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Seems like a pretty poor way to really understand math anyway. If you memorize some formula you may learn how to do a specific problem faster but if you teach k

Seems like a pretty poor way to really understand math anyway. If you memorize some formula you may learn how to do a specific problem faster but if you teach kids to understand how the formula was built from first principals, not only can they solve the problem, but they understand how to build the solution from scratch rather than pulling a premade solution from the memory bank. Memorizing solutions isn't useful anymore. We have google to list out formulas. A deep understanding of problem solving is far more important and something you cant trivially search.

varjag 5y ago
Right now there are students who have trouble opening up algebraic expressions or forget to cancel negatives in multiplication while doing exercises on advanced concepts. All for lack of practice.
- bigbillheck 5y ago
  Those kinds of kids were common 10, 20, 50, 100, and more years ago.
  - varjag 5y ago
    Now they are ubiquitous. Downplaying it to 'dumb ones' is not helpful when they can solve polynomials without much trouble but are getting burned on concepts that should have been drilled down properly in middle school.
    - bigbillheck 5y ago
      > Now they are ubiquitous They were saying that back in the day as well: https://en.wikipedia.org/wiki/Why_Johnny_Can%27t_Add https://en.wikipedia.org/wiki/Why_Johnny_Can%27t_Add
JackFr 5y ago
The deep understanding comes after knowing the facts. At a low level, you can point out all the patterns that are in multiplication tables, but they won’t be remembered until the student has internalized the facts. At a higher level, teaching epsilon-delta proofs isn’t a good way to learn calculus. Memorizing the building blocks and the chain rule is.
TeMPOraL 5y ago
You can't understand a formula without repeatedly applying it to great many problems, playing with it until you get a feel for how it behaves. Without that, you'll only be "understanding" your own imaginary version of a formula, a simulation in your mind with no grounding in reality. Same with understanding anything else in life - you don't really understand anything until you get to the point you can, in your head, predict a specific outcome, test it, and be proven correct, repeatedly. (At some point you may learn to gain robust understanding purely from simulating things in your head, deriving insight from lower-level principles. But this itself is a skill, a hard one, which few people master. It's not something a random kid, or adult, can do.)

varjag 5y ago

Right now there are students who have trouble opening up algebraic expressions or forget to cancel negatives in multiplication while doing exercises on advanced concepts. All for lack of practice.

bigbillheck 5y ago
Those kinds of kids were common 10, 20, 50, 100, and more years ago.
- varjag 5y ago
  Now they are ubiquitous. Downplaying it to 'dumb ones' is not helpful when they can solve polynomials without much trouble but are getting burned on concepts that should have been drilled down properly in middle school.
  - bigbillheck 5y ago
    > Now they are ubiquitous They were saying that back in the day as well: https://en.wikipedia.org/wiki/Why_Johnny_Can%27t_Add https://en.wikipedia.org/wiki/Why_Johnny_Can%27t_Add

JackFr 5y ago

The deep understanding comes after knowing the facts. At a low level, you can point out all the patterns that are in multiplication tables, but they won’t be remembered until the student has internalized the facts. At a higher level, teaching epsilon-delta proofs isn’t a good way to learn calculus. Memorizing the building blocks and the chain rule is.

TeMPOraL 5y ago

You can't understand a formula without repeatedly applying it to great many problems, playing with it until you get a feel for how it behaves. Without that, you'll only be "understanding" your own imaginary version of a formula, a simulation in your mind with no grounding in reality. Same with understanding anything else in life - you don't really understand anything until you get to the point you can, in your head, predict a specific outcome, test it, and be proven correct, repeatedly. (At some point you may learn to gain robust understanding purely from simulating things in your head, deriving insight from lower-level principles. But this itself is a skill, a hard one, which few people master. It's not something a random kid, or adult, can do.)