> No longer can teachers be reasonable by allowing you to solve a problem your own way, as long as you show your work and get the right answer.
Suppose after a week of lectures on sorting, you ask your students to implement a sorting algorithm. From one student, you get back a 400 line monstrosity that somehow, miraculously, does the right thing. Do you shrug it off and say "as long as it works", or do you grow very concerned that the student is somehow missing the forest for the trees, even though they arrived at an apparently correct answer?
In my experience teaching, it's far more likely that the student doesn't understand some basic, necessary underlying concepts than that the student is very bright and was trying to come up with a super optimized sorting algorithm. Both will exist, and you have to differentiate. The worst bit is that often the idiots know this, and imagine themselves to be super intelligent, so they're impossible to teach.
IMHO "just get the right answer" has never been a reasonable way to teach math.
> All this has done is remove parents from the teaching process.
I hear this a lot. We're basically just talking about different ways of doing arithmetic or multiplication.
It's akin to bitching and moaning because someone taught your kid insertion sort, and you only know bubble sort so now you can't teach your kid sorting.
Is the problem that the curriculum developers are being obtuse, or is the problem that many parents and teachers never really had a deep enough understanding addition/multiplication/division in the first place?
It's pretty scary how few of our elementary/middle school teachers -- who teach math -- cannot differentiate from the definition of addition (a set of axioms), and algorithms which implement addition. Because they don't know the difference between a specification and an implementation, teaching multiple implementations seems silly. But it's not silly at all, and the difference between the definition of a thing and an algorithm matching the definition is something our elementary, middle and high school students can, should, and hopefully will understand -- unmotivated and stubborn teachers/parents be damned.
Suppose after a week of lectures on sorting, you ask your students to implement a sorting algorithm. From one student, you get back a 400 line monstrosity that somehow, miraculously, does the right thing. Do you shrug it off and say "as long as it works", or do you grow very concerned that the student is somehow missing the forest for the trees, even though they arrived at an apparently correct answer?
In my experience teaching, it's far more likely that the student doesn't understand some basic, necessary underlying concepts than that the student is very bright and was trying to come up with a super optimized sorting algorithm. Both will exist, and you have to differentiate. The worst bit is that often the idiots know this, and imagine themselves to be super intelligent, so they're impossible to teach.
IMHO "just get the right answer" has never been a reasonable way to teach math.
> All this has done is remove parents from the teaching process.
I hear this a lot. We're basically just talking about different ways of doing arithmetic or multiplication.
It's akin to bitching and moaning because someone taught your kid insertion sort, and you only know bubble sort so now you can't teach your kid sorting.
Is the problem that the curriculum developers are being obtuse, or is the problem that many parents and teachers never really had a deep enough understanding addition/multiplication/division in the first place?
It's pretty scary how few of our elementary/middle school teachers -- who teach math -- cannot differentiate from the definition of addition (a set of axioms), and algorithms which implement addition. Because they don't know the difference between a specification and an implementation, teaching multiple implementations seems silly. But it's not silly at all, and the difference between the definition of a thing and an algorithm matching the definition is something our elementary, middle and high school students can, should, and hopefully will understand -- unmotivated and stubborn teachers/parents be damned.