I read the first 1⁄3 of the post and then skimmed the rest, because I think that you yourself are “glossing over important bottlenecks”.
As I see it, for you the main problem with education is that students don’t learn effectively in schools and you try to treat this problem. However, you should be asking: how did this problem appear? What could be done to solve the real problems? And those are in fact more difficult questions and require much deeper changes than creating a dependency tree and applying it to the students.
Creating and following a dependency tree with pupils implies that you consider 5-, 6- or 7-year-old children who enter the school system tabula rasas, which is not true. What is more, during my pedagogy studies one of the lecturers mentioned that 7-year-old children may be 2 years ahead or behind in development in any area (gross motor, fine motor, memorization, social skills, knowledge, you name it) and these differences are normal. This in turn means that the primary school teacher has to manage and teach not a uniform group of tabula rasa children, but a highly differentiated collective of individuals ranging in mental age from 5 to 9 years.
If you are not starting with a uniform group, you cannot follow a dependency tree, because each child is in a different place of this tree. First you would have to sort the children, so that each group is at some level of your tree. But how would you do that? As I said, sorting by age is one of the worst ideas, it has only one advantage: it’s cheap. You don’t even have to see the kid, you just find one number about her and decide about her life. So, maybe do some tests? (now let’s just not talk about how much it would cost and how much time it would take). Sure, but now you can clearly see that some of those kids can read but not count and some can count but not read, so you should either put them in separate classes or order them to go to different classes for different subjects (the former unrealistic and the latter being very frowned upon in elementary schooling; my country even tries to forbid separation of lessons with bells for 7-9-year-olds).
Suppose that you in fact solved that problem and have a group of children on a very similar level in the area that you are going to teach them. Soon you notice one more phenomenon. The same differences that made some of your pupils start education a year earlier and some a year later cause the kids to learn at a different pace. You could be working with some of the pupils on harder problems, advance your tree faster than the average set by bureaucrats, but other kids need more explanation, more time practicing before they advance. If you comply with the needs of the faster kids, the slower ones will completely stop learning, because they will stop understanding what is going on. If you accomodate the slower kids, the faster ones will get bored and unmotivated to learn anything. How do you solve this problem? My lecturers said that teachers should teach the lesson at such a pace that 3⁄4 of the class can understand it, effectively stiffling half of the class. Maybe you would divide the class further?
But then, how many times can you divide the class without forcing half of the adult population to work as teachers?
This comment is already longish, but let me point to another problem. When learning anything, a dependency tree is an oversimplification.
Active vocabulary: Vocabulary that students actually use in speaking and writing.
Passive vocabulary: Vocabulary that students have heard and can understand, but do not necessarily use when they speak or write.
When learning a language, students commonly have much larger passive vocabularies than active. Some textbooks are designed in a way that is supposed to minimize this difference, but at the same time they offer an extremely slow pace of learning. I observe that this concept of active and passive knowledge applies to any field of study. It’s quite intuitive: you first have to learn about something before you can use your knowledge. Following a dependency tree means that you cannot expand your passive vocabulary in a given field of study before you master active vocabulary of the lower level, and this in turn slows down you learning. You can learn about multiplication and division when you have not yet mastered calculating addition and subtraction; you only need to understand the concepts of addition and subtraction, have them in your passive vocabulary.
These are just two sample problem with education, but as a newbie, I only wanted to point that you’re missing your own point, not solve the whole mess of institutionalized education.
I read the first 1⁄3 of the post and then skimmed the rest, because I think that you yourself are “glossing over important bottlenecks”.
As I see it, for you the main problem with education is that students don’t learn effectively in schools and you try to treat this problem. However, you should be asking: how did this problem appear? What could be done to solve the real problems? And those are in fact more difficult questions and require much deeper changes than creating a dependency tree and applying it to the students.
Creating and following a dependency tree with pupils implies that you consider 5-, 6- or 7-year-old children who enter the school system tabula rasas, which is not true. What is more, during my pedagogy studies one of the lecturers mentioned that 7-year-old children may be 2 years ahead or behind in development in any area (gross motor, fine motor, memorization, social skills, knowledge, you name it) and these differences are normal. This in turn means that the primary school teacher has to manage and teach not a uniform group of tabula rasa children, but a highly differentiated collective of individuals ranging in mental age from 5 to 9 years.
If you are not starting with a uniform group, you cannot follow a dependency tree, because each child is in a different place of this tree. First you would have to sort the children, so that each group is at some level of your tree. But how would you do that? As I said, sorting by age is one of the worst ideas, it has only one advantage: it’s cheap. You don’t even have to see the kid, you just find one number about her and decide about her life. So, maybe do some tests? (now let’s just not talk about how much it would cost and how much time it would take). Sure, but now you can clearly see that some of those kids can read but not count and some can count but not read, so you should either put them in separate classes or order them to go to different classes for different subjects (the former unrealistic and the latter being very frowned upon in elementary schooling; my country even tries to forbid separation of lessons with bells for 7-9-year-olds).
Suppose that you in fact solved that problem and have a group of children on a very similar level in the area that you are going to teach them. Soon you notice one more phenomenon. The same differences that made some of your pupils start education a year earlier and some a year later cause the kids to learn at a different pace. You could be working with some of the pupils on harder problems, advance your tree faster than the average set by bureaucrats, but other kids need more explanation, more time practicing before they advance. If you comply with the needs of the faster kids, the slower ones will completely stop learning, because they will stop understanding what is going on. If you accomodate the slower kids, the faster ones will get bored and unmotivated to learn anything. How do you solve this problem? My lecturers said that teachers should teach the lesson at such a pace that 3⁄4 of the class can understand it, effectively stiffling half of the class. Maybe you would divide the class further?
But then, how many times can you divide the class without forcing half of the adult population to work as teachers?
This comment is already longish, but let me point to another problem. When learning anything, a dependency tree is an oversimplification.
From Glossary of language teaching terms and ideas
Active vocabulary: Vocabulary that students actually use in speaking and writing.
Passive vocabulary: Vocabulary that students have heard and can understand, but do not necessarily use when they speak or write.
When learning a language, students commonly have much larger passive vocabularies than active. Some textbooks are designed in a way that is supposed to minimize this difference, but at the same time they offer an extremely slow pace of learning. I observe that this concept of active and passive knowledge applies to any field of study. It’s quite intuitive: you first have to learn about something before you can use your knowledge. Following a dependency tree means that you cannot expand your passive vocabulary in a given field of study before you master active vocabulary of the lower level, and this in turn slows down you learning. You can learn about multiplication and division when you have not yet mastered calculating addition and subtraction; you only need to understand the concepts of addition and subtraction, have them in your passive vocabulary.
These are just two sample problem with education, but as a newbie, I only wanted to point that you’re missing your own point, not solve the whole mess of institutionalized education.