I am teaching a math class where the students, most of them, tell me that they can understand the materials given by me during the course. I test them during the course too and they seem to get it. However, when it is time to face quiz or exam problems, they don't know what to do.
At first, I thought that my exam is too hard. However, I usually, definitely, give problems that need the understanding of materials I give in the class to solve, but add some "spices" to them. By spices, I mean I always assume that in an exam, there should be a little bit of challenge, not just repeating exercises. It is a test after all, right? I will not repeat problems I gave previously during the course. Sometimes, even when I intentionally give the same problems, they still don't know what to do, most likely because they do not repeat until they understand after class.
For example of the problem, instead of just asking how many ways we can arrange a group of 4 letters, I ask how many ways we can arrange a group of n letters. The point is that I won't repeat and will give a small added challenge during exam.
I thought I should give them homeworks and also tutorial sessions, but the math program is new (just two batches now), so we have no tutor..nor grader. I do it myself almost always. We have no money for tutors either. Thus, I can't do anything else (like finishing paper, doing administrative task, etc) other than helping my students. Indeed, it's gonna be so tiring.
I genuinely want them to succeed and this is just my second year of formal lecturing. So happy knowing they understand me when I teach, but no idea yet how to make them exercising more often, other than reducing the covered materials maybe? Doesn't seem wise. Or should I make the exam..a repetition of problems, where only the information about the numbers given is different? It will kinda help but I am just a little bit afraid they will only be able to do specific problems with no small added restriction, resulting in less flexibility of problem solving.
ADDED: It could also be due to my experience as an undergrad student in one of the leading universities in my country. I am still so fresh to remember my days in college where I was given problems in exams (most of them) that was served more like challenges rather than competency tests. Hence my mindset was like "Exam is supposed to challenge you with extra work". Now I am teaching in a not so well-known university where I should've known the standard set would be much lower, which is in the form of fewer materials given. Hence, I am still in the mindset that while university is a place to learn, it is also a place for those who can flexibly apply what they learn, now matter how high or low the standards are.
Any suggestion on how do I demonstrate flexibility to students other than by having them learn the basics and giving nonrepeated problems (in exam) to test them?
Some of my students do fine with the extra work exams, but most of them, predicted from quizzes, still need more work and guidance before midterm.