I agree. It's because of "math debt" that it's essential first to fill in gaps when helping math students. As you eluded to, I'm sure the "math debt" is fine for some circumstances. As in, if a student doesn't memorize the decimal equivalent of 7/8, they will probably be fine. Or if a student doesn't know the 3-4-5 Pythagorean Triple, they can still solve these problems using other skills. Or learn how to use Algebra to prove that 0.111... is 1/9. But there is other mathematical knowledge that prevents students from proceeding.
A couple of essential skills include being able to formulate all the different ways that numbers add to 10, one-digit multiplication, and the related divisions. Many students use calculators instead of memorizing these facts, but, as you said, they won't be able to factor or simplify later, and often solving these problems will take so much time that the enjoyment of doing the problem is lost.
And many students struggle with subtraction with borrowing, but the idea of regrouping shows up in adding and subtracting mixed numbers, and conversions like changing between hours and minutes.
While it might seem easier to gloss over these as nonessentials - "Oh, we can use a calculator for this," or "I can just search up the answer." But then the skills don't get developed.
I remember a time when it was laughable that people couldn't figure out how to make change with a 10-dollar bill. But now, no one uses cash for payments and these skills seem unimportant.
But what about our students who want to go into engineering, medicine, or other precision or technical fields? It seems a shame that students might grow up thinking that they don't need this information, only to find out that their jobs (or dream jobs) depend on what they thought was unimportant.
And I think, as a society, we also benefit so much more from a "math literate" society in minute ways - from efficiencies, improvements, and numerical checks and balances - that maybe this "math debt" isn't just a debt collected by one person. It can potentially be a debt to our society as a whole.
I agree. It's because of "math debt" that it's essential first to fill in gaps when helping math students. As you eluded to, I'm sure the "math debt" is fine for some circumstances. As in, if a student doesn't memorize the decimal equivalent of 7/8, they will probably be fine. Or if a student doesn't know the 3-4-5 Pythagorean Triple, they can still solve these problems using other skills. Or learn how to use Algebra to prove that 0.111... is 1/9. But there is other mathematical knowledge that prevents students from proceeding.
A couple of essential skills include being able to formulate all the different ways that numbers add to 10, one-digit multiplication, and the related divisions. Many students use calculators instead of memorizing these facts, but, as you said, they won't be able to factor or simplify later, and often solving these problems will take so much time that the enjoyment of doing the problem is lost.
And many students struggle with subtraction with borrowing, but the idea of regrouping shows up in adding and subtracting mixed numbers, and conversions like changing between hours and minutes.
While it might seem easier to gloss over these as nonessentials - "Oh, we can use a calculator for this," or "I can just search up the answer." But then the skills don't get developed.
I remember a time when it was laughable that people couldn't figure out how to make change with a 10-dollar bill. But now, no one uses cash for payments and these skills seem unimportant.
But what about our students who want to go into engineering, medicine, or other precision or technical fields? It seems a shame that students might grow up thinking that they don't need this information, only to find out that their jobs (or dream jobs) depend on what they thought was unimportant.
And I think, as a society, we also benefit so much more from a "math literate" society in minute ways - from efficiencies, improvements, and numerical checks and balances - that maybe this "math debt" isn't just a debt collected by one person. It can potentially be a debt to our society as a whole.
I agree! And it's true -- we need lots of math literacy as citizens as well, both for professions and public life.