I was not in the habit of solving problems, so I thought of understanding/analysing the importance of problem solving. I thought learning theory properly to be the shortest route to understand any concept, which I felt will enable me to answer or solve any problem/numerical (formally given as exercise in a textbook). In my course of understanding the concept by thinking, I never had lot of experience in solving problems as I was never used to complete thinking completely. I thought understanding concept by solving problems to be a long route.
Sometimes theory will not be properly tailored for explanation and may not succeed in explaining the concepts, at that time problems are going to help in explaining the concept or bringing out new relations. And even problems can also be used to find out problems in the theory itself! If someone don't have the program in the head which analyses the concept, then problems are going to be the one which are going to make one analyse things, but one should not depend on problems to make their brain think, they should be taken as a starting step for thinking; what if one comes to see new theory which doesn't have problems for them to "make them" think, then it is going to be "problem" for them. In other ways problems can be used as a supporting stand to get perfect in theory. Yeah, it may be anything "problem solving" is important. Importance of problem solving can be conceived as a function of the concept being learnt, clearly understood theory may not need problem solving except for exercise (while most of the time problems are really for exercise of your brain), while some of the concept can be understood clearly only by doing problems; so, one should be flexible in analysing when the "problem solving" is important or in other words one should know when the value of the function of importance of "problem solving" is high. I remember +Vasanth kumar B , +rahul kalose and others saying problems to help us applying theory, yeah they will for sure. If we are not able to solve a problem we should either confirm that we haven't learnt the theory (either mathematical tool theory or the theory of the concept in problem) properly or that we have failed to apply the theory which is learnt. One should notice that sometimes quality of explanation of (mainly physics) theory may not to be precise but the numerical problems will be precise in explanation. It came to me as a flash that I studied things to understand the world and problems in, say physics are application based, for example in electrodynamics we find fields inside sphere and many many other things, which can be used as "ready-made" source to understand/analyse the world.
So, this is what I got when I tried to analyse the importance of problem solving. Of course all these views are not of too matured one, I might require your views on this to get a better view, in case you feel something is missing, please comment below. We shall together build a better view. All these things seem to be known before, but recollecting them helps us to have a satisfaction on what we are doing and also helps us to do things in a better way.
Sometimes theory will not be properly tailored for explanation and may not succeed in explaining the concepts, at that time problems are going to help in explaining the concept or bringing out new relations. And even problems can also be used to find out problems in the theory itself! If someone don't have the program in the head which analyses the concept, then problems are going to be the one which are going to make one analyse things, but one should not depend on problems to make their brain think, they should be taken as a starting step for thinking; what if one comes to see new theory which doesn't have problems for them to "make them" think, then it is going to be "problem" for them. In other ways problems can be used as a supporting stand to get perfect in theory. Yeah, it may be anything "problem solving" is important. Importance of problem solving can be conceived as a function of the concept being learnt, clearly understood theory may not need problem solving except for exercise (while most of the time problems are really for exercise of your brain), while some of the concept can be understood clearly only by doing problems; so, one should be flexible in analysing when the "problem solving" is important or in other words one should know when the value of the function of importance of "problem solving" is high. I remember +Vasanth kumar B , +rahul kalose and others saying problems to help us applying theory, yeah they will for sure. If we are not able to solve a problem we should either confirm that we haven't learnt the theory (either mathematical tool theory or the theory of the concept in problem) properly or that we have failed to apply the theory which is learnt. One should notice that sometimes quality of explanation of (mainly physics) theory may not to be precise but the numerical problems will be precise in explanation. It came to me as a flash that I studied things to understand the world and problems in, say physics are application based, for example in electrodynamics we find fields inside sphere and many many other things, which can be used as "ready-made" source to understand/analyse the world.
So, this is what I got when I tried to analyse the importance of problem solving. Of course all these views are not of too matured one, I might require your views on this to get a better view, in case you feel something is missing, please comment below. We shall together build a better view. All these things seem to be known before, but recollecting them helps us to have a satisfaction on what we are doing and also helps us to do things in a better way.
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