Instead of 120/6, you'd end up writing, "I'm on lunch with a few friends, we got the bill and it was $120. There are 6 of us here. How much should each of us pay if we want to split the bill?"

Now imagine how complicated the prompt would get with a problem that's actually difficult and how easy it could be to state the question in a way that provided the wrong context. When this happens, without a foundation, you won't have any idea of the answer is way off or not.

Back when I was in school we'd have answers given to us and had to determine if they made sense without doing the exact calculation. This is very useful. With the 120/6 example. If the LLM said to pay $0.05 each, it should trigger something in a person to think that's not right and to examine the question that was asked. This may be an extreme example, but this stuff happens all the time.

There are also quick calculations that are useful, but where asking an LLM every time isn't practical. Price comparisons in a store, measuring stuff in your home to make sure a piece of furniture fits. Without any math foundation would they be able to read and understand a tape measure enough to actually measure and enter in the right stuff? Do you want them to need to consult an LLM to know that a wall that is 5 1/4" long will accommodate a cabinet that is 5 1/16" wide? These are things some people can't figure out today, and they had math class.

I can't imagine how helpless someone would feel if they had to reach for a phone with billions of dollars worth of infrastructure behind it just to answer basic questions that everyone around them can figure out in their head.

The foundation should always be there. It's more a question of how high do you go with it. But if the kid likes it and is good at it, why take that away from them? Also, remember that you're cherry picking exceptional examples of where it worked. There are a lot of examples where the LLMs have been embarrassingly bad at math (counting the number of "r" in "strawberry"). Math is built on rules, and LLMs are a text prediction engine... they don't necessarily know the rules or have real logic. LLMs also tend to look smart to someone who doesn't know the subject, and kind of dumb to the experts in a field.

As an aside, my high school had some kind of new math program that failed to go into depth on each topic of mathematics that people normally learn. I had been really good at math, but this screwed me over in college and now, 25 years later, I'm still upset that a solid foundation in math is taken from me. I could self-study, but it's harder to prioritize that when there are so many things competing for attention. When the kids are young is the time to do it.