4 ms·

Change is hard. When computers were first introduced to schools there were similar arguments and complaints. When calculators were brought in instead of the sli

Change is hard. When computers were first introduced to schools there were similar arguments and complaints. When calculators were brought in instead of the slide rule we heard it would be the end of actually "knowing" math. Teachers who are great find ways to use technology and tools available to inspire their students and create engaging lessons. This teacher just sounds resistant to change.

jacquesm 11y ago
But calculators actually did negatively impact basic arithmetic skills. The number of people that can't do 9x14 without reaching for a calculator is scary.
- delecti 11y ago
  The number of people who need to do 9x14 when they have no access to a calculator is pretty much zero.
  - pc86 11y ago
    To be fair though, that's the math version of "I don't need to know JavaScript at all because I will always have jQuery." Technically accurate but lazy.
    - lmm 11y ago
      Javascript or 9x14 is not the kind of knowledge that's valuable for its own sake. http://unreasonable.org/Feynman_and_the_map_of_the_cat http://unreasonable.org/Feynman_and_the_map_of_the_cat
  - untog 11y ago
    That doesn't mean it isn't a valuable skill. Mental arithmetic can also improve other brain skills.
    - gregweng 11y ago
      No? As an Asian student I have seen countless people try to push their children to exercise arithmetic skills because they believe that does good to their brains. However, it only misleads children to hate "math" and sometimes even their lives based on this the most important subject again and again. Moreover, children would wholly waste their exercised brain on the ruined confidence because some of them just cannot "recite" the patterns well among questions in tests, because you're required to answer too much questions during too short time, which means if you cannot recite the solution patterns from textbook and calculate the answers right at first time, you barely have no chance to try it again. Even those who did excellently in those high-school tests will face another crash at the beginning of university, because the "real math" no matter cares your arithmetic skills, but your abstract thinking and the feeling to grab and deduct rules from axiom. After all, except those real geniuses can conquer these two very different requirements and continuously get payback from that, I don't see any benefits from focusing on arithmetic with so high-strength training.
  - thearn4 11y ago
    That's too application focused. The primary value of arithmetic is that it forces you to exercise parts of your mind in a way which would otherwise be difficult. The same can be said of general mathematics, and literary analysis, etc.
    - marcosdumay 11y ago
      Hum, basic arithmetics is mechanical repetition. There may be some benefit to the brain in doing it, but I'm doubting it until I get evidence. The main benefit is that knowing arithmetics well makes higher mathematics easier to learn. That's because one won't get distracted doing calculations. That's still true on the calculator era, just a bit less so, thus I do think it's important to learn arithmetics... It just the "it improves your brain" that I find highly suspect.
- pc86 11y ago
  To this point is there an easier way to do this than mentally do (9x10)+(9x4), which is what I've done since I was in elementary school (29 now)?
  - davnicwil 11y ago
    Hmm that's interesting - I'd tend to round one of the numbers, whichever is closest to a '5' or '10', to make an 'easier' multiplication, then add / subtract the extra value lost / gained by rounding. Example 9 x 14 = (<10> * 14) - ([1] * 14) = 140 - 14 = 126 key: <> easier rounded number [] deal with rounding 'error'
    - pc86 11y ago
      I've done that before too, but for whatever reason my mind just defaults to adding two numbers rather than subtracting. Probably either habit or I just find it easier.
    - pavel_lishin 11y ago
      Weird, I did it the other way - 9x10 + 9x4 = 90 + 36 = 126
  - nkrisc 11y ago
    I do the same. However, recognizing you can do that is part of learning arithmetic and problem solving in general. I learned that method at an early age and it taught me that most big, scary problems in general are really just a bunch of small problems that can be identified and solved more easily.
  - jacquesm 11y ago
    10 times 14 - 14.
    - neffy 11y ago
      (9* 7) * 2 :)
  - eterm 11y ago
- Retra 11y ago
  The number of people who can do it quickly in their head, maybe. I don't know a single adult who would look at that problem and say they don't know how to solve it. Math is a perishable skill. You get slow at it if you don't use it.
  - matwood 11y ago
    It is just a matter of remembering the tricks. (9x10) + (9x4)
- dagw 11y ago
  But calculators actually did negatively impact basic arithmetic skills. Sure, but the interesting question is if they negatively impacted math skills.
  - a-saleh 11y ago
    Depends what kind of math skills are you looking for. I remember my classmate, 1st year at university, that passed one of his classes just because his calculator was capable of precise enough numeric integration. Next semester he was required to construct proofs as well and he flunked the class.
- w8rbt 11y ago
  I do 9 x 14 in my head by breaking it down. I assume others do this too. Anyone should be able to break a problem down (pre or post tech generation) and do the small parts, then put them together to answer the bigger question. In general, that's the essence of learning. If we stop teaching that, then we're all in trouble ;) 9 x 10 = 90 9 x 4 = 36 90 + 36 = 126
  - gambiting 11y ago
    Ha, very interesting, I do something very similar, although for multiplication by 9 I would multiply by 10(since it requires no mental effort, you just add a zero at the end) then subtract one. So: 14 x 10 = 140 140 - 14 = 126
- theinternetman 11y ago
  > negatively impact basic arithmetic skills Yep and that skill was rendered completely obsolete. Always remember being told "you won't always have a calculator with you!!" because I couldn't be bothered showing my working on my maths work. How did that work out... oh everyone now always has calculators with them. Glad I didn't waste my time memorising multiplication tables.
mhurron 11y ago
Change also doesn't just happen because you dumped a computer in a room. I personally haven't seen a computer used effectively in a classroom, in a large part because the teachers don't know how to integrate them into their lessons. They were given devices and then given no instruction on how to use them.
- jerf 11y ago
  Education is just barely starting to come out of what I call the "... but on a computer!" [1] era, which is when you try to do exactly the same thing you did before, but now it's on a computer (or a tablet in this case). There's basically no advantage to taking existing classroom practices, but sticking them on a computer. You'll have to rewrite the entire education process to figure out how to harness computers. Let me give a concrete example. I am now a fantastic speller, of a language that is one of the harder languages to spell. Am I fantastic because I'm just that awesome? No! Am I fantastic because I have spent years studying lists of words and taking spelling tests? Hell no! I'm fantastic now because every major text input I use now has the red-squiggly line, and the instant I misspell a word and hit space, bam, red line. Backspace & correct. Right-click and select if I really, really can't work it out. (But with backspace & correct actually being way faster, I prefer that.) With instant feedback comes a high rate of learning. I can tell this isn't "cheating", because when I do function in an environment where I don't have this functionality, I retain my spelling skill, the golden standard of whether a skill exists in the tools or the brain. In fact I write many of my blog posts in emacs with no spelling support on, and while I still scan over my posts with a spell checker before posting them, I routinely experience writing several thousand words without a single misspelling, because I have harnessed solid technology to train my brain. I also spell well with handwriting. This is unbelievably fantastic technology for teaching spelling so efficiently and so effectively that it hardly even need be explicitly taught; sit students down in front of this technology and have them simply write and let the red squiggly handle the spelling training. (You'll still need vocabulary training, but, again, let the red squiggly handle the spelling of the vocabulary while the vocabulary training focuses on meanings.) By contrast, doing spelling tests "but on a computer" is a terrible way of doing business! First of all, if the students have to "turn in" the test before they get feedback, you've already missed the sub-second feedback rate that would have been so much better anyhow, but second of all, the fact that you're having a spelling test at all is a huge waste of their time. That's the sort of second-order effect we need to be harnessing with computers in the classroom, and we are only at the very, very beginning of that road. My first grader is just starting spelling tests. He's not quite computer savvy enough to start writing on a computer yet, but you can believe I'll be setting him up with a red squiggly as soon as is practicable. I still believe computers are going to rewrite education from top-to-bottom, but I find it is proving to be one of the most entrenched, hidebound, nearsighted, and even perhaps terrified of real change elements of society we can possibly imagine. We're so scare of what bad things might happen if we don't stuff a conventional education into our children's heads (moreso than ever, thanks to ever-more test-based education) that we're terrified of experimenting with anything new, and the only acceptable change to the "conventional" education is to precommit even more time to it, making it that much harder to work any experimentation into the system. There are major religions that treat their holy texts as more flexible than the way our culture treats the official line of How Children Are Taught. [1]: http://www.jerf.org/iri/post/2916 http://www.jerf.org/iri/post/2916
alistairSH 11y ago
Two counter-points... 1. Computers in classrooms have rarely, if ever, been deployed to entire classrooms in the way that tablets can be. Typically, you'll see one or two PCs in a class, plus a computer lab. PCs don't distract in the same way iPads can. 2. Calculators do make people worse at math. I saw this first-hand with my son. As he went through school, they used calculators for everything. Students began to rely on the calculators for simple arithmetic and took the answers provided as gospel, not realizing that garbage in = garbage out. He, along with many of his peers, never really developed the fluency in math to say to themselves "hmm, that answer looks suspect. Let me try again."
- jacquesm 11y ago
  But you as a parent could easily fix that. Schools don't have a monopoly on education.
  - alistairSH 11y ago
    Of course, and we did. But, I continue to believe that allowing calculators on ALL mathematics work from a young age does the student a disservice. Calculators certainly have their place, but elementary school arithmetic is not that place.
    - jacquesm 11y ago
      Agreed. So I taught my eldest arithmetic at home and discouraged the schools from giving him more calculators until the sums involved more than two digits and other operators than the basic four. After the third calculator they got the message. Interesting aside: the teacher couldn't do anything beyond single digit arithmetic without reference to a calculator either. Pretty sad affair, and I really wonder how someone who does not understand the basics gets to be a teacher.
- Vraxx 11y ago
  Counter anecdote to your calculator anecdote. I grew up using calculators all through school and excelled in knowing math. Using a calculator did not inhibit my ability to question the result of the calculator whatsoever. I don't think calculators are necessarily to blame here.
kps 11y ago
> When calculators were brought in instead of the slide rule > we heard it would be the end of actually "knowing" math. Plato argued in Phaedrus that literacy would be the end of anyone actually "knowing" anything. Why learn if you can just google^H^H^H^H^H^H read it? Same shit, different millennium.

jacquesm 11y ago

But calculators actually did negatively impact basic arithmetic skills. The number of people that can't do 9x14 without reaching for a calculator is scary.

delecti 11y ago
The number of people who need to do 9x14 when they have no access to a calculator is pretty much zero.
- pc86 11y ago
  To be fair though, that's the math version of "I don't need to know JavaScript at all because I will always have jQuery." Technically accurate but lazy.
  - lmm 11y ago
    Javascript or 9x14 is not the kind of knowledge that's valuable for its own sake. http://unreasonable.org/Feynman_and_the_map_of_the_cat http://unreasonable.org/Feynman_and_the_map_of_the_cat
- untog 11y ago
  That doesn't mean it isn't a valuable skill. Mental arithmetic can also improve other brain skills.
  - gregweng 11y ago
    No? As an Asian student I have seen countless people try to push their children to exercise arithmetic skills because they believe that does good to their brains. However, it only misleads children to hate "math" and sometimes even their lives based on this the most important subject again and again. Moreover, children would wholly waste their exercised brain on the ruined confidence because some of them just cannot "recite" the patterns well among questions in tests, because you're required to answer too much questions during too short time, which means if you cannot recite the solution patterns from textbook and calculate the answers right at first time, you barely have no chance to try it again. Even those who did excellently in those high-school tests will face another crash at the beginning of university, because the "real math" no matter cares your arithmetic skills, but your abstract thinking and the feeling to grab and deduct rules from axiom. After all, except those real geniuses can conquer these two very different requirements and continuously get payback from that, I don't see any benefits from focusing on arithmetic with so high-strength training.
- thearn4 11y ago
  That's too application focused. The primary value of arithmetic is that it forces you to exercise parts of your mind in a way which would otherwise be difficult. The same can be said of general mathematics, and literary analysis, etc.
  - marcosdumay 11y ago
    Hum, basic arithmetics is mechanical repetition. There may be some benefit to the brain in doing it, but I'm doubting it until I get evidence. The main benefit is that knowing arithmetics well makes higher mathematics easier to learn. That's because one won't get distracted doing calculations. That's still true on the calculator era, just a bit less so, thus I do think it's important to learn arithmetics... It just the "it improves your brain" that I find highly suspect.
pc86 11y ago
To this point is there an easier way to do this than mentally do (9x10)+(9x4), which is what I've done since I was in elementary school (29 now)?
- davnicwil 11y ago
  Hmm that's interesting - I'd tend to round one of the numbers, whichever is closest to a '5' or '10', to make an 'easier' multiplication, then add / subtract the extra value lost / gained by rounding. Example 9 x 14 = (<10> * 14) - ([1] * 14) = 140 - 14 = 126 key: <> easier rounded number [] deal with rounding 'error'
  - pc86 11y ago
    I've done that before too, but for whatever reason my mind just defaults to adding two numbers rather than subtracting. Probably either habit or I just find it easier.
  - pavel_lishin 11y ago
    Weird, I did it the other way - 9x10 + 9x4 = 90 + 36 = 126
- nkrisc 11y ago
  I do the same. However, recognizing you can do that is part of learning arithmetic and problem solving in general. I learned that method at an early age and it taught me that most big, scary problems in general are really just a bunch of small problems that can be identified and solved more easily.
- jacquesm 11y ago
  10 times 14 - 14.
  - neffy 11y ago
    (9* 7) * 2 :)
- eterm 11y ago
Retra 11y ago
The number of people who can do it quickly in their head, maybe. I don't know a single adult who would look at that problem and say they don't know how to solve it. Math is a perishable skill. You get slow at it if you don't use it.
- matwood 11y ago
  It is just a matter of remembering the tricks. (9x10) + (9x4)
dagw 11y ago
But calculators actually did negatively impact basic arithmetic skills. Sure, but the interesting question is if they negatively impacted math skills.
- a-saleh 11y ago
  Depends what kind of math skills are you looking for. I remember my classmate, 1st year at university, that passed one of his classes just because his calculator was capable of precise enough numeric integration. Next semester he was required to construct proofs as well and he flunked the class.
w8rbt 11y ago
I do 9 x 14 in my head by breaking it down. I assume others do this too. Anyone should be able to break a problem down (pre or post tech generation) and do the small parts, then put them together to answer the bigger question. In general, that's the essence of learning. If we stop teaching that, then we're all in trouble ;) 9 x 10 = 90 9 x 4 = 36 90 + 36 = 126
- gambiting 11y ago
  Ha, very interesting, I do something very similar, although for multiplication by 9 I would multiply by 10(since it requires no mental effort, you just add a zero at the end) then subtract one. So: 14 x 10 = 140 140 - 14 = 126
theinternetman 11y ago
> negatively impact basic arithmetic skills Yep and that skill was rendered completely obsolete. Always remember being told "you won't always have a calculator with you!!" because I couldn't be bothered showing my working on my maths work. How did that work out... oh everyone now always has calculators with them. Glad I didn't waste my time memorising multiplication tables.

mhurron 11y ago

Change also doesn't just happen because you dumped a computer in a room. I personally haven't seen a computer used effectively in a classroom, in a large part because the teachers don't know how to integrate them into their lessons. They were given devices and then given no instruction on how to use them.

jerf 11y ago
Education is just barely starting to come out of what I call the "... but on a computer!" [1] era, which is when you try to do exactly the same thing you did before, but now it's on a computer (or a tablet in this case). There's basically no advantage to taking existing classroom practices, but sticking them on a computer. You'll have to rewrite the entire education process to figure out how to harness computers. Let me give a concrete example. I am now a fantastic speller, of a language that is one of the harder languages to spell. Am I fantastic because I'm just that awesome? No! Am I fantastic because I have spent years studying lists of words and taking spelling tests? Hell no! I'm fantastic now because every major text input I use now has the red-squiggly line, and the instant I misspell a word and hit space, bam, red line. Backspace & correct. Right-click and select if I really, really can't work it out. (But with backspace & correct actually being way faster, I prefer that.) With instant feedback comes a high rate of learning. I can tell this isn't "cheating", because when I do function in an environment where I don't have this functionality, I retain my spelling skill, the golden standard of whether a skill exists in the tools or the brain. In fact I write many of my blog posts in emacs with no spelling support on, and while I still scan over my posts with a spell checker before posting them, I routinely experience writing several thousand words without a single misspelling, because I have harnessed solid technology to train my brain. I also spell well with handwriting. This is unbelievably fantastic technology for teaching spelling so efficiently and so effectively that it hardly even need be explicitly taught; sit students down in front of this technology and have them simply write and let the red squiggly handle the spelling training. (You'll still need vocabulary training, but, again, let the red squiggly handle the spelling of the vocabulary while the vocabulary training focuses on meanings.) By contrast, doing spelling tests "but on a computer" is a terrible way of doing business! First of all, if the students have to "turn in" the test before they get feedback, you've already missed the sub-second feedback rate that would have been so much better anyhow, but second of all, the fact that you're having a spelling test at all is a huge waste of their time. That's the sort of second-order effect we need to be harnessing with computers in the classroom, and we are only at the very, very beginning of that road. My first grader is just starting spelling tests. He's not quite computer savvy enough to start writing on a computer yet, but you can believe I'll be setting him up with a red squiggly as soon as is practicable. I still believe computers are going to rewrite education from top-to-bottom, but I find it is proving to be one of the most entrenched, hidebound, nearsighted, and even perhaps terrified of real change elements of society we can possibly imagine. We're so scare of what bad things might happen if we don't stuff a conventional education into our children's heads (moreso than ever, thanks to ever-more test-based education) that we're terrified of experimenting with anything new, and the only acceptable change to the "conventional" education is to precommit even more time to it, making it that much harder to work any experimentation into the system. There are major religions that treat their holy texts as more flexible than the way our culture treats the official line of How Children Are Taught. [1]: http://www.jerf.org/iri/post/2916 http://www.jerf.org/iri/post/2916

alistairSH 11y ago

Two counter-points... 1. Computers in classrooms have rarely, if ever, been deployed to entire classrooms in the way that tablets can be. Typically, you'll see one or two PCs in a class, plus a computer lab. PCs don't distract in the same way iPads can. 2. Calculators do make people worse at math. I saw this first-hand with my son. As he went through school, they used calculators for everything. Students began to rely on the calculators for simple arithmetic and took the answers provided as gospel, not realizing that garbage in = garbage out. He, along with many of his peers, never really developed the fluency in math to say to themselves "hmm, that answer looks suspect. Let me try again."

jacquesm 11y ago
But you as a parent could easily fix that. Schools don't have a monopoly on education.
- alistairSH 11y ago
  Of course, and we did. But, I continue to believe that allowing calculators on ALL mathematics work from a young age does the student a disservice. Calculators certainly have their place, but elementary school arithmetic is not that place.
  - jacquesm 11y ago
    Agreed. So I taught my eldest arithmetic at home and discouraged the schools from giving him more calculators until the sums involved more than two digits and other operators than the basic four. After the third calculator they got the message. Interesting aside: the teacher couldn't do anything beyond single digit arithmetic without reference to a calculator either. Pretty sad affair, and I really wonder how someone who does not understand the basics gets to be a teacher.
Vraxx 11y ago
Counter anecdote to your calculator anecdote. I grew up using calculators all through school and excelled in knowing math. Using a calculator did not inhibit my ability to question the result of the calculator whatsoever. I don't think calculators are necessarily to blame here.

kps 11y ago

> When calculators were brought in instead of the slide rule > we heard it would be the end of actually "knowing" math. Plato argued in Phaedrus that literacy would be the end of anyone actually "knowing" anything. Why learn if you can just google^H^H^H^H^H^H read it? Same shit, different millennium.