Students are just like me. They (typically) will do what is expected, the minimum expected. Let me explain through an example from my life.
My example at home is my wife and I have a fairly clear set of chores that we each "own." But when I am really busy with school some of those things slide to my wife, mainly setting the table for dinner. I am suppose to set & clear the table, but sometimes I "let her" cause I am grading quizzes or whatever (and she is super supportive). And these busy times usually run in 2 day sprints, so I won't set for 2 days -- then even though I know I should set the table for supper for some reason I don't. My wife then has learned to ask. Cause I am a space-case? No! Because I quickly adjust to my new expectation -- I really appreciate the help she gives when I need it , but I quickly revert to the minimum I can "get away with." (And I really appreciate when she asks me to set the table once I am through my busy spot). Students are exactly the same....
I can talk about why math and understanding is important, but that does not drive many students at all. But the consequences of not learning the material is what keeps the average student going, translation they want to pass. They will learn whatever the minimum needed to survive, to get their minimum grade overall (whatever they set for themselves). So as long as they want to pass they will work only hard enough to meet their minimum letter grade (not try-ers require different things, their learning cannot be about a grade, their consequences need to intrude on what they want).
So I have to remind students to "set the table" often -- to learn the material, I never talk about grades - my favorite saying about grades is that they take care of themselves. Thus my courses must require knowledge and application of that knowledge so that every student who passes actually knows the math. Meaning a D student must have enough knowledge to be ready for the next class without a lot of remediation. I believe too often math teachers don't get their C and D students ready for the next course in math sequences. Heck, if 40% of incoming Freshmen in most UWs need remedial math (9th grade Algebra), and they had to take Alg 1, Geometry & Alg 2 to get into any UW; how could we say that our D, C or even B students really understand the material. I am really proud of my results at Juda the last 2 years. Any student that has received a D- or better has not been remedial at college the last 3 years. (Confession: During my first 3 years I had students who earned Cs and Ds but could not really do the math.)
The above statistic is why I often remind my students and myself that they want to have me be their toughest math teacher. And since I work for them (their future-selfs, I work for the student when they are 28) I don't let them get away without the knowledge. By doing that I don't have to care about grades, cause grades prove little. It proves knowledge at a time, it may show the ability to plan but not too much. But often it only shows the students who best "play the game of school." I have had many A students that I would not have wanted in my machine shops prior to teaching but plenty of D and C students I wanted (I miss ya - Tim).
Effort is more important than the ability to "play school." Drive to learn is more important than grades. Understanding more important than speed. I use these thoughts every day, I remind myself to make sure the students understand math, I encourage, I push, I dry tears and then encourage some more, but I do give grades without skills. I remind myself that once they leave Juda I am no longer there - so I must follow my cliche "Be less helpful" during quizzes/tests (which means I offer no help on assessments - I always say "Don't worry come in before/after school we will review and work through so you understand so you can do on the next one.")
So as I sit here on an early Sunday morning planning my week of courses I remind myself::
Make the students set the table....