The main ideas of the article -- (1) you must teach the prerequisites first; (2) it could be useful to make an explicit “knowledge tree”; (3) you should test whether the knowledge was properly understood—are good. But the ideas (1) and (3) are what almost every teacher already knows and does. So you’re kinda reinventing the wheel here. It’s worth mentioning it explicitly to people who already don’t know. But those who teach, already do (which doesn’t mean they always follow it; people compartmentalize).
Even the idea (2) is known on an intuitive level; most teachers would probably think about it as a linear sequence, not a directed acyclic graph; or at best case a very simple graph consiting of long linear parts. But that’s because in a typical school, you teach linearly. To use the graph structure fully, you would have to allow each student to progress individually… but then you can’t have in the same classroom, listening to the teacher. So the full use of the graph requires individual learning, which could be achieved by a web application, as you say. (And the Khan Academy already does this.)
So, the ideas are good, but you are trying to sell them as something new, which they are certainly not.
Then you jump across many topics in a very simplified way. E.g. the part about motivation is… well, do you believe that progressing through a “tech tree” is the thing that makes a real difference between a motivated and unmotivated student? Because you could write such “tech tree” even for things which are taught in schools now. I believe it would be a nice thing to have, but it would make almost zero difference. You ignore other relevant facts, for example the large inferential distances and uncertainty. It’s difficult to see how knowing the “2 + 2 = 4” contributes to anyone’s dreams. (And even if it does, they may object that it’s enough to write that fact on a piece of paper, and they don’t have to memorize it. And the only problem with that is that at some moment the heap of such papers would just become too big to handle.) On the other hand, motivation can be created by completely irrational things, e.g. role-playing with small children that they are “pirates, lost in the magical Island of Numbers (and they must solve the problems to get back to their pirate ship)”.
If you propose a common project, I applaud the attitude, but you haven’t done your homework. Also it seems like you underestimate the size of the project. How long would it take you with, say, 10 volunteers? Twenty years? At least you could outsource the creation of the rationality curriculum to CFAR.
My advice:
Start with something smaller. (It is okay to keep in mind the big picture. But focus on one thing at a time.)
Research what already exists.
Write an article about what you found (focusing on only that topic) and ask for more info. In the discussion people will tell you about dozen other things you missed. Research them, and write another article.
If you completed all the parts, and the Singularity is not here yet, start the project. Now you have the necessary information.
Possible starting points: (A) Has someone already created the “tech trees”? Where can I find them? What are their strengths and weaknesses? How could I improve them? When I discuss my ideas of the improvement with a real teacher, what is their first reaction? (B) What web based teaching programs are out there? What are their similarities and differences? What are their successes and failures?
Both of these topics can be interesting on your own, and if you want to do a project, you certainly wouldn’t waste your time, because (A) means researching your product, and (B) means researching your competitors and learning from their failures. Which a successful project would have to do anyway.
EDIT: Another thing, be specific. Create a “tech tree” for a selected subject or two you know. (Feel free to steal ideas from Khan Academy.) Maybe you will discover some less obvious issues—for example that to create a proper tree of knowledge you would have to split the information into too many parts. For example are “solving quadratic equations (without complex solutions)” and “solving quadratic equations (with complex solutions)” two different nodes, or just one? Is “finding rational solutions of quadratic equations” worth creating a separate node? Or is it just a subset of “finding rational solutions of polynomial equations” node?
do you believe that progressing through a “tech tree” is the thing that makes a real difference between a motivated and unmotivated student?
Seeing a visual representation of that “tech tree” probably would. One thing lacking in school is a clear communication of the intended skills to master and progress towards that mastery.
for example that to create a proper tree of knowledge you would have to split the information into too many parts.
The tree would need to be able to be displayed at multiple levels of hierarchical composition.
(Feel free to steal ideas from Khan Academy.)
Anyone know what Khan Academy already has in this regard? Or other educational software?
Research what already exists.
That really should have been his starting point—study what’s already been done.
I am not doubting that seeing the visual representation of the “tech tree” would make some students somewhat more motivated. But I am thinking about many other things which make students unmotivated (such as: the student’s parents are preparing for a divorce right now, and the student cannot focus on learning at school), so I doubt how many % of the total “unmotivation” can be fixed specifically by showing the students the “tech tree”. 5%? I’m probably being too optimistic here.
Anyone know what Khan Academy already has in this regard?
This. I don’t know if they have other subjects than math processed in this way.
That Khan Academy tree is pretty demotivating for me, and it’s actually less math than I know (it looks like it only goes up through derivatives in a more traditionally structured series of classes). Now imagine that there are similar, more comprehensive trees for every major field of knowledge. To truly face the fact that you will only ever be able to learn a tiny fraction of any given field is pretty depressing. Of course, this is partially a reflection of the scale at which the tree is made and the way it’s presented, but motivation is not at all a sure thing.
To truly face the fact that you will only ever be able to learn a tiny fraction of any given field is pretty depressing.
First, if that reality depresses you, you need an attitude adjustment. I got a PhD in EE which taught me that neither I nor anyone else knows squat. That’s just the way reality is.
Second, the graph isn’t enough without identifying levels of competency against some standard, which could be population statistics, or grade level. That’s what’s needed for education—realistic goals, and a way to track progress toward completing them.
That should be sufficient for schooling. After that, experts could recommend material based on desired specialties.
In tough times, the advantage of habits of achievement and monitoring developed in good times should provide significant help, if not a guarantee of success, which I don’t think anyone promises or expects.
To use the graph structure fully, you would have to allow each student to progress individually… but then you can’t have in the same classroom, listening to the teacher
Well, yes and no. There are methods (usually called within-class groups) that allow students to progress at different paces while being in the same classroom. These methods usually depend a lot on small-group instruction and peer helping. So no, they won’t be simply listening to the teacher, at least not all at the same time.
But the ideas (1) and (3) are what almost every teacher already knows and does.
Maybe, but probably at level 1, maybe level 2, but surely not level 3.
So, the ideas are good, but you are trying to sell them as something new, which they are certainly not.
I don’t see anyone else emphasizing the importance of the dependency tree and of making sure that at a small enough level, students know the prerequisite information.
E.g. the part about motivation is… well, do you believe that progressing through a “tech tree” is the thing that makes a real difference between a motivated and unmotivated student?
At a small enough level, yes. But I don’t think we’ll really be able to understand this level well enough to use it. So I think that the idea is just something to keep in mind when thinking about how to motivate students.
Also it seems like you underestimate the size of the project.
Not at all! If I thought that this could be done with 10 volunteers I’d be trying to do it right now. I think that this would need hundreds, probably thousands of people. Consequently, I think that the best thing I could be doing is making enough money to (help) pay for all of this, so I’m starting a startup: http://www.collegeinsideview.com/.
Maybe, but probably at level 1, maybe level 2, but surely not level 3.
When I was a student, teaching other students privately math, I automatically started explaining any topic by testing whether they understand the prerequisites. -- I started one step before the new topic, and if they failed the test, I backtracked another step before the failed test. I didn’t have a complete map in my mind, but at each moment I simply thought: “what are the immediate prerequisities for this?”.
I doubt I was the first person to think about this. Does the fact that I don’t remember anyone explaining this to me explicitly (before I came to university) make it somewhere between the levels 2 and 3?
I don’t see anyone else emphasizing the importance of the dependency tree
You know what all teachers do in summer, before the school year starts? They prepare the sequence in which they will explain the topics during the year. (At least if they teach for the first time, because later they usually reuse the stuff from the previous year.)
As I said, they probably don’t think about this as a “directed acyclic graph”, but rather as a “linear sequence where some parts can be reordered” (because most of them are not computer science people). The idea that the topics have some prerequisites, and you need to explain them in the proper order, is out there at least for decades.
The main ideas of the article -- (1) you must teach the prerequisites first; (2) it could be useful to make an explicit “knowledge tree”; (3) you should test whether the knowledge was properly understood—are good. But the ideas (1) and (3) are what almost every teacher already knows and does.
Let’s just say American education isn’t as good as Slovak.
moved to Discussion (writing quality insufficient for Main)
Meaning the ideas, or my ability to communicate them? Tell culture—hit me hard.
Uhm, both.
The main ideas of the article -- (1) you must teach the prerequisites first; (2) it could be useful to make an explicit “knowledge tree”; (3) you should test whether the knowledge was properly understood—are good. But the ideas (1) and (3) are what almost every teacher already knows and does. So you’re kinda reinventing the wheel here. It’s worth mentioning it explicitly to people who already don’t know. But those who teach, already do (which doesn’t mean they always follow it; people compartmentalize).
Even the idea (2) is known on an intuitive level; most teachers would probably think about it as a linear sequence, not a directed acyclic graph; or at best case a very simple graph consiting of long linear parts. But that’s because in a typical school, you teach linearly. To use the graph structure fully, you would have to allow each student to progress individually… but then you can’t have in the same classroom, listening to the teacher. So the full use of the graph requires individual learning, which could be achieved by a web application, as you say. (And the Khan Academy already does this.)
So, the ideas are good, but you are trying to sell them as something new, which they are certainly not.
Then you jump across many topics in a very simplified way. E.g. the part about motivation is… well, do you believe that progressing through a “tech tree” is the thing that makes a real difference between a motivated and unmotivated student? Because you could write such “tech tree” even for things which are taught in schools now. I believe it would be a nice thing to have, but it would make almost zero difference. You ignore other relevant facts, for example the large inferential distances and uncertainty. It’s difficult to see how knowing the “2 + 2 = 4” contributes to anyone’s dreams. (And even if it does, they may object that it’s enough to write that fact on a piece of paper, and they don’t have to memorize it. And the only problem with that is that at some moment the heap of such papers would just become too big to handle.) On the other hand, motivation can be created by completely irrational things, e.g. role-playing with small children that they are “pirates, lost in the magical Island of Numbers (and they must solve the problems to get back to their pirate ship)”.
If you propose a common project, I applaud the attitude, but you haven’t done your homework. Also it seems like you underestimate the size of the project. How long would it take you with, say, 10 volunteers? Twenty years? At least you could outsource the creation of the rationality curriculum to CFAR.
My advice:
Start with something smaller. (It is okay to keep in mind the big picture. But focus on one thing at a time.)
Research what already exists.
Write an article about what you found (focusing on only that topic) and ask for more info. In the discussion people will tell you about dozen other things you missed. Research them, and write another article.
If you completed all the parts, and the Singularity is not here yet, start the project. Now you have the necessary information.
Possible starting points: (A) Has someone already created the “tech trees”? Where can I find them? What are their strengths and weaknesses? How could I improve them? When I discuss my ideas of the improvement with a real teacher, what is their first reaction? (B) What web based teaching programs are out there? What are their similarities and differences? What are their successes and failures?
Both of these topics can be interesting on your own, and if you want to do a project, you certainly wouldn’t waste your time, because (A) means researching your product, and (B) means researching your competitors and learning from their failures. Which a successful project would have to do anyway.
EDIT: Another thing, be specific. Create a “tech tree” for a selected subject or two you know. (Feel free to steal ideas from Khan Academy.) Maybe you will discover some less obvious issues—for example that to create a proper tree of knowledge you would have to split the information into too many parts. For example are “solving quadratic equations (without complex solutions)” and “solving quadratic equations (with complex solutions)” two different nodes, or just one? Is “finding rational solutions of quadratic equations” worth creating a separate node? Or is it just a subset of “finding rational solutions of polynomial equations” node?
Seeing a visual representation of that “tech tree” probably would. One thing lacking in school is a clear communication of the intended skills to master and progress towards that mastery.
The tree would need to be able to be displayed at multiple levels of hierarchical composition.
Anyone know what Khan Academy already has in this regard? Or other educational software?
That really should have been his starting point—study what’s already been done.
I am not doubting that seeing the visual representation of the “tech tree” would make some students somewhat more motivated. But I am thinking about many other things which make students unmotivated (such as: the student’s parents are preparing for a divorce right now, and the student cannot focus on learning at school), so I doubt how many % of the total “unmotivation” can be fixed specifically by showing the students the “tech tree”. 5%? I’m probably being too optimistic here.
This. I don’t know if they have other subjects than math processed in this way.
That Khan Academy tree is pretty demotivating for me, and it’s actually less math than I know (it looks like it only goes up through derivatives in a more traditionally structured series of classes). Now imagine that there are similar, more comprehensive trees for every major field of knowledge. To truly face the fact that you will only ever be able to learn a tiny fraction of any given field is pretty depressing. Of course, this is partially a reflection of the scale at which the tree is made and the way it’s presented, but motivation is not at all a sure thing.
First, if that reality depresses you, you need an attitude adjustment. I got a PhD in EE which taught me that neither I nor anyone else knows squat. That’s just the way reality is.
Second, the graph isn’t enough without identifying levels of competency against some standard, which could be population statistics, or grade level. That’s what’s needed for education—realistic goals, and a way to track progress toward completing them.
That should be sufficient for schooling. After that, experts could recommend material based on desired specialties.
In tough times, the advantage of habits of achievement and monitoring developed in good times should provide significant help, if not a guarantee of success, which I don’t think anyone promises or expects.
Well, yes and no. There are methods (usually called within-class groups) that allow students to progress at different paces while being in the same classroom. These methods usually depend a lot on small-group instruction and peer helping. So no, they won’t be simply listening to the teacher, at least not all at the same time.
Maybe, but probably at level 1, maybe level 2, but surely not level 3.
I don’t see anyone else emphasizing the importance of the dependency tree and of making sure that at a small enough level, students know the prerequisite information.
At a small enough level, yes. But I don’t think we’ll really be able to understand this level well enough to use it. So I think that the idea is just something to keep in mind when thinking about how to motivate students.
Not at all! If I thought that this could be done with 10 volunteers I’d be trying to do it right now. I think that this would need hundreds, probably thousands of people. Consequently, I think that the best thing I could be doing is making enough money to (help) pay for all of this, so I’m starting a startup: http://www.collegeinsideview.com/.
When I was a student, teaching other students privately math, I automatically started explaining any topic by testing whether they understand the prerequisites. -- I started one step before the new topic, and if they failed the test, I backtracked another step before the failed test. I didn’t have a complete map in my mind, but at each moment I simply thought: “what are the immediate prerequisities for this?”.
I doubt I was the first person to think about this. Does the fact that I don’t remember anyone explaining this to me explicitly (before I came to university) make it somewhere between the levels 2 and 3?
You know what all teachers do in summer, before the school year starts? They prepare the sequence in which they will explain the topics during the year. (At least if they teach for the first time, because later they usually reuse the stuff from the previous year.)
As I said, they probably don’t think about this as a “directed acyclic graph”, but rather as a “linear sequence where some parts can be reordered” (because most of them are not computer science people). The idea that the topics have some prerequisites, and you need to explain them in the proper order, is out there at least for decades.
Let’s just say American education isn’t as good as Slovak.
I agree with Eliezer that this shouldn’t be in Main, but I think your “ability to communicate” is fine.