My thoughts on learning are derived mostly from my experience with mathematics, which I have been doing for quite a while, and salsa dancing, which I have been doing since January 2005. Learning tasks in salsa is relatively easy since I try to learn only a few moves at a time, and I don't perform. Learning new mathematical tasks is difficult because math is hard!

Some words about Task Learning: I believe that task learning follows the following steps, which I will break down along with the example of learning to drive a car.

1. Unconscious incompetence. Here you don't even know what you're supposed to do. You're completely lost. Imagine getting behind the wheel for the first time if you had never even seen a car before.

2. Conscious incompetence. Now your conscious mind is working to understand the task, yet you're still incompetent. This is the point where you are spending all of your mental energy keeping track of the pedals and the steering wheel, yet you still can't get it.

3. Conscious competence. Your conscious mind can be relied upon to perform the task with reasonable competence. You would be able to drive the car, yet you must devote all your attention to this task. Your driving will often not be smooth.

4. Unconscious competence. You can now drive and talk on your cell phone and adjust the radio with little or no trouble. You don't need to think about when to slow down and when to start your turns.

Let's examine these steps in more detail from the student's perspective.

1. Unconscious incompetence is a necessary first step. You may pass by this step very quickly (maybe you paid attention to how your parents drove and imagined yourself driving for quite a while). However, you must start here. Many students become disillusioned at this point and want to give up. They feel that the real learning involves the actions performed in steps 2 and 3 (the way material is presented in the classroom has something to do with this), and think that they are on the wrong path when in this stage. Many give up.

2. During conscious incompetence the analytical mind gets to show it's stuff.

3. Habits, good or bad, are largely formed during conscious competence. Once this stage is reached you have the ability to move around and reformat the procedure you use to accomplish the task. Sometimes this is hard to do since if you feel that you have (finally) got it down, you can be reluctant to change. Analytical types can also often get stuck here because they wish to tinker with their task performing until the unobtainable goal of perfection is reached. Remember: Sometimes you need to learn a new task in order to master an old one.

4. Reaching this stage requires rote memorization of elements in (subtasks of) the task. This is why algebra homework drilled you with so many similar problems. This is why it is helpful to step through a turn pattern many times. Reaching this stage can become addictive.

Now from the teacher's perspective.

1. Unconscious incompetence is the time to give encouragement to students. Your expectations should be low here and you should promote an atmosphere of, “it's ok to mess up”, just get your hands dirty.

2. As teachers are often masters of the art, they will mostly be in step 4. So it is easy for them to push students toward this level too fast. If one sees a student struggling while using their conscious mind, it is tempting to tell them, “you're thinking too hard, just feel it.” But are they thinking too hard (as in being stuck in conscious competence), or are they spending legitimate time in steps 2 and 3?

3. Re-examination is one key to passing through steps 2 and 3. Letting students teach each other is a good tool here.

4. It is important for a teacher to promote good habit formation during steps 2 and 3 (especially 3). Habits should be re-enforced through repetition.

5. A teacher should tell students that perfection is impossible, and encourage them to move on to unconscious competence when they are ready.

One further note: Some tasks are not important enough to merit the time necessary to reach unconscious competence. I often do this in mathematics: I'll follow some proof and see some technique, but decide that my time would be better spent moving on. I still retain an overview of the method, and hopefully can remember to recall (and then completely learn it) when necessary. This is why courses without homework can still be useful.

A level of learning that occurs on a deeper level than task learning is abstraction and generalization. This...