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Why does that matter? LLMs are going to be increasingly important tools, so it's valuable for educators to help students understand how to use them well. If you

Why does that matter? LLMs are going to be increasingly important tools, so it's valuable for educators to help students understand how to use them well. If you choose to exclude modern tools in your teaching to avoid disadvantaging those who don't want to use them, you disadvantage all the students who do want to use them. To put it another way, modern high school level math classes disadvantage students who want to learn without using a calculator, but it would be quite odd to suggest that we should exclude calculators from math curricula as a result.

l33t7332273 2y ago
Many high school classes are taught in such a way that your calculator rarely helps you.
- skydhash 2y ago
  My high school math classes were mostly about solving problems. The most important was learning the formulas and the steps of the solution. The calculator was mostly a time saver for the actual computation. And once I move to university, almost all the numbers were replaced by letters.
bigstrat2003 2y ago
> but it would be quite odd to suggest that we should exclude calculators from math curricula as a result. That wouldn't be odd at all. Calculators have no place in a math class. You're there to learn how to do math, not how to get a calculator to do math for you.
- Der_Einzige 2y ago
  Math class has no place without calculators. You're there to learn how to do math in the real world, not how to do math in a contrived world where we pretend that the ability to do calculations isn't ubiquitous. There are almost certainly more calculator capable devices on earth than people today. Ludditism is the human death drive expressed in a particularly toxic fashion.
  - dmonitor 2y ago
    When speaking of Math class, are you ignoring everything up to pre-calculus or do you think everything from addition flashcards, times tables, and long division is useless? I'd argue those exercises are invaluable. Seeing two numbers and just knowing the sum is always faster than plugging into a calculator.
    - casey2 2y ago
      This is the same fallacy that people make when they learn a new language, so they pick up anki spend a ton of time on it and most burn out, some don't, but neither see any real benefits greater than if they just spent that time on learning the language. The fallacy comes from the fact the goal of learning isn't to finish problems quickly, but to understand what is trying to be said or taught. For example you claim that addition flashcards and times tables are invaluable, but you don't specify a base, in base 2 you have 4 addition flashcards, in base 100 you have 10,000, clearly understanding addition isn't related to the base, but flashcards increase as base increases, thus there is a relation, implying of course that understanding addition isn't related to the number of addition flashcards you understand. Oh but of course they aren't invaluable in understanding addition, they are invaluable in understanding concepts that use addition, cause ... why exactly? You saved 1 second finishing the problem that you may have understood before you completed that addition step? You didn't have to "context switch" by using a calculator? Students who don't know the sum often give unused name and go back at the end of the problem and solve it later. This behavior is of course discouraged since students can't understand variables until much later if ever and not knowing something you were taught represents the failure of the student and thus the teacher, school, government and society. Infinitely better is learning from someone who speaks the language. A 30 minute solo tutoring session once a week for a month, in a no distraction environment (aside from a snack), even just working through homework, is more than enough for most students to go from Fs to As for multiple years.
    - cmontella 2y ago
      Personally I have dyscalculia and to this day I need to add on my fingers. Still, I ended up with degrees in physics and computer engineering. I don't think those things you mention are useless, but they never worked for me so I don't view them as invaluable.
- dmonitor 2y ago
  Calculators in early math classes, such as algebra, would be 100% detrimental to learning. Getting an intuitive understanding of addition and multiplication is invaluable and can only be obtained through repetition. Once you reach higher levels of math, the actual numbers become irrelevant so a calculator is fine. But for anything below that, you need to do it by hand to get any value.
frakt0x90 2y ago
I disagree. I see an LLM as less calculator and more as cheating. I think there's a lot of value in creating something entirely yourself without having an LLM spit out a mean solution for you to start from. LLMs have their place and maybe even somewhere in schools but the more you automate the hard parts of tasks, the less people value the struggle of actually learning something.
- cmontella 2y ago
  FWIW I teach upper level courses. I see LLMs as almost sufficiently advanced compilers. You could say the same thing about gcc or even standard libraries. "Why back in my day we wrote our own hash maps while walking uphill both ways! Kids these days just import a lib and they don't learn anything!" They are still learning, just at a higher level of abstraction.

l33t7332273 2y ago

Many high school classes are taught in such a way that your calculator rarely helps you.

skydhash 2y ago
My high school math classes were mostly about solving problems. The most important was learning the formulas and the steps of the solution. The calculator was mostly a time saver for the actual computation. And once I move to university, almost all the numbers were replaced by letters.

bigstrat2003 2y ago

> but it would be quite odd to suggest that we should exclude calculators from math curricula as a result. That wouldn't be odd at all. Calculators have no place in a math class. You're there to learn how to do math, not how to get a calculator to do math for you.

Der_Einzige 2y ago
Math class has no place without calculators. You're there to learn how to do math in the real world, not how to do math in a contrived world where we pretend that the ability to do calculations isn't ubiquitous. There are almost certainly more calculator capable devices on earth than people today. Ludditism is the human death drive expressed in a particularly toxic fashion.
- dmonitor 2y ago
  When speaking of Math class, are you ignoring everything up to pre-calculus or do you think everything from addition flashcards, times tables, and long division is useless? I'd argue those exercises are invaluable. Seeing two numbers and just knowing the sum is always faster than plugging into a calculator.
  - casey2 2y ago
    This is the same fallacy that people make when they learn a new language, so they pick up anki spend a ton of time on it and most burn out, some don't, but neither see any real benefits greater than if they just spent that time on learning the language. The fallacy comes from the fact the goal of learning isn't to finish problems quickly, but to understand what is trying to be said or taught. For example you claim that addition flashcards and times tables are invaluable, but you don't specify a base, in base 2 you have 4 addition flashcards, in base 100 you have 10,000, clearly understanding addition isn't related to the base, but flashcards increase as base increases, thus there is a relation, implying of course that understanding addition isn't related to the number of addition flashcards you understand. Oh but of course they aren't invaluable in understanding addition, they are invaluable in understanding concepts that use addition, cause ... why exactly? You saved 1 second finishing the problem that you may have understood before you completed that addition step? You didn't have to "context switch" by using a calculator? Students who don't know the sum often give unused name and go back at the end of the problem and solve it later. This behavior is of course discouraged since students can't understand variables until much later if ever and not knowing something you were taught represents the failure of the student and thus the teacher, school, government and society. Infinitely better is learning from someone who speaks the language. A 30 minute solo tutoring session once a week for a month, in a no distraction environment (aside from a snack), even just working through homework, is more than enough for most students to go from Fs to As for multiple years.
  - cmontella 2y ago
    Personally I have dyscalculia and to this day I need to add on my fingers. Still, I ended up with degrees in physics and computer engineering. I don't think those things you mention are useless, but they never worked for me so I don't view them as invaluable.
dmonitor 2y ago
Calculators in early math classes, such as algebra, would be 100% detrimental to learning. Getting an intuitive understanding of addition and multiplication is invaluable and can only be obtained through repetition. Once you reach higher levels of math, the actual numbers become irrelevant so a calculator is fine. But for anything below that, you need to do it by hand to get any value.

frakt0x90 2y ago

I disagree. I see an LLM as less calculator and more as cheating. I think there's a lot of value in creating something entirely yourself without having an LLM spit out a mean solution for you to start from. LLMs have their place and maybe even somewhere in schools but the more you automate the hard parts of tasks, the less people value the struggle of actually learning something.

cmontella 2y ago
FWIW I teach upper level courses. I see LLMs as almost sufficiently advanced compilers. You could say the same thing about gcc or even standard libraries. "Why back in my day we wrote our own hash maps while walking uphill both ways! Kids these days just import a lib and they don't learn anything!" They are still learning, just at a higher level of abstraction.