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That's silly. None of my (I'm a math major) university calculus courses (calc 1, calc 2, calc 3, differential equations) allowed calculators on quizzes or exams

That's silly. None of my (I'm a math major) university calculus courses (calc 1, calc 2, calc 3, differential equations) allowed calculators on quizzes or exams. Graphing calculators are a zombie technology kept alive by completely bogus, artificial means. There's no reason to use a calculator on a properly-designed calculus exam. We were doing everything from Taylor series to triple integrals without them. Teaching kids to rely on a calculator from a young age severely limits their ability to develop the basic arithmetic "muscle memory" (for lack of a better term) needed to manipulate equations quickly in more advanced math classes. It's a real shame.

drdaeman 6y ago
But what's the value of this arithmetic muscle memory, in a world of ubiquitous computing? As long as you don't treat this computing as magic that somehow solves your math problems (hah, true I was guilty of that when I was a school kid), but is fully aware about how it does it (the algorithm) and just let the machine do the boring bits.
- jeffbee 6y ago
  Are you joking? Number sense is hugely useful in daily life. What if I have a recipe for three servings but five dinner guests? If I just passed milepost 472 and I average 55 miles per hour, how long will it take me to reach Mexico? How many bottled liters of water can I fit in this box? How much is the 1.35% annual property tax on a million-dollar house, per month? You really want to whip out your laptop for all that?
  - dTal 6y ago
    >How much is the 1.35% annual property tax on a million-dollar house, per month? You really want to whip out your laptop for all that? I'll bite. In what scenario would it be useful to do this calculation in my head?
    - jeffbee 6y ago
      You're trying to figure out if you can afford that house based on your monthly pay?
  - Jach 6y ago
    > What if I have a recipe for three servings but five dinner guests? Doubling is a useful skill, sure. > If I just passed milepost 472 and I average 55 miles per hour, how long will it take me to reach Mexico? This would never come up, because my phone navigation will tell me at any point along the trip how long it will take, more accurately because it has my full speed data plus knowledge about traffic and other hazards ahead. > How many bottled liters of water can I fit in this box? Unless I have another box under consideration, then I probably intend to fit as many as possible, so I'll just fill. Complicating this problem can make a need to calculate (or count) more apparent, but further complications can also make a need to compute with a program more apparent too. > How much is the 1.35% annual property tax on a million-dollar house, per month? About 1e6/1e2/1e1, or $1000. If I want to be more accurate then I would use a computer -- 1. because I'm likely at my computer already when this comes up, 2. because if not I still likely have a phone. Both you and chongli ought to consider this argument (ignore the stuff about violent video games): https://theodoregray.com/BrainRot/ https://theodoregray.com/BrainRot/
  - deleted 6y ago
    [deleted]
- chongli 6y ago
  But what's the value of this arithmetic muscle memory, in a world of ubiquitous computing? It’s the same as knowing the editor commands, of whatever text editor you’re using, so that you don’t have to look them up constantly while working. It’s the same as knowing the basic functions and methods of the libraries and frameworks you use so that you can type them quickly without going to look them up. Auto completion is a powerful tool but, in general, it’s not very helpful if you don’t know at least a prefix of the name of the function you’re looking for. Basic arithmetic skills are like math literacy. If you’re constantly having to look words up in the dictionary then you probably won’t get through Lord of the Rings.
mycall 6y ago
Thank you for saying what I was thinking. I had the same experience.
Jach 6y ago
Have you used Mathematica yet? I linked further downthread but I think you should consider this argument (ignoring the stuff about violent video games): https://theodoregray.com/BrainRot/ https://theodoregray.com/BrainRot/
- chongli 6y ago
  No, I haven't used Mathematica. It doesn't hold much use for me (yet) because it's not allowed on any of my exams. Being able to diagonalize a matrix by hand may not be a useful real world skill but the ability to do it on an exam demonstrates that you understand the process. On the other hand, typing the matrix into Mathematica and calling the diagonalize function demonstrates very little other than that you know how to command the magic box to give you the answer. Mathematics is a tower of abstractions. In the course of my education, I am learning how all of the layers fit together. Skipping all that and teaching people how to use Mathematica is not teaching mathematics, it's teaching dependence on a tool (and a proprietary one at that). It's like teaching people how to use Microsoft Word instead of how to write their own word processor. I'm very critical of the way technology has infiltrated the modern classroom. I think we're in danger of raising a generation of Eloi [1]. [1] https://en.wikipedia.org/wiki/Eloi https://en.wikipedia.org/wiki/Eloi
  - Jach 6y ago
    Surely you're not in mathematics just to pass exams and absorb/explore at whatever rate teachers and classes set? You should really give such tools a try. If proprietary ones aren't your cup of tea, play with Octave (and its Octave Forge package collection), Maxima, and R, and if you want throw in Julia, SymPy, Axiom, or Metamath too. See what they offer and what people have done with them. Or what if you programmed your own diagonalize function and used it thereafter (knowing over time you'd forget how to do it by hand)? Or would you insist on going through something like nand2tetris before writing in a high level language like, say, C? I have more questions but they're mostly rhetorical at this point. Re my previous link, are you so smart that you can learn all that has been made known so far as a neat tower floor by floor (despite it not being discovered/invented that way), and still have room for anything new? Are you sure you haven't skipped anything? Are you sure there's a singular tower? So you know how to diagonalize a matrix, either by hand or by using a magic box, do you know why you'd want to diagonalize a matrix? As a final external recommendation, check out chapter 9, "Forget It!", in Asimov's book On Numbers: http://www.arvindguptatoys.com/arvindgupta/asimov-on-numbers.pdf http://www.arvindguptatoys.com/arvindgupta/asimov-on-numbers... (e-page 75) If you haven't studied and passed an exam on compound addition (and subtraction, multiplication, division) how can you live with yourself?
0xabe 6y ago
My university math class experience was the same as yours. No calculators allowed, and we learned to not need them. But as has been said repeatedly, these calculators put Computer Science and BASIC terminals in the pockets of grade school and high school children and encourage learning in areas other than math.

drdaeman 6y ago

But what's the value of this arithmetic muscle memory, in a world of ubiquitous computing? As long as you don't treat this computing as magic that somehow solves your math problems (hah, true I was guilty of that when I was a school kid), but is fully aware about how it does it (the algorithm) and just let the machine do the boring bits.

jeffbee 6y ago
Are you joking? Number sense is hugely useful in daily life. What if I have a recipe for three servings but five dinner guests? If I just passed milepost 472 and I average 55 miles per hour, how long will it take me to reach Mexico? How many bottled liters of water can I fit in this box? How much is the 1.35% annual property tax on a million-dollar house, per month? You really want to whip out your laptop for all that?
- dTal 6y ago
  >How much is the 1.35% annual property tax on a million-dollar house, per month? You really want to whip out your laptop for all that? I'll bite. In what scenario would it be useful to do this calculation in my head?
  - jeffbee 6y ago
    You're trying to figure out if you can afford that house based on your monthly pay?
- Jach 6y ago
  > What if I have a recipe for three servings but five dinner guests? Doubling is a useful skill, sure. > If I just passed milepost 472 and I average 55 miles per hour, how long will it take me to reach Mexico? This would never come up, because my phone navigation will tell me at any point along the trip how long it will take, more accurately because it has my full speed data plus knowledge about traffic and other hazards ahead. > How many bottled liters of water can I fit in this box? Unless I have another box under consideration, then I probably intend to fit as many as possible, so I'll just fill. Complicating this problem can make a need to calculate (or count) more apparent, but further complications can also make a need to compute with a program more apparent too. > How much is the 1.35% annual property tax on a million-dollar house, per month? About 1e6/1e2/1e1, or $1000. If I want to be more accurate then I would use a computer -- 1. because I'm likely at my computer already when this comes up, 2. because if not I still likely have a phone. Both you and chongli ought to consider this argument (ignore the stuff about violent video games): https://theodoregray.com/BrainRot/ https://theodoregray.com/BrainRot/
- deleted 6y ago
  [deleted]
chongli 6y ago
But what's the value of this arithmetic muscle memory, in a world of ubiquitous computing? It’s the same as knowing the editor commands, of whatever text editor you’re using, so that you don’t have to look them up constantly while working. It’s the same as knowing the basic functions and methods of the libraries and frameworks you use so that you can type them quickly without going to look them up. Auto completion is a powerful tool but, in general, it’s not very helpful if you don’t know at least a prefix of the name of the function you’re looking for. Basic arithmetic skills are like math literacy. If you’re constantly having to look words up in the dictionary then you probably won’t get through Lord of the Rings.

mycall 6y ago

Thank you for saying what I was thinking. I had the same experience.

Jach 6y ago

Have you used Mathematica yet? I linked further downthread but I think you should consider this argument (ignoring the stuff about violent video games): https://theodoregray.com/BrainRot/ https://theodoregray.com/BrainRot/

chongli 6y ago
No, I haven't used Mathematica. It doesn't hold much use for me (yet) because it's not allowed on any of my exams. Being able to diagonalize a matrix by hand may not be a useful real world skill but the ability to do it on an exam demonstrates that you understand the process. On the other hand, typing the matrix into Mathematica and calling the diagonalize function demonstrates very little other than that you know how to command the magic box to give you the answer. Mathematics is a tower of abstractions. In the course of my education, I am learning how all of the layers fit together. Skipping all that and teaching people how to use Mathematica is not teaching mathematics, it's teaching dependence on a tool (and a proprietary one at that). It's like teaching people how to use Microsoft Word instead of how to write their own word processor. I'm very critical of the way technology has infiltrated the modern classroom. I think we're in danger of raising a generation of Eloi [1]. [1] https://en.wikipedia.org/wiki/Eloi https://en.wikipedia.org/wiki/Eloi
- Jach 6y ago
  Surely you're not in mathematics just to pass exams and absorb/explore at whatever rate teachers and classes set? You should really give such tools a try. If proprietary ones aren't your cup of tea, play with Octave (and its Octave Forge package collection), Maxima, and R, and if you want throw in Julia, SymPy, Axiom, or Metamath too. See what they offer and what people have done with them. Or what if you programmed your own diagonalize function and used it thereafter (knowing over time you'd forget how to do it by hand)? Or would you insist on going through something like nand2tetris before writing in a high level language like, say, C? I have more questions but they're mostly rhetorical at this point. Re my previous link, are you so smart that you can learn all that has been made known so far as a neat tower floor by floor (despite it not being discovered/invented that way), and still have room for anything new? Are you sure you haven't skipped anything? Are you sure there's a singular tower? So you know how to diagonalize a matrix, either by hand or by using a magic box, do you know why you'd want to diagonalize a matrix? As a final external recommendation, check out chapter 9, "Forget It!", in Asimov's book On Numbers: http://www.arvindguptatoys.com/arvindgupta/asimov-on-numbers.pdf http://www.arvindguptatoys.com/arvindgupta/asimov-on-numbers... (e-page 75) If you haven't studied and passed an exam on compound addition (and subtraction, multiplication, division) how can you live with yourself?

0xabe 6y ago

My university math class experience was the same as yours. No calculators allowed, and we learned to not need them. But as has been said repeatedly, these calculators put Computer Science and BASIC terminals in the pockets of grade school and high school children and encourage learning in areas other than math.