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My problem with the "new math" is the lack of volume. Developing a sense for the numbers is best done by working more with numbers; in the "old math" kids had t

My problem with the "new math" is the lack of volume. Developing a sense for the numbers is best done by working more with numbers; in the "old math" kids had to do thousands of additions in the first and second grade, and developed ten times the sense of numbers compared to kids today. Theory is theory, but practice is practice. Just get over the addition and multiplication, please. That's not where the true math is. Don't spend so much time on finding the true meaning of addition by carry, you won't have time to teach kids logarithms and integrals later.

empath75 9y ago
Learning by rote doesn’t teach you anything.
- yorwba 9y ago
  Spending lots of time on the treadmill won't make you a great soccer player, but still trains a basic skill useful for the game. Similarly, doing lots of arithmetic by hand isn't enough to solve all kinds of real-world problems, but it does help develop an intuition for numbers, which then helps with the problem-solving part.
  - zaphar 9y ago
    Rote arithmetic may help you develop an intuition for numbers. It's hit or miss though and there are more effective and efficient methods than just doing a large volume of arithmetic. I believe the current trend in Math education is intended to take advantage of the more effective and efficient methods. Your treadmill is a good example actually. Much of the exercise world has realized that just jogging for a long period of time while effective is also not the most efficient way to exercise. Instead mixing periods of hi intensity workout with periods of lower pace workout can allow you to get more value with less time from you routine.
- credit_guy 9y ago
  Are you sure that it doesn't teach you anything? Somehow the students of "old math" were able to put a man on the Moon.
  - boomboomsubban 9y ago
    So you're advocating the return of the slide rule? As that's what was used for most calculating, the "old math" method being too cumbersome for such large problems.
    - ghaff 9y ago
      As someone who actually learned to use a slide rule before pocket calculators became available, that's probably not the best example. Slide rules were good for getting "[EDITED: precise not accurate] enough" results in various situations where they could do so more quickly than solving by hand. You still needed to understand orders of magnitude, precision, and generally having a feel for numbers to use one. Note also that a lot of calculations on the Apollo program were actually done in part by hand by human "computers." There was even a whole movie about it a couple years ago: https://en.wikipedia.org/wiki/Hidden_Figures https://en.wikipedia.org/wiki/Hidden_Figures
      - boomboomsubban 9y ago
        Those human computers used slide rules, as even with them the problems were so ridiculously complex they took months. Their were many different slide rules with varying degrees of precision https://www.nasa.gov/audience/forstudents/k-4/home/calculate_feature_k4.html https://www.nasa.gov/audience/forstudents/k-4/home/calculate...
  - watwut 9y ago
    Only a fraction of them. And those of their generation who were that good talked about math as something to be understood rather then memorized.
- ghaff 9y ago
  Really? In the case of math, it provides you with the ability to add/multiply/etc. Now, maybe you don't think that being able to do fast and reasonably accurate mental or paper-based arithmetic is important in a world in which calculators are ubiquitous but rote learning does help give you that ability even if you don't understand deeper mathematical concepts. Asimov's short story "A Feeling of Power" is a fun read by the way. Rote learning also has a role in things like language vocabulary but in that case there are certainly differing approaches to developing language skills. My understanding is that there's a lot of memorization in things like medicine as well.
- dahart 9y ago
  All humans learn their first language by rote. Much more of higher ed is rote learning than you think. If it wasn't rote, we would never have to see examples or practice something, but the majority of what we actually spend our time doing in school is seeing examples and practicing. If there was no rote learning in math, doing long division would be an order of magnitude more painful, and you would always derive your formulas from scratch. I believe critical thinking is as important as anyone does, but there's no critical thinking without foundational skills and knowledge. Education simply cannot be 100% critical thinking, even if we wanted it do. "Rote learning is widely used in the mastery of foundational knowledge." https://en.m.wikipedia.org/wiki/Rote_learning https://en.m.wikipedia.org/wiki/Rote_learning
dahart 9y ago
> the "old math" kids had to do thousands of additions in the first and second grade, and developed ten times the sense of numbers compared to kids today. This must be variation from school to school or state to state. My kids are stuck with more homework than I had when I was a kid. I actually wish they had less homework, they're not getting enough exploratory time during their school days. They also have a better intuitive sense of numbers than I did. > Just get over the addition and multiplication, please... you won't have time to teach kids logarithms and integrals later. Generally speaking, I think calculus is being taught earlier now than when I was in grade school. My kids (grades 5&7) are being introduced to some interesting arithmetic concepts that I didn't get when I was a kid that I think will complement higher math. As a parent, I'm not seeing any issue with lack of volume or of progression toward higher math concepts, FWIW...
dragonwriter 9y ago
> in the "old math" kids had to do thousands of additions in the first and second grade, and developed ten times the sense of numbers compared to kids today. I don't think that's generally true; the kids that were particularly successful in math certainly developed more sense of numbers than mod kids today, but AFAICT very many developed almost no sense of numbers.

empath75 9y ago

Learning by rote doesn’t teach you anything.

yorwba 9y ago
Spending lots of time on the treadmill won't make you a great soccer player, but still trains a basic skill useful for the game. Similarly, doing lots of arithmetic by hand isn't enough to solve all kinds of real-world problems, but it does help develop an intuition for numbers, which then helps with the problem-solving part.
- zaphar 9y ago
  Rote arithmetic may help you develop an intuition for numbers. It's hit or miss though and there are more effective and efficient methods than just doing a large volume of arithmetic. I believe the current trend in Math education is intended to take advantage of the more effective and efficient methods. Your treadmill is a good example actually. Much of the exercise world has realized that just jogging for a long period of time while effective is also not the most efficient way to exercise. Instead mixing periods of hi intensity workout with periods of lower pace workout can allow you to get more value with less time from you routine.
credit_guy 9y ago
Are you sure that it doesn't teach you anything? Somehow the students of "old math" were able to put a man on the Moon.
- boomboomsubban 9y ago
  So you're advocating the return of the slide rule? As that's what was used for most calculating, the "old math" method being too cumbersome for such large problems.
  - ghaff 9y ago
    As someone who actually learned to use a slide rule before pocket calculators became available, that's probably not the best example. Slide rules were good for getting "[EDITED: precise not accurate] enough" results in various situations where they could do so more quickly than solving by hand. You still needed to understand orders of magnitude, precision, and generally having a feel for numbers to use one. Note also that a lot of calculations on the Apollo program were actually done in part by hand by human "computers." There was even a whole movie about it a couple years ago: https://en.wikipedia.org/wiki/Hidden_Figures https://en.wikipedia.org/wiki/Hidden_Figures
    - boomboomsubban 9y ago
      Those human computers used slide rules, as even with them the problems were so ridiculously complex they took months. Their were many different slide rules with varying degrees of precision https://www.nasa.gov/audience/forstudents/k-4/home/calculate_feature_k4.html https://www.nasa.gov/audience/forstudents/k-4/home/calculate...
- watwut 9y ago
  Only a fraction of them. And those of their generation who were that good talked about math as something to be understood rather then memorized.
ghaff 9y ago
Really? In the case of math, it provides you with the ability to add/multiply/etc. Now, maybe you don't think that being able to do fast and reasonably accurate mental or paper-based arithmetic is important in a world in which calculators are ubiquitous but rote learning does help give you that ability even if you don't understand deeper mathematical concepts. Asimov's short story "A Feeling of Power" is a fun read by the way. Rote learning also has a role in things like language vocabulary but in that case there are certainly differing approaches to developing language skills. My understanding is that there's a lot of memorization in things like medicine as well.
dahart 9y ago
All humans learn their first language by rote. Much more of higher ed is rote learning than you think. If it wasn't rote, we would never have to see examples or practice something, but the majority of what we actually spend our time doing in school is seeing examples and practicing. If there was no rote learning in math, doing long division would be an order of magnitude more painful, and you would always derive your formulas from scratch. I believe critical thinking is as important as anyone does, but there's no critical thinking without foundational skills and knowledge. Education simply cannot be 100% critical thinking, even if we wanted it do. "Rote learning is widely used in the mastery of foundational knowledge." https://en.m.wikipedia.org/wiki/Rote_learning https://en.m.wikipedia.org/wiki/Rote_learning

dahart 9y ago

> the "old math" kids had to do thousands of additions in the first and second grade, and developed ten times the sense of numbers compared to kids today. This must be variation from school to school or state to state. My kids are stuck with more homework than I had when I was a kid. I actually wish they had less homework, they're not getting enough exploratory time during their school days. They also have a better intuitive sense of numbers than I did. > Just get over the addition and multiplication, please... you won't have time to teach kids logarithms and integrals later. Generally speaking, I think calculus is being taught earlier now than when I was in grade school. My kids (grades 5&7) are being introduced to some interesting arithmetic concepts that I didn't get when I was a kid that I think will complement higher math. As a parent, I'm not seeing any issue with lack of volume or of progression toward higher math concepts, FWIW...

dragonwriter 9y ago

> in the "old math" kids had to do thousands of additions in the first and second grade, and developed ten times the sense of numbers compared to kids today. I don't think that's generally true; the kids that were particularly successful in math certainly developed more sense of numbers than mod kids today, but AFAICT very many developed almost no sense of numbers.