9 ms·

San Francisco reverses 'equitable' ban on middle school algebra

43 points by tomohawk 3y ago

colanderman 3y ago
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.
- purpleflame1257 3y ago
  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?
  - brianwawok 3y ago
    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.
    - colanderman 3y ago
      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.
  - WarOnPrivacy 3y ago
    > 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.
  - colanderman 3y ago
    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.
  - bdjsiqoocwk 3y ago
    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.
    - whelp_24 3y ago
      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.
      - bdjsiqoocwk 3y ago
        > 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.
    - everforward 3y ago
      > 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. 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.
- gedy 3y ago
  Honestly, what is the value of algebra if a child can’t even subtract?
  - ITB 3y ago
    The point is that they forbid the children that can subtract from learning algebra
    - sollewitt 3y ago
      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.
      - colanderman 3y ago
        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.
        bdjsiqoocwk 3y ago
        > 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.
        jjk166 3y ago
        If only there were some way of doing math where different symbols were substituted such that people could recognize patterns that they had difficulty understanding with the original symbols.
- morkalork 3y ago
  >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?
  - qeternity 3y ago
    Imagine trying to teach students year after year. Disgusting. /s
    - morkalork 3y ago
      Imagine highschoolers being too burnt out from failing to learn subtraction to learn subtraction. OP's comment reeks of the soft racism of low expectations.
      - colanderman 3y ago
        You don't know anything about me, the school I worked at, or the kids I worked with. 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.
  - notmyuserlogin 3y ago
    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.
    - colanderman 3y ago
- sokoloff 3y ago
  > 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".)
  - colanderman 3y ago
    Syntactic pattern matching is straightforward and visual.
    - engcoach 3y ago
      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
      - colanderman 3y ago
        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 struggled with).
        sokoloff 3y ago
        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".
ITB 3y ago
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.
- PreachSoup 3y ago
  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.
  - benf76 3y ago
    How can you say that eliminating algebra for all students ‘only’ affects the poor it literally is the opposite it is all Students no subset.
    - ImJamal 3y ago
      Wealthy people can get private tutors or send their kids to a private school. The poor are stuck with the public schools.
      - PreachSoup 3y ago
        > The poor are stuck with the 'bad' public schools. Minor suggestion, there are good ones
        ImJamal 3y ago
        I don't think mentioning the quality of the public schools is relevant. Poor people are almost always stuck in public schools (on occasion they can get aid for private schools). This rule on banning certain math classes applies to all public schools regardless of how good or bad they are. This means even if a poor kid went to the best public school in the world, they would still be impacted.
up2isomorphism 3y ago
This is probably one of the mostly racist thing in the name of “equitable “.

43 points by tomohawk 3y ago

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.

purpleflame1257 3y ago
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?
- brianwawok 3y ago
  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.
  - colanderman 3y ago
    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.
- WarOnPrivacy 3y ago
  > 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.
- colanderman 3y ago
  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.
- bdjsiqoocwk 3y ago
  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.
  - whelp_24 3y ago
    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.
    - bdjsiqoocwk 3y ago
      > 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.
  - everforward 3y ago
    > 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. 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.
gedy 3y ago
Honestly, what is the value of algebra if a child can’t even subtract?
- ITB 3y ago
  The point is that they forbid the children that can subtract from learning algebra
  - sollewitt 3y ago
    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.
    - colanderman 3y ago
      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.
      - bdjsiqoocwk 3y ago
        > 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.
        jjk166 3y ago
        If only there were some way of doing math where different symbols were substituted such that people could recognize patterns that they had difficulty understanding with the original symbols.
morkalork 3y ago
>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?
- qeternity 3y ago
  Imagine trying to teach students year after year. Disgusting. /s
  - morkalork 3y ago
    Imagine highschoolers being too burnt out from failing to learn subtraction to learn subtraction. OP's comment reeks of the soft racism of low expectations.
    - colanderman 3y ago
      You don't know anything about me, the school I worked at, or the kids I worked with. 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.
- notmyuserlogin 3y ago
  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.
  - colanderman 3y ago
sokoloff 3y ago
> 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".)
- colanderman 3y ago
  Syntactic pattern matching is straightforward and visual.
  - engcoach 3y ago
    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
    - colanderman 3y ago
      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 struggled with).
      - sokoloff 3y ago
        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".

ITB 3y ago

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.

PreachSoup 3y ago
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.
- benf76 3y ago
  How can you say that eliminating algebra for all students ‘only’ affects the poor it literally is the opposite it is all Students no subset.
  - ImJamal 3y ago
    Wealthy people can get private tutors or send their kids to a private school. The poor are stuck with the public schools.
    - PreachSoup 3y ago
      > The poor are stuck with the 'bad' public schools. Minor suggestion, there are good ones
      - ImJamal 3y ago
        I don't think mentioning the quality of the public schools is relevant. Poor people are almost always stuck in public schools (on occasion they can get aid for private schools). This rule on banning certain math classes applies to all public schools regardless of how good or bad they are. This means even if a poor kid went to the best public school in the world, they would still be impacted.

up2isomorphism 3y ago

This is probably one of the mostly racist thing in the name of “equitable “.