I truly believe limiting educational attainment for our smartest (or privileged, if you want) children is among the most obviously harmful things we can do as a society. It’s shocking to me that anyone can vote to make moves like that with a straight face. Of course we want everyone to get better education. But under-leveraging our highest potential children is a crime that takes future well-being from everyone.
It only affect the poor. The competitive parents regardless left or right will do whatever they can to get their children ahead. When it comes down to children, all bets are off.
After so many years, I can't say that these kinds of policies aren't malicious.
Hot take (having taught algebra to disadvantaged youth in a previous life): a lot of kids who struggle with algebra do so because it is taught in a way that assumes a solid grasp of arithmetic. But many kids do not.
I've worked with high schoolers who couldn't subtract, and weren't about to learn to, because they are completely burnt out on the concept from having it attempted to be taught to them year after year.
But algebra does not depend on arithmetic. Nor on the arcane precedence rules employed by traditional notation. Algebra is just a term rewriting system following a small set of strict syntactical rules, and it can be taught that way successfully. (It can then be linked back to standard curriculum by teaching precedence rules and applying arithmetic reductions as an extra step.)
When taught this way, even kids who can't subtract actually get it, because it stands alone and has clear, simple rules.
> Algebra is just a term rewriting system following a small set of strict syntactical rules, and it can be taught that way successfully.
What are the percentage of kids who can't handle subtraction but can handle Algebra taught this way? (I don't have to squint very hard to cast subtraction in the light of "a term rewriting system following a small set of strict syntactical rules".)
>high schoolers who couldn't subtract, and weren't about to learn to, because they are completely burnt out on the concept from having it attempted to be taught to them year after year.
Sorry, but what in the actual fuck kind of excuse is this?
My youngest is in honors algebra. Can't multiply or divide to save himself. My wife and I are both teachers. No amount of flashcards, extra work, summer tutoring can get it to stick.
But Algebra he can do. If you ask him to multiply or divide by hand he gets derailed loses the big picture and can't move forward.
So I don't know what percentage of students have this kind of problem. But they are certainly out there.
I'm speaking from experience. The kids I've worked with who struggle here protest loudly any attempt to "return to basics" because they have done that every year from 4th to 10th grade without success and by that age see it as infantilizing.
As to why any individual struggled in the first place is different for every kid. But scar tissue around the subject builds year after year until it's painful for them to return to the subject.
> Wait, how can algebra not depend on arithmetic? Something simple like x+20=3x+8.
If your Q could be restated as: How can a student struggle with one while excelling at the other?
The answer is: When we learn the answer we'll be able to help more dyslexic kids than we are now.
I failed basic 3rd grade math tests for so long they finally quit testing me. Eventually, I was the only one of those kids doing algebra in the 6th grade.
My longish life is loaded with similar discontinuity-of-ability. Adult me obfuscates it so well I rarely experience other people's incredulity. Grade school me could have put that to good use.
Frustrating that op doesn't straight answer the question. I think what he's getting at is that you can do the usual steps without having to interpret what the mean. For example, you don't have to say that you're subtracting 8 from 20. Instead you say that all things without x must be on the same side, and signs change when you move across. So one step is x+20-8=3x. Nevermind what those symbols mean, you just memorize the rules. At the end you have x=(20-8)/(3-1) and you put that into the calculator.
To me this seems that you're hacking the system. You're avoiding learning how to think and understand, you're just learning how to pass the class.
That said, I cannot concieve that some kids don't understand 20-8. I wish I could chat to some of them to see what's going on.
The way I taught was to delay the arithmetic to the end, then use a calculator (if necessary).
Moreover -- the concepts taught in algebra are only loosely related to arithmetic. The important concept being taught is that of principled symbolic manipulation; the domain just happens to be over real numbers.
Readit News
After so many years, I can't say that these kinds of policies aren't malicious.
I've worked with high schoolers who couldn't subtract, and weren't about to learn to, because they are completely burnt out on the concept from having it attempted to be taught to them year after year.
But algebra does not depend on arithmetic. Nor on the arcane precedence rules employed by traditional notation. Algebra is just a term rewriting system following a small set of strict syntactical rules, and it can be taught that way successfully. (It can then be linked back to standard curriculum by teaching precedence rules and applying arithmetic reductions as an extra step.)
When taught this way, even kids who can't subtract actually get it, because it stands alone and has clear, simple rules.
What are the percentage of kids who can't handle subtraction but can handle Algebra taught this way? (I don't have to squint very hard to cast subtraction in the light of "a term rewriting system following a small set of strict syntactical rules".)
Sorry, but what in the actual fuck kind of excuse is this?
But Algebra he can do. If you ask him to multiply or divide by hand he gets derailed loses the big picture and can't move forward.
So I don't know what percentage of students have this kind of problem. But they are certainly out there.
As to why any individual struggled in the first place is different for every kid. But scar tissue around the subject builds year after year until it's painful for them to return to the subject.
/s
The normal way to solve this is just separate terms, but you need to subtract 8 from 20. Is there another way to do this?
If your Q could be restated as: How can a student struggle with one while excelling at the other?
The answer is: When we learn the answer we'll be able to help more dyslexic kids than we are now.
I failed basic 3rd grade math tests for so long they finally quit testing me. Eventually, I was the only one of those kids doing algebra in the 6th grade.
My longish life is loaded with similar discontinuity-of-ability. Adult me obfuscates it so well I rarely experience other people's incredulity. Grade school me could have put that to good use.
To me this seems that you're hacking the system. You're avoiding learning how to think and understand, you're just learning how to pass the class.
That said, I cannot concieve that some kids don't understand 20-8. I wish I could chat to some of them to see what's going on.
Moreover -- the concepts taught in algebra are only loosely related to arithmetic. The important concept being taught is that of principled symbolic manipulation; the domain just happens to be over real numbers.
But I’m not sure of the end goal. Seems like in the real world, you need to subtract way more than solve algebra.