4 ms·

>IMO, it's the focus on the micro steps that's the problem. No, the micro-steps are the solution, not the problem. Those who "get" math intuitively break probl

>IMO, it's the focus on the micro steps that's the problem. No, the micro-steps are the solution, not the problem. Those who "get" math intuitively break problems down into smaller steps, often unconsciously. For those that can't intuitively do this (most students), they need to be taught explicitly the micro-steps. The micro-steps build the foundation for the higher level steps and the problem solving. Learning the micro-steps well is like learning an abstraction in a program. Once you learn the abstraction to the point that your understanding of it is unconscious, then your thought processes are lifted to a higher level. This is true understanding of math.

happy4crazy 16y ago
Learning the micro-steps well is like learning an abstraction in a program. Once you learn the abstraction to the point that your understanding of it is unconscious, then your thought processes are lifted to a higher level. This is true understanding of math. Exactly. The argument is not to "do things in micro-steps", it's to do things in appropriately-sized steps. As your understanding of math improves, you can (and should!) take bigger and bigger steps. The point is that, for presumably a variety of reasons, a really large percentage of students don't drop down a level in abstraction when they get stuck--they get depressed and give up. I see a large part of education's role being the inculcation of good habits, and this is just a sucky, sucky habit.
simpleTruth 16y ago
There are plenty of useful things to memorize that let you flat out skip steps. Some of this stuff might feel like party tricks, but don't assume people are using the same steps subconsciously.
- hackinthebochs 16y ago
  I don't mean to say that people use the micro-steps all the time. What I mean is that, on initially learning something, those that "get" it subconsciously break it down into micro-steps that are just small enough for them. This builds the bridge from what they know to what they're learning. Once the abstraction or technique makes sense, then you apply it as a whole on further usage. I think one of the main things that separates the quick learners from the slow learners is how much breaking steps into micro-steps can be done unconsciously. The data lends weight to this. Teaching a concept in micro-steps doesn't help the smartest people learn it better, but it brings the slow learners up to speed. The difference is how small the steps have to be for the students' unconscious to make the connections and thus reach "understanding".

happy4crazy 16y ago

Learning the micro-steps well is like learning an abstraction in a program. Once you learn the abstraction to the point that your understanding of it is unconscious, then your thought processes are lifted to a higher level. This is true understanding of math. Exactly. The argument is not to "do things in micro-steps", it's to do things in appropriately-sized steps. As your understanding of math improves, you can (and should!) take bigger and bigger steps. The point is that, for presumably a variety of reasons, a really large percentage of students don't drop down a level in abstraction when they get stuck--they get depressed and give up. I see a large part of education's role being the inculcation of good habits, and this is just a sucky, sucky habit.

simpleTruth 16y ago

There are plenty of useful things to memorize that let you flat out skip steps. Some of this stuff might feel like party tricks, but don't assume people are using the same steps subconsciously.

hackinthebochs 16y ago
I don't mean to say that people use the micro-steps all the time. What I mean is that, on initially learning something, those that "get" it subconsciously break it down into micro-steps that are just small enough for them. This builds the bridge from what they know to what they're learning. Once the abstraction or technique makes sense, then you apply it as a whole on further usage. I think one of the main things that separates the quick learners from the slow learners is how much breaking steps into micro-steps can be done unconsciously. The data lends weight to this. Teaching a concept in micro-steps doesn't help the smartest people learn it better, but it brings the slow learners up to speed. The difference is how small the steps have to be for the students' unconscious to make the connections and thus reach "understanding".