But what's the value of this arithmetic muscle memory, in a world of ubiquitous computing?
As long as you don't treat this computing as magic that somehow solves your math problems (hah, true I was guilty of that when I was a school kid), but is fully aware about how it does it (the algorithm) and just let the machine do the boring bits.
Are you joking? Number sense is hugely useful in daily life. What if I have a recipe for three servings but five dinner guests? If I just passed milepost 472 and I average 55 miles per hour, how long will it take me to reach Mexico? How many bottled liters of water can I fit in this box? How much is the 1.35% annual property tax on a million-dollar house, per month? You really want to whip out your laptop for all that?
> What if I have a recipe for three servings but five dinner guests?
Doubling is a useful skill, sure.
> If I just passed milepost 472 and I average 55 miles per hour, how long will it take me to reach Mexico?
This would never come up, because my phone navigation will tell me at any point along the trip how long it will take, more accurately because it has my full speed data plus knowledge about traffic and other hazards ahead.
> How many bottled liters of water can I fit in this box?
Unless I have another box under consideration, then I probably intend to fit as many as possible, so I'll just fill. Complicating this problem can make a need to calculate (or count) more apparent, but further complications can also make a need to compute with a program more apparent too.
> How much is the 1.35% annual property tax on a million-dollar house, per month?
About 1e6/1e2/1e1, or $1000. If I want to be more accurate then I would use a computer -- 1. because I'm likely at my computer already when this comes up, 2. because if not I still likely have a phone.
But what's the value of this arithmetic muscle memory, in a world of ubiquitous computing?
It’s the same as knowing the editor commands, of whatever text editor you’re using, so that you don’t have to look them up constantly while working. It’s the same as knowing the basic functions and methods of the libraries and frameworks you use so that you can type them quickly without going to look them up.
Auto completion is a powerful tool but, in general, it’s not very helpful if you don’t know at least a prefix of the name of the function you’re looking for.
Basic arithmetic skills are like math literacy. If you’re constantly having to look words up in the dictionary then you probably won’t get through Lord of the Rings.
As long as you don't treat this computing as magic that somehow solves your math problems (hah, true I was guilty of that when I was a school kid), but is fully aware about how it does it (the algorithm) and just let the machine do the boring bits.