Besides the 2 mathematicians quoted below and me, who else has touted free dissemination to students of detailed solutions, to EVERY exercise and problem (like in textbooks)? I uphold this wholeheartedly! This free dissemination ought to be the norm!

I do NOT refer to snippety one-line answers at the back of a textbook, student solution manuals that solve merely some or half of the exercises, or solution manuals restricted to instructors.

1. Robert Ash (1935-2015), Preface to Real Variables with Basic Metric Space Topology.

I rely especially on one of the most useful of all learning devices: the inclusion of detailed solutions to exercises. Solutions to problems are commonplace in elementary texts but quite rare (although equally valuable) at the upper division undergraduate and graduate level. This feature makes the book suitable for independent study, and further widens the audience.

1. David Patrick, Introduction to Counting and Probability (2005), page v.

However, if you are using this book on your own to learn independently, then you probably have a copy of the solution book, in which case there are some very important things to keep in mind:

1. Make sure that you make a serious attempt at the problem before looking at the solution. Don't use the solution book as a crutch to avoid really thinking about a problem first. You should think hard about a problem before deciding to give up and look at the solution.

2. After you solve a problem, it's usually a good idea to read the solution, even if you think you know how to solve the problem. The solution that's in the solution book might show you a quicker or more concise way to solve the problem, or it might have a completely different solution method that you might not have thought of. [emboldening mine]

3. If you have to look at the solution in order to solve a problem, make sure that you make a note of that problem. Come back to it in a week or two to make sure that you are able to solve it on your own, without resorting to the solution.

• Put me in the "This is a profoundly bad idea" column. It is even worse for math than CS though. Reading an answer isn't nearly the same for learning as doing it. And, point 3 under the Patrick quote is just foolish. Rote memory is for eight year olds, not for mathematicians or computer scientists. Nov 16, 2022 at 14:26
• Neither quote says "to every exercise". Nov 17, 2022 at 4:57
• @Buffy, I'm not quite following how you got "rote memory" from point 3. I read it entirely differently; it seems to me Patrick is saying that the student should do their best to solve the problem on their own, but if they fail to do so, they should consult the solution, attempt to understand and internalize the approach taken there, and then after a while (when they forgot the exact details of the solution) to assess whether they have indeed successfully adopted the technique into their toolbox. I don't see anything rote about this. Nov 17, 2022 at 9:58
• [...] If we're considering graded assignents, I think the solutions for them should also be published, but only after the deadline of the tasks in question. By the time the deadline is over, the execrise becomes an ungraded, optional work for everyone who wishes to improve their solution / complete it. The only problem I see with sharing solutions to pretty much everything is that every year we need to come up with slightly new problems for graded work, because students will have easy access to exercises from the past. For example I would be against publishing solved exams and tests. Nov 21, 2022 at 14:48
• Just curious, are you an instructor? Do you use a textbook? How do you grade exercises for which the solutions are available? Nov 21, 2022 at 19:20

The lure to recycle past problems is great. It's so great to save work. It's so great to reduce risk by using exercises that worked well in the past. I used to succumb to that lure early on. Students told me decades ago that this is a terrible mistake. Especially the good/ambitious students become disenfranchised in courses where it's known that problems are recycled. The students argued that recycling exercises that are worth marks - be it for exams or graded homework - rewards being well-connected rather than able to solve the problems themselves. That's when I changed. I never regretted the change.

If one resists that lure, there's more work to create new problems every session, more risk that the problems are not that good, but there are also sizeable benefits:

• discussing solutions in detail leads to learning (I used to ask for volunteers who wanted their solutions discussed, anonymised 2 of those solutions, typically a good and a bad one, and then discussed the good and the bad of each in class)
• cheating by copying from previous cohorts is eradicated
• contract cheating is more expensive and easier to spot on the usual sites such as freelancer.com
• Good arguments. (And I still disagree.) I guess it partly depends on what sort of material you are teaching. For my own courses I find it very hard to come up with many good exercises. I can make totally-made-up-exercsie-for-the-sake-of-exercise problems, I have some exercises that bear some relation to reality, and the next step up is embedding the material in some humongous real context that will be impssible to explain in finite time. Feb 22 at 14:08
• I agree with @VictorEijkhout that it really must depend on what you're teaching. Some topics are a LOT harder than others when it comes to generating reasonable problems.
– Ben I.
Feb 22 at 20:27

I'm against publishing answers to exercises. Credentials: I'm in the situation that I have several textbooks to my name, all of which have exercises with not-published solutions. (Only if an instructor mails me, from an .edu address, and with promises of confidentiality, I will send them the solutions manual. Maybe.)

I teach from my textbooks multiple times. So I'd like to assign exercises this year, and again next year, maybe with a minor tweak. I can not do that if the answers are out in the wild.

Designing good exercises is hard! I do not have the time to come up with a dozen (number of weeks in a typical semester) brand-new problems every time I teach my courses.

So what do I give students after they have been graded? I discuss their submissions, point out what's good, and what they missed. But I still don't give them full worked-out solutions.

• Dec 4, 2022 at 8:50
• "Designing good exercises is hard! " indeed it is! FWIW sometimes I do the assignment in front of the students in real-time in a lecture/seminar. It isn't recorded and I don't provide notes etc. It has the advantage of demonstrating not only what the solution looks like, but how to go about the programming task - e.g. breaking down the problem, problem solving, writing small test programs to work out how to do something, testing and debugging. Dec 13, 2022 at 19:17

In a world with ChatGPT and other similar tools, publishing detailed solutions to all exercises and problems will lead to a world where there is no problem that can be set where the student can't get ChatGPT to give them the answer (and explanation). The only way to avoid that is likely to be to set abstruse exercises that are hard to understand, hard for students to grasp, and of low educational value.

At the end of the day, there are skills, such as maths and programming that you can only really learn or be good at by doing them for yourself. Looking at worked solutions is a bit like going to the gym and watching someone else pump iron. It will teach you how to use the gym equipment, but it won't make you any stronger.

• A world with ChatGPT needs a world where students are graded on their ability to explain their code. For that matter, so does a world without ChatGPT. Jan 29 at 2:56
• @candied_orange ChatGPT can explain the code it poduces, so that won't work. Jan 29 at 9:06
• @downvoter some feedback on why you disagree with my answer would be appreciated. Feb 25 at 14:21