31–40 of 89 posts
Yes we should start my six year old with group theory. When we go to the farmer's market I can ask him under what transformations is an apple invariant, and then pay for it by having him solve a Rubiks cube.
Because you need to be able to run numbers in your head for a lot of practical tasks, and inability to do napkin math can cost you very dearly
This isn't just folk wisdom either. There's an active subfield of cognitive science that focuses on working memory/cognitive load and math instruction. Broadly speaking, it's hard for students to successfully transition to even basic algebra if they don't have basic calculations down.
If you don't get the basics of arithmetic it is incredibly hard to grasp the idea of "equals" as a pivot point. Division by hand helps to give us a hint that numbers can be broken up into constituents and still be the same.
You internalise a whole set of behaviours, typically via repetition, and it unlocks understanding beyond itself imo
Because being able to do basic order-of-magnitude arithmetic in one's head is a critical thinking tool essential to detecting nonsense claims in real time.
Earlier quoted context omitted.
There must be ruggedized calculators out there, so that argument doesn't seem very compelling. People use their phones at construction sites, and you can run whatever type of calculator you want on a cell phone.
If you run every basic calculation through a calculator, you'll make every task take 3x time it requires today, in best case. I have seen people eyeball measurements and taking notes, and bringing in perfectly manufactured goods (blinds, cupboards, etc.) in return. Esp, in construction, nothing is precise, so being able to eyeball correctly after a quick measurement with a tape and doing some basic math on the number…
Tell me you have never built a thing[1] in your entire life that was more complex than an IKEA bookshelf without telling me that challenge: I do hobby projects all the time and I couldn't even tell you how many mental-math problems I do per hour while doing so. It's a LOT. Depending what I'm making I might well spend more time doing math in my head and on paper than I do actually putting tools to materials to build the thing.
[1]: by this I mean actually building. With your hands.
Because being able to do basic order-of-magnitude arithmetic in one's head is a critical thinking tool essential to detecting nonsense claims in real time.
Because you need to be able to run numbers in your head for a lot of practical tasks, and inability to do napkin math can cost you very dearly
And calculators get broken very quickly on construction sites. And you must be capable of adding and subtracting and finding the LCD and GCD of fractions to read a tape measure in US customary units.
Well, that's what tolerances are for. I don't need a perfectly accurate answer. Just one that's within 1/32" or more likely 1/4" to 1/8".
Because being able to do basic order-of-magnitude arithmetic in one's head is a critical thinking tool essential to detecting nonsense claims in real time.
Mental arithmetic is vital to mental self defense.
to me this seems very ill-thought through, and doesn't feel like they actually remember what math was like. they are suggesting letting the computers do the computation part, but we already do that once that skill has been mastered. i.e.: simple calculators are allowed in calculous exams. the problem with bad ideas in education is the system might be stupid enough to follow through with it, like that new math nonsens…