This got me thinking, I really wish school had looked more like unlocking a tech tree in a game like Civilization than completing ordered stages in a game like Super Mario Brothers (with occasional warps/shortcuts for the clever).
Maybe with AI tutors it can. Study a subject. Take a test. If you pass, (and passing here means demonstrating mastering, not getting some score that’s “good enough” to meet some standard for much you have to know to be allowed to move on to the next grade with all your peers even though you clearly don’t have full mastery of the topics) you move on, and if you don’t, you keep studying until you can master the test. No need to learn subjects in lockstep with same-sage peers, because everyone can be studying what they need to learn with their own, independent AI teacher.
I tried to make the “tech tree” for elementary-school math, and it turned out to be much more complicated than I expected.
Consider this: as a first approximation, we could make nodes for “addition”, “subtraction”, “multiplication”, and “division”. But if you look closer, there is actually not one node for “addition”, but there is a separate node for “integer addition up to 10, e.g. 3+5″ (which children can calculate using their fingers), “integer addition across 10, e.g. 8+7” (which depends on basic subtraction, because to calculate 8+7 you use 10-8=2 and 7-2=5 as intermediate steps), and then there is a general skill of “adding two integers of arbitrary length”. Should we also make separate nodes for “addition is commutative”, “addition is associative”, and “adding a negative number means subtracting its absolute value”? I think we should, because ultimately we need to teach these concepts to the kids, but… you get the idea about how large the resulting tree will be.
Large trees are inconvenient to work with. A tree with 10 nodes is a nice picture. A tree with 1000 nodes is an intricate network of lines. You could arrange it into categories (e.g. put all the “addition” nodes next to each other, or maybe make an “addition and subtractions” cluster), that would allow you to easier locate a node, but you would have many lines between the categories. This could be handled by a computer, for example the nodes you have already mastered (and took an exam for) would be checked, and if you click on a new node, all nodes between your current knowledge and the selected node would be highlighted, to give you an idea about how much would you need to learn in order to get there.
This is not an argument against constructing such tree. I definitely would like to see it! I am just saying that it is a lot of work, and difficult to use without a computer, so I understand why teachers are not doing this, and instead handle the complexity by creating groups of nodes, and arranging those groups in linear order.
This got me thinking, I really wish school had looked more like unlocking a tech tree in a game like Civilization than completing ordered stages in a game like Super Mario Brothers (with occasional warps/shortcuts for the clever).
Maybe with AI tutors it can. Study a subject. Take a test. If you pass, (and passing here means demonstrating mastering, not getting some score that’s “good enough” to meet some standard for much you have to know to be allowed to move on to the next grade with all your peers even though you clearly don’t have full mastery of the topics) you move on, and if you don’t, you keep studying until you can master the test. No need to learn subjects in lockstep with same-sage peers, because everyone can be studying what they need to learn with their own, independent AI teacher.
I tried to make the “tech tree” for elementary-school math, and it turned out to be much more complicated than I expected.
Consider this: as a first approximation, we could make nodes for “addition”, “subtraction”, “multiplication”, and “division”. But if you look closer, there is actually not one node for “addition”, but there is a separate node for “integer addition up to 10, e.g. 3+5″ (which children can calculate using their fingers), “integer addition across 10, e.g. 8+7” (which depends on basic subtraction, because to calculate 8+7 you use 10-8=2 and 7-2=5 as intermediate steps), and then there is a general skill of “adding two integers of arbitrary length”. Should we also make separate nodes for “addition is commutative”, “addition is associative”, and “adding a negative number means subtracting its absolute value”? I think we should, because ultimately we need to teach these concepts to the kids, but… you get the idea about how large the resulting tree will be.
Large trees are inconvenient to work with. A tree with 10 nodes is a nice picture. A tree with 1000 nodes is an intricate network of lines. You could arrange it into categories (e.g. put all the “addition” nodes next to each other, or maybe make an “addition and subtractions” cluster), that would allow you to easier locate a node, but you would have many lines between the categories. This could be handled by a computer, for example the nodes you have already mastered (and took an exam for) would be checked, and if you click on a new node, all nodes between your current knowledge and the selected node would be highlighted, to give you an idea about how much would you need to learn in order to get there.
This is not an argument against constructing such tree. I definitely would like to see it! I am just saying that it is a lot of work, and difficult to use without a computer, so I understand why teachers are not doing this, and instead handle the complexity by creating groups of nodes, and arranging those groups in linear order.