[Hermitian909]

> fractions are taught not until FOURTH GRADE. That is almost 3 years too late.

Former math educator: This is not the problem at all. Finland has great Math Education and they wait till 5th grade. If you ever try teaching a large number of 1st graders (or 3rd graders) fractions it becomes clear most of them are not developmentally ready and they'd be better served firming up foundations that would let them more quickly learn fractions when they're ready.

More pertinent problems are that much of our k-6 teaching staff are themselves math illiterate, our culture of disliking mathematics is enforced by a teaching style that makes math incredibly stressful for kids and disengage from the subject, we don't allow any tracking of where students actually are which causes slow students to fall behind more and fast students to be bored out of their mind, and that we make no use of "developmental priming" to speed up later learning later (e.g. you can learn many of the concepts of calculus long before your brain is capable of the necessary algebraic operations, if you know them, you can learn calculus faster)

[euroderf]

There's a lot of talk about how A.I. can be used as individual language tutors on a large scale.

Is there any reason why this could not work for mathematics too ?

[davnn]

I would be highly surprised if LLMs would NOT be used as individual math tutors. In fact ChatGPT would likely already be very helpful.

[pro-kythera]

The PLATO system for so-called "programmed instruction" was available in the 1970s, IIRC. Meanwhile, math pedagogy, AFAIK, tends to more rigorous reference to "scope and sequence". These seem compatible even without AI, and if only to better identify gaps.

[klooney]

It's a good idea, it's probably not compatible with the public school system as-is.

[nyrikki]

Turing and Gödel proving that whenever a mathematical system is rich enough to describe the arithmetic we learn at school, it cannot prove its own consistency is a bit of a barrier.

ML is sophisticated pattern matching and finding.

As we know that even defining simple rules of arithmetic is impossible, how will pattern finding do so.

Sure some company could pay slave wages to make LLMs better at it, but correctness is important in math and LLMs have no concept of truthfulness.

[Dylan16807]

> As we know that even defining simple rules of arithmetic is impossible

That's not what it means. You can evaluate systems, you just have to do it from outside.

> how will pattern finding do so.

What are you talking about? We're not asking the computer to invent its own number system.

[nyrikki]

Feed forward Neural Networks, like LLMs using attention are effectively Directed acyclic graphs, so it has little it can do to 'evaluate from the outside'

Even if you can move to second-order logic logically-valid formulas in second-order logic is not recursively enumerable. AS RE problems are those which a Turing machine can answer "YES" in a finite amount of time, but a "NO" answer might never come, moving out of RE spaces like DAGs is not computationally feasible.

The problem with 'pattern finding' is that it can learn some even HoL problems if it is in the corpus, but will fail on even simpler problems that weren't.

Here is one paper that explains this. https://arxiv.org/abs/2301.09723

"A persistent problem in corpus-based ML, in all its applications, is that the patterns that the AI finds do not actually reflect the fundamental characteristic of the problem, but rather superficial regularities in the training data, known as “artifacts”.

LLMs aren't doing the 'logic' of the math problems, they are finding patterns in their training data that are hopefully close enough to work for the presented problem.

This is why you can use AI to say learn about intervals on the real line, as those are of finite VC dimensionality, but algebra questions that are outside of it's corpus tend to be very difficult for LLMs to be correct on.

And obviously issues like the Entscheidungsproblem don't magically go away because we have a tool like ML that is far more computationally efficient than brute force, but still insufficient.

As LLM's will confidently present wrong answers as correct, how is that helpful for students?

[Dylan16807]

> Feed forward Neural Networks, like LLMs using attention are effectively Directed acyclic graphs, so it has little it can do to 'evaluate from the outside'

I thought you were talking about the math that's being taught.

No, you can't prove the tutor is mathematically consistent. Is that supposed to be a problem? No tutor in the history of the world has ever met that standard.

No matter what you think of the current state of LLMs, that bar is so high it's meaningless.

[jakderrida]

> stressful for kids and disengage from the subject

In my limited experience, stress and disengagement are almost always the main culprit. Once someone decides, "I'm not good at math", it becomes a lost battle that they'll pretty much never revisit or seek to relitigate.

In my family growing up, we were all taught Algebra as early as 4th grade by our mom because the Philadelphia Catholic School system taught some absurd system where everything a simple education in Algebra can solve is replaced with a massive blackboard-covering table of rules to memorize that I wish I had a picture of because nobody believes me. Anyway, knowing Algebra helped all of my siblings get far enough ahead of the class that most everyone else disengaged while we excelled and younger siblings were frequently helped to advance even better because they had a house packed with people that liked math.