San Francisco reverses 'equitable' ban on middle school algebra
freebeacon.com
freebeacon.com
After so many years, I can't say that these kinds of policies aren't malicious.
Minor suggestion, there are good ones
No. They will do whatever they can to make sure their children get the education. They will pay extra. Some will teach their children themselves.
Again, this is regardless of race/religion/lgbtq or anything. It's all hands on deck when it comes to providing for the children.
Sometimes I really doubt whether people are really that naive online? Or are they arguing for the sake of the argument? Tbh, I have never seen anyone in real life doesn't understand the situation and the parents that I am talking about.
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.
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?
But I’m not sure of the end goal. Seems like in the real world, you need to subtract way more than solve algebra.
1. All operators are written explicitly, and parentheses are used around every operation. (Order of operations is a huge tripping stone.)
2. All allowed algebraic manipulations were clearly named and diagrammed, and we applied them step by step (no leaps of intuition allowed -- another tripping stone).
3. Save all arithmetic to the end. I.e. numbers and variables function identically. But -- try to move numbers around so they're in operators together.
4. Once the equation is solved (or whatever task is required), now take out the calculator and do the arithmetic required.
I completely agree subtraction is a more useful real world skill. But like you said -- calculators exist. So no reason to let that be the reason to hold kids back from learning algebra.
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.
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.
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.
Doing this way means that you've actually understood algebra, and honestly, the only step of memorization is the substraction itself.
Whether you pull out the calculator at 2 +3, or (23449)/(!6 + root(34/5) ) is sorta irrelevant.
No, not really. If you understood what an equality and a variable means, then you could solve it without having to go thru algorithmic steps.
> More often, students find the difficulty in trying to do arithmetic on things that can't be(what's x +y? it isn't xy and it isn't some new letter).
I'm beginning to suspect that you yourself struggle with arithmetics.
I can certainly grasp that these are literally different, but are they practically different for most people?
Eg I know that some of my clothes need to be washed with cold water. I don't know why, but it's never made a difference in my life.
I know my car needs oil changes, but I don't specifically know why. Some kind of lubrication, but for what and why it goes bad I have no idea.
We all do hundreds of things algorithmically without really understanding what we're doing or why. We know enough to get the answer we want and that's good enough.
The kids that do algebra algorithmically probably aren't going to be math professors, but neither am I, and there are plenty of lucrative and productive professions that are fine with getting the right answer without knowing why.
On some level, most people are doing arithmetic algorithmically anyways, based on rules structured around base 10. Ask some people you think have passable arithmetic skills to do addition and subtraction in like base 5 and watch the smoke come out of their ears. I'm not casting aspersions, I'd have a hard time too past a couple digits.
I would wager most of them can't explain why we carry numbers over, they just know it needs to happen to get the right answer. I don't think I'm much better; I'm sure there are dozens of things in basic math that I just do without really understanding why.
> That said, I cannot concieve that some kids don't understand 20-8.
I would almost put money down that it's around carrying the 1's. I've met a few people that struggled with arithmetic, and they almost always get lost around carrying over numbers.
But if the point of school isn't "teach them practical algorithms", but instead learning how to think, then it makes perfect sense to teach them equations, and have them actual understand.
I'm short, if the point of school is to learn how to think, teaching them some mysterious algorithms isn't going to achieve that. If the point is to learn useful algorithms, I can think of 100 better things than algebra.
So which one is it?
Isn't this the actual core of the problem then? If a kid can do $100-$100 but can't do 20-8, the problem is he doesn't understand how to map the things in real life he knows, to the symbols you're showing him.
Sorry, but what in the actual fuck kind of excuse is this?
/s
These are kids who we were lucky to have show up to class each day, each failed by the traditional school system in some way. So rather than force feed them material they hated and knew they hated because they didn't get it before and were now so far behind they felt like failures, we taught them material which was at their grade level that didn't depend on areas they struggled with and was interesting to them.
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.
My experience is somewhat slanted as the context I worked on was a charter high school for students who were being failed by traditional schools for one reason or another. This meant I saw a high percentage of students who (almost by definition) struggled with elementary and middle school subjects, yet were perfectly capable learners when their individual learning styles were accounted for.
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.
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".)
Not to mention that becoming proficient in algebra helps these kids realize they're not "bad at math" and hopeless (as you seem to think they are). It's easier to fill in knowledge gaps when you're looking backwards than forwards (speaking from my own experience with subjects I've struggled with).
In this subthread, I'm trying to understand how even Algebra I can be taught to proficiency to someone who is not capable of subtracting two numbers.
Even graphing a simple linear y = x - 3 requires subtraction. Division is based on subtraction. We might not think of 6 / 2 as requiring subtraction, but 114 / 6 does as does "How many slices of pizza are left over if you start with 8 slices and divide slices evenly among 3 people?". "2 pizzas with 8 slices each and 5 people?" Multiplying out y = (x + 2) * (x - 4). Find the x intercepts of y = x² - x - 6. Find the intersection of two lines.
Maybe I'm "bad at imagination" and hopeless, but I don't see it likely that many students who can't subtract will thrive in Algebra I and from that recognize "oh, I'm actually good at math; let me see if I can find those old flash cards and figure out this subtraction thing..."
IMO, kids who cannot subtract need to be assessed to see if it's a capacity issue or a path/background issue. If it's the latter, giving them support and teaching them arithmetic seems far more likely to succeed than trying to teach them Algebra, and will far more valuable to them in life (budgeting, credit, taxes, etc.).
I greatly respect that you have experience teaching Algebra to disadvantaged youth. I wonder if the success cases you saw were those who absolutely could subtract but just couldn't be bothered to do classroom tricks to perform for other teachers. "Could do arithmetic but just couldn't be bothered" tracks for me much more than "Can't do arithmetic but can thrive in Algebra".