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San Francisco reverses 'equitable' ban on middle school algebra

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Re: San Francisco reverses 'equitable' ban on middle school algebra

#21

Post by WarOnPrivacy »

purpleflame1257 wrote: post #3
colanderman wrote: post #2

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. B…

Wait, how can algebra not depend on arithmetic? Something simple like x+20=3x+8. 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?

> 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.

Re: San Francisco reverses 'equitable' ban on middle school algebra

#22

Post by colanderman »

brianwawok wrote: post #4
purpleflame1257 wrote: post #3

Earlier quoted context omitted.

Wait, how can algebra not depend on arithmetic? Something simple like x+20=3x+8. 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?

Allow calculators? But I’m not sure of the end goal. Seems like in the real world, you need to subtract way more than solve algebra.

Essentially that's what I did -- the way I taught this was:

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.

Re: San Francisco reverses 'equitable' ban on middle school algebra

#23

Post by colanderman »

sollewitt wrote: post #11
ITB wrote: post #7

Earlier quoted context omitted.

The point is that they forbid the children that can subtract from learning algebra

I suspect if you told these 8 graders who “can’t subtract” you were going to give them $100 and ask them for $110 back you’d find they understand both subtraction and negative numbers.

It's different when it's written down as a math expression or word problem. 100-110 becomes 110-100. 17-9 becomes a finger counting exercise. Small errors get propagated in ways that make a distracting mess to sort out. None of this is conducive to learning algebra.

Re: San Francisco reverses 'equitable' ban on middle school algebra

#24

Post by colanderman »

purpleflame1257 wrote: post #3
colanderman wrote: post #2

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. B…

Wait, how can algebra not depend on arithmetic? Something simple like x+20=3x+8. 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?

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.

Re: San Francisco reverses 'equitable' ban on middle school algebra

#25

Post by bdjsiqoocwk »

purpleflame1257 wrote: post #3
colanderman wrote: post #2

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. B…

Wait, how can algebra not depend on arithmetic? Something simple like x+20=3x+8. 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?

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.

Re: San Francisco reverses 'equitable' ban on middle school algebra

#26

Post by bdjsiqoocwk »

colanderman wrote: post #23
sollewitt wrote: post #11

Earlier quoted context omitted.

I suspect if you told these 8 graders who “can’t subtract” you were going to give them $100 and ask them for $110 back you’d find they understand both subtraction and negative numbers.

It's different when it's written down as a math expression or word problem. 100-110 becomes 110-100. 17-9 becomes a finger counting exercise. Small errors get propagated in ways that make a distracting mess to sort out. None of this is conducive to learning algebra.

> It's different when it's written down as a math expression or word problem

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.

Re: San Francisco reverses 'equitable' ban on middle school algebra

#27

Post by whelp_24 »

bdjsiqoocwk wrote: post #25
purpleflame1257 wrote: post #3

Earlier quoted context omitted.

Wait, how can algebra not depend on arithmetic? Something simple like x+20=3x+8. 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?

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 memoriz…

With this explanation, you've inadvertently convinced me of the op. Being able to get to the "x = number" is the whole point of algebra. 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).

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.

Re: San Francisco reverses 'equitable' ban on middle school algebra

#28

Post by bdjsiqoocwk »

whelp_24 wrote: post #27
bdjsiqoocwk wrote: post #25

Earlier quoted context omitted.

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 memoriz…

With this explanation, you've inadvertently convinced me of the op. Being able to get to the "x = number" is the whole point of algebra. 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). Doing this way means that you've actually understood algebra, and honestly, the only step of memorization is the substraction itself. W…

> Doing this way means that you've actually understood algebra, and honestly, the only step of memorization is the substraction itself.

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.

Re: San Francisco reverses 'equitable' ban on middle school algebra

#29

Post by snypher »

notmyuserlogin wrote: post #14
morkalork wrote: post #6

Earlier quoted context omitted.

>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 still can't add 43 + 7 that quickly but would say I have a decent grasp of algebra. Maybe I leant too heavily on a calculator at school.

Re: San Francisco reverses 'equitable' ban on middle school algebra

#30

Post by sokoloff »

colanderman wrote: post #20
engcoach wrote: post #17

Earlier quoted context omitted.

And what will these folks who can do algebra but not arithmetic do with their skill? Are there any applications that don’t involve other math knowledge? Someone who can’t subtract is functionally retarded in modern society and it’s not meaningful to invest outside remedial education

You're asking, what skill could someone possibly develop on a foundation of symbolic reasoning... on a software development forum ? 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 strugg…

Whether or not they're "hopeless" at math is a subjective/open question, but someone in their teens who cannot subtract is objectively "bad at math" at that moment.

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".

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