I often had a similar experience in grade school; teachers would present a concept for the first time as if they were reviewing it.
So far as I could tell, the teachers were saying the words that allowed them to refresh their memory of how a technique worked, rather than words that would allow someone with no prior experience of the technique to give it a try. E.g., frequent flyers here on LW can say things to each other like “don’t forget to test your ideas,” or “update your probability estimates” and the words have meaning, because they are handles that we have all built and designed to pull on a whole cluster of related memories and skills. But if you said that to someone with little or no exposure to the modern Enlightenment, they wouldn’t be able to follow along unless they could infer all of the intermediate steps from the skeletal verbal outline you’re providing.
I’ve done some occasional tutoring and so on, and my pupils are usually impressed, but all I’m doing is listening to people to find out what they already know, and then explaining the next few steps, one step at a time. It helps me to have an outline or a diagram showing all of the steps that I want the student to be comfortable with, and then we can look at it together and decide what the student will learn next.
Even when I am unable to acknowledge that a subject is hard, I can at least acknowledge that it is made up of many parts, each of which is necessary for mastery, and then make an effort to teach each of those parts.
Hm! Nobody has ever asked me to teach them how to teach. It’s very difficult to formalize the knowledge without a context, but here are some questions to ask yourself that may help you think of subtopics:
(1) What data or inputs do I typically need to solve a problem in this subject? E.g., if you want to send a robot to the moon, you need to know the mass of the robot, the location of the moon, the cost of fuel, the gravitational co-efficient, and so on. Each of these inputs can be a subtopic of “rocketry”—you might want to teach your students how to weigh a robot, how to trace the moon’s orbit, how to comparison shop for fuel, and how to look up a universal constant. Only after learning all four of these skills would a beginning rocketry student be in a position to independently (i.e, don’t hire somebody else to do it) and directly (i.e., don’t just judge based on past accomplishments / perceived difficulty) assess the likelihood that an arbitrary moon-launch project would succeed.
(2) What are the prerequisites for attacking a problem in this field? Any ordinary group of Americans will have a median student who is woefully deficient at one or more prerequisites. No matter how much it might “make sense” to assume that people in your class know what they are “supposed” to know, if your goal is to actually teach them the next step, then you can best achieve your goal by discarding this assumption, testing for competency at the prerequisites, and then making subtopics out of any prerequisites where people seem weak. E.g., if you are trying to teach people how to compost their domestic food waste, you might think that the most important information to convey relates to the size, shape, and composition of a compost pile—what to put in each layer, how big to make each layer, etc. But the task “add a layer of dead foliage that’s two feet thick and six feet around” is not a primitive task. It assumes that people know how to, e.g., operate a shovel, identify which foliage is dead, and measure distances with rough accuracy. Chances are, at least some of your audience can’t do these things well, or at all. Think about what concrete actions your students will need to take in order to follow each of your instructions, and then make each of those concrete actions a subtopic.
(3) Is this really a single problem, or is a related cluster of problems? There’s nothing wrong with teaching related problems in close (geographical or temporal) proximity to each other so that people will find it easier to cross-apply skills, but that’s different from trying to teach a group of related problems all at the same time. “Being rational,” e.g., turns out to subdivide into “seeing things as they really are” and “doing what actually achieves my goals.” Although these two skills have similar prerequisites and are deeply complementary, they’re still distinct: you can imagine being good at one but not the other. Try to identify the smallest subset of your topic that would still be a useful skill to have if you had it independently—if I’m training a soccer player, and the big game starts in two minutes, and I have an empty bench, it’d be at least somewhat handy if my protege had figured out how to boot the ball down the field, even if she was still hopeless at all other soccer-related tasks. That means “booting” is a sub-topic. Don’t teach “soccer” except in some meditative/spiritual sense; at the algorithmic level, teach booting, running, passing, teamwork, etc.
(4) Mix and match the questions to get narrower sub-topics. E.g., suppose booting is a subtopic of soccer. Well, what are the inputs that a student will use in deciding how to boot? At a minimum, you need to know where your own goal is and where the ball is so that you can move the ball away from your goal. So, I will probably give an instruction like “find the ball.” What are the prerequisites of “finding the ball?” It helps a whole lot if you are consciously following the ball as it moves from one person to the next; this skill is generally easy, but some absent-minded people don’t realize that they should be doing it, and some unusually absent-minded people might not know how to do it. It turns out that it helps to see which direction people are running in; they tend to run toward the ball. So we have soccer > booting > finding ball > visually following ball > visually following people. When you dig four levels down, it’s easy enough to get to twenty or eighty sub-sub-subtopics within “soccer,” and if you spend a few minutes teaching each of those, you’ll usually have exhausted your audience’s attention span.
Hmm. Nobody’s ever asked me to try to teach them that before, but here’s my advice:
Think about what dimensions or components success at the task will include. E.g., if you’re trying to play a song on the guitar, you might decide that a well-played song will have the correct chords played with the correct fingering and the correct rhythm.
Think about what steps are involved in each of the components of success, with an eye toward ordering those steps in terms of which steps are easiest to learn and which steps are logical prerequisites for the others. E.g., in order to learn how to play a rhythm, you first need an understanding of rhythmic concepts like beats and meters. Then, once you have a language that you can use to describe a rhythm, you need some concrete examples of rhythms, e.g., a half note followed by two quarter-notes. Then you need to translate that into the physical motions taken on the guitar, e.g., downstrokes and upstrokes with greater or lesser emphasis. Those are two different steps; first you teach the difference between a downstroke and an upstroke, and then you teach the difference between a stressed beat and an unstressed beat. You might change the order of those steps if you are working with a student who’s more comfortable with physical techniques than with language, e.g., demonstrate some rhythms first, and then only after that explain what they mean in words. In general, most values will have a vocabulary that lets you describe them, a series of examples that help you understand them, and a set of elements that constitute them; using each new word in the vocabulary and recognizing each type of example and recognizing each element and using each element is a separate step in learning the technique.
Leave some room at the end for integration, e.g., if you’ve learned rhythm and fingering and chords, you still need some time to practice using all three of those correctly at once. This may include learning how to make trade-offs among the various components, e.g., if you’ve got some very tricky fingering in one measure, maybe you simplify the chord to make that easier.
I often had a similar experience in grade school; teachers would present a concept for the first time as if they were reviewing it.
So far as I could tell, the teachers were saying the words that allowed them to refresh their memory of how a technique worked, rather than words that would allow someone with no prior experience of the technique to give it a try. E.g., frequent flyers here on LW can say things to each other like “don’t forget to test your ideas,” or “update your probability estimates” and the words have meaning, because they are handles that we have all built and designed to pull on a whole cluster of related memories and skills. But if you said that to someone with little or no exposure to the modern Enlightenment, they wouldn’t be able to follow along unless they could infer all of the intermediate steps from the skeletal verbal outline you’re providing.
I’ve done some occasional tutoring and so on, and my pupils are usually impressed, but all I’m doing is listening to people to find out what they already know, and then explaining the next few steps, one step at a time. It helps me to have an outline or a diagram showing all of the steps that I want the student to be comfortable with, and then we can look at it together and decide what the student will learn next.
Even when I am unable to acknowledge that a subject is hard, I can at least acknowledge that it is made up of many parts, each of which is necessary for mastery, and then make an effort to teach each of those parts.
Have you had any success teaching the ability break topics down into small steps? This is not something that seems trivial to me.
Hm! Nobody has ever asked me to teach them how to teach. It’s very difficult to formalize the knowledge without a context, but here are some questions to ask yourself that may help you think of subtopics:
(1) What data or inputs do I typically need to solve a problem in this subject? E.g., if you want to send a robot to the moon, you need to know the mass of the robot, the location of the moon, the cost of fuel, the gravitational co-efficient, and so on. Each of these inputs can be a subtopic of “rocketry”—you might want to teach your students how to weigh a robot, how to trace the moon’s orbit, how to comparison shop for fuel, and how to look up a universal constant. Only after learning all four of these skills would a beginning rocketry student be in a position to independently (i.e, don’t hire somebody else to do it) and directly (i.e., don’t just judge based on past accomplishments / perceived difficulty) assess the likelihood that an arbitrary moon-launch project would succeed.
(2) What are the prerequisites for attacking a problem in this field? Any ordinary group of Americans will have a median student who is woefully deficient at one or more prerequisites. No matter how much it might “make sense” to assume that people in your class know what they are “supposed” to know, if your goal is to actually teach them the next step, then you can best achieve your goal by discarding this assumption, testing for competency at the prerequisites, and then making subtopics out of any prerequisites where people seem weak. E.g., if you are trying to teach people how to compost their domestic food waste, you might think that the most important information to convey relates to the size, shape, and composition of a compost pile—what to put in each layer, how big to make each layer, etc. But the task “add a layer of dead foliage that’s two feet thick and six feet around” is not a primitive task. It assumes that people know how to, e.g., operate a shovel, identify which foliage is dead, and measure distances with rough accuracy. Chances are, at least some of your audience can’t do these things well, or at all. Think about what concrete actions your students will need to take in order to follow each of your instructions, and then make each of those concrete actions a subtopic.
(3) Is this really a single problem, or is a related cluster of problems? There’s nothing wrong with teaching related problems in close (geographical or temporal) proximity to each other so that people will find it easier to cross-apply skills, but that’s different from trying to teach a group of related problems all at the same time. “Being rational,” e.g., turns out to subdivide into “seeing things as they really are” and “doing what actually achieves my goals.” Although these two skills have similar prerequisites and are deeply complementary, they’re still distinct: you can imagine being good at one but not the other. Try to identify the smallest subset of your topic that would still be a useful skill to have if you had it independently—if I’m training a soccer player, and the big game starts in two minutes, and I have an empty bench, it’d be at least somewhat handy if my protege had figured out how to boot the ball down the field, even if she was still hopeless at all other soccer-related tasks. That means “booting” is a sub-topic. Don’t teach “soccer” except in some meditative/spiritual sense; at the algorithmic level, teach booting, running, passing, teamwork, etc.
(4) Mix and match the questions to get narrower sub-topics. E.g., suppose booting is a subtopic of soccer. Well, what are the inputs that a student will use in deciding how to boot? At a minimum, you need to know where your own goal is and where the ball is so that you can move the ball away from your goal. So, I will probably give an instruction like “find the ball.” What are the prerequisites of “finding the ball?” It helps a whole lot if you are consciously following the ball as it moves from one person to the next; this skill is generally easy, but some absent-minded people don’t realize that they should be doing it, and some unusually absent-minded people might not know how to do it. It turns out that it helps to see which direction people are running in; they tend to run toward the ball. So we have soccer > booting > finding ball > visually following ball > visually following people. When you dig four levels down, it’s easy enough to get to twenty or eighty sub-sub-subtopics within “soccer,” and if you spend a few minutes teaching each of those, you’ll usually have exhausted your audience’s attention span.
Hope some of this helps; feedback is welcome.
Thanks, that was surprisingly informative.
Hmm. Nobody’s ever asked me to try to teach them that before, but here’s my advice:
Think about what dimensions or components success at the task will include. E.g., if you’re trying to play a song on the guitar, you might decide that a well-played song will have the correct chords played with the correct fingering and the correct rhythm.
Think about what steps are involved in each of the components of success, with an eye toward ordering those steps in terms of which steps are easiest to learn and which steps are logical prerequisites for the others. E.g., in order to learn how to play a rhythm, you first need an understanding of rhythmic concepts like beats and meters. Then, once you have a language that you can use to describe a rhythm, you need some concrete examples of rhythms, e.g., a half note followed by two quarter-notes. Then you need to translate that into the physical motions taken on the guitar, e.g., downstrokes and upstrokes with greater or lesser emphasis. Those are two different steps; first you teach the difference between a downstroke and an upstroke, and then you teach the difference between a stressed beat and an unstressed beat. You might change the order of those steps if you are working with a student who’s more comfortable with physical techniques than with language, e.g., demonstrate some rhythms first, and then only after that explain what they mean in words. In general, most values will have a vocabulary that lets you describe them, a series of examples that help you understand them, and a set of elements that constitute them; using each new word in the vocabulary and recognizing each type of example and recognizing each element and using each element is a separate step in learning the technique.
Leave some room at the end for integration, e.g., if you’ve learned rhythm and fingering and chords, you still need some time to practice using all three of those correctly at once. This may include learning how to make trade-offs among the various components, e.g., if you’ve got some very tricky fingering in one measure, maybe you simplify the chord to make that easier.