As I’ve mentioned in the past, I don’t have full control of my finite mathematics course. I asked for certain leeway in my grade breakdown, but had to settle on leaving the four class tests at 60% of the overall grade (in contrast to my precalculus where there are two tests making up 30% of the grade). Consequently, the students still treat my class as if nothing counts until exam week. Sure standards comprehension make up 30% of the overall grade, but they aren’t EXAMS!!!! How do I convince these kids that the typical college attitude will not cut it? They have an opportunity to spend four years living the life of the mind. Instead, they spend four years taking their mind off life. The night before a quiz, I stayed up late making screencasts of linear programming problems. One student told me how much he appreciated it, only he hadn’t had time to watch it because, “you know, the Yankees were on.” Guess how he did on the quiz?
Maybe I have to follow the rules and set my percentages like everyone else, but is there a chance that I could change the name (retention assesments?) and de-emphasize the importance of exams so that the day-to-day stuff gained relevance? Or are students socially constructed to work this way: slack, slack, slack, cram, rinse, repeat?
GL(s,R) 
If I remember right, “finite mathematics” at your school is not “applied discrete math”, but “math for kids unready even for pre-calculus high school math”. Motivating those students to study is going to be an uphill chore, no matter how you structure your assessments of fiddle with scoring schemes.
It’s true. The odds are stacked against me from the beginning. On the other hand, I just caught a fly with my hands I’d been chasing for ten minutes, so maybe this is possible too!