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I love, "Learning by invention". Basically, you start with a problem, than the teacher "helps" to come up with a solution, (by hints / guides), which casually

I love, "Learning by invention". Basically, you start with a problem, than the teacher "helps" to come up with a solution, (by hints / guides), which casually ends up at the solution implemented. I think it's one of the reasons people love to reinvent the wheel. When they invent something themselves they truly know it inside out. You can somewhat do it yourself, if say, you want to learn a new library, by first trying to implement the problem yourself, then take hints from the library and finally use the library.

mynameismon 5y ago
Learning by invention is also my favourite way to learn. However, I find it rather unappreciated among both teachers and textbook writers. What is usually done is the result is presented on a silver platter to regurgitate and reproduce, and important details are glossed over in favour of 'simplicity', creating a (dangerous) knowledge gap.
- MathMonkeyMan 5y ago
  You remind me of something a Physics professor once told me. He said (I'm paraphrasing) "when you get to really learning the Physics, it's not an incremental logically consistent picture rooted in mathematics like in the textbooks. It's mostly a bunch of little tricks that you learn when to apply, and sometimes you get somewhere." He wasn't making a pedagogical point, but I wonder if being compelled by the "learn by invention" style is in some way detrimental to learning how to solve hard novel problems.
  - mynameismon 5y ago
    To be fair, 'Learn by invention' can be detrimental if one is trying to derive a result which requires significant prior knowledge that the learner lacks. However, quoting a simple physics example of what I mean: One can prove the Work-Energy theorem with simple manipulations of the basic definitions of displacement, velocity and acceleration without having to learn it like a law. One cannot derive Newton's three laws, on the contrary.
    - lyaa 5y ago
      Most of physics is not a great counter-example to learning by invention. There are several ways to derive Newton's three laws. It's a fun exercise in Lagrangian mechanics. Perhaps quantization or the curvature of space would be better examples as they require prior knowledge of experimental data (assuming we ignore proposed philosophical arguments that stray a bit too far from physics imho.)
- AussieWog93 5y ago
  First thing I thought of when you said that: https://www.youtube.com/watch?v=yYAw79386WI https://www.youtube.com/watch?v=yYAw79386WI Done properly, it's an amazingly powerful way of explaining things.
zhengyi13 5y ago
This is exactly how Syntax 1 was taught at UC Santa Cruz when I attended. We started with a general question of "What is the simplest sentence you can think of?", and then moved to "How could you represent that symbolically? Generically?". With the professor's guidance, the solutions and systems of representation evolved over the course of the quarter to become more rich and complex, and just so happened to trace the development of syntactic theory from roughly the 50s to the 70s. Then you took Syntax 2 tracing roughly the 70s to the 90s, and by the end of that time, you were ready to look at modern problems.

mynameismon 5y ago

Learning by invention is also my favourite way to learn. However, I find it rather unappreciated among both teachers and textbook writers. What is usually done is the result is presented on a silver platter to regurgitate and reproduce, and important details are glossed over in favour of 'simplicity', creating a (dangerous) knowledge gap.

MathMonkeyMan 5y ago
You remind me of something a Physics professor once told me. He said (I'm paraphrasing) "when you get to really learning the Physics, it's not an incremental logically consistent picture rooted in mathematics like in the textbooks. It's mostly a bunch of little tricks that you learn when to apply, and sometimes you get somewhere." He wasn't making a pedagogical point, but I wonder if being compelled by the "learn by invention" style is in some way detrimental to learning how to solve hard novel problems.
- mynameismon 5y ago
  To be fair, 'Learn by invention' can be detrimental if one is trying to derive a result which requires significant prior knowledge that the learner lacks. However, quoting a simple physics example of what I mean: One can prove the Work-Energy theorem with simple manipulations of the basic definitions of displacement, velocity and acceleration without having to learn it like a law. One cannot derive Newton's three laws, on the contrary.
  - lyaa 5y ago
    Most of physics is not a great counter-example to learning by invention. There are several ways to derive Newton's three laws. It's a fun exercise in Lagrangian mechanics. Perhaps quantization or the curvature of space would be better examples as they require prior knowledge of experimental data (assuming we ignore proposed philosophical arguments that stray a bit too far from physics imho.)
AussieWog93 5y ago
First thing I thought of when you said that: https://www.youtube.com/watch?v=yYAw79386WI https://www.youtube.com/watch?v=yYAw79386WI Done properly, it's an amazingly powerful way of explaining things.

zhengyi13 5y ago

This is exactly how Syntax 1 was taught at UC Santa Cruz when I attended. We started with a general question of "What is the simplest sentence you can think of?", and then moved to "How could you represent that symbolically? Generically?". With the professor's guidance, the solutions and systems of representation evolved over the course of the quarter to become more rich and complex, and just so happened to trace the development of syntactic theory from roughly the 50s to the 70s. Then you took Syntax 2 tracing roughly the 70s to the 90s, and by the end of that time, you were ready to look at modern problems.