I think the availability of solutions to the homework online does give people advantages when looking at the homework part of the grade, but the fact of the matter is when those people take exams they are not as prepared as people who actually take the time to do the homework instead of copying it.
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Usually I would agree, however, personally I have gained a lot from having solutions posted online. Though I use it as a tool to help me when I am stuck and I have no direction on how to solve a problem. I use it as a self tutoring system, which helps me learn the processes of the specific math problems and helps me overall with my understanding. I know that you do not want students merely using the 'cookie cutter' method, but I think that the majority of students would benefit from such a resource.
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This could be beneficial for some, but I know a lot of people would probably just copy most of it. Especially if they wait until the last minute to do the homework.
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I agree i think that most people would copy the solutions from online however, some people may be actually doing the homework themselves and get stuck on a part. If the solutions were posted you could get a little help. On the other side if you are stuck on a problem you can ask for help on Rhea or go to office hours as long as you dont wait till the last minute to start the homework.
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I have always felt that having online solutions or at least answers to problems is beneficial. No one is perfect, especially when learning new material. Therefore, sometimes checking one's work as they go along or their answer at the end, is an important building block and confidence booster that I believe helps the learning process. Yes, any student can simply copy posted online solutions and can probably get away with it, getting a 100% on homework, but unfortunately for them, no test are posted online.....
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I believe that the homework solutions should be available online because then people who are having difficulty with a certain problem, can then go see how it is done. There will be people that will just copy down the answers without even looking at how to do the problem, but that will hurt them in the long run since they probably will not do that well on the exams. The people that use the solutions the right way will in my opinion will be able to learn much faster and easier because there will be a step by step for the problem right there rather then either going in to office hours or sending an email to the professor for a small question and waiting for a response. I think that there will be more people benefiting from the online solutions then those that use it just to get their homework done faster.