It's really important in reading: if you were sounding out every word, could you read Moby Dick? Definitely not, and not just because it'd take forever. The larger chunks are that you can process with relatively little effort, the more mental energy that you have to make connections between them and do other higher-order thinking.
It's also important in both reading and writing music. Why do musicians practice scales so much? part of it is so that you can think "that run is in F minor: Ab up to G down to F," instead of "OMG: Ab Bb C D E F G F Eb Db C Bb Ab G F". When you do that, you can play it faster, think about your rhythm, tone, balance, blend, and intonation, and do all of the other things that make it music and not just notes. When you're composing, if you have to think about voice leading, scales and modes, rhythms, instrument ranges, counterpoint, etc. very consciously, then you have no mental energy left for the big picture - theme, development, form, etc.
This applies to just about every human endeavor.
In physics and math, students can get lost in the trees and miss the forest very easily. There are at least two prominent forms that this takes:
Completely missing the point of the problem:
Students sometimes do a ton of work, but using tools that don't apply to the problem. If they're not consciously looking at the situation, evaluating which models do and don't apply ("OK, there's a net external force from the rope pulling the box, so momentum isn't conserved and the rope is adding energy to the box-system, so it's not conserved, but it's not accelerating in the vertical dimension, so the forces are balanced and it's in constant v motion in that dimension, but the forces are unbalanced in the x-dimension, but the pull force isn't constant, so I can't use the constant acceleration kinematics that I know."), then sometimes they'll go completely off track.
This model determination is something that we have to foster in students. Some ways to start doing this:
- If you work example problems or the class does them together, with you writing, make this part of the process really explicit, and make it happen before you do anything else. Don't start writing your IF chart or conservation equation and then off-handedly say "well, there's no friction, so we'll use CopM, right?". Do it every time.
- Give students - early and often - chances to get it wrong. It's easy to fall into the trap of only giving practice and assessment problems using the concept du jour, but it hobbles them later. Ever have great unit assessments and terrible comprehensive exams? This'll do it. This opportunity is why I went back to a CVPM CAPM BFPM UFPM sequence (instead of CVPM BFPM CAPM UFPM) - it gives students (in the second unit) a chance to differentiate between models. I really like to introduce models in pairs and emphasize that: CVPM vs. CAPM, BFPM vs. UFPM, pTM vs. CopM, ETM vs. CoEM. Having choices to make between just two competing models is a good stepping-stone to the bigger choices when all of the model are in play, and if you don't emphasize it when the choice is easy, then they won't be able to do it suddenly later. This part can easily get lost in the planning. I do a good job of using 'older' concepts when they apply in the new context, but I need to give more practice and assessment of those skills just for their own sakes later in the term.
- Make articulating model choice a part of assessment - consistently.
Incomplete Mastery (conscious competence):
When students don't fully master a skill (or don't practice it periodically after mastering it), they have loose ends. Maybe they don't even have that - maybe that can do it accurately, but they just have to think it through and put a lot of effort into it to get it right. That doesn't only take time, but it takes mental effort, which is a finite resource. This goes back to some of the things in the posts about fluency here and here and here.
- This comes up a lot with skills that are used often, like symbolic algebra, trig (breaking vectors into components and the reverse), graph-making, unit conversions and prefixes, etc.
- It derails the more important thought processes that we're trying to get to - it's that mental energy allowance, in addition to the time issue, for assessments.
- It builds a poor foundation for later concepts. In math and physics, everything (should) build on what came before. Having middling understanding of something means that whatever application or extension comes next already starts out on shaky ground.
Both of these cut down on the level of complexity of situations that students can analyze: they need to be able to quick dissect the situation into models (maybe several different time intervals with differing models) and then have the fluency to apply those models accurately. That's a tall order, and they can't do it if their brains are exploding trying to remember some details of each skill or concept simultaneously. The ballistic pendulum's a great one to work on with this: you have at least three different sets of models applying to different time intervals over the course of the motion, and we all-too-often blow past that determination step. The same goes for the Atwood machine. Once you're through introducing mechanics, have students model it with forces/kinematics, momentum/impulse, and energy/work. It's a brain-buster for them trying to determine why the force exerted upward by the pulley on the string DQs conservation of momentum but not conservation of energy.
Here's a video game analogy: if physics is like Mega Man (or a million other games), then the tools (graphs, IF charts, LOL diagrams, FBDs, etc.) that we learn are like the weapons that you get when you conquer a level. Didn't beat Fire Man? Then you don't get to use Fire Storm. (OK, I had to look that up - high school was a long time ago. Also, feel free to update with more relevant video game references. :) This is another way to help kids chunk in their physics analysis - those kinematics toolkit equations might be handy, but they only apply in certain situations, and if determining which models apply isn't part of their process from the beginning, they'll be trying to use them later, when the acceleration's not constant.
One more thing: don't keep understanding about the learning process to yourself - talk about it with your kids, and often! Many students think that they know how they learn best, but they frequently fool themselves into thinking that something's solid when it really isn't. If you can convince, cajole, exemplify, and otherwise harp on meta-cognition consistently, then you can change how some students learn. Once they really can evaluate for themselves whether their mental models are solid, the subject material's beside the point.