I don't know of any studies, I'd love to see some!
But, I'm a little torn on the concept you're getting at, which is whether seeing answers is less helpful than struggling to find answers and arriving at them yourself without having seen the answer first.
We do have a strong and pervasive belief in our society that the struggle itself is important, and that struggling to derive how to get to the answer without someone giving it to you is the only "right" way to learn.
(The same goes for money, btw, but that is a meta topic for another time...)
In many ways, I believe in struggle myself, but I don't have any concrete scientific evidence, I'm just becoming aware that it's a belief and not necessarily a truth. Recently, as a parent, I think I'm seeing some evidence to the contrary. When my kids ask for math help and I force them to struggle through each step and think about how to do it and explain and show their work, it works eventually, but it takes a long time and it is a struggle for all of us. When I show them the answer first, and then we talk about it later, they learn quicker with less struggle. Usually I will make them rewrite anything I show, but I'm starting to feel that learning by example without the forced struggle is a lot more efficient.
I still want them to be curious and interested in researching their own solutions, so of course I'm a little worried that by doing too much handing out of answers, I might do damage to their desire to explore math (or any subject). But so far, I'm not seeing that, I'm seeing increased interest and enjoyment in math, we spend more time talking about subjects beyond homework.
In some ways it makes sense, we learn how to talk and eat and behave by example, some subjects we can only learn by example (like, say, history). Math and physics are weird ones where we pile on extra struggle to derive the rules because we think it's helpful for learning.
Anyway, I'm certain struggling to learn rules is important, I'm just becoming less certain that it's always important. I do believe that learning by example works and is useful and sometimes more effective than learning rules.
But, I'm a little torn on the concept you're getting at, which is whether seeing answers is less helpful than struggling to find answers and arriving at them yourself without having seen the answer first.
We do have a strong and pervasive belief in our society that the struggle itself is important, and that struggling to derive how to get to the answer without someone giving it to you is the only "right" way to learn.
(The same goes for money, btw, but that is a meta topic for another time...)
In many ways, I believe in struggle myself, but I don't have any concrete scientific evidence, I'm just becoming aware that it's a belief and not necessarily a truth. Recently, as a parent, I think I'm seeing some evidence to the contrary. When my kids ask for math help and I force them to struggle through each step and think about how to do it and explain and show their work, it works eventually, but it takes a long time and it is a struggle for all of us. When I show them the answer first, and then we talk about it later, they learn quicker with less struggle. Usually I will make them rewrite anything I show, but I'm starting to feel that learning by example without the forced struggle is a lot more efficient.
I still want them to be curious and interested in researching their own solutions, so of course I'm a little worried that by doing too much handing out of answers, I might do damage to their desire to explore math (or any subject). But so far, I'm not seeing that, I'm seeing increased interest and enjoyment in math, we spend more time talking about subjects beyond homework.
In some ways it makes sense, we learn how to talk and eat and behave by example, some subjects we can only learn by example (like, say, history). Math and physics are weird ones where we pile on extra struggle to derive the rules because we think it's helpful for learning.
Anyway, I'm certain struggling to learn rules is important, I'm just becoming less certain that it's always important. I do believe that learning by example works and is useful and sometimes more effective than learning rules.