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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

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".
- engcoach 3y ago
  I really doubt folks who can’t subtract will get an engineering job, it’s almost certainly the tip of the iceberg of intellectual insufficiency. Doesn’t mean they’re bad people or even dumb.

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".
engcoach 3y ago
I really doubt folks who can’t subtract will get an engineering job, it’s almost certainly the tip of the iceberg of intellectual insufficiency. Doesn’t mean they’re bad people or even dumb.