I am teaching a 3rd year undergraduate algebra course, and I have told my students that I would not be giving out solutions to the weekly exercises that I set. Instead,
- one question per week will be graded and detailed written feedback will be given by way of continuous assessment, and
- there are weekly tutorials where they can ask questions if they struggled to solve something or if they are unsure if their solution is correct.
Many students are extremely unhappy about it, so I would like to get 2nd/3rd/etc opinions from other experienced educators here. I will provide my reasoning below, but first the question:
Do you give out model solutions to your exercises, say one or two weeks after they were set? This is primarily aimed at educators in science subjects, where there is a correct solution to each exercise.
My reason for not giving out solutions
My main purpose in teaching a mathematics course is to teach students to solve problems; to be stuck and to persevere; to seek creative approaches. I am pretty sure that if the model solution is one click away, or even if they just know that it will arrive in a few days' time, they will, on average, spend less time on the exercises, and some of them will just give up when they cannot solve something within 10 minutes. One student explicitly told me that they like to use model solutions to "work backwards" to complete their understanding of the course material. This is simply not the intended use of the exercises.
A little more background
I was student at Oxford UK, I taught at Cambridge UK, Warwick UK, and Postech Korea. At none of these institutions did students expect to be handed out model solutions. Now I am at Glasgow, where students' expectations are wildly different. However, due to a research grant I have not taught for a few years, and I do not know how much of this difference is not just due to geographical variation, but also to a temporal gap. I can certainly see infantilisation and bureaucratisation of university education on a wide spectrum of issues, I just don't know whether this is one of them, so one answer could be "wake up, you are stuck in 2015 with your ideas about university mathematics education; these days we are all expected to give out model solutions".
I did check what the School policy is on solutions to exercises. There is no need to go into details, but suffice it to say that both decisions, to give out full solutions and not to give out almost any, would be compatible with the official policy.
Frequent arguments for giving out solutions and my response to them
- These are responsible adults, don't treat them like kids. They know that they are supposed to first attempt the exercises themselves. The solutions are there for when they get truly stuck or to check the correctness of their solution at the end.
Contrary to popular opinion and superficial appearance, this is not really an argument, but a rhetorical device dressed up as an irrefutable argument. The fact that they are of legal age is irrelevant here. Firstly, they simply have little experience at independent learning. We do not say about a patient "They are an adult, they can choose their therapy themselves", but leave that choice to experts; the age or legal status of the patient is irrelevant, only their experience in that particular domain is. Secondly, even adults can have a hard time overcoming temptation. I am sure I do not need to elaborate on this last point.
- Everybody studies differently. It is unfair to impose your personal choices on others.
Actually, this is precisely what a pedagogue is paid to do: to impose certain choices on their students. We do that through selection of the material, of the order in which to present it, of the exercises that we set and don't set to our students, and yes, through the mode of delivery and the resources that we make available or choose not to make available. Of course what distinguishes a good pedagogue from a bad one is how good those choices are, hence this question.
- How can the students know if they have solved an exercise correctly?
I have to confess that I underestimated this one. I always thought that in mathematics one knows when one has proven something, but many students obviously don't. However, that is what the tutorials are for. It might be relevant to add here that the tutorials are happening via zoom, and the engagement, so far, has been pretty lacklustre. Many students don't switch on their mic or camera, and about 1/3 of them show no signs of life through the entire tutorial. Certainly, the percentage of students that say "I would like to see how this question is done" is much lower than of those complaining about the lack of model solutions.
Anyway, I could say more on this, but I would like to hear your experiences and thoughts!