Tuesday, April 9, 2013

Our first remedial course


College Algebra


“It’s called College Algebra because nobody would pay for a course called The Algebra You Should Have Learned in High School.”

--Faculty member (not me, though I wish it were).


Algebra is the basic language of mathematics, it’s all but impossible in the modern world to accomplish much in math without some familiarity with the syntax of algebra. I was a bit slow in math, and a year behind the “top” students. Thus, I took algebra in the 11th grade, instead of the 10th grade like the better students, but the point is college material today used to be early high school material.


“[That professor]’s math class is hard. You’ll have to come to class for it.”

--overheard student comment, defining what makes a course hard, relative to other courses, no doubt.


     College Algebra is a necessary course, the language, notation, and attention to detail learned there is critical to almost every other field. It is the prerequisite to over a 100 courses, and yet administration is perpetually trying to get rid of it, unable to understand that doing so shuts students out of many of the most profitable fields of study.

     The “College Algebra” course offered at my college (and elsewhere) is little different than the remedial algebra course that I taught at University of South Florida in the 80s…it’s also little different than the algebra course I took in high school. The primary differences are that College Algebra has less information than my high school course, lacking discussion of several topics, like matrices, circles, hyperbolas, inequalities, and a few other things. This is actually representative of many low level college courses: they have less than what used to be taught in high school courses of the same name. I also teach a college trigonometry course for example, and it similarly covers far less material than the trigonometry I took in high school. In any event, I include a discussion of College Algebra in the chapter on remedial courses because, at one point, it was a remedial course.


Passing rates in College Algebra courses usually run a bit more than 50%, although not much more (at one university I taught, the rate went from 50% to above 85% from one semester to the next, due to extensive pressure and threats from administration to pass more students). This is certainly lower than many other classes, especially the classes where, like my student quoted above, attendance (or, likely, any learning of the material) isn’t needed for passing.


Pitchman: “What we know for sure is, the students who score high enough for College Algebra usually took courses past College Algebra in high school. The students who don’t quite make it into College Algebra took it in high school, and so on down the line.”


Faculty: “Wait a minute. You mean there’s hard evidence for what we know to be true: that to achieve a goal in learning, you must push past that goal to succeed? Why haven’t these results been published?”


Pitchman: “That was off the record.”


--Exchange between faculty and pitchman, discussing results learned from a very popular standardized test very often used to place students.


Because the passing rate of College Algebra is so unsatisfactory in administration eyes, many campuses offer an “Explorations in Algebra” type course, a fake course with “Algebra” in the title so it at least sounds like it might be a real course. These courses are rationalized by “removing material the students don’t need,” and it’s no small amount of material. There are variations, but the course seldom has significantly more in it than a remedial course, but it’s for college credit all the same. Well, sort of college credit: the course is seldom transferrable and doesn’t prepare the student for anything (remember, College Algebra is a prerequisite for over 100 courses). That said, the fake Algebra course generally has a much higher passing rate, which makes administration very happy…and is worthless when the student tries to apply it towards most any degree anyone would be willing to pay for.

     The quote above hints at a truth, at least in mathematics and probably in other fields: the most advanced skill a person has mastered cannot be the most recent skill that was learned. In order to be comfortable with high school algebra, a student must push past the concepts in high school algebra. After years of diligently working to make a college degree represent no more than a high school diploma of years ago, college administrators, by promoting “Explorations” type courses, are now working to make a college degree as meaningful as graduating from the 8th grade.


“Dammit. I studied for two hours and STILL failed that test.”


--student angrily telling me my test was too hard. The two hours represented all the time he’d put into the course over the last month. How did he get the idea that two hours of study would be sufficient to understand a month of material? Hint: other courses he was taking.


Although the passing rate is relatively low, College Algebra really isn’t that tough a course. Every semester, I’ve had multiple students that failed the course before take it again, come back and pass the course, often with a B or better. They’re only too willing to tell me the difference is they actually studied the second time around. For most students, passing this course is simply a matter of study and effort, which can be quite the confusing barrier when compared to other courses.


On the other hand, there are absolutely people (perhaps 10% of the population) that have a real problem with math. They’ve come to my office literally unable to tell me the slope-intercept equation for a line (“y = mx + b”), and then shown me a page where they’ve copied “y = mx + b” hundreds of times the day before. It doesn’t matter how hard they study, they just won’t get it.


The most common issue they claim to have is they “can’t remember anything” when it comes time to take the test. They are not lying about this lack of memory, but in speaking with them, asking for demonstrations of knowledge outside of test time, they can’t remember anything outside of test time, either. It’s a real problem, and I do think it’s cruel of administration to force such people to take this course, but in administration’s defense, for accreditation, they have no choice to force students to take it. Quite often, these students eventually pass by taking an “Independent Study” course, “fishing” for an easy instructor, or some less reputable means. I’m glad these students eventually find a way, but I do wonder what kind of education a person can have when he remembers none of it, and how administration can claim to be acting with integrity when they go out of their way to sell an education to such a person.


“How much is 2/5?”


--Student question, a high school graduate who passed a remedial course the previous semester. I tried to explain via a pie graph and other examples, but I’m not convinced I helped her even a little. A history professor jokingly offered the best answer: “3/5.”


Many students come into College Algebra unprepared, either by catching a break from a remedial teacher, getting lucky on the placement exam, or by simply not wishing to take a remedial course in the first place. I try to accommodate these students as much as possible (for example, for every single problem that has a fraction, I have no choice but to stop and review how to work with fractions), but the end result despite my efforts is most unprepared students fail the course. With no ability to work with fractions or distinguish between multiplication and addition in algebraic notation, there’s little chance they can pass. I’m hardly the first faculty to complain how hard it is to teach a class with such unprepared students, and complaints like mine led to the creation of remedial courses, to address the material that all students, theoretically, learned in public schools. This leads to our first official remedial (nowadays) course: to be addressed next time.