I think the transition from Type 2 to Type 1 is very important for teaching.
When I was teaching, my students often complained why do they have to make exercises, if they already understand the topic. I felt that there are some good reasons, but I missed one of them. 1) Doing exercises is good for finding student’s “bugs” in understaning the theory, if you think about exercises as unit tests in programming. 2) Doing many exercises means repeating the topic, and repeating leads to remembering. But the reason not obvious to me was: 3) Repeating converts the skill from Type 2 to Type 1 skill.
If a complex skill is built from dozens of subskills, it is necessary to have the subskills in Type 1 mode before trying to master the big skill. Otherwise the subskills will require so much attention that it is impossible to see the big picture and do the big task correctly. (As a programmer I would use a metaphor that Type 1 thinking is like a one-line function call, while Type 2 skill is like writing the algorithm. If I cannot use function calls, my algorithm’s code will span across several screens, and will be a nightmare to edit or debug.) For example in mathematics it is difficult to explain solving quadratic equations to someone who still has problems with “why minus times minus equals plus” or “why minus in front of parenthesis changes inside all minuses to pluses and pluses to minuses”; because in the middle of explanation it will be necessary to explain these subtopics, and the the explanation is just too long and too complex to follow. Similarly it is difficult to explain algorithm design to someone who is still strugling with the “semicolon after each command”.
So in order to teach complex skills, it is necessary to explain the subskills in Type 2, and then do enough exercises to convert them to Type 1. Otherwise students will understand the subskills, but will be unable to move to the big skill. I think this is real danger of some proposed school reforms—less memorizing, more creative thinking; problem is, how could one creatively think about things they do not understand because they lack the basics.
I think the transition from Type 2 to Type 1 is very important for teaching.
When I was teaching, my students often complained why do they have to make exercises, if they already understand the topic. I felt that there are some good reasons, but I missed one of them. 1) Doing exercises is good for finding student’s “bugs” in understaning the theory, if you think about exercises as unit tests in programming. 2) Doing many exercises means repeating the topic, and repeating leads to remembering. But the reason not obvious to me was: 3) Repeating converts the skill from Type 2 to Type 1 skill.
If a complex skill is built from dozens of subskills, it is necessary to have the subskills in Type 1 mode before trying to master the big skill. Otherwise the subskills will require so much attention that it is impossible to see the big picture and do the big task correctly. (As a programmer I would use a metaphor that Type 1 thinking is like a one-line function call, while Type 2 skill is like writing the algorithm. If I cannot use function calls, my algorithm’s code will span across several screens, and will be a nightmare to edit or debug.) For example in mathematics it is difficult to explain solving quadratic equations to someone who still has problems with “why minus times minus equals plus” or “why minus in front of parenthesis changes inside all minuses to pluses and pluses to minuses”; because in the middle of explanation it will be necessary to explain these subtopics, and the the explanation is just too long and too complex to follow. Similarly it is difficult to explain algorithm design to someone who is still strugling with the “semicolon after each command”.
So in order to teach complex skills, it is necessary to explain the subskills in Type 2, and then do enough exercises to convert them to Type 1. Otherwise students will understand the subskills, but will be unable to move to the big skill. I think this is real danger of some proposed school reforms—less memorizing, more creative thinking; problem is, how could one creatively think about things they do not understand because they lack the basics.
And in my case, sometimes it’s easier to understand the theory after I’ve done the application a number of times.
Another argument for drill is that it can make theory easier to remember.
However, it’s also important to have some way of telling whether a person has done enough drill and is ready to move on.