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Why do some math (and science) textbooks/solution books only include answers to odd- or even-numbered problems?

Some textbooks have a separately purchased answer book with the missing answers, while others only include odd or even-numbered answers in the solutions book (and none in the textbook). Why is this the case and how do publishers decide this stuff?

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    $\begingroup$ A better question is why aren't the answers given where the problem is stated? Don't we all hate the flipping back and forth? Indeed, this is one of the joys of Churchill's complex variables text. Answers with problems can be very nice. Unfortunately, students misuse answers. $\endgroup$
    – James S. Cook
    Nov 27, 2017 at 2:45
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    $\begingroup$ @DaveLRenfro The question was asked, so presumably it is not obvious. $\endgroup$
    – Tommi
    Nov 27, 2017 at 7:28
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    $\begingroup$ I think it is a commercial thing with instructors finding it better for them but students finding it worse (harder to practice). Very few teachers grade th number of drill problems needed for fluency. And if they do, the feedback lags. Also it makes it harder for people to self study, which again is a commercial thing that empowers paid instructors. [This is not a popular view with paid instructors but should be considered. Economics drives things--just look at editions creep for another example.] $\endgroup$
    – guest
    Jan 18, 2018 at 1:21
  • $\begingroup$ I’m particularly mystified by Gallian providing the odd answers in the back of the book (OK fair) and then the “solutions manual” (!) also only gives the odd answers. $\endgroup$
    – Alper
    Jan 18 at 20:08
  • $\begingroup$ Oh OK. The Gallian book can't make up its mind. Sometimes it does a bunch of even numbered answers as well just randomly. $\endgroup$
    – Alper
    Jan 29 at 10:43

1 Answer 1

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Having answers to all the problems in a book is often inconvenient for teachers.

  1. For very elementary topics in which not much work needs to be shown by students (such as what is the domain of $f(x) = \frac{x}{x^2 – 4}),$ allowing students to have the answers makes it more difficult to grade homework. For example, suppose a student has the correct answer and the student work is not clear, but the work might be on the right track. How much partial credit do you give? If the students are not given the answers, then you can lower your "show your work" bar in deciding on how much credit to give.

  2. For more difficult problems, especially when an intuitive “trick” is needed, if a student has the answer, then the student might be able to reverse engineer the answer to come up with a solution. Counting problems (i.e. combinatorics) can sometimes be tricky, but if you know the answer, then you might be able to make educated guesses as to whether permutations or combinations are used, and whether additional modifications are needed (such as when certain objects treated as identical).

  3. If students have all the answers, then they will not get practice in making safety checks to see if their answers make sense, a skill especially important when the answer sought is very important, which is often the case in real life situations, such as how much is it going to cost the company if such-and-such policy is put in place.

  4. If answers are given to all the problems in the book, then for certain topics at least, this can prevent teachers from using these questions on tests, which makes the book less useful for the teacher than a book that doesn’t give answers to all the problems.

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    $\begingroup$ I think that (3) is really the most important point here: we are trying to teach students to solve problems that they don't know the answer to. They will never be able to do this if they don't have practice with it. That is the hardest thing that we teach, mathematical confidence and how to tackle an unknown problem. Students need to learn how to understand for themselves if their answer is correct without checking it. They will have to on tests and in the real world. If we don't do it in our classes we're going to make math useless to them. $\endgroup$
    – Nate Bade
    Nov 27, 2017 at 23:24
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    $\begingroup$ I also have to +1 for (3). In my current job, I probably spend as much (or more) time checking my answers as actually solving them. $\endgroup$
    – PGnome
    Nov 28, 2017 at 22:56
  • $\begingroup$ @NateBade So how should self-studiers approach this? I don’t have access to the “we” you speak of. $\endgroup$
    – Alper
    Jan 18 at 20:16
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    $\begingroup$ @Alper Take your list of problems with answers and portion them up into a group A and a group B. Do the group A problems, checking the answers. When you feel like you know how to do the problems, start on those without answers (you can even start sooner for practice). They key is to learn how to check your steps - are there two ways of doing the problem? Try both and compare answers. Do sanity checks (the sphere has radius 1, but the volume is 10^10?) and parity checks (does an odd answer make sense?). Convince yourself the answers is correct. Then do some of the problems from set B. $\endgroup$
    – Nate Bade
    Jan 19 at 22:53
  • $\begingroup$ That's more or less what I'm doing. I just can't really motivate myself to solve problems that I can't check. $\endgroup$
    – Alper
    Jan 21 at 10:03

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