How University Students Use Claude

If kids don't go through the struggle of understanding arithmetic, higher math will be very very difficult. Just because you can use a calculator, doesn't mean that's the best way to learn. Likewise for using LLMs to program.

I have no anecdata to counter your thesis. I do agree that immersion in the doing of a thing is the best way to learn. I am not fully convinced that doing a lot of arithmetic hand calculation precludes learning the science of patterns that is mathematics. They should still be doing something mathematical but why not go right into using a calculator. I have no experience as an educator and I bet it's hard to get good data on this topic of debate. I could be very wrong.

There's a wealth of research on how children learn to do math, and one of the most crucial things is having experiences manipulating numbers directly. Children don't understand how the symbols we use map to different numbers and the operations themselves take time to learn. If you just have them use a black-box to generate answers, they won't understand how the underlying procedures conceptually work and so they'll be super limited in their mathematical ability later on.

Can you explain further why you think nobody has tried teaching first graders math exclusively using calculator in the 30 years they've been dirt cheap?

That's after all the implication from your assessment that there would be no good data.

I'm not an educator but I know from teaching my own children that you don't introduce math using symbols and abstract representations. You grab 5 of some small object and show them how a pile of 2 objects combined with a pile of 3 objects creates a pile of 5 objects.

Remember, language is a natural skill all humans have. So is counting (a skill that may not even be unique to humans).

However writing is an artifical technology invented by humans. Writing is not natural in the sense that language itself is. There is no part of brain we're born with that comes ready to write. Instead, when we learn to write other parts of our brain that are associated with language and hearing and vision are co-opted into the "writing and reading parts".

Teaching kids math using writing and symbolism is unnatural and often an abstraction too far for them (initially). Introducing written math is easier and makes more sense once kids are also learning to read and write - their brains are being rewired by that process. However even an toddler can look at a pile of 3 objects and a pile of 5 objects and know which one is more, even if they can't explicitly count them using language - let alone read and write.