This is a question for mathematics instructors: How do you feel about having solutions available for the exercises in a math textbook? What if the solutions are available on the internet?

Some colleges and universities have guidelines for how instructors should treat the possibility of cheating on homework (e.g. looking for solutions on the web rather than working problems out). I taught at about five different colleges and universities. Four of them had honor codes, which gave the instructor the luxury of giving students their assignments and instructions and assuming that they complied honestly, whether they did or not. It was up to the administration to sort out egregious problems and the students’ own consciences to deal with mild ones.

My favorite tactic was to simply make homework count for only a small part of the grade, and place more emphasis on in-class tests and quizzes. The homework is useful for studying, students could work together or work with a solution guide as they pleased.

And there is a third option: to give homework problems whose solutions are not available or very difficult to access online or in books. Is this the high ground approach, or is it simply impractical and too much trouble considering questionable benefits?

What do you think? Should textbooks contain solutions to problems, or should the problems only be made available to instructors in a separate manual, or online accessible only by password?

**Featured Book of the Day**

**Integers, Fractions and Arithmetic **by Judith Sally and Paul Sally. This book was co-published by the AMS and MSRI as part of a Math Circles Program for K-8 teachers. The book consists of twelve interactive seminars, and gives a comprehensive and careful study of the fundamental topics of K–8 arithmetic. The guide aims to help teachers understand the mathematical foundations of number theory in order to strengthen and enrich their mathematics classes.

I would describe the approach to exercises in this book as: use very few and explain the solutions carefully and completely.

1. Let me define: Problems, trivial or not, call for some awareness of other, variously related concepts, understanding of the relationships with other concepts, etc. Exercises, trivial or not, call for a direct reference to some very specific piece of information, a “show and tell” explanation or, even worse but quite usual, a Template Example.

2. A text ought to convey some “understanding” of some chunk of knowledge, particularly of the relationships among the various constituents of the chunk and, insofar as possible, with constituents of other chunks. It can do that in at least two ways. One is by way of careful explanations. Another is by giving what is known as “Illustrative Examples”—as distinguished from Template Examples. Which to use depends at least in part on who the learners are. But the two reinforce each other.

3. The conveying/acquisition of that understanding is, at least partially, a separate issue. But one known difficulty is that students do not really read the text, certainly not “pencil in hand”. So, Exercises can be redefined as forcing the reader to really read the text.

4. It follows in any case that neither problems nor exercises ought to be included in a text as they both detract, if in different manners, from the intent of the text.

5. Exercises and problems, then, ought to be given separately from the text. It gives them importance. They can be fruitfully worked on by several people—as long as the final write-up is individual. They can be discussed in class—at least if the instructor is not wasting everybody’s time by lecturing.

6. When I decided not to include problems and exercises in my own texts, I found out that it completely changed my writing.

Thank you for your input!

I’ve found complete solution manuals on paid “help” sites, sometimes with incorrect solutions and/or glaring typos. Quite a few student submissions are exactly word for word the same, including the typos. I haven’t had any luck with plagiarism checkers for math solutions.

I’ve tried your third option of rewriting problems, including putting a strict no-posting no-copying warning. However, often within one term, the problems and solutions appear on these cheating web sites, including my warnings! I’ve had students cheat on exams using their cell phones.

Because these solutions are paid for outside the school systems, I don’t see any way of limiting access. Of course many professors post solutions too and they are easy to find via search engines. It feels like an “elephant in the room” situation where many know that it’s there but few are willing to acknowledge it.

I think you are voicing the concerns of many. Thanks for your comment.

You may be interested in this thread on academia.stackexchange concerning solutions to graduate-level textbooks.

https://academia.stackexchange.com/q/56739

In particular, Paul Garrett makes an interesting case for why solutions should be included.

https://academia.stackexchange.com/questions/56739/why-dont-graduate-math-texts-have-solutions-to-their-exercises

Thank you for this link. The discussion there is very interesting.