Stopping the "Will I need this for the test" question [closed]

I am a college professor in the American education system and find that the major concern of my students is trying to determine the specific techniques or problems which I will ask on the exam. This is the typical "will this be on the test?" question.

I find this to be a major detraction from students education. Students seem to have the notion that they can discard a lot of ideas and just memorize a few specific problems in order to pass the class. Given the philosophy of some teachers to "teach to the test" when in a standardized testing environment, this does not surprise me.

This stressful approach to education seems to make student overlook major themes in each class and themes in the subject as a whole. Even worse, once they land in classes like calculus 3 and real analysis, the effects of this point of view rears its head in an ugly way.

My question is:

How can we turn students away from this way of thinking?

Solution 1:

The psychology of all this is quite simple, IMHO: no matter how much a student may WANT to learn mathematics, the fact is that she MUST earn acceptable grades, and success in the former doesn't always guarantee the latter. It's a basic hierarchy-of-needs issue. If a student strives wholeheartedly to learn the material with no specific thought given to exam results, the result is often a worse grade than if the student had striven solely to do as well as possible on exams. Any responsible student should and must ask endless questions about what's going to be on each exam, and is given no choice but to prioritize grades over learning, since a student's academic reputation, financial aid, and prospects for employment and/or admissions to successive levels of schooling all depend much more on GPA than on less tangible qualities like subject matter mastery. Of course, taking a long view, one easily understands how crucial such mastery will be in the long term, but students rarely have the luxury of adopting such a perspective when they know that a single red "73" scrawled at the top of the next exam may literally cost them thousands of dollars in the short term. The solution? There isn't one, practically speaking. Theoretically, we'd just have to scrap our entire model of education and replace it with something new.

Solution 2:

I don't think the root problem here has anything to do with mathematics. It has more to do with the conception that education is a process of transferring facts from people who know them to people who don't know them. This is true in a way, but it's not merely students memorizing facts and behaviors.

To really fight this problem, you would have to change the entire culture. You would have to get students, their parents, and educators to support the idea that there is more to learning than just behavior like memorization and routine algorithms. You'd have to get support for that in a big way, and that's very hard.

The parts of learning that people most often overlook are things like

• critical thought and decision making processes in an unfamiliar situation
• transfer of ideas between contexts (to the type of students you're talking about, there is only one context: the test. They only care about transferring class to the test.)
• thinking about learning itself (and observing how you learn things)
• Recognition that you usually learn more than just the contents of what you are told (Even if you don't ever use the specifics of what you learn, you will most likely use some meta-idea you learned during the process of learning.)

Unfortunately, cognitive studies have shown that decision making processes are among the hardest to transfer from experts to nonexperts. It simply takes time and experience. Ultimately achieving mastery of something relies on the student's willingness to keep at it.