I know that in my department we teach THOUSANDS of students each year, and we only have a few dozen majors. Almost all of our teaching is to freshmen in other departments. These other departments tell us which topics they want their students to see and how many semesters we have to cover it (and it’s often too much stuff in too little time). Completing these sequences in math certifies that the student knows some basic facts, can be trusted to be in a certain place at a certain time more often than not, and can follow basic directions.
…as long as intro-level courses continue to be service courses taken by freshmen who haven’t yet learned how to study, think, or learn, nothing is going to change.
It took me six months to figure it out, but I finally realized that teaching precalculus is not merely a challenging task: it is an impossible one. And that’s a big part of the source of my stress over this course – even if you do an impossible task well, it’s still and impossible task and at the end of the day, you’ve still failed. You can’t win.
My job description, according to the sample syllabus I was given at the beginning of the term, is to teach thirty students how to factor quadratics, solve simple algebraic equations, solve algebraic inequalities, graph various types of functions, approximate roots of polynomials, and solve exponential and logarithmic equations. That’s certainly tractable with an audience of students who come with the prerequisite knowledge and experience.
But students who haven’t learned any of the basics in math, and who haven’t learned to “study, think, or learn” aren’t ready to do what’s required by the syllabus unless I limit myself to showing step-by-step how to do a very limited array of questions, which they will then mimic when they see those exact same questions on the test.
But that’s not math, and I refuse to do it. So, my real job – which I have three months to accomplish – is to teach thirty students (most of whom have failed at least one math class before) how to do five years’ worth of math (remember, these are the students who can’t add fractions), how to read mathematics, how to think about and study the subject…and only then can I teach them what I’m technically required to teach them.
They have another test this coming week. They’re going to do poorly. And it’s not because they’re not working hard, and it’s not because I am a bad teacher. It’s because I am not a miracle worker.