"hook" - There's your problem, right there. Try "inviting" them, instead.
High School Teachers who CARE, certainly help. Sadly, they are not as common as perhaps they once were.
Sorry but a serious omission on my behalf is that I have just become Admissions Tutor and will struggle to get students to study mathematics with the hike in tuition fees. Just looking for ideas to inform students why mathematics is a good subject to study.
From Why Study Math? we have the following, quoting from and commenting on "The Republic" of Plato:
Not comfortable reading for our current political "masters"In his view, mathematics should be taught both because it "compels the soul to turn her gaze toward that place, where is the full perfection of being, which she ought, by all means, to behold" [VII], and because it prepares people for the responsibilities of a citizen and soldier. "Plato maintained that only those individuals who survive this program are really fit for the highest offices of the state and capable of being entrusted with the noblest of all tasks, those of maintaining and dispensing justice." [EB] For Plato, the 'interesting' and 'important' arguments are bound together: citizens imbued with an appreciation of what is true and eternal are the best defense against tyrants and demagogues.
Furthermore, Plato considers mathematics to be an important subject of study not only in its own right but also for the salutary benefits in abstraction, insight, and intelligence that carry over to all studies: "Even the dull, if they have had an arithmetical training, although they may derive no other advantage from it, always become much quicker than they would otherwise have been."
CB
As math student in university I blame the grading policy I feel it places to much emphasis on test. For example test in my math class tests are 55 percent of the grade and homework and quizzes I think are only 20 percent.
It is a bit unfair because I do all my homework and study but I make 70-75 percent on the tests. And in test there are variable that can make you do worse nervousness, people coughing, distracting noises.
I would advocate getting rid of grades and evaluating the student some other way.
I don't know about the situation in other countries, but in America, apathy (or even outright hate) towards mathematics is a systemic problem. Mathematics (if you can even call it that) in public schools usually consists of phrases like "Here is a formula. Just do it and don't ask where it came from." Students only memorize formulas and crunch numbers; they aren't encouraged to investigate mathematical structures and ask why things should be the way they are. (And this kind of mentality links back to CaptainBlack's Plato quote.) Everything is done for no reason at all.
I can 100% understand the students' frustration toward mathematics in the lower levels with the current state of things. I think that nothing can be done to encourage them to enter mathematics at the university other than doing a complete reformation of mathematics education.
i studied math for the girls. i was apparently misinformed.
the state of mathematics in the united states is just abysmal.
father: so, son, how are you doing in school?
son: ok, except i'm failing calculus.
father: don't feel too bad, i failed calculus, too.
I've always considered the benefits of mathematics to be purely about changing the way you think - developing the `skill' of mathematics rather than the knowledge of mathematics. Yes, Linear Algebra has applications but they are secondary to what learning Linear Algebra teaches you: the concept of proof, how to think critically, etc.
For example, I have a friend who studied maths and then went to a `big-four' auditing company to become an accountant. The skills she learned studying maths put her in a better position to become an accountant than the knowledge that the accounting graduates had! She came top of her year, beating all the accountancy graduates in all the exams...