“Hey. We’re selling a plot of land, and thought we could ask our math professor friend for help. The land is a rectangle, 120’ on one side, and 300’ on the other. I know you need that much. What’s the square footage and how do you get it?”
--question from the wife of a longtime friend, valedictorian at her school, and a bright person. She and her husband just didn’t take math in high school.
Now, it’s easy to blame the high schools for the unprepared students entering college, but that’s not fair. High schools offer College Algebra-level material, and often more advanced math, and also simpler courses, as well as other options. They tell students “this is what you need for college, this what you need to get by, and this is what you need to pump gas” giving their students the option to take the challenging material, something simpler, or no math at all. Students choose (or are advised by counselors or parents) not to take the challenging coursework, improving their GPA and chances of graduating high school. I don’t blame students for taking the easy way out when asked to do so; I would have myself if my parents had let me. A student who puts effort into it can avoid having a math class for his last few years of high school, if he wishes; I commonly get students that tell me they haven’t taken math since the 8th or 9th grade, and looking at their tests, I am in no position to disagree.
“Find the exact area under the curve of the graph of y = 3x2 + 2 between x = 2 and x = 4, using the limit of sums method.”
-- High school calculus problem. Using sums in this way is way beyond what I would attempt in an elementary college calculus course, where I often spend considerable time going over how to add fractions.
I’ve certainly heard tales of bad teachers, teachers not doing their jobs, teachers that don’t care about students, and, of course, teachers that succumb to the immense pressure to pass unprepared students. While I believe such teachers exist, I’ve met quite a few public school teachers, and through tutoring many high school students, I can only conclude that the vast majority of teachers are dedicated, hardworking, knowledgeable, and do a legitimate job in offering real mathematics courses to their students. In short, the vast majority of students that want to learn have a fair opportunity to do so.
Perhaps public schools shouldn’t give students the opportunity not to learn, but I suspect they’ve long since figured out that forcing students into classes they have no interest in taking doesn’t really help the students. If only that knowledge could be passed up to postsecondary institutions.
If a student chooses not to be prepared for college, it’s no great surprise that such a student, when tricked into going to college, is not prepared for it. A student shouldn’t be made to suffer forever for a poor choice made in high school, but…recall how years ago getting into college was not a certain thing. It was reserved for those who worked hard and studied, demonstrating they were willing to do what it takes to achieve higher learning. The great slobbering greed of colleges with open admission policies, and the “increase the student base at all costs” major goal of administration, has led to a massive influx of unprepared, often wildly unprepared, students onto college campuses.
These students, being unprepared for college, naturally do very poorly in college courses, and administration (with “graduation rate” being a goal of what makes a college good) clamps the pressure down on faculty to increase passing rates, as well as opening up an array of less regulated remedial courses, with no restraints on what goes into such courses. Unfortunately, the remedial faculty (often with less qualifications and job security than other college faculty) are bullied into having high pass rates, and the only surefire method of doing so is to lower the difficulty as much as possible.
(Two students at my door): “Hi. We’re in your statistics class, and we have a question about lines of regression.”
(Me, welcoming them in): “Certainly, those are some rough formulas, the key is to be very careful and not try to skip steps.”
(I take out some paper and start setting up a typical problem)
Student: “No. We’re not even going to try that. Our question is for when you already have the line, like for y = 2x + 1, because we can get that on our calculator. How did you get the points, and how do you graph the line? We’ve both had 6 hours of developmental and got A’s in College Algebra, and neither of us had to do anything like that.”
--Students at an accredited institution where developmental math wasn’t handled at all by the math department, and College Algebra wasn’t either, to some extent.
With no restraints, “reduce difficulty as much as possible” is results in very low difficulty indeed, which is why at one campus, it was quite common to have students with 4.0 GPAS, 9 hours of passed math courses…and still completely overmatched by what should have been basic concepts.
Since the flood of unprepared students doesn’t stop at remediation, faculty in the higher level courses have no choice but to likewise reduce course requirements, or lose their position. So, in my case, it isn’t just statistics students that can’t handle graphing a line, nearly half of the students I have in calculus, for years now, are unable to add fractions, despite the high GPA and multiple prerequisites.
As long as administrators view everyone with a pulse as a source of a government check, with no concerns about how such a person can end up trapped in a lifetime of debt, remedial students will be a common feature on “higher education” campuses.