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I am in the following situation. I got a class with theory an exercise once a week. The students do the exercises at home and have the opportunity to discuss them at the exercise sessions. In each session, there is a test about the exercises from the previous week (similar, but different questions).

I am unsure if I should provide the solutions of the exercises directly after the session, the week before the test.

Pros: They could see if they solved the exercises correctly before the test. (They may think they got them correct and don’t ask). Unfortunately, I cannot correct all exercises individually as there are too many students. I have about 130 students and 2 TAs.

Cons: There is little motivation to work hard on the exercises, as they see the solution before the test. (Yes, good students know they should do them on their own. The problem are the not-so-good students.)

Is there better solution that encourage students to work on exercises on their own?

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    What subject is this? – candied_orange Nov 17 '20 at 20:47
  • How can you be unsure about providing solutions to the exercises directly after the session, the week before the test or anywhen else? Is that not laid down by your school or area or education authority? If it's not laid down already, why not gather together teachers in similar situations and make a joint policy? – Robbie Goodwin Nov 18 '20 at 0:51
  • I moved the discussion about the best student/TA ratio to chat. Please read this FAQ before posting another comment. – Massimo Ortolano Nov 18 '20 at 15:00
  • @RobbieGoodwin, I wouldn't expect that to be obviously a matter of policy. We have no such policy at my university, and, given the different pedagogical approaches of my colleagues, neither I nor they would want to be bound to a single way of approaching problems and solutions. – LSpice Nov 18 '20 at 22:16
  • @LSpice Are you suggesting "Motivating students to work on exercises if solutions are provided" or "providing solutions to the exercises directly after the session" mean being "bound to a single way of approaching problems and solutions…" or what? – Robbie Goodwin Nov 18 '20 at 22:38
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The way for a "not so good" student to become better is to work harder and solve more exercises. Reading a solution is not at all like finding a solution. Your test becomes one of memorization rather than skill if you test on exercises for which the students have already seen correct solutions.

I would suggest that if you provide solutions, rather than individual help on finding solutions and seeing where the students went wrong, that you post them after the test.

And, the key, post those answers with additional exercises for those who did poorly on the test to get some additional practice. If you want to incentivize them to solve those exercises, provide some bonus to the test scores for submitting correct solutions to the follow-up exercises.

But you have an additional problem in that your "practice sessions" are probably ineffective if they depend on students knowing that their supposed solutions are wrong and that they need help. Students have misconceptions often enough and need to be pushed past them. If they "solve" exercises but no one checks the solutions, then they are unlikely to see where they made a mistake. The exam only tells them that the are wrong, but may not indicate why and it probably won't help them dispel those misconceptions for the next try.

The combination of a bit of stick and a bit of carrot might help. You have the stick (the exam) but you are missing the carrot. Give points not just for success but for hard work, even if it is re-work.

I often learned lots of math by doing lots of exercises beyond what was required. It was only through that extra work that I was able to achieve insight. Luckily I was self motivated in those instances, but not everyone is. In another course the professor provided lots of external "motivation" through "pop quizzes" which we hated but knowing they were coming, forced us to be ready every day. Remember "flash cards" from early elementary school? Lots of repetition. Lots of feedback.


An option that I've never used, but might consider in your situation is to require that students who did below a certain mark on one weekly quiz, submit their work for review in the following week (or two). This might reduce the number of papers you need to give feedback on and also make it feel like a reward for the better students who don't need to submit. Or even, make submission optional to everyone. And comment on the papers you do get.

With TAs, have them comment on exercise papers and pass them to you for review.

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    Tip: Don't describe extra work as, "required if your test score is too low." Describe it as, "optional if your test score is high enough." – Brian Nov 18 '20 at 16:47
  • @Brian, actually, I am referring to the normally assigned exercises, not any additional ones. Submitting them permits the instructor to provide feedback. – Buffy Nov 18 '20 at 16:51
  • If the exercise is always required, making submission optional is not a "reward for the better students who don't need to submit." Mind you, I would hesitate to call something "required" if you aren't even asking students to submit it. – Brian Nov 18 '20 at 17:00
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The underlying concern that you raise seems to be how you can best engage students to become self-motivated in their own learning processes, especially "the not so good students", with the resources that you have at hand.

Perhaps you might first reframe this as a question back to the students. What will help you (students) become more self-motivated in your own learning processes? After all, what good will you ultimately do in your quest to give away anything that is either not desired, not understood, or not appreciated for its intent? You may also discover that what you believe about the desire of your students to be self-motivated in their own learning processes is a chimera compared to the desire of your students to just get a good grade in your class. As disappointing as the latter finding is, it can serve as a reality check to recalibrate where you might better spend your time to reach those students who sincerely want to do what is needed to learn and yet still be honest with those students who are just passing through your course for whatever reason.

One solution is to provide no solutions to the exercises at any point in time. Instead, give the exams with questions drawn directly from a portion of the exercises. The self-motivation is the commensurate statement "If you do all of these exercises, you will have done at least X% of the upcoming exam questions". Finally, you could address your desire to motivate self-learning by having an open-door policy to students who want to review the answers to their work.

Another solution is to provide all solutions to all exercises at some point. Realize that, in this day of internet and with the interactions that occur among students, the minute that you open this door for even one student or one portion of the class, you have essentially opened the door for all students at that moment and for all students in advance for all future offerings of your course. You can in this case address your desire to motivate self-learning by stating that exams will have a (smaller) Y% of the questions from the exercises and a corresponding Z% of questions that stay within the scope of the course but go beyond the exercises. Essentially, exam questions from the exercises would test how well students know the material (even if that is only rote memorization) while exam questions not from the exercises would be designed to test their mastery of (knowledge of, understanding of, and ability to apply) the material.

Finally, an intermediate solution is to give only a portion of the answers to the exercises. Again, with reference that students will have these next time around, when you decide this option, you may as well give the selected answers directly along with the exercises. Here, you can also balance how you distribute the questions for the exams. One potential advantage of this approach is that you can reserve some questions from the exercises that you do not give answers so that you can use them on exams. You might also simply give some exam questions that are already answered as exercises just to discover how many students will not even commit to studying what they are given to know it let alone studying to learn it.

In summary, each of the above three options has its own balance of resources and outcomes. I think that none of them are inherently wrong or right. I think that your first calibration point to decide which option you will use is first to discover what your students believe about the concepts of self-motivation as applied to learning.

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    exam questions not from the exercises would test their UNDERSTANDING of the material — "Understanding" is the wrong target. The right target is mastery of (for facility with) the material—not what they "understand", but what they can actually DO. – JeffE Nov 17 '20 at 15:01
  • @JeffE I've restated accordingly. Thanks. – Jeffrey J Weimer Nov 17 '20 at 15:22
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As an instructor, I can assign readings to students, but I cannot actually force students to read. I can only provide consequences in the form of good/bad grades by, for instance, testing students over the reading. I believe it would help you to similarly identify which actions you have control over with regards to giving practice exercises.

Students who attempt the exercises before comparing their answer to the solutions could benefit from formative self-assessment, i.e. identifying where they went wrong and how to correct it, or validating correct approaches.

  • You could withhold solutions, which would make it difficult for students to self-assess their work, but would also prevent students from only reading the solutions without attempting the exercises.
  • You can provide the solutions as well as instructions on how students should use them for the best learning. You cannot force students to follow those instructions, but the reward of good grades (assuming your exam assesses the desired learning outcomes) is a motivation you can provide.
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Generally I think it's good for the students to get some but not all solutions. It is sometimes helpful to see how an exercise is done properly, for orientation, and for learning certain things (including how to write). On the other hand providing too many solutions implicitly communicates that the exercises are not about "exercising" but about knowing the right answers, which in my view they are not. Also it will encourage the idea that studying is about learning what's right rather than about understanding and developing one's own thinking. (I regularly have exercises that don't only have one unique true solution, and I don't want to communicate through an official solution that "this is how you have to do it all the time".)

I will only decide afterwards which solutions the students get, sometimes based on student requests (including doing surveys about "for which one of the five exercises do you want to have a fully worked through solution", of course after they have done them).

Another thing is that one can make active work on exercises a condition for passing the course in one way or another. Versions of this are "everyone has to present on own solution in class at some point", or giving marks on exercises that count toward the final course mark. I have given marks for "serious attempts to solve exercises" regardless of whether they are right or wrong, then only contributing a small percentage to the overall course mark, such as 10%.

Actually your tests do this in a way, but as you correctly state, the problem is then that students may be tempted to solve the test based on the given out solutions rather than their own work... so this approach combined with giving out all solutions is problematic exactly for the reason you state. Keeping the tests I'd probably publish selected solutions in a somewhat unpredictable manner, see above.

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You are doing two things wrong. (1) You have been provided with two TAs, but you are not using them to give students feedback on their exercises. (2) You are not handing out solutions.

The result of this is that students are operating in a complete vacuum. On the day they walk into an exam, they have absolutely no information about whether their own work has been correct.

You complain that "I cannot correct all exercises individually as there are too many students." No. You have 130 students and 2 TAs. That is a very generous level of support. You may not be able to give detailed feedback to every student on a large number of problems, but you can certainly give detailed feedback on some fraction of the problems, or less detailed feedback on all of them.

There is little motivation to work hard on the exercises, as they see the solution before the test. (Yes, good students know they should do them on their own. The problem are the not-so-good students.)

This is why you have been provided with two TAs. Their job is to grade the exercises in order to provide this motivation for the less mature students.

Depending on what this class is, you may also be deluding yourself about whether students already have access to solutions. For lower-division math and physics classes, for example, any student who pays $20/month for a chegg account has access to essentially every homework problem in every popular textbook.

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  • Note that not everywhere can one use TAs to check students' homework. In some places, TAs may be required to do other duties. – Massimo Ortolano Nov 18 '20 at 15:04
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It depends on the subject, but in some of my physics classes for example, solutions were often provided for at least half the homework problems in advanced.

However, knowing the final value of a solution isn't the same as providing a walkthrough for how to complete the problem, which is itself more difficult and more important for having a grasp of the topic.

Often times, having the solution in hand was more incentive for me to work through the problem, because I would be able to tell if I ended up in the right spot, and if not, I would have to rethink how I approached the problem. Without a solution in hand, I was less likely to reevaluate my work, because I didn't know if I was converging or diverging from the correct solution.

tl;dr Providing the solutions can provide good motivation to complete the problems, depending on the subject.

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  • I might be confused: what is a solution if not a walkthrough for how to complete the problem? – Denis Nardin Nov 18 '20 at 10:44
  • @DenisNardin For example a physics problem might ask you to solve for how far a cart will slide, so the answer in the book might be 2m. But this won't tell you how to set up for solving conservation of energy or momentum or what have you and working through, which is often a significant part of the grade as well. – spacetyper Nov 19 '20 at 10:14
  • Oh I understand what you mean. I think I would not consider those solutions (certainly I would give a student who provided only the numerical answer 0 points, while I could give full marks to a student who wrote a correct solution but did a silly arithmetic mistake in the last step). It's a bit moot for me, because almost none of the class I teach have such numerical answers. – Denis Nardin Nov 19 '20 at 11:51

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