Stopping the "Will I need this for the test" question 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?

 A: Kudos!!!
For starters, I appreciate that you're asking this question. It shows that you are among the rare breed that deeply cares about teaching and what the students learn. Because you do, I'll give you my opinion and some cases that prove my point.
I'm a student, and my honest opinion is that you need to stop weighing so much of the class on the test and focus more on growth. The biggest problem in today's schooling systems is that educators focus so much on the numeric portion(grading) of schooling that we often forget about the main goal of grading, which is to measure the progress a student makes and to know if a student reached a certain level of competence. 
Many students like myself want to focus more on learning than exams, but we often have to place so much emphasis on the grade because that's what we need to get in and stay in college, get and keep scholarships, get a good first job, and have a good social standing among a lot of people(nobody wants to seem like a nobody). This is especially true for jobs. With the job market getting ever more competitive every year, we need those grades to have a more secure life.
You see why we only learn to the test now? 
There's a solution you can enact in your class however. When you have the time read the book Great By Choice & Good to Great. I cant remember which one of the two books said it (I think Good To Great), but by enforcing constant growth that isn't too fast or too slow and using fun as a driving factor within your classroom while only having test to measure the progress (not worth any points), you'll get better results than just teaching to the curriculum. This is because each student will eventually have a sense of confidence in what they're doing. By the end you'll have better students. I can almost promise that the students will worry more about learning. 
Example 
In the book Good to Great the author interviewed a track coach that helped her students reach Nationals within 3 years. Before they never even reached state. When the author's team asked what her secret was, she said that it was that she boosted the confidence each student had by having them run consistently everyday for fun, no matter the conditions;everyday constantly growing by a certain amount each time. She was never too critical when a person wasn't as good as the and others, she simplily said "It's okay as long as you get better next time, " and she pushed them to do so. When the students reached a certain confidence, they all looked at the Nationals and said "I think that we can win Nationals." She said, "Okay, let's do it" and all did. Sure enough, the team not only won nationals, they had more people sign up for the team. 
So how do you do this in the classroom?
State it simply, "It doesn't matter if you do good or bad on exams, if you don't improve constantly as time progress, you'd miss the point of the class and you wont get a good grade." That's how artist teach their classes, at that works out very well. That way a person will grow considerably from your class on and the pressure will be taken off of exam grades and more on the growth from the beginning at the class. Also, try making the smartest person in your class help out everybody else for an extra points. Everything will be balanced by the end.
Huge Edit
I totally forgot to add that by showing a lot more care towards the students you instantly get better results. I use this second example a lot.
One of my professors used to tell me the story of his educational childhood. He grew up in an unknown town, is dyslexic, and his single mom had 3 boys and a 5th grade education (extremely horrible in thing in the 50s and 60s). By no means should he be successful in the educational world. All odds were against him. What steered him straight on to graduating in Electrical Engineering on the deans list at Michigan State University and attending grad school at MIT was that a teacher in second grade sat down with his mom and said, "Your son has a reading problem, but we'll work together and solve this problem and bring out his best potential" -- and of course she did --, he instantly became more attached to school and learning. It meant something more to him. He felt less like a number and more like an individual. 
Sit down and work with each of the students a lot more. Basically force a 10 - 20 office hour and work with them. They'll feel like you care, even while you might be tough on them and you'll notice every single one of them will do better.
If you have a big class, show care to a small group of students then set the expectation for them to do the exact same.
A: A lot of students are concerned about, oh, losing their scholarship if they miss something. Others actually believe (or are aware of the fact, depending on your point of view and/or experience) that what you ask on the test is the really important stuff. Not only from a GPA point of view, but what they'll need to pass the next course, or to do their job well in the future.
The other side if that comes down to crappy scheduling on the part of faculty. In my senior year of EE undergrad, I had, in ONE class:


*

*A design project, with a demonstrable, physical product, which took about 30 hours to construct,

*Matlab simulation of said product (~10 hours, but I was already a professional programmer, others took much longer for this)

*A homework assignment with 10 questions, each of which had at least 5 "parts" (ie, 50 questions), the easiest of which took about 10 minutes. Do the math.

*A test over said homework assignment.


Now, here's the kicker:


*

*The project was assigned the Wednesday before Thanksgiving (a holiday in the US rivaled only by Christmas)

*The labs were closed over the break. We had to collectively bribe the facilities manager for a key. (Really. There was flack later, but at least we passed.)

*All of this was due on the same day (including the homework assignment, which was covered on the test. So we had no grading feedback on the homework before being tested on it. It would have been more efficient and has as informative to treat the homework assignment as the test, and skip the extra stress.)

*All of this was due on the Tuesday following Thanksgiving. It would have been Monday but the school was closed due to inclement weather. And it's hard to submit a breadboard through email.
Now, this was a three credit-hour class. I was taking 16 hours at the time. These were not the only major assignments that were assigned and due during the surrounding two-week period. Things were made worse by the fact that I had a wife and a full-time job at the time (this wasn't night school - but that's a different conversation), but the other students, some of the smartest, most motivated people I've ever met (even 10 years later) - were about to throw themselves off of the building.
To wit:


*

*They want to know what's on the test so they can find out what you think is important,

*Even the most dedicated fanboy who wants to master every thing you teach will not, in reality, have the time to dedicate to such a task if he/she is taking multiple courses,

*Professors rarely coordinate to avoid crunches where every course has a major commitment due at the same time,

*They have realized that not everything that is taught is actually going to come up again. As in, ever. At all. This is the sign of an intelligent student - be grateful. 


*

*If they're wrong, and every topic you cover will come up in the future, your course should probably be split into multiple parts. This seems unlikely. Trim the fat.

*If they're correct, stop wasting everyone's time and focus on the important things.
A: Actually, I think you're wrong. This is not necessarily any indication of a problem.


*

*I have had instructors for the most challenging and interesting classes of my life themselves voluntarily state "You will not be tested on this material."
They have also answered the same question quite honestly when asked.  

*I have asked this question myself, and I can assure you that I have rarely had any "notion that I can discard a lot of ideas and just memorize a few specific problems in order to pass the class".

*I have seen many other students ask the same question, and I know they were not the types of students who would fall into your category, either. In fact I have seen some of the best students in the class ask this question.
The most common reason I have asked this question is that the pace of a lecture can be too fast to take notes and understand the material at the same time. Either you take detailed notes and review them later -- which can make you lag behind by a few minutes -- or you save the energy and instead use it to try to follow every step in the lecture. Many people (myself included) just can't do both.  
In fact, sometimes instructors clearly follow the sentence "you will not be tested on this" with the sentence "you don't need to take notes". The goal here is to just listen and focus on the (perhaps intended-to-be-interactive) lecture, rather than to save it for future learning.  
Similarly, if I know I'm not going to be tested on some material, that means I know it is outside the scope of the class. In that case, I will probably take less detailed notes, and instead try harder to follow your explanations as you go along. Why? Because there probably isn't that much detail for me to write coherent notes anyway -- taking notes wouldn't help because I'll have to repeat that again in a subsequent class that actually covers the material. So I might as well just listen and try to follow what you're saying.
A: 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.
A: Do nothing but open book tests.  Give them fact/equation sheets.  This question is caused by students being tested on things that they can memorize.  This question should never come up if they're given everything and the test is on their application of what they've learned.
If you don't want to see people study by memorizing, then don't make them memorize things.  It doesn't make sense to test them on that stuff any more either, since you can Google the basics of pretty much any subject and there's no reason they couldn't just use their textbook at any other point in life, except for those 1-3 hours in "normal" testing situations.
Your answer will then be, "You will have all the tools/equations/facts you need given to you on your test/exam.  Practice, and make sure you know how to use them."
A: The trouble with most educators , in my humble opinion, is that they know little about cognitive psychology and its relationship to how we learn. I am a retired college teacher of some 27 years  and I have seen much poor teaching, including my own.
The brain is poor at thinking
Firstly the brain is designed to save us from thinking, that is , the brain is designed so that things become automatic so that the limited working memory we have can be used more effectively. So practice becomes an important part of any effective teaching strategy. Ask any concert pianist or professional athlete or any top notch scientist. The basic skills of any subject must become automatic. This then allows the working memory to deal with new and unusual problems. An expert in  any field is one who constantly practices, either overtly or indirectly many basic skills and strategies. 
Cognitive research has shown that when solving new problems the  "expert" - engineer, scientist, mathematician, physician- recalls from longterm memory similar problems.
So to answer the question "Will this be on the test?" I would make it clear to the student what the relevant basic skills and facts are and what must be mastered for the particular course. I would also make clear, by giving relevant examples,  how these basic facts and skills can be applied to specific problems so that the student can demonstrate how such basic skills and strategies can be applied to similar problems.
Critical thinking is difficult to teach.
If it is implied in the question that we want students to be critical thinkers Daniel Willingham  shows in his paper (  http://www.aft.org/pdfs/americaneducator/summer2007/Crit_Thinking.pdf
) why it is difficult to teach this skill and ways to get around this problem.
Willingham  http://www.danielwillingham.com has a lot to say on effective teaching practices.
A: Students want to do as little work as necessary - either because they're truly lazy and don't care about learning the material or because they are taking five other classes plus working a job plus two other things plus trying to maintain some semblance of what can be called a social life. Appeal to their laziness and explain that learning concepts is in their best interest, in the present as well as the future.
As a student, I found that learning concepts rather than the rote memorization of facts both 1) reduced my workload and 2) increased my test scores.
1) It is much more difficult to memorize two dozen facts than to learn the three concepts that develop/discover those facts. I spent less time learning because concepts build upon other concepts - learning becomes progressively easier (or at least, it never becomes more difficult) as I already know the foundation of what I'm learning. The concepts stick with me much better than the facts I've long forgotten, and I often find myself applying what I learned in one field while solving a problem in another field (and isn't that the whole purpose of general education?).
2) I have always scored higher on tests than my actual knowledge - given my understanding of the underlying concepts, I was able to either figure out new things or make educated guesses and get pretty close (most of the time).
A: I had an economics professor state on the first day of class (and within his syllabus) that any topic/material for which this question was asked would be on the test.  He further stated he already has tests written up for the course, but would add additional questions to the test(s) every time this question was asked.  The additional questions would cover the material related to that for which the question was asked.  Lastly, to ensure everyone understood, he explicitly stated that by asking the question "Will this be on the test", the students were only making the test longer and harder.
A: Distribute practice exams a week or so before the test. Make them represent the style and difficulty of the exams, but make sure that one couldn't pass the real exam just by memorizing the specific set of techniques used to solve the practice test. Make the tests dramatically more complex than the homework. Fashion them in a way that leverages the course material and relevant prerequisite knowledge in a cumulative way.
I had a professor who would do this. At first it would seem like I'd gotten the practice test for the wrong class. Then I'd realize that the problems built on several different techniques learned throughout the class (and in the prerequisite classes). It would take hours upon hours to get through the practice exam. In the end I learned far more about the material and how to really apply it, and had a lot of success on the real exams.
And there would have been no point in asking whether something would be on the test. Everything covered in class, on the homework, or even in the prerequisite classes was fair game.
A: I am student (in Germany not in America, but the situation is the same...) and for me the origin of your problem is the way the lectures are organized resp. structured. There are weekly worksheets in each lecture and most of the time these worksheets consist of very, very specific applications of some theorems and definitions that were given in the lecture. At the end of a semester there is a lot of stuff, more common one and more specific one and for a student it is very difficult to decide, which things within the semester were more important than other contents, which were done to get details and which were taught to get an overview. So according to my opinion the only possibility to handle all this stuff as a student is to ask, what will be important in a test and what rather not.
On the other hand there are lectures in which one chapter needs the chapter before and so on so that it is obvious that indeed all is need for the test. If a lecture is well structured and the work sheets really have to do with contents of the lecture (and are not too detailed so that one does not see the connection to the lecture) students do not ask what is needed and what not. This is my impression based on my own experiences.
The question "Will I need this?" is always an expression of the confusion of the students when going through the semester's exercises and therefore nothing else than a kind of feedback to the way the lecture was.
A: I like the answer "Maybe" or "What do you think?" -- or perhaps "Maybe", followed by "What do you think? Will it be on the test?" after the students hound you for a more definite answer. And if they glibly answer "Yes" or "No" to your query, then immediately ask them "Why?" or "Why do you think it will be on the test?" (or won't be) -- the goal is to throw it into a Socratic dialog to make them think about the importance and context of the knowledge you're trying to pass on. Or maybe it will at least slow down the little bastards from asking that dumb "will it be on the test" question next time.
A: I think a number of the answers here are completely missing the point.
Why does a student ask "will this be on the test"?  A student, of any discipline, has one of two motivations depending on their situation.  The first motivation is that the class directly applies to the career they are pursuing.  These students will indeed try to get everything they can out of the class for the simple reason that they care.
The second motivation is when a class is a prerequisite for something else that they actually are interested in.  In this case, students will try to get by on the bare minimum of facts and for them "is this on the test" is a crucial question as to whether they are going to devote time on this subject instead of time on something they find far more interesting.
Now, of course, complicating these are two situations at the extreme of each motivation.  The first being the situation of someone who is merely trying to get a degree, where almost any will do, in order to move on with their life.  They will never want to dive in and instead will always just want to know what they have to study.  
The second one is almost as bad, but is a really critical point.  This person is in a highly competitive environment and understands that a few points on a test may have major repercussions in their chosen field.  Any advantage, such as knowing what to focus on and what to ignore, is paramount.   Unfortunately grading, and the pressure put on each grades meaning, is responsible for this.
If you really wanted to get rid of the question, the only viable way is to get rid of grades and established time frames (semesters) for absorbing the material and instead focus on helping students with the acquisition of skills necessary to get a degree in their chosen field.  In other words, a "subject" is instead geared around having the student perform it's mastery, regardless of how long it takes or how many times it takes to do the demonstration, prior to allowing them to proceed.  By the same token, a student who shows mastery early on shouldn't need to spend months going over it and instead should be able to bypass the subject.
Unfortunately, this is a radical change that a great number of universities are simply not interested in pursuing.  It's certainly a far better way of teaching, similar to a journeyman, but it takes far more effort on the part of the educator, among other issues.
As a side challenge, consider this.  If you knew your boss was going to grade you on a particular set of skills (ie: performance review) wouldn't you want to know what was going to be part of the review process?  In the corporate world this is usually spelled out.

So, for today, I'd say, let them ask the question and simply don't be perturbed by it.  Because now you might have an idea of why they ask.
A: Make your teaching more broad. When you introduce or refer in your classes knowledge from physics, astronomy, information technology, music, and any other field of human activity students know the question "Will I need this for the test?" is inherently invalid. And they just don't ask it.
Examples:


*

*differential equations, solve a simple one-dimensional equation of motion with viscous resistance $\frac{d^2x}{dt^2} = -\alpha \frac{dx}{dt}$ with some initial speed.

*combinatorics, how many bits in pointer we need to address any cell in 8GB RAM memory?

*logarithms, calculate distance in semitones between 5th and 6th harmonic (should be around minor third)

*trigonometry, calculate length of comet's tail if you know: angle between sun and the comet, distance from Earth to comet, and apparent length (angle) of the tail as seen from the Earth

*integrals, what is the approximate surface area of paintings on Sistine Chapel ceiling?


Every area of mathematics is used somewhere. You need only few words to introduce a problem.
The only issue is principal's and parents' attitude. Be strong, say this is your way of making job done.
A: The approaches Cambridge adopts is giving out a syllabus at the beginning of the year for each course and everything on that piece of paper is maximal for examination, minimal for lecturing. see: http://www.maths.cam.ac.uk/undergrad/course/schedules.pdf
You, of course, only need it write one for your course and hand it out at the beginning of the course. Of course, you may decide to strike out a few things at the end of the course in exceptional circumstances.
I think this is a good approach, because every time you get a question on 'if we need to look at this for exam', just tell them look at the schedule. Notice the schedule I linked to your is pretty vague. This tells them what they need to know, but keeps them guessing how much they need to grasp and also gives you leeway if they argue your exam is too hard.
One of our lecturers actually made it clear to us that deciding for yourself what is important and what isn't, is an important skill in mathematics. You can (and should) do the same and make it clear at the beginning of the course that you will not be spoon feeding them and summarising for them what is important.
A: 
How can I stop the "Will I need this on the test question"?

Your options are:


*

*Don't teach things that won't be on the test.

*Put things you teach in the test.

*Don't have a test (weekly quizzes, participation, projects/assignments are still fair game), and if assessing performance is necessary, do it through other means.

*Don't use the threat of low grades to motivate students. Have tests that are easy enough (given some basic amount of effort) that students can stop worrying about the test and start worrying about actually learning.

*Make your material interesting enough that students value actually learning it more than they value a high GPA. This can be because they see the immense practical utility, because they are impressed by the theoretical beauty, or any other such reason.


These options can be combined. The main idea is this: Imagine a student at 8:45 am. He is thinking, "My lecture starts in 15 minutes. Should I go to the class or should I read some random book about the history of science fiction because I enjoy learning about that?" How will the student decide? He will probably go to the lecture, because not learning about the history of science fiction may or may not lead to problems in the future, but not going to the lectures will certainly lead to problems.
To a student, learning some concept which may or may not be useful is less optimal than studying for the test. Studying for the test has obvious, clear benefits. Not studying for the test has obvious, clear disadvantages. Both of these are not the case for "actually learning". You must either decrease the payoff from studying for the test, decrease the cost of not studying for the test, increase the (perceived) payoff from learning, or increase the (perceived) cost of not learning.
Finally, realize that not every student taking your course can be made to want to learn the material. Some of them hate your course and want nothing to do with it, but are forced to take it because their program requires them to.
A: I have been a German teacher and in my opinion, this only works with "open problems". That means problems where there is no one and only way of solving them. Also several techniques have to be combined to solve them. 
I'm not sure if I can make this clear, so let me give you an example. The problems have to be motivating. The solution must not be clear at sight. 
Bad example (an exageration): Calculate $\left(a+5x\right)^2$
This is not thrilling and the students know right away it is the binomial formula. 
Good example: A rope is hanging from the ceiling. There is 1m of rope left on the ground. If you take the rope and go $1,5$ to the left, the rope is straightened (no rope on the ground). How high is the room?
I think those open questions bear motivation. And thats what it is about: the motivation must not be the next test. 
A: If your classes are small enough to permit it, I'd suggest replacing the tests by oral exams. 
In my experience, they can better judge if a student has a broad understanding of the topic in question that a written test, and I think students understand this, too. Therefore they might be less inclined to find the "set of calculations to learn by heart" and more inclined to understand concepts or proof ideas and such.
A: Give them interesting real world problems to solve with the maths that you're teaching them. They'll still want to know what's on the test, but they'll also start to see maths as something useful and interesting.
A: I'm a current Math undergrad (a junior).  I've gotten to the point where most of my GenEd requirements are met, so now I can focus on Math and Computer Science.  As I'm sure you know, these courses are very time intensive.  It helps to be able to focus on what's important for a grade so I'm not wasting time.  For instance, in the Spring I'm taking Modern Algebra, Number Theory, Complex Analysis, and an algorithm course (and Spanish).  It's going to be a ridiculous amount of work, but I want to graduate on time and hopefully go to grad school. 
Yes, I want to learn and understand every concept being taught. And, no, I don't think I have the faculties or the time to be "test-ready" on all concepts especially during a final exam week. 
A: This question to some extent implies that students have an infinite time to acquire every piece of specific knowledge that is required to master the subject. 
Even the best students have only a finite amount of time and energy/focus they can devote in a year to a specific subject and thus it is perfectly natural to try and ascertain where they should focus their most valuable commodity (which is time) on. It's all about supply and demand.
The easiest way to solve this problem is to give students as much time as they want to write exams (even if it takes days or weeks), and to allow them to use any resources at their disposal (such as the internet, other students or even yourself). This will probably never happen though.
A: This reminds me of something Neil Tyson said in twitter: "When Students cheat on exams it's because our School System values grades more than Students value learning.". In a nutshell, they ask you: “Will I need this for the test” because their interest goes in obtaining a good grade on that test and not for the purpose of learning maths.
So if you could change the latter, by convincing them that 'maths are better than grades' and that its beauty is hidden by the 'memorization rules', then they will surely stop asking such questions.
Terence Tao adds in his blog:

When learning mathematics as an undergraduate student, there is often a heavy emphasis on grade averages, and on exams which often emphasize memorisation of techniques and theory than on actual conceptual understanding, or on either intellectual or intuitive thought. There are good reasons for this; there is a certain amount of theory and technique that must be practiced before one can really get anywhere in mathematics (much as there is a certain amount of drill required before one can play a musical instrument well). It doesn’t matter how much innate mathematical talent and intuition you have; if you are unable to, say, compute a multidimensional integral, manipulate matrix equations, understand abstract definitions, or correctly set up a proof by induction, then it is unlikely that you will be able to work effectively with higher mathematics.
However, as you transition to graduate school you will see that there is a higher level of learning (and more importantly, doing) mathematics, which requires more of your intellectual faculties than merely the ability to memorise and study, or to copy an existing argument or worked example. This often necessitates that one discards (or at least revises) many undergraduate study habits; there is a much greater need for self-motivated study and experimentation to advance your own understanding, than to simply focus on artificial benchmarks such as examinations.

A: This response should work better for mathematics than other subjects:

"You might need it.  But if you can't remember it, you can derive it on the spot."

Not only does it answer the student's question in an open-ended way, it also communicates the idea that mathematics is discoverable, not just handed-down knowledge.
A: 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.
A: One word: Incentive.  I'm guessing their exam scores are highly significant in terms of their overall grade, which in turn influences their financial aid packages, relationship with their parents or academic advisers, and meeting prerequisites for subjects in which they are actually interested.
Students will worry about the exams less if their test results have a smaller impact on their lives.  The easiest way for the instructor to do this is to reduce the weight of their exam scores.  Here's an example:
Problem sets / homework: 50%
Class Participation: 20%
Daily reviews: 15%
Exams: 15%
This way, exams can be used for their intended purpose, which is to EXAMINE the knowledge of the student.
Another option may be to let the students propose their own exam questions.  You could answer the question "Will this be on the test?" with "I don't know.  Would you like it to be?"
A: Asking what will be on the test usually means someone isn't smart enough/ paying enough attention to have an idea of what would be on the test (if you are in Calculus class, you aren't going to have to prove anything, proofs being what even better students don't understand when presented), or they think you will give them an even better idea, because you have an interest in seeing them "succeed"/take away what you want them to. Every student is to some extent after a grade; even the super smart ones who ask deep questions and get Bs are motivated to some extent to assure they do well enough. I don't think you can turn everyone on to math, and make them forget about their grade, nor would you want to because then many people would just "entertain" Calculus in their mind and not practice it (me in high school). Thus I think the best idea is to have some clarity, probably just from having homework.  
A: Students want to know a 'purpose' so that they can find the meaning to create that motivation. 
Give them an application, and relate to real-life stories. People remember stories better and hence, they may recall the lesson.
Relate to adventures of hacking for example, using statistics to explain how mathematics are used in cracking systems, eg. computational load to crack in GSM, Bluetooth, DVD (CSS), and Wifi, etc; or how the ancients use mathematics to calculate and construct structures.
Then ask them to think how they may apply in their lives. Give them a different mind and eye to see things, see the world with - mathematics. If their eyes light up, you know they are listening.
A: Thank you for asking :) That rarely happens anymore.
Pass students based on quality of project based learning which encompasses the things you want students to learn.


*

*In high school I was part of US FIRST Robotics students were there every day working their butts off learning programming and all sort of math that go into that stuff.  When it came time to compete not a single person asked what would be on the test.  Our project had to be able to compete well in the arena and work with a team. http://www.usfirst.org/

*In web development NO ONE reads a book and then takes a test to learn a new framework or language.  People learn by DOING not READING. When I start using a framework or language guess what happens, the reading naturally occurs because I want to learn and I'm building a project.
When I was in Computer Science they taught us from a book and then tested us, what a gawd awful way to learn I hated it and dropped out.  I'm now involved in my business and build our software I love it and I love learning!
Leave test driven development to programming, humans are creative not machines, with machine minds and machine hearts! You are not machines! You are not cattle! You are men! You have the love of humanity in your hearts! You don’t hate! Only the unloved hate - the unloved and the unnatural! Soldiers! Don’t fight for slavery! Fight for liberty!
A: "Will I need this for the test?”
Being a student myself, I know that the moment the teacher answers this question with a 'Yes/No' I am already in the mindset that I should only focus on learning the things that I know will be on the exam, whilst completely ignoring anything I don't need to know. Extra knowledge might be useful to me in the future, but right now what matters to me is getting a good grade.
That being said, if the teacher were to say to me "Everything I have taught you in class is examinable" everything changes.
My mindset suddenly changes to paying attention to everything, trying my best to understand everything. If getting my grade is what matters, I can now only achieve this by building on my knowledge of everything I have been taught in class. This is also useful in the way that I now find every class important, making me want to pay attention more and more relectunt to skip classes where I know I could be missing important things related to the exam.
A: Make them love what they learn. There is no other better methods to help the students. A lot of people are not interested in learning better things because it feels like it is a 'punishment'. :)
A: In my data structures and algorithms course at university, the lecturer solved this by releasing model questions for the entire syllabus, and drawing the exam as a subset of those questions. Accordingly, everything was actually examinable, and the only way to "game" the system was by actually learning the material, one way or another.
I realise that this may not be applicable to every course, but is one way of solving the problem.
A: Yeah, about the test:
http://www.youtube.com/watch?v=Yocja_N5s1I&feature=youtu.be&t=12s
From Crash Course: World History, Episode 1: The Agricultural Revolution hosted by John Green.
