For a student, what is the optimal usage of a solution manual?

During coursework if a solution manual is available for the textbook, it is always a huge bonus for the student. While the student is exposed to a variety of relevant applications and tricks in the problems, the solution manual ensures the student's hard work spent trying out the problems does not go waste. The solution manual's availability is akin to the presence of a "Cheat" button in crossword applets - the earlier you press the less you try, but still the presence of the button is useful as such. What are some useful tips for a student who wants to utilise the solution manual optimally?

4 Answers 4

1. Never use the solution manual before trying everything else; talk to friends, visit the professor, go to class and listen (!), check the internet. Once you use the solution manual for a problem, the potential gain from that problem is significantly and irrecoverably reduced.
2. Use the solution manual to check your work. (Duh.)
3. For problems you aren't planning on solving, you can use the solutions manual to create flashcards and other learning aides (if the course material is anemable to such a construct).
4. If you have a friend/roommate/spouse/trained monkey who can compare your answers to the manual for you, such that you don't actually read through the manual, that may be useful for certain topics.
5. You can make some good money selling it when the semester is over :)

Ignore it and write a new one.

Looking at the solution manual is not useful; it only gives you answers. The point of homework isn't the answers, but the struggle to find them.

If the manual only gives answers, then it isn't worth much. However, if the manual shows how to find the answers, then it can be useful. If you're really stuck on a problem (and have worked on it for a while), you could try just peaking at the manual to get an idea to help you get unstuck, then try to work out the details on your own (without reading the manual).

There were times during maths class in school that I checked my answer in the back of the book, realised I was wrong & reattempted the problem looking out for where I could've made a miscalculation or misunderstood something. Normally, it ended up giving me a better understanding of the problem space. It also meant that I was able to come to the right answer myself (albeit after being told that I was wrong, but not how I was wrong) — without that I would've been shown the correct method anyway (when the class went over the homework), but I think I would've learned less.

Is believing this a requirement to obtain tenure? That would explain some of my former professors. If the solutions to homework exercises are not important, then why does every good university course provide students with feedback on their homework in the form of written corrections or tutorials where a TA or professors demonstrates the solutions?

@Peter Solutions can be useful after the students have already struggled to solve them, if for no other reason than to sanity-check their own grades. At least, that's why and when I give my students solutions (and advice on how to find them).

Don't just read the solutions. This is counterproductive. Work the problems yourself.

However, after finishing, use the answer (not the worked solution) as a check. It is psychologically reinforcing to have a feedback loop and know that you did it right.

If you were wrong, rework the problem. Often the reason will have been a minor calculational mistake (in STEM). You will usually be able to fix this on your own (without even seeing the detailed solution) just by being more careful. If not, sometimes the format of the answer will suggest a more conceptual thing that you missed or prompt you to relook at the textbook description/examples. This is crucial, that you fully redo even "dumb mistake" attempts. Doing this means you won't make them again. It's like music or sports. If you make a mistake, do it over. Do the entire exercise, not just the part you messed up.

In the few cases where the above is not sufficient, look at the actual worked solution to see how they do it. But STILL. Then put the manual down and rework the missed problem yourself. You need to actually practice the solution process. Not just read it. Even though it seems hokey, it will help your learning, versus reading and saying "OK, that was the trick".

I do disagree with other answers that say you should prioritize outreach to friends, Chegg, instructors, SE, before checking the solution manual. It is a tool for you and is extremely convenient for the disciplined drilling problem solver. I would reserve that sort of personalized outreach for when you are baffled by the written solution itself. (Keep a written list and then see your instructor with them.)

But absolutely do use the disciplined drill, check, repeat (if wrong) method that I espouse above.