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In view of recent developments of AI-based adaptive math learning systems like Squirrel, Aleks, Knewton Alta, or Math Academy:

Does a human math teacher play any reasonable role, or will those systems make human math teachers completely unnecessary?

It seems to be clear that human pedagogic, psychological, and technical support may needed. But what is or will be the role of someone who knows math and knows how to teach it?

Edit in response of the comment of Adam Rubinson: I might differentiate two versions of my question:

  • Based on how good those systems actually work today.
  • Based on what is advertised, of how good they work.

For example Math Academy advertises:

"Our adaptive, fully-automated platform is 4x more efficient than a traditional math class"

I don't know any good, independent peer reviewed papers, that evaluate in depth of how well those systems work.

Some work that indicates that it might be quite effective:

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    $\begingroup$ Actually being capable of giving answers that are in any way correct. $\endgroup$
    – Guest
    Oct 30, 2023 at 1:55
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    $\begingroup$ I have downvoted and voted to close due to lack of context and lack of clarity. AI learning is obviously a very recent development in the history of mankind. AI is not very well-developed, so one should not expect an AI program to teach as well as teachers do. You should include in the body of the question evidence that AI learning systems can be as effective or more effective at teaching maths than traditional teaching methods. Basically, your question lacks context or evidence for why maths teachers will become obsolete any time soon, which is more-or-less what your question is about. $\endgroup$ Oct 30, 2023 at 11:22
  • $\begingroup$ @Guest: As far as I understand, the material used in the AI systems I mentioned in my question is human made (i.e. the explanations, exercises, problems and solutions are (or may be) made by humans). So humans can assure that answers are right (maybe additional to machine checks). The AI comes in of how to choose the appropriate material for the individual student from a large pool. So it's not something chatgpt, which gets lots of math wrong (at least in 2023). $\endgroup$
    – Julia
    Nov 4, 2023 at 10:46
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    $\begingroup$ One of the critical challenges of AI is that it has no universal tether to the human experience. This means that it can't not be pathological eventually. It is going to run into places that a physical intution, and the human contraints would never lead to, where the real world does not meaningfully apply and where the rules of the place do not apply to the real world. The game of "go" has perfect information, so superhuman is easy. Applied to real life, requires some information that might never be available for AI, so it can't learn or perform like it would in perfect information cases. $\endgroup$ Nov 12, 2023 at 22:18

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I'm the Director of Analytics & Algorithms for Math Academy; of particular relevance to this question, I also spent about a decade teaching/tutoring math human-to-human, as well as several years working hands-on with students who were using the Math Academy system.

I don't think math teachers will be made completely unnecessary. At least, not for all students.

It's true that as we've refined our content and algorithms over the years to better scaffold the instruction, personalize the learning experience, and adapt to the needs of individual students, we've enabled more and more students to achieve comprehensive mastery without the need for a human math teacher in any capacity. (For instance, many students get a 5 on the AP Calculus BC exam working solely on our system, no human teacher needed.)

This works for surprisingly many students. But the thing is -- despite our best efforts, there are also many students who will go off the rails without a human teacher or tutor to keep them on track. For example:

  • Some students have major attention issues and need a human to reel them back in when they get distracted every minute.

  • Some students have severe math anxiety and will totally freeze up if they don't have a human next to them providing encouragement.

  • Some students find basic math extremely hard and need a human to help them work with physical manipulatives (e.g. counting blocks) and/or explain a concept a hundred different ways until something sticks.

There are also students who are "on the edge" in the sense that most of the time, they are fine learning without a human teacher, but every once in a while, they need some human support. Some teachers whose students are like this use Math Academy as the primary resource in their classroom and walk around checking in and helping students as needed.

Additionally, there are other students who are capable of learning without a human teacher but who enjoy the environment of a classroom with a human teacher where they can have ad-hoc enrichment discussions about various aspects of math that interest them.

All this to say, when it comes to teaching math, I think humans and machines can enjoy a symbiotic existence. There is so much demand for math learning that goes unserved -- so much that even if machines are capable of serving a lot (or even most) of it, there will still be more than enough demand to require a supply of human teachers.

Human-vs-machine reliance in education is on a spectrum, and while the distribution will likely drift towards less human involvement over time, I think the following things will always be true:

  • Some students will learn entirely from machines.

  • Some students will learn their core curriculum entirely from machines but will enjoy ad-hoc enrichment discussions with humans.

  • Some students will learn primarily from machines but will need human support every once in a while.

  • Some students will need humans throughout most or all of their learning.

And if you replace the word "machines" with "books" in the above, they have always been true. The distribution has always existed; new technology (books ⟶ computers ⟶ adaptive learning software) just shifts it upwards.

(I'm happy to answer any follow-up questions anyone might have.)


Response to Follow-Up Question 1

Doesn't help from humans during ai learning confuse the ai feedback loop?

Sure, if a human is sitting down with a student and carrying them / correcting them on every problem so that they get everything right, then without any explicit mechanism for detecting this, the AI is going to pass them through and treat them as stronger than they really are. The same will happen if the student is relying on online calculators as a crutch (e.g. WolframAlpha, SymboLab).

However, in practice, students' overreliance on outside resources isn't as huge an issue as it may seem in theory. There are a handful of forces working in our favor:

  1. It's rare that a student would be getting that much help from another human. Teachers usually have too many kids in their class to spend an inordinate amount of time with any particular student, and it would be unusual for a parent to work with their kid on the system all the time (or hire an expensive tutor to do so) because one of the big value propositions of the system is that it frees up the parent's bandwidth while remaining way less expensive than tutoring.

  2. We measure knowledge repeatedly into the future. Our system does not take a "one-and-done" approach to learning. Even if a student gets carried (by another human) through a lesson, they'll still receive spaced reviews and quizzes on the topic in the future, and if they do poorly on those, they'll move backwards in the spaced repetition process, potentially back to the very beginning when they initially got carried through the lesson.

  3. We are often able to structure questions in a way that prevents or makes it much harder to cheat using online calculators. Here's the first example that comes to mind: instead of asking a student to select the graph of the transformed function $2\sin(-3x)+4,$ we might give them the graph, tell them the graphed function takes the form $a \sin (bx) + c,$ and ask them to compute $a + b + c.$

  4. Because math is so hierarchical, knowledge debts quickly come due. Most mathematical topics feed into more advanced topics. If a student manages to get through topic X by relying on an online calculator, then they're not going to be able to get through the more advanced topics that depend on X unless they find an online calculator for those too. They quickly run into topics where there is no online calculator and they're unable to do the topic by hand because they never learned how to do the prerequisites by hand. So the only way forward is to go back to the prerequisites and actually learn those properly.

Interestingly, item 4 above is such a barrier to continued overreliance on outside resources that the overreliance tends to manifest primarily as a customer support issue:

  • student uses an online calculator for topic X,
  • student runs into "post"-requisite topic Y that they're unable to do by hand but there is no online calculator,
  • student tells their parent/teacher that topic Y is too hard for them,
  • parent/teacher sends a support message,
  • we look into it and pick up on clues indicating that the student used an online calculator for prerequisite topic X,
  • we explain this to the parent/teacher and help them get their student back on track.

What a headache!

To avoid these kinds of support issues, we have recently started working on explicit mechanisms for detecting overreliance on outside resources. (This will also increase learning integrity, which is always a plus, though it wasn't too much of a problem for us in the first place.)


Response to Follow-Up Question 2

Teaching is much more than delivering knowledge to a student's brain. A teacher is a secondary parent. Children imitate their role models and become like them. 90% of being a math teacher is just being (at whatever level) an adult who likes math. I don't think AI will ever be able to act in the capacity of a passer-on of passion. We can't enculturate children without human adults. Optimizing instruction strategies and holding students accountable is the easy, mindless part of teaching. And these things are rarely neglected. Instruction strategies and accountability don't need to be optimized. They just need to be good. Trying to fine tune them is being penny wise and pound foolish.

I do agree that there is a dimension of "passion" along which teachers can be very positive or negative, while AI (at least in the current conception) is more neutral.

However, if a math teacher spends "90% of their time/effort just being an adult who likes math" at the exclusion of optimizing instruction strategies and holding students accountable for learning, then the outcome is still a disaster.

I've seen this on multiple occasions -- a well-intentioned teacher focuses all their energy on class discussions about mathematical beauty and cool applications, thinks that because they're so good at that they don't have to optimize instruction strategies and hold students accountable, and graduates students who can't solve even the most basic kinds of problems that they were supposed to have learned in the class.

And that leads to situations like the one that came up a few weeks ago: What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?

In my experience, when you weight instruction/accountability versus passion, you get the following outcomes:

  • best outcome: HIGH instruction/accountability, HIGH passion

  • good outcome: HIGH instruction/accountability, NEUTRAL passion

  • bad outcome: HIGH instruction/accountability, NEGATIVE passion

  • bad outcome: LOW instruction/accountability, HIGH passion

  • very bad outcome: LOW instruction/accountability, NEUTRAL passion

  • worst outcome: LOW instruction/accountability, NEGATIVE passion

So I would argue that, even though there is value to be had from a passionate human teacher, even students who learn solely from an AI machine can still enjoy good educational outcomes (which is better than most students receive from most human teachers).

And that's even an understatement. In our experience, optimizing instruction/accountability has allowed us to accelerate student learning by 4x -- meaning that on our system, serious students learn 4x the amount of material in the same time (or the same amount of material in a quarter of the time) as compared to traditional classrooms. And that's being conservative, since our courses tend to be even more comprehensive than what you'd find in a traditional classroom (our courses aim to cover the superset of all content that one could reasonably expect to find in any major textbook or standard class syllabus).

Of course, it's hard for a human teacher to achieve this level of effectiveness by optimizing instruction/accountability. Using long-known learning strategies (like mastery learning, spaced repetition, the testing effect, varied practice, interleaving, layering, cognitive noninterference, cognitive load minimization) to their fullest extent requires an infeasible amount of effort for any human teacher. But just because a human can't do that, doesn't mean that there's little to gain from it.

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    $\begingroup$ Nothing to do with math; it's about being a teacher, +1. $\endgroup$
    – Mazura
    Oct 27, 2023 at 6:02
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    $\begingroup$ I'm very curious to see what the site can do for me once tensors, differential forms, and topology have been added. $\endgroup$ Oct 28, 2023 at 5:28
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    $\begingroup$ Teaching is much more than delivering knowledge to a student's brain. Children imitate their role models and become like them. 90% of being a math teacher is just being (at whatever level) an adult who likes math. They pick up a viewpoint of math (or history or music) from the teacher that an AI doesn't have. My students learn from me how to react to an error, how to have confidence in their work, and which bits of math are fun and which are boring. We can't enculturate children without human adults. $\endgroup$
    – B. Goddard
    Oct 28, 2023 at 17:05
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    $\begingroup$ ^ "90% of being a math teacher is just being (at whatever level) an adult who likes math." Well, this viewpoint certainly explains a lot about why the state of math education is the way it is! ;) $\endgroup$ Oct 28, 2023 at 18:14
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    $\begingroup$ @JustinSkycak Yes. More than half the people teaching math below 8th grade hate math. They pass on their hatred. Just as good teachers pass on their love of math. I don't think AI will ever be able to act in the capacity of a passer-on of passion. Whether that passion is love OR hate. $\endgroup$
    – B. Goddard
    Oct 28, 2023 at 21:50
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Many (most?) mathematics learners benefit immensely from social, mathematical discussions, and often multi-modal ones where people speak, write, point at things, explain what is happening by using their hands and bodies, and so on.

There is still some way to go before an AI manages to be a partner in such a discussion, and even longer way before they manage to moderate such a mathematical discussion, which requires skills also in mathematics didactics. The psychology and the mathematics are not orthogonal.

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    $\begingroup$ There's a chance (but not a certainty) that AI's not going to be able to do that unless it can persuade a learner that it's a 3D thinking feeling person actually right in front of them in person. And that phenomenon will increase not decrease after a bump in users being able to suspend their disbelief in AI making them feel they are doing this in non-face-to-face online learning. $\endgroup$ Oct 27, 2023 at 22:30
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I joined this community just so that I could answer this question.

I work in AI and I am big proponent for it. However I do not believe that it is ready to replace math teachers, nor do I think it is a good idea in the first place.

Learning mathematics is not about finding the right answers. It is about a journey of discovery! Some of my best math teachers, inspired me with their knowledge, ideas and creativity. They motivated me to explore and find new and exciting ideas. They challenged my beliefs and showed me new viewpoints. They supported me and encouraged me. There was a lot of human emotion and human touch involved. Frankly I don't think that machines are yet capable of any of this.

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I'll address a narrow aspect: Access to quality, minimum-standard instruction in math. Two hundred years ago, access to quality math instruction was limited, at least in the US. General public education was still decades off. By 1918, all US states had passed a compulsory education law, and most had done so by the 1870s or 1880s. The ages for which attendance was required ranged from 7 or 8 to 14–16 years old, and attendance rates ranged from 80-99%, tailing off considerably after age 13. One significant factor was the need for children to work, a need that has greatly diminished from then until now, it seems. Another is the affordability, not so much to individual persons, which was a factor 200 years ago, but to communities, some of which struggled to have good school facilities and teachers. This factor has evolved but persists today. If we look outside the US, it is not hard to find many places in which facilities and teachers are poor or absent.

The potential accessibility of the internet would address, or ameliorate, poor facilities by giving cheap access to texts, if nothing else. The potential of AI teachers would ameliorate the lack of good teachers, which is the relevant factor in this Q&A. (That is, I wish to set aside other important factor underlying the internet hypothesis, even though lack of access to electricity and computing prevents access to AIs.) Even if AI teachers are merely mediocre, they probably represent an improvement that could not be accomplished in any other way, simply because we will never train so many teachers as needed and place them in the locations where they are required.

In other words, instead comparing AI to the best (or good) teachers, compare them to the other end, where teachers are lacking or poorly trained in mathematics. My child's Algebra I teacher started a lesson on inequalities by asking the bunch of 14-year-olds in the class, "Does anyone in here know how to teach this?" I give them credit for "doing no harm" instead barging ahead mis-teaching them. One friend's child was told by their teacher that the placement of parentheses don't matter in algebra. The teacher of another friend's child was so concerned with maintaining control by suppressing the curiosity of the child, that the child got angry and refused to learn (in Algebra I in eighth grade). No doubt an AI can be trained better than this, but then so can a teacher. My doubt is whether everyone will pay the expense for well-trained AIs, or will they opt for a cheaper one in the face of imperfect knowledge about whatever AIs happen to be available.

I also think an important consideration, not central to the above remarks but relevant to the OP's question, is that most (or all) learning is accomplished by the individual person. I was more-or-less told this by one of my high school English teachers. It's more or less obvious, on a literal level, when considering the biology of the brain. A teacher has a role in the individual's learning, and it's good to think about what that role is. I spent a few years, ages 12–14, learning math from books without the aid of a teacher. I have a student currently who did something similar and is very good and interested in mathematics. Maybe we're rare exceptions. Still it is possible to learn by reading, calculating, and thinking. I wonder if books that always say the same thing, no matter what question you ask them, are so much better than an AI that can interact with you. It doesn't seem likely that a better AI is impossible.

People once asked me, "Won't the internet make teachers unnecessary?" I'd say, "They've been unnecessary for a long time. You can always go the library and find out what you want to learn. But people prefer teachers for some reason." I guess they always will. But if you don't have access to them, then libraries, the internet, and AIs may be the best alternatives.

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  • $\begingroup$ (+1) I especially like your last paragraph, although in my opinion "I guess they always will" is futurical (made-up companion word for "ahistorical"), since if we don't destroy ourselves or enter into a serious dark age, probably within 200 to 300 years the dichotomy of "organic human" and "AI" will no longer exist, and probably not much afterwards (another couple of hundred years?), maybe even the notion of individuality (e.g. analogy with development of multicellular life). $\endgroup$ Oct 30, 2023 at 20:07
  • $\begingroup$ @DaveLRenfro Thanks. Re a dark age: In 2006, when my daughter was learning to count past 20, she asked me about the date on a test I was grading, and I told her. "Does that mean next year will be two thousand and seven?" "Yes," I said. "And the year after that will be two thousand and eight?" "Yep, and it keeps on going." Then she said, "I guess it depends on how many years there are." $\endgroup$
    – user1815
    Oct 30, 2023 at 22:09
  • $\begingroup$ Then she said, "I guess it depends on how many years there are." --- She might be a budding finiteist, or perhaps even an ultrafiniteist! FYI, in the mid 1980s I happened to come across Dantzig's 1955 paper Is ${10^{{{10}^{10}}}}$ a finite number?, making a photocopy of it. Then later, in my 2nd job interview "after" my Ph.D. (in March or April 1993, before I had technically finished) (continued) $\endgroup$ Oct 31, 2023 at 7:32
  • $\begingroup$ at this university (probably "college" when I interviewed), during an interview with several of their faculty members (not all in math) a philosophy faculty member mentioned something about a paper dealing with the nature of "existence" for large finite numbers (possibly this was because the conversation had drifted to set theory and cardinal numbers), and I mentioned Dantzig's paper (author and title, although perhaps not the year), (continued) $\endgroup$ Oct 31, 2023 at 7:33
  • $\begingroup$ to which he said something along the lines of "Yes, that's the paper". They were a bit surprised at my coming up with this reference (not a math paper, and while still not all that well known now, it was much less known in those pre-Wikipedia and limited math discussion web page days), but nonetheless I didn't get offered the position. Searching now in sci.math, going back to 1981 or so, it appears Dantzig's paper is only mentioned twice, both times by me (of these 4 sci.math posts, see the 2002 and 2006 posts). $\endgroup$ Oct 31, 2023 at 7:33
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Interesting question. But, is it at all a new question ? If you look at the way that online education is delivered then isn't it already the case that "instructors" are just there for "pedagogic, psychological, and technical support". If your school has online classes where you're just using textbook resources to funnel the kids through homework, then they take online tests and you never even have so much as a required online synchronous meeting with the class... are you teaching ?

At least I feel like I'm not teaching when I "teach" online. At least not yet.

So, have online classes supplanted the need for residential classes ? Sure, for what, maybe 20% of all US higher education credits ? ( I made that up, I'd be curious the real number if it's available). Do these credits earn degrees ? Sure. Do these credits represent actual learning on the part of the students who are enrolled in such classes ? Sometimes. Do these credits represent educational success in view of metrics created and referenced by the progenitors of such products ? Oh, most certainly. We can always prove a new educational product by checking appropriate boxes. Accreditation is the ultimate example of this scam.

So, to turn the question over, can AI do a better job at scamming education then humans ? Probably. Given time we'll be able to pretend we're getting an education more efficiently and convincingly with AI tools than with human tools. But it seems to me now that I think about it for a bit, the real endangered part is the more counterfeit realms of education. Those programs which are not authentically thinking for themselves and requiring their students to do the same.

When will an AI earn the first online degree ? Someone should offer a prize and see how many months it takes.

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