# Making solutions to all problems freely available

I teach at a community college, almost all physics but also a math course now and then. My current practice is that I assign homework worth a very small number of points (1 point per problem, as opposed to about 20-25 points per problem on exams), and I withhold solutions until students have turned in their problem sets.

There is an different set of practices which I think is more common in math courses than physics courses. Full solutions are available (e.g., in the book) for all problems. Problem sets are assigned but not collected or graded. At the beginning of each class, there is a short quiz, in which the students are asked to solve one problem that is of the same flavor as the ones on the problem set. I'm toying with the idea of switching to this system.

Can anyone give pros or cons based on their experience with such a system? Are there common pitfalls in implementing such a system?

Is this system more likely to work well at a school with selective admissions, where students are more likely to be willing to put in many hours of work every week without immediate grade incentives? Or, conversely, does this system work better in the type of course that does not require much critical thinking or higher-level reasoning, so that students are simply differentiating $2x^3+1$ on the homework and then differentiating $2x^4+1$ on a quiz?

[EDIT] Some clarifications on what I'm asking: (1) I'm not talking about changing the intellectual level of the course. There would still be the same high level of critical thinking and higher-level reasoning that I've been requiring for the last 22 years. (2) I'm not talking about abdicating what I see as my responsibility to provide written feedback to students on their work. The written feedback would just be on their quizzes rather than their homework. (3) My question is about what outcomes people have experienced with students when they tried such a system, their impressions of pros, cons, and pitfalls, and how it works out in terms of different students' levels of motivation, response to rewards, and levels of maturity. (4) I'm not asking for recommendations of some other system besides the one described in the question. (5) I'm asking for descriptions of people's personal experience with using this system, which is specifically one in which all solutions are freely available.

• Working problems is the key for student learning. Either system is fine, but I would go with miniquizzes. Make them easy to grade or just do "pass the paper" exercises to lower workload. If you do collect HW, just grade it for completion. AND provide the solutions ahead of time. (Yes, people can game this, but most will either do the work or completely blow it off. And given the point value is low, who cares. At least they are looking at the stuff.) As far as solutions, my advice is to provide the answers ahead of time, but not the worked solutions (maybe later, if you have them.) – guest Jan 1 '18 at 4:47
• I don't think there is anything wrong with the course being mostly practicing derivatives versus "concept" type questions. People here are in love with it because for them the mechanics is easy. But for the kids, even the mechanics is new. And it better serves them for physics classes and the like. Would say this for any demographic but especially for community college. Be efficient with the students' time and horsepower. – guest Jan 1 '18 at 4:49
• In my B.A. math program, I certainly had homework to do outside of class and not collected. However, I never experienced the quiz-in-class-to-verify practice. So this question as given might be very narrow in its range of observations. – Daniel R. Collins Jan 2 '18 at 2:03
• Dan, unless you are teaching bachelor's math students, it's not the appropriate comparable. [I would actually argue that we do a disservice in MANY bachelors majors courses by not emphasizing drill and progression also, leaving "maturity" for true labs and project courses and actual seminars (real actual ones, not in name). But that's a minority view. Go look at how professional athletes are trained. Many of the techniques are very similar from high school to college to the pros.] – guest Jan 2 '18 at 17:36
• @guest: At any rate, I think the burden of proof would be on someone asserting that daily-quiz-on-homework is a "common" practice. I'm pretty sure that none of my colleagues at a large community college do that, nor have I heard anyone at various city-wide math (not math major) conferences relating that. – Daniel R. Collins Jan 4 '18 at 22:53

This is an opinion, but perhaps worth sharing:

When I assign that I expect students (particularly lower division students, such as those in calculus or precalculus classes) to do on their own time, I assume that they are going to collaborate, ask the Google, and otherwise use all of the resources that are available to them. Demanding that they do the work on their own is a fool's errand, and can be rather paternalistic. As such, I don't like to make homework a huge proportion of the final grade in a class, as I want a student's grade to reflect their individual ability and learning, rather than their ability to find the answers on the internet. I would prefer to base a student's grade on work that they do in class, under better controlled circumstances, e.g. exams or presentations (with moderately intense questioning).

That being said, most students cannot learn and internalize new material without having had a good deal of practice. Homework provides that practice. As such, homework is a vital part of class, and cannot be ignored. In an ideal world, I would assign homework, and my students would be mature and well-motivated enough to recognize that working through the problems is to their benefit. In this ideal world, it would be entirely unnecessary to grade (or even collect) this work—the effort that the students put into it would be reflected in their exam scores. Since we don't live in an ideal world, and not all students are mature or well-motivated enough to do work on their own without some kind of Pavlovian reward, I typically give some minimal credit for homework.

Returning to my ideal world, once I have assigned homework, I would collect it, and give feedback to all of my students in detail. However, if I have a large class, there are not enough hours in the day to give that kind of feedback. As such, there are a few ways that I can assign work (this is not meant to be exhaustive, but should hit the major points):

1. Use a computer driven system, such as MyMathLab, WebWork, or ALEKS, then using the scores returned by the system for the homework component of my gradebook. Such a system has the advantage of requiring very little input from me (once the class is set up), and gives students instantaneous feedback. On the downside, these systems are only good for low-level drill-and-kill style questions, and tend to do a poor job of forcing students to use higher order thinking. I think that the questions also have a tendency to break down problems too much, and give students the idea that there are different problem "types" that, once mastered, give them mastery over the material.
2. Assign homework with answers (but not solutions) given, and grade that on the basis completion. Here, the students know if they have obtained the correct answer (since the answers are given), and my workload is tractable, since I only have to check off the assignments. I can also give deeper questions in the homework. The disadvantage is that the students get very little feedback, unless they choose to come and discuss the problems during office hours. I have also observed that students seem not to value work that is graded on the basis of completion—they do the minimum necessary to get the points, then move on. This hurts them, come exam time.
3. Assign problems with no answers given, then grade either entirely on the basis of completion, or pick a few problems on which to give feedback and give completion credit for the rest. From the point of view of giving good feedback, this is likely the best that can be done for a large class. Again, office hours are good for addressing problems. On the downside, students are only getting feedback on a few problems, and may have serious misconceptions that are never addressed. This can be somewhat ameliorated by providing solutions once the assignments are handed in.
4. As you suggest, assign work but do not collect or grade it. You can then assess their homework performance on the basis of short quizzes (I wouldn't give them answers in advance, as this defeats the assessment). My strategy is to give them 5–10 minutes to answer one or two questions taken more-or-less directly from the homework. Sometimes I even let them keep their homework out to answer these questions (if they did it right, it is a simple copy-pasta). I then grade these quizzes fairly harshly, with the justification being that they had plenty of time to discusses troublesome problems during office hours.

Note that all of this is for a lower division mathematics class, where there is a often a significant requirement that students be able to perform basic computations, which may or may not require deeper understanding, but which does require a fairly large number of problems for practice (perhaps not quite drill-and-kill, but close). As courses get more abstract and the students become more mature (both mathematically and as self-motivated learners), a greater emphasis can be placed on written work (e.g. nicely written or typed work in a proofs-based course).

• Thanks for your thoughts, but the only part of this answer that seems responsive to the question is the one paragraph near the end, beginning with "As you suggest..." And this is very short and not very specific, e.g., you don't state whether or not solutions are made available in advance. – Ben Crowell Jan 1 '18 at 19:55
• @BenCrowell Your original, unedited question was quite broad and unfocused. I did my best to address the question which seemed to be asked, i.e. how do you deal with homework in math classes? The pros-and-cons of any particular system, it seems depend on how that system compares to other systems, hence preamble and breakdown of different strategies which I have employed in the past. The edits that you made significantly focus the question, but I am loath to discard an hour's worth of work to address the changed emphasis of the question. – Xander Henderson Jan 1 '18 at 20:08
• I thought Xander's answer was responsive. – guest Jan 1 '18 at 23:04
• I also think this is a worthwhile response. One thing I had trouble parsing was use of the phrase "drill-and-kill", which is usually meant as a pejorative, whereas you're presenting it as a requirement of the course in question. In the positive it's more common to use the word "practice", e.g.: apa.org/education/k12/practice-acquisition.aspx or teched2010.wikispaces.com/Drill+and+Kill – Daniel R. Collins Jan 1 '18 at 23:38
• @DanielR.Collins I've amended the last paragraph. I stand by the pejorative earlier use. ;) Thanks for the comment. – Xander Henderson Jan 1 '18 at 23:56

I teach a highly selective Liberal Arts College. If you don't assign a component of the final grade to the homework, the majority students in a typical introductory class just won't do it or, if they do it, they'll do it carelessly. They'll rely on their previous knowledge for the quizzes and it won't go well for them.

In my classes I assign and collect daily homework through WebWork and make it worth 5% of the final grade. This encourages them to do it, makes them prepared for class and class discussions go better. In my experience, since WebWork problems are randomized, students seem to have a harder time finding the solutions on line. Also, WebWork has no solutions manual (as far as I know), making it harder to find online. Also, the students know if they got things right because WebWork will indicate whether or not their answer is correct. In summary, then, I find it better to assign daily homework with neither solutions nor answers available. The students who want to work, get a lot out of it and the students who don't are no worse off.

I give weekly quizzes based on the previous week's homework. I find that making the quizzes weekly and the homework daily gives the students a chance to review a whole week's worth of material at a time, something that would be missing in your proposed scheme. I've given daily quizzes before but believe that students who did the homework were just relying on muscle memory to complete the quizzes rather than thinking more broadly or deeply about the material. I make the total of these quizzes about 10% of the final grade. This is the mechanism by which students get feedback on their work (I also almost-weekly Team Homework assignments where I give extensive feedback on their writing and argumentation).

Edit: This doesn't seem that different to @Xander Henderson's response, so maybe I misunderstood the question.

• I liked it anyways. – guest Jan 2 '18 at 14:27
• +1 for using WebWorK! – BobaFret Jan 3 '18 at 4:48

I'm not sure that I understand your question well: you talk about replacing homework by a small quiz at the beginning of each class, based on variations on freely available solved problems?
One of the reasons is your experience that some students don't do their homework themselves.

I have teached in a technical school and I can tell you that, in that particular environment, your system would fail heavily:
Imagine you start each class by a short quiz, then this would automatically take away some teaching time (an average class takes 50 minutes, if you start with a written quiz you easily lose 15 minutes, or 30%). In order to compensate this, you might need to speed up, with a high risk of weaker students (who already have problems following the course), to get even more into problems.
Imagine you start each class by a short oral quiz (just ask one or two questions and let the class find an answer), then you risk that the highly motivated students (who generally are the smartest ones) give the answers very quickly, and the weaker ones won't even bother looking for the answer as they know that they can't win/lose points whether or not they know the answer to the question.

I also don't like the whole idea: you say that there are two ways to learn mathematics: - listen to the teacher and then, at home, try to do it yourself (the homework way) - listen to the teacher, read it and try to make variations (the quiz way)

I don't believe the last way can work: the whole idea of mathematics is to learn how to reason, and how difficult this may seem for some students, the only way to learn it is by doing it themselves. You are right that in some cases some students are just copying from other ones, but sometimes they ask to each other "But how did you even think of doing that?", and in that case, just by getting it explained by someone of their own age, is enough to get them understand it.
The most common argument against this is, as you say yourself, that students just copy from each other or just get it from Google (which is most probably the reason for you to propose this new method), but in my opinion there is one simple "solution" for this: don't let students write their homework via a computer, but they need to do it in handwriting. I know, it is old-fashioned and they might dislike it, and oké, some students might still look up via Google or via their friends, but at least they will be forced to write the solutions down them-selves, and simply by doing this, even if they are just copying, they might actually learn from it.

Good luck

I think the problem with homework generally is that when we assign problems from almost any book published by a mainstream publisher there are "solutions freely available".

Most of my colleagues assign problem from the textbook and give weekly quizzes based on that homework for the homework grade. Unfortunately, there are just too many solution manuals etc. freely available and all too often we get mindless copying of "answers". Similar problems exist for WebAssign, or WebWork etc. again these have the added undesirable trait of de-emphasizing the importance of cataloging work. I think the process of them assembling their own catalog of solutions is as or more important than us giving them feedback. They need to learn to assess their own progress if they are to thrive long term.

I once tried posting required homework for physics which was then quizzed so the could copy down their solutions. What I found was that there was still a significant portion of the students trying to do the problems in the 3-5 minutes I gave them. The others often had not really thought out the problems for themselves either. In short, to answer your question I did not find this motivated the class better than when I made them use Web Assign. But, it was not a significant increase in apathy. If I had to put a number on it, I'd say I experienced an apathy level of 50 whereas the usual level was 40.

The only solution I know which is reliable is to write your own problems each semester and find human graders to either comprehensively or selectively grade the work. To my knowledge, this is the gold standard of homework which gets the most genuine effort from many of the students. I just spent about 4 days crafting 162 mostly new problems for my linear algebra class. It will take me another 30-40 hours to write solutions as the semester unfolds. Fortunately I have a grader to help. It certainly does improve the general aptitude on tests.