I think we should aim for "quantitative intuition" by teaching how to do rough calculations instead of spending time teaching precise calculations.
This is like saying we should teach children how to swim by letting them splash around in the wading pool.
In real life there is often so many uncertainties in the source numbers that a 'precise' answer is not meaningful anyway.
Math is precise. That's the whole point of it. I don't want my banker, accountant, civil engineer, pilot, cartographer, or architect working on "good enough". I want them to be precise. Consistently.
Your brain is not. I've seen a lot more evidence of people bootstrapping from intuition up to mathematical precision than simply starting with mathematical precision. Taken to its logical conclusion (and I do mean that I believe this is the logical conclusion), this leads to trying to teach number and set theory to kindergarteners, berating them for failing to get it, throwing your hands up and declaring they just aren't suited for math. You have to start with quantitative intuition, the alternative is not to teach math at all. There isn't a "start them out on correct pedagogy immediately" choice. You can and should argue about what tradeoffs are best, but you will have to have tradeoffs.
I don't seen how quantitative intuition and precision are somehow opposed to each other. 4*5 is 20. Not 21. Not 18. 20.
That is logical, and it's vitally important in the understanding of all future concepts. You don't need to understand advanced calculus to grasp the concept that 2 3/4 oranges + 2 1/3 oranges is not 5 oranges altogther, but actually more, and that left over bit is in fact meaningful and relevant.
It's when you start to play with abstractions that mathematics becomes confusing, not when you are being precise.
I think you misunderstood my example. My point was that knowing that there is 5 1/12 oranges (as opposed to 5) is the important precision, and it works logically to a child's mind.
It's quite a bit more complex to expect the child to discard the 1/12 and suggest there are 5 oranges. It's not that the 1/12 is useful for anything, it's the fact that it exists, and is accounted for.
No, this statement is too strong. There are many examples in mathematics where one cannot exactly calculate a result (e.g. because one doesn't know all inputs), but one can give an estimation and prove that it is good enough for a certain purpose.
Certainly, but in order to properly appreciate these more advanced aspects, you need to have an appreciation of the precision and logic of more basic math.
More importantly, I'd suggest that you need to know very basic math (simple addition, subtraction, multiplication and division) on the same level that you can type at your keyboard or drive a stick shift.
If you're spending brain effort on the basics, you've got less of it left for the complexities, making the entire exercise much more difficult.
This is like saying we should teach children how to swim by letting them splash around in the wading pool.
In real life there is often so many uncertainties in the source numbers that a 'precise' answer is not meaningful anyway.
Math is precise. That's the whole point of it. I don't want my banker, accountant, civil engineer, pilot, cartographer, or architect working on "good enough". I want them to be precise. Consistently.