math PHDs living off of ramen. But there's a damn good reason that brain drain is a concern in many places, and other places favour immigration candidates with higher education.
Also, writing a computer program because you are slow at solving math problems is a sign that you may need more math practice. It's not like you were handing my in your homework with solutions your wrote for harder problems that you wrote.
> Also, writing a computer program because you are slow at solving math problems is a sign that you may need more math practice.
I didn't say I was slow, I just realized Python was faster than doing the same boring problem with different numbers. I seriously doubt there are people that can do high school level math faster than a computer at any level.
In retrospect a 13 year old knowing the problem area and programming well enough to get a computer to do their homework was a sign of mastery and boredom rather than a need for more practice. You can't get a python script to do your algebra homework without a pretty good understanding of the subject. So much so that in later math courses you are required to buy a programmable calculator to avoid wasting your time on the basic and tedious parts of math problems.
On the other hand, I know there are people who enjoy math but struggle to pay attention and learn from a "sit quietly and listen" lecture-based model. (My husband is in this camp.) I can see how the back-and-forth conversational approach of these AI tutors could be really helpful for students like this.
They're still a small minority of the student population, but maybe a different minority from the students who are already excelling academically. If Khanmigo helps only 5% but it's a slightly different 5% from the students who are best served by the current system, I see that as a win, even if it's not the educational revolution that is being hyped.
[0] https://danmeyer.substack.com/p/the-kids-that-edtech-writes-...
A lot. A lot, lot. There are entire states full of people in India who don't have access to good teaching. Who travel absurd distances and stay away from their family for years to get access to good education. In the last few years as kids in my extended family grew up, I am amazed by how much they just learn from YouTube. One of the biggest educational startups started from a free education YT channel.
This is supported by the fact that there are hard limits to computation, in terms of both Computability Theory, and Complexity Theory that are often disregarded by the novice and magical thinker alike despite being largely solved fields by experts in Computer Science, at least in terms of Computability Theory.
Most of this work was completed in the 1950s.
This is not a difficult a subject, but most people online simply are unwilling to do the work to rationally learn this and instead choose to try and hide their own ignorance because they feel inadequate, or perhaps they are engaging in something more malevolent. The reasoning (false justification) doesn't really matter.
It is, however; quite telling when expert's have validated these things, and yet any mention contrary to a narrative provokes downvotes in a public forum to remove it from view. A perfect example of intentional actions done by third-parties trying to misinform others about the risks (by those parties actions removing legitimate and valid information).
For those with the cajones to actually learn this stuff. Here is a link. It seems very jaron laden but it provides a true understanding of how computers actually work which is sorely lacking in the youth of today.
MIT 18.404J Theory of Computation https://www.youtube.com/watch?v=9syvZr-9xwk&list=PLUl4u3cNGP...
The only net benefit AI has towards society is towards destructive ends because there are far more destructive people whose efforts scale more in general when compared to the good people today. These people often do things which cannot be undone (salting the earth and burning the bridge).
Simply not having a sufficient background, or failing to perform basic due dilligence often will place most people in that destructive cohort regardless of their own personal beliefs.
Outcomes matter more than intentions, and the devil is always in the details.
A perfect example of this potential landmine of a field would be anything dealing with the underlying mechanisms involved in human to human communication.
There is an uncanny valley, and distorted reflected appraisal will occur inevitably in any human to AI interface seeking to mimic human communication.
Case studies from torture during the Korean Conflict (1950s) show that distorting reflected appraisal leads to either psychotic or dissociative behavior that progresses as exposure increases, it can permanently break people to the point where they cannot recover. Often, the first thing to go is rational thought.
Multiple experts cover this and confirm the findings (Lifton, Meerloo).
So what do you suppose will happen when AI distorts reflected appraisal (because it can't be tested sufficiently to the contrary) and its then used on the next generation of children? (who are inherently vulnerable to permanent change at that stage of development).
If as a result, they end up either killing themselves or others, or become people incapable of rational thought (which impulse control is correlated with), do you think they'll be alive or survive very long? What indicators would there be that this is happening (none, other than increasing chaotic violence)
Who do you think will be responsible for crippling them if that were to come to pass? Would any kind of justification ever be able to justify that outcome? Could we even recover from intentional crazy-making as a society? (likely not, insanity cannot be cured).
These things are not toys. Outcomes matter.
This is complete bullshit, and computability theory has nothing to say about which (if any) cognitive tasks people can do that AI cannot.
That may be your belief, but it is not, and beliefs mean little in the face of reality.
Saying the same thing in a more formalized way (so there can be no ambiguity), it is inherent in the 1:1 unique input to output relationship that is required for each state transition on a state graph, for the system's property of determinism to be preserved.
No disrespect intended, but you don't seem to have actually taken or learned important parts regarding this subject matter.
> computability theory has nothing to say about which (if any) cognitive tasks people can do that AI cannot.
You are incorrect. The very first video in that linked coursework (from MIT) provides a counterexample to this statement. The professor clearly states this is impossible, and the proofs that come later in the class prove it.
This statement is an over-generalization based in fallacy.
If I hadn't mastered the concepts of computability and deterministic finite automata, I wouldn't've written what I did.
We will have to disagree.
I feel my position still stands correct on solid rational foundation, since you haven't provided any rational basis other than an appeal to authority, and there remain several unanswered contradictions in the supposition you made.
However, I think its reasonable to say that if you think that some fundamental thing keeps computers from doing what people do then you believe that people are somehow magic. This isn't a super unusual perspective among humans, but its certainly not a particularly common scientific one.
This is improper paraphrasing (its ambiguous), the claim was, "computability theory has nothing to say about which (if any) cognitive tasks people can do that AI cannot."
This claim is a statement based in irrational fallacy. Computability Theory discusses the limits of the underlying mathematical operations performed by a computer (DFA). A Counter-example is provided in the very first lecture of that linked playlist that includes a task that humans can verify (in practice), that is not possible for computers. Formal verification is a very tricky subject with regards to computation, and is an open area of research but it provides a tidy contradictory example that the claimed statement must be false (a priori).
There is no sound or valid claim or proof that AI can somehow exceed the limitations of its dependent and underlying architecture (which is based in mathematical properties), once those properties are broken.
Additionally, taking isolated subject matter, overgeneralizing it in isolation, and ignoring the dependent abstraction layers is fallacious and magical thinking. It is a simple cognitive mistake that often occurs when people don't have expert knowledge of the whole system (sans abstraction).
As for my perspective, it is based in a decent amount of mathematics and science. Aside from the mathematical proofs, and properties, on to something you might find a bit more interesting, how familiar are you with wave collapse theory in neuroscience?
There are certainly problems which are hard for computers which are easy for people (and vice versa) but I don't know of any formal version of the claim that people can perform actions which are in principal impossible for human beings. You seem to be alluding to the claims of Penrose that humans can somehow do things machines cannot, but this isn't even what Penrose is claiming in the book. Instead, Penrose claims humans _somehow perceive_ the truth of propositions which cannot be proven in a given formal system, but this is a very vague claim which few scholars take seriously. He also thinks quantum mechanics is involved somehow, but this is also entirely vague. Even if one were to demonstrate that quantum mechanics were somehow involved in cognition there isn't any account that I know of that would describe how, per se, merely having a quantum computer involved would somehow introduce computations that classical computers could not do. I mean for one thing one can always simulate any quantum process on a classical computer. I'm not an expert in complexity theory, but as far as I know there are no known problems for which it is proven that there are no non-deterministic classical algorithms that perform as well as quantum algorithms. So we cannot even demonstrate with certainty that quantum computers are in fact better than classical computers with randomness. We only have situations where quantum algorithms are theoretically better than any known classical algorithm. It is also worth noting that most neuroscientists are dubious about the importance of quantum mechanical effects in cognition.
All that said, some people believe that there is some property of people that allows them to do things that computers cannot do (at the very least generate or have consciousness). But I don't know of any way of supporting that idea that doesn't involve dualism of some kind. That is, that asserts that there is something more than material that somehow constitutes a person. Like I said, a lot of people believe that there is. Most people. But a plurality of scientists do not believe this. I do not believe it. While I wouldn't say I'm a materialist, I would say I am a monist and that belief basically makes the assertion that a machine can do what a person does trivially true.
All that aside, I agree with you that language models cannot reason, almost certainly have no consciousness, and are have the propensity to be bad for people "spiritually" (speaking loosely of course). I'm not sure things are quite as dire as you assert. The moral rot of working in a call center, indeed, the existence of call centers, is surely worse than the imposition of an AI agent between the caller and the worker.
As for formal verification of software, there are often common problems with decidability that go ignored, or design problems within the model being tested where similar looking but ultimately different objects are treated the same in error (apples to oranges). This latter part is often quite common with abstraction and its acting as a conceptual black box.
Unfortunately, this is not just a simple brute force problem. Required properties for the system need to be preserved, and these properties may or may not be explicitly defined in the formal model under test, not to mention that many tools designed for this purpose also have a corresponding combinatorial explosion with regards to complexity in many cases. Termination as a property is one that is quite common, and famous in Computer Science (i.e. the Turing Halting problem).
We can design a model that will guarantee termination, but we cannot easily determine if an arbitrary model will terminate without first running it. The hard part is in the definition and coming up with the proof of correctness, not necessarily the actual verification of correctness part.
The former as far as I'm aware is always done by humans because machines above a trivial complexity will get stuck in loops largely due to the halting problem, or the predictability paradox (which also has roots in halting). They will chug away without realizing they've repeated the same steps ad infinitum. Inductive proofs as a class are one that a lot of machines choke on or run forever.
It seems to me like you may be confounding my meaning of 'non-determinism' in a context from Floyd, instead of from a system's property context (such as found in EE coursework on Signals and Systems).
The former context is a bit more relaxed than the latter (i.e. its similar to the same way as describing the absence of time in-variance [system property]), while the latter requires unique inputs to unique output maps (i.e. preserving that 1:1 function test at each step of a computation) The property basically acts as a virtual rail for the CPU states to follow some computational graph with at most only one edge being followed based on inputs.
Von Neumann Architectures are all inherently deterministic at the signal domain level, the instructions are static and usually in the same place, and its processed in the CPU (also a single fixed place, at a single time). The preserved property guarantees that each unique instruction will will always have a single unique output (given care with the design of the instructions), and will provide that same output regardless of time, absent further compromises as you go up the abstraction layers of the architecture.
Non-determinism can be introduced through coding of interfaces and other methods of abstraction that may break the property (such as flattening, shifting, etc).
Overall non-determinism's usefulness is vanishingly small (mostly being bugs, errors, and undefined behavior), and its introduction breaks any guarantees that further automation (which may be passed output from non-deterministic code) may work at all.
Non-determinism is largely uncharacterizable (outputs don't corresponding to input as potential causes) and as a result lacks the properties for troubleshooting (aside from a guess and check model), and in practice exception handling cannot generally correct these type of errors given the unpredictability.
Troubleshooting of digital systems is largely just an application of the structured properties. Absent those properties, you cannot isolate the problem without full knowledge of the system including its design spec for inputs and outputs (which often isn't available, or economic).
Unfortunately, the role of determinism or its absence as a system's properties doesn't allow any direct comparison without knowledge of the architecture. While we can make some assumptions, we wouldn't have any sound basis because the devil really is in the details with regards to how superposition can be leveraged, and the instruction set.
Sorry if this seemed a bit run-on. I find it is important to be clear without ambiguity with the meaning of the words which is why I'm clarifying (also given that I may not be able to respond timely if YN keeps blocking me). Hopefully this was sufficiently clear in identifying any discrepancies of underlying meaning.
> I'm not sure things are quite as dire as you assert.
The direness of the assertion comes from long experience and intimate understanding of feedback systems, and a realization of the dependencies for acting on problems.
Generally speaking, Feedback systems are normally considered broken when they no longer appropriately react to signals they should normally react to.
Perception in people is just one such feedback system, and there are structures of stimuli that can bypass it in most people. Cialdini has documented a number of these in his book Influence. Other areas such as Reflected Appraisal and its distortion, along with destructive interference have also been investigated related to our biological stages of development for self concept the main way we transfer culture to our offspring (Ericksonian Identity), as well as some subtle applications of Sapir-Whorf in the 1950s on PoWs (which follow Cialdini's Consistency Principle).
The general rule of thumb for feedback systems are when they continue running, once broken the longer they take to catastrophic breakdown the higher the overall cost.
In an ecological overshoot environment, where failure of society to organize (such as happens in a breakdown) or even react leads to a failure to feed ourselves, it requires a critical view based solely on the existential risk.
Now if your perception is changed without you recognizing or alerting to it, such that you no longer recognize certain problems and discount them from your awareness, you become blind, and without knowing/being able to react you cannot act to correct it. Critically thinking people may be able to cope better than others, but no one I know is hyper-rational all the time.
Perception underlies most of what we do, so when these structures and the following consequences happen, you ultimately get stuck in a feedback loop as an unthinking automata without realizing it. You may perform regular fixed action patterns but its still the same output oblivious to the danger signals you may be receiving.
Associative priming of unrelated things is one such method discovered in the past 70 years, similar to attenuating signals (jamming), or front of line blocking (more common in bureacracy); those are the two most common ways these systems fail.
Would you not consider a subtle, indirect, and blinding madness that is uncharacterizable but spreading and overtaking people, and chaotically increasing across a population a greater imposition than an AI agent crudely disrupting people's ability to communicate (which the underlying mechanic this agent performs has been shown to break people; with a cohort trending towards this type of psychotic behavior or alternatively dissassociating completely as automata)?
Its been well documented that the first thing to go in torture is often rational thought, which would be our sole defense.
Authors Meerloo and Lifton both cover case studies of these type of mental torture structures which have been used both by Nazi's and Mao, as well as so haphazardly and carelessly today by businesses towards manipulating sentiment and marketing, none more commonly than social media and adtech.
Meerloo covers WW2 Nazi Thought Reform through Mao (where they broke perception). Lifton documents in detail the case studies from victim POWs in the Korean Conflict (Mao). These structures are even commonly found in schools.
Personally, I think a blinding illness that spreads subtly through communication, that you can't react to without first being inoculated against is a pretty dire threat.
Predictability Paradox and links to Halting (overview) https://link.springer.com/content/pdf/10.1007/s10670-020-003...
One other note:
> Overall non-determinism's usefulness is vanishingly small .
This is really not true. There are many problems which have no useful deterministic solution but for which non-deterministic solutions exist which can get very close to an optimal answer, and non-determinism is extremely important. In fact, in complexity theory Turing machines with and without a random oracle are distinguished precisely because the former is so useful and, in many respects, the big question in the complexity theory of quantum computers comes down to: is the randomness of a quantum computer more powerful than mere classical randomness?
People perform certain kinds of proof tasks in practice better than computers, in my opinion, only because we have a large volume of heuristic strategies for proving things which are embedded in the culture of mathematics and which are difficult but in principal not impossible to embed in a machine. In a sense, humans prove things by _guessing correctly_ which turns out to be how we get computers to do these kinds of non-trivial search tasks as well.
Anyway, on the cultural end of things I agree with the basic idea that some applications of language models and other AI are probably bad for society, but I think you're just overstating the case that this particular technology is so catastrophic. In fact, this technology merely takes effort out of a person and puts it into a machine: in a call center situation if a person gets angry at the call center employee, that is itself an error on the part of the caller, since the person at the center isn't personally responsible for anything and is, in fact, placed there almost entirely to sop up the emotional energy of the customer. The call center employee in turn has to do the internal work of "throwing away" the emotions of the customer so as to continue to respond in the robotic way that their bosses require them to perform. Merely being in a call center is intensely dehumanizing and, presently, places the burden of that dehumanization on the employee: they must dehumanize _themselves_ or face the economic consequences. This technology displaces some of that labor. Does it make the entire "call center" locus more dehumanizing? Hard to say, in total, but if so, its marginal. The employee in this situation is by far the one with the shortest end of the stick and I have trouble getting really bent out of shape about a technology which might make their lives slightly more pleasant.
If the product in question here were a secret AI agent that intermediated between a partners in a romantic relationship or between parent and child (especially) then I would get your point, but the call center is such a moral morass that this piece of technology hardly matters.
Speaking more broadly: you have a grand narrative, clearly, in your mind, but I think its preventing you from looking closely at the things that are really happening and responding rationally to them. In particular, in the cases to which you refer, where various sorts of strategies to disrupt cognition were so damaging, one thing stands out in particular: the overwhelming, credible, threat of actual violence to the subject from a difficult or impossible to escape force. Without that critical ingredient I would expect most of the effects you describe to be missing or highly attenuated.
> We’ve upgraded parts of Khanmigo to a more capable large language model, which is the software that generates human language. The more capable large language model is called GPT-4 Turbo. Our internal testing shows an improvement in math after we made the switch.
> We are beginning to test the capabilities of a new large language model called GPT-4o, and we’re evaluating other models too to see if they are stronger at math.
> We’ve improved the way AI “thinks” during a tutoring session before responding to a student. We have instructed the AI to write out all the ways in which the student may have arrived at their answer. This approach mimics how a tutor in real life works with a student. We’ve found it significantly improves the quality of math interactions.
> We’ve built new tools to track our progress on math.
> We’re sharing math examples and learnings with others in our field so that we can learn from each other.
> We’re studying the latest research papers on math performance.
Sounds like most of what they're doing is related to prompting, chain-of-thought reasoning and similar, on top of a 'vanilla' foundation model. Sounds like something an ambitious student could replicate / improve upon, so given their mission, it'd be cool if they published the exact techniques they're using and their benchmark results.
This was not their objective though.
Facebook managed to shoehorn itself into the public and private school system of a nation with over a billion people.
That is tangible (for facebook) and way cooler than a million.
Renting a 24GB VRAM Runpod is ~0.5$ per hour. How can the math work out unless you have to have a non-profit energy company and a server farm attached?
[1] https://osboncapital.com/khanmigo-ai-public-vs-private/ [2] https://www.runpod.io/gpu-instance/pricing
I heavily use ChatGPT via a desktop client and my own key, and I am at $3.90 for the month after making a mistake where I accidentally was sending a 30k token prompt repeatedly, that cost me about $2. Using an optimized approach, it is VERY hard to incur a $4/month bill.
I imagine that Khan academy has a much better bulk-pricing agreement with openAI, and that they can probably have a caching layer that can look for previously asked questions.
If it actually works, this is the ideal outcome.
I tried Khanmigo. It is counterproductive junk.
It simply doesn't understand what a student knows and it has to idea how to give examples or provide perspective shifts that help students. That's what a good tutor does. It gets stuck explaining the same things in the same ways but with different words over and over again.
It has no idea how to think geometrically vs algebraically and how to switch between the two. And it can't carry out even simple proofs.
Are people consulting only one book/source on any given subject? I remember learning Python and C, and it was such a mixture of books/articles/forums/wiki, I can't even remember the process. I do remember understanding pointers easily because of a chapter of another book about memory models in OS. Learning is an iterative process and the expert is just there to shorten the way, not to carry you through it.
I've found Wikipedia to be an excellent resource for math/physics once you're ~halfway through a math degree to have a good baseline level of knowledge to understand it.
The trouble with math is one of the important goals is to teach people not to produce nonsense and to be able to tell the difference between and argument that sounds good vs. an argument that's sound and good. A nonsense generator (presented as authoritative) is perhaps not the best way to do that. Obviously its abilities could change in the span of a couple years, so it's probably still worthwhile to explore how we would use it if it were useful.
this to me is an insane way to think. I do not consider something better because I can ask it a question, something is better because it is more correct.
The good version was heavily guided by a single human.
1. Improve sample efficiency of generated plans to get to the right goal while meeting all the subgoals for a plan.
2. Enrich engineered and correct neuro-symbolic models of reasoning with better knowledge representations.
3. Quantitative psychometric systems that use metrics like proficiency could only be as good as the underlying “factor” model and hypothesis, but one could test multiple more interesting hypothesis more quickly: "Are you mentally tiered?", "Here is a hint: ___. Does that help?".
The median price of an existing single-family home in the Califoria Bay Area in February 2024 was $1.25 million. The range of teacher salaries in the Bay Area is $50K - $100K. A reasonable downpayment on that home would be ~$250,000, followed by yearly payments in the range $64K (30-year) to 80K (15-year). Following the 'housing should consume 30% of income' - allowing teachers to have children and buy a car and go on vacations and so on - this would require salaries of $200K - $250K per year under current market conditions. Thus, anyone wanting their own home and a family will probably not be considering a career in teaching - you'd end up as a lifelong two-room apartment renter.
AI tutoring is a great idea - but a tutor isn't a teacher. The job of the teacher is to excite and motivate the students, provide overall guidance and appropriately difficult problem sets for the students to work on. The one-one-one tutor is there to help with the problem sets, especially when students get stuck.
Unfortunately, here in the USA we have a system that values the CEO of McDonalds - which delivers very unhealthy food to the population - at $19 million per year - and teachers are valued at the same rate as garbage truck operators (at least in the Bay Area).
The result is that most students entering higher education need one-two years of remedial math education before being able to grasp the higher math, e.g. vector calculus, linear algebra, complex analysis etc., which is needed for modern engineering and scientific disciplines. This results in competitive disadvantage relative to China and other countries that invest heavily in childhood education.
Following that trend line, it seems quite possible to me that in five years AI will be the teacher. (Of course it may replace CEOs also.)
Followed by:
> As we come to the end of our first full pilot school year,
Did they not monitor students' performance? Do they not have concrete numbers like the ones quoted in the first paragraph? What better way to demonstrate effectiveness than to evaluate students and see how much improvement they made?
Are there RCT results (or any results) showing the impact on students?
https://blog.khanacademy.org/multiple-studies-show-khan-acad...
It would be interesting to compare it against how Khan Academy helps students right now.
The same researchers of the Khanmigo trial published the results of a different trial in May 2024: https://blog.khanacademy.org/university-of-toronto-randomize...
Its AI turtles all the way down...
Think how much you learned playing sim city (assuming it was realistic). Imagine effortlessly learning any skill by having fun.
If AI is good enough to teach people to drive, then it should be good enough to drive the car itself. At that point, it would be pointless to teach the masses to drive when the AI can do it for them. If AI is good enough to cook, ... So on and so forth.
The intention is noble but where does it all lead?
Are you arguing that people should not be able to take the initiative to move themselves from one place to another of their own volition? (driving)
Being able to read, write, do math and think and do things for myself is very improtant to me - it's even more imprtant to me that I live in a vibrant society full of people who can do likewise. I don't want to live on the Axiom in Wall-e.
If the OpenAI data use policy applies to Khan Academy students, they implicitly require every student user of this to not use the output to compete with OpenAI (taken literally, you can’t use what your tutor says to you for anything, since it’s always going to compete with OpenAI)
Imagine how dumb it is to say “our thing can do everything. You can use it, but you can’t use it to do anything that competes with us.”
Let that sink in. Can you name one thing you can do using the output of a thing that does everything which doesn’t compete with the everything thing?
What a shame to flush Khan academy just to hop aboard the hype train. I know I’ll probably get downvoted for being negative but to write so much without clarifying what the “Open” AI legal terms mean for students is actively harmful to student trust.
If anyone needs a reason to pity OpenAI, just remember how they betray their true name. That is a profound failure and I would not wish it on anyone.
I kinda love how it doesn't lose patience with my stupidity
What I would have had to give up to get that luggage, if that was even possible, or where I was supposed to store it in my tiny apartment, were not concerns that computed for them.
The limitation is price. Many listings for reputable math tutors are greater than $60 USD per hour. If you go by the CAP's minimum for "high-dosage tutoring" of a 30-minute session three times a week, that sums to at least $360 USD per month. Many parents do pay for this for children, but it's an unaffordable expense for many people. There is an initiative to provide free tutoring (via the "Schoolhouse" project founded by Khan Academy's Sal Khan to have volunteer tutors, who are often university students), but it's not yet clear to me whether the quality of volunteer tutors will be sufficient to make a difference in the success of students.
I've also read elsewhere that one of the most important factors in tutoring effectiveness is the frequency of consistently meeting with the tutor. An AI tutor would help with frequency via lowering the price—though then again, there may be more feelings of accountability with meeting a human person at a scheduled time, versus using a software tool consistently.
[1] https://www.americanprogress.org/article/fact-sheet-scaling-...
The origin of Khan academy was Sal Khan filming lessons for his younger cousins, it was easier to host the videos on YT than anywhere else. When he realized that other people were watching his videos and learning from them he took a leap of faith, and quit his job to start a non-profit with the goal of providing free educational materials to anyone.
If you find a way to hire and fund thousands or millions of tutors worldwide to provide no charge education, get in touch with Sal Khan, since that's what he has been trying to do for the past 2 decades.
To add on to this, this is actually an existing project founded by Sal Khan in 2021 called "Schoolhouse" at https://schoolhouse.world/about. There was a recruitment drive to try and encourage undergraduate students at my university to volunteer as tutors, in exchange for a letter of reference and tutoring experience. I suppose that the program was effective at recruiting volunteers at my university, as it had official support from my university's administration—students received recruitment emails from a faculty member, rather than from an external email address.
But I'm unsure about the quality and effectiveness of the program with tutors as volunteers, as I wasn't involved in the program myself. I also predict that it's hard to retain talent, as professional tutors can earn a very high hourly rate—I've seen many independent tutors charge more than $60 per hour.
It’s fortunate that it is cheaper than paying people.
May it never end!
The "why" is obvious, it's cheaper than paying people, and the article didn't have anything interesting to say.
[0] https://projects.propublica.org/nonprofits/organizations/261...
Those expenses could be anything and anyone.
They could be increasing rev to further increase expenses like salaries and exec pay. Not "shareholders" in a typical corporate business way, but still driving profits for a handful of key stakeholders.
Not a bad thing, just don't think non-profit = altruistic orphan saving factory.
Regardless, the idea that Sal Khan specifically isn't fundamentally serious about education and sees this as his personal golden goose is a special kind of cynicism.
https://www.irs.gov/charities-non-profits/charitable-organiz...
None of that means that employees of 501(c)(3) organizations can't earn competitive compensation. But I think they'd be on pretty slippery ground if any part of compensation was tied directly to revenue increases.