My groundbreaking idea: make sure that students know A1…An before teaching them A.
I disagree.
Just getting a personal pet project is frequent advice for people who want to start to learn to program.
Working on the project leads you to learn the things that are necessary to solve the problem.
You also should explain how this interacts with what you say about essay writing. To me it seems like you advocate two distinct ideas that sound reasonable on the surface without having thought deeply about how they interact with each other.
Have students tackle projects and learn what they need along the way.
Teach students A1 before teaching them A.
3 requires 1.
3 is not necessarily optimal, since it still implies a set curriculum. IOW, teachers teaching to students instead of students learning what they need.
2 is made more efficient by 1. If I’m trying to learn how to do a high-level thing like build a machine learning algorithm, normally, schools would require me to take calculus and statistics courses beforehand, however, I could just learn what a gradient is (and all the pre-reqs for that like partial derivatives).
I disagree.
Just getting a personal pet project is frequent advice for people who want to start to learn to program. Working on the project leads you to learn the things that are necessary to solve the problem.
You also should explain how this interacts with what you say about essay writing. To me it seems like you advocate two distinct ideas that sound reasonable on the surface without having thought deeply about how they interact with each other.
Mu: (I agree with both of you).
Make a dependency Map of topics.
Have students tackle projects and learn what they need along the way.
Teach students A1 before teaching them A.
3 requires 1. 3 is not necessarily optimal, since it still implies a set curriculum. IOW, teachers teaching to students instead of students learning what they need. 2 is made more efficient by 1. If I’m trying to learn how to do a high-level thing like build a machine learning algorithm, normally, schools would require me to take calculus and statistics courses beforehand, however, I could just learn what a gradient is (and all the pre-reqs for that like partial derivatives).