3 ms·

The Teaching of Arithmetic I: The Story of an experiment (1935)

39 points by barry-cotter 5y ago

barry-cotter 5y ago
> In the fall of 1929 I made up my mind to try the experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite - my new Three R's. > I was so delighted with the success of the experiment so far that in the fall of 1930 we started six or seven other rooms along the same line. The formal arithmetic was dropped and emphasis was placed on English expression, on reasoning, and estimating of distances. > In other words these children, by avoiding the early drill on combinations, tables, and that sort of thing, had been able, in one year, to attain the level of accomplishment which the traditionally taught children had reached after three and one-half years of arithmetical drill
- andi999 5y ago
  It might just be that older children learn faster. And same results might happen in any subject. Here they started to teach a foreign language from grade 1. After 4 years kids usually reach the same level the would have had end of grade 5 when instruction started at beginning of grade 5.
WalterGR 5y ago
(1935) Actual title: The Teaching of Arithmetic I: The Story of an experiment
Raidion 5y ago
I did fairly well in maths, and I still resonated with this. It wasn't until I was deep into university that I realized that higher level maths were a game of sorts. I enjoyed it to a point, but found myself asking "what's the point?". Calculus was an exception because it really does start with "how do we find an area under a curve" and ties in closely with the physics concepts of finding velocity/acceleration/jerk. I think bringing interesting problems to students and enabling them to think about those problems naturally before introducing abstract concepts is always the way to go. Teaching inquisitiveness and building confidence that they can solve problems will serve them far better than more multiplication memorization.
andai 5y ago
I really like the writing style used here. Nobody writes like that anymore, although it was considered normal for centuries. What happened to make it go away, and when?
- lisper 5y ago
  Twitter. 2007. Wrtng hz nvr bn the sm snc.
  - andai 5y ago
    It's not a phase, mom!
kwhitefoot 5y ago
It's a pity that primary education isn't done this way now. As far as I can tell it is worse than ever with children being regularly tested but never taught how to think.
- lkbm 5y ago
  It's not quite the same, but there've been several efforts in the US to shift math education away from "memorize this algorithm for addition, this one for multiplication, etc." and instead get kids to understand our number system. New Math was ridiculed for it[0], and now Common Core[1]. "Why are you teaching kids these inefficient ways of multiplying instead of memorizing the standard algorithm?" Despite it being the focus of Tom Leher's song, my go-to test for "Do you understand our number system?" is "Can you work out a multiplication problem in base 8?" If you understand the concept of digits, you can solve multiplication in other bases, and likely have solid grasp on how our number system work. From there, you'll understand both the standard arithmetic algorithms and will be able to figure out your own shortcuts. If you lack this understanding, you're likely stuck just mindlessly using the algorithm you were taught. (One other thing I'd also like for us to add is Fermi problems. Physics students learn to estimate everything from the mass of the earth to the number of dogs in their city. Seems like something everyone would benefit from practicing and that kids would really enjoy.) [0] Tom Leher has a famous and delightful song about it: https://www.youtube.com/watch?v=UIKGV2cTgqA https://www.youtube.com/watch?v=UIKGV2cTgqA [1] https://www.youtube.com/watch?v=tBkQAxt1JXA https://www.youtube.com/watch?v=tBkQAxt1JXA (This is more a defense of Common Core, but in response to the common complaint.)
mtdewcmu 5y ago
What's the TL;DR of this? I finished part 1 and and I lost faith that this was heading toward any conclusion.
- rjmunro 5y ago
  Kids who are taught less formal maths end up doing better at questions that have extra information to throw you off. The distance from Boston to Portland by water is 120 miles. Three steamers leave Boston, simultaneously, for Portland. One makes the trip in 10 hours, one in 12, and one in 15. How long will it be before all 3 reach Portland? So 15 hours. People who learn more plain arithmetic maths assume that the 120 miles and the fact that all the figures divide into it exactly must be significant, and try to do calculations when none are needed.
  - mtdewcmu 5y ago
    Thanks for your reply. I thought there was a point being made about education at a more meta level, since the piece was very old and it begs the question of why a really old essay is on hackernews.
andrepd 5y ago
This echoes my feelings on the matter. It's infuriating how useless much of the curriculum is. Kids spend hundreds or thousands of hours of their lives sitting in chairs absolutely bored out of their minds having to cram useless stuff to spill on the test and then forget. Meanwhile there's no time and place to learn reasoning skills, critical reading, actual in-depth history (not just memorising names of kings and dates of battles), philosophy (again, being able to make a reasoned argument, not cramming stuff), economics, etc. > For some years I had noted that the effect of the early introduction of arithmetic had been to dull and almost chloroform the child's reasoning faculties. There's something very wrong when you suck out all the natural curiosity and will to learn from a group of children.

39 points by barry-cotter 5y ago

> In the fall of 1929 I made up my mind to try the experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite - my new Three R's. > I was so delighted with the success of the experiment so far that in the fall of 1930 we started six or seven other rooms along the same line. The formal arithmetic was dropped and emphasis was placed on English expression, on reasoning, and estimating of distances. > In other words these children, by avoiding the early drill on combinations, tables, and that sort of thing, had been able, in one year, to attain the level of accomplishment which the traditionally taught children had reached after three and one-half years of arithmetical drill

andi999 5y ago
It might just be that older children learn faster. And same results might happen in any subject. Here they started to teach a foreign language from grade 1. After 4 years kids usually reach the same level the would have had end of grade 5 when instruction started at beginning of grade 5.

WalterGR 5y ago

(1935) Actual title: The Teaching of Arithmetic I: The Story of an experiment

Raidion 5y ago

I did fairly well in maths, and I still resonated with this. It wasn't until I was deep into university that I realized that higher level maths were a game of sorts. I enjoyed it to a point, but found myself asking "what's the point?". Calculus was an exception because it really does start with "how do we find an area under a curve" and ties in closely with the physics concepts of finding velocity/acceleration/jerk. I think bringing interesting problems to students and enabling them to think about those problems naturally before introducing abstract concepts is always the way to go. Teaching inquisitiveness and building confidence that they can solve problems will serve them far better than more multiplication memorization.

andai 5y ago

I really like the writing style used here. Nobody writes like that anymore, although it was considered normal for centuries. What happened to make it go away, and when?

lisper 5y ago
Twitter. 2007. Wrtng hz nvr bn the sm snc.
- andai 5y ago
  It's not a phase, mom!

kwhitefoot 5y ago

It's a pity that primary education isn't done this way now. As far as I can tell it is worse than ever with children being regularly tested but never taught how to think.

lkbm 5y ago
It's not quite the same, but there've been several efforts in the US to shift math education away from "memorize this algorithm for addition, this one for multiplication, etc." and instead get kids to understand our number system. New Math was ridiculed for it[0], and now Common Core[1]. "Why are you teaching kids these inefficient ways of multiplying instead of memorizing the standard algorithm?" Despite it being the focus of Tom Leher's song, my go-to test for "Do you understand our number system?" is "Can you work out a multiplication problem in base 8?" If you understand the concept of digits, you can solve multiplication in other bases, and likely have solid grasp on how our number system work. From there, you'll understand both the standard arithmetic algorithms and will be able to figure out your own shortcuts. If you lack this understanding, you're likely stuck just mindlessly using the algorithm you were taught. (One other thing I'd also like for us to add is Fermi problems. Physics students learn to estimate everything from the mass of the earth to the number of dogs in their city. Seems like something everyone would benefit from practicing and that kids would really enjoy.) [0] Tom Leher has a famous and delightful song about it: https://www.youtube.com/watch?v=UIKGV2cTgqA https://www.youtube.com/watch?v=UIKGV2cTgqA [1] https://www.youtube.com/watch?v=tBkQAxt1JXA https://www.youtube.com/watch?v=tBkQAxt1JXA (This is more a defense of Common Core, but in response to the common complaint.)

mtdewcmu 5y ago

What's the TL;DR of this? I finished part 1 and and I lost faith that this was heading toward any conclusion.

rjmunro 5y ago
Kids who are taught less formal maths end up doing better at questions that have extra information to throw you off. The distance from Boston to Portland by water is 120 miles. Three steamers leave Boston, simultaneously, for Portland. One makes the trip in 10 hours, one in 12, and one in 15. How long will it be before all 3 reach Portland? So 15 hours. People who learn more plain arithmetic maths assume that the 120 miles and the fact that all the figures divide into it exactly must be significant, and try to do calculations when none are needed.
- mtdewcmu 5y ago
  Thanks for your reply. I thought there was a point being made about education at a more meta level, since the piece was very old and it begs the question of why a really old essay is on hackernews.

andrepd 5y ago

This echoes my feelings on the matter. It's infuriating how useless much of the curriculum is. Kids spend hundreds or thousands of hours of their lives sitting in chairs absolutely bored out of their minds having to cram useless stuff to spill on the test and then forget. Meanwhile there's no time and place to learn reasoning skills, critical reading, actual in-depth history (not just memorising names of kings and dates of battles), philosophy (again, being able to make a reasoned argument, not cramming stuff), economics, etc. > For some years I had noted that the effect of the early introduction of arithmetic had been to dull and almost chloroform the child's reasoning faculties. There's something very wrong when you suck out all the natural curiosity and will to learn from a group of children.