By Professor Doom
A new year begins, and that means a new semester begins. As always an avalanche of new students comes onto campus, and is funneled into remedial courses. So, again, I’ll write an essay, hoping against hope that the one pebble I toss will actually affect the avalanche.
Now, I’ve already addressed that remedial students should just leave college. More than that, I’ve said that such students should just read the books and study on their own, rather than pay full college price for sub-college material.
“But that’s not fair to the students that had sucky schools and sucky teachers!” cries those in defense of remedial students. There’s truth to this, but, alas, the current situation isn’t fair, and it won’t be fair any time soon.
For thousands of years, the primary, best, way for a human being to learn a skill has been to stand next to a knowledgeable human being and pay attention while the knowledgeable demonstrate the skill. Personal attention is the best way to learn something new. It would be fair for those in bad situations to get the best possible choice for education.
The best choice is just not an option in higher education. I wish it were, because when I tutor 1 on 1, I often make real progress with a student (for much less than college tuition, and for more money for myself; it’s a real sign how broken the system is that both student and teacher are better off if there’s no school involved). A distant, but still viable, second to learning from another human being is to learn from a book. I know, it’s hard to learn from a book, but ultimately in higher education, learning from books is how it’s done.
Is it unfair for our weakest students to learn the second-best way? Absolutely. Nevertheless, this is the only way that makes sense right now. Here are some numbers to reinforce why in higher education today, the best choice for a remedial student is to open up the book on his own time, and study:
This number represents the typical amount of experience your remedial teacher will have, if you go to university. See, administrators have figured out the easy way to increase their own salaries is to cut costs by forcing incoming graduate students to teach these courses. English is often not the first language of new graduate students, and they have little experience teaching the material they haven’t seen in ten years, anyway. You might as well read the book.
This number represents the amount of actual mathematics knowledge your teacher will have, if you go to community college. See, in community college, administrators hire Education majors to teach; even a Math Education major might not have taken a math course since the 10th grade. The only thing these guys know how to do is go very, very, slow, and eliminate as much course material as possible. You won’t be prepared for college courses this way, and if you don’t read the book and learn on your own, you’ll be destroyed when you get to any real college courses.
This is the number of hours you might be forced to spend alone at the computer every week. The most successful program for teaching remedial students makes them go and sit in front of a computer, which tracks how much time the student spends studying like this. To pass the course, the student must spend three hours a week practicing, to the satisfaction of the computer. You’re paying real money to have a computer stare at you while you study? Just read the book, honest, there’s no reason to shovel thousands of bucks into tuition for this.
This is the enrollment for an entry-level mathematics course, one section, at a nearby university. Yes, 200 students in a class. Hey, you can only cut pay so much, past that you double the class size…then double it again…then double it again. If each student requires 5 minutes a week of effort by the teacher, that’s about 16 hours a week. That doesn’t sound bad? Well, faculty teach four courses at a time, and there’s more to it than just answering questions…you may as well read the book on your own time, because there’s just no reason to expect even 5 minutes a week of personal attention.
This is very high end pay that an adjunct might receive for teaching an entry level course. Isn’t it bizarre that tuition skyrockets every year when overhead is so minimal? An adjunct could literally be in a course with two hundred students, representing a quarter of a million dollars of tuition, and only get a couple thousand bucks for it, no benefits or anything else. In much the way that people should avoid buying products from those brutal Asian clothing mills, a remedial student really should just crack open the book instead of support borderline slave labor.
This is the chance a remedial student will manage to get a 2 year degree, even if he’s allowed 3 years to get it. Sure, it happens, but ultimately the very few who succeed are those that are able to read a book all alone. Why wait 3 years to figure that out? Find out now if you can read a book all by yourself…if you can’t, college isn’t for you.
“…a course whose purpose was to teach teachers how to teach mathematics using teaching kits that made it possible to teach math without actually knowing it. My suggestion that they should teach the prospective teachers math was voted down,…”
Another faculty member trying to slow down what’s going on in education. Seriously, why would anyone pay for this?
For the most part, I’m preaching to the choir with these essays. The bulk of college students are remedial students, and will never come here and read the truth of what’s going on in higher education, will never realize how screwed they are until they’re deep in debt. All they know is what the college administrators tell them—“take our courses and then you’ll get piles of moolah for a magic rainbow job.”
That’s a shame, because the numbers make it very clear that, at the bare minimum, a remedial student would do himself far more good by reading the course textbook on his own time, rather than signing up for stupid expensive oversize classes led by an inexperienced teacher, possibly one with very limited knowledge.
I've nothing but contempt for education majors but think you're being a bit harsh on math education majors. At least in my state (Minnesota) they'll have completed the usual calc sequence, taken combinatorics, at least one algebra course (linear or abstract), one college-level geometry course, college-level stats and probability. Admittedly it's not very much compared to a math major -- no real and complex analysis, no differential geometry, no topology, maybe no diff eqs. But still -- more than 10th grade level.ReplyDelete
The other thing is: Where is an autodidact supposed to get the books to teach himself with? Have you seen the current crop of algebra, trig, pre-calc, calc, and stats books out there? The quality is abysmal. They are verbose, ill-organised, ill-written. See, it's not just poor teaching that accounts for poor math results in community college -- it's cruddy books as well. It takes quite a bit of experience with math and with math literature to know which books to use and where to get them. For example, if I'm teaching high school algebra (simple equations, simultaneous equations, quadratic equations), the book I'd use would be Peterson's "Intermediate Algebra for College Students" -- which was published back in the mid '50s. The modern texts are no good.
I have little choice but to be hard on Math Education degree holders...they should know better than to teach college. I acknowledge it's *possible* for a Math Education graduate degree holder to know math, but it's not necessary. Such graduate schools put the whole curriculum online (Concordia has a 1 year Master's program, in fact), so you can see for yourself. Then see for yourself that entrance into the program also requires no knowledge of mathematics.ReplyDelete
Now, as soon as there's one legitimately accredited school giving such degrees, that means there's no reason to expect anyone holding that degree to actually know what they're teaching. Having seen SO MANY incompetent Math Education degree holders, I guess I just haven' seen any from Minnesota.
I don't think the books are that bad, myself...and one advantage to the college textbook scam is you can pick up an "old" (i.e. 2 years) textbook identical to what's being used in college pretty cheap. It's not the best way, I easily concede...but paying for college to learn 6th grade math is flat out insane, especially since it's not taught decently in any event.
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From what I've seen, the foundations themselves are utterly lacking -- something also pointed out by more expert observers than myself. Thus students aren't picking up calc not because of the inherent difficulty in calc (though that is there also) but because they lack the requisite algebraic and trig skills, sometimes even arithmetical skills. For example, most students today cannot compute square roots manually -- most teachers cannot, either. Ask someone to calculate the square root of 3 or 7 to three decimal places and they won't be able to do it. As another example, ask a student (or teacher) to prove the Pythagorean theorem -- the very bedrock of trig and analytic geometry -- and they won't be able to. And even worse, their minds often blank out when you try to explain it to them -- all they've acquired from the American school system is terror of the quantitative and learned helplessness. This allows me to segue to a suggestion.ReplyDelete
It might be an idea to indicate what books people should use. I've already suggested an algebra text. For an even more basic algebra text -- one that I grew up on and that I used with my son -- I'd suggest Hall and Knight's "Elementary Algebra for Schools," which was published in the mid- and late 19th century. For basic geometry I'd suggest "Ruler and Compass," by Andrew Sutton, published by Walker in 2009. And then Avery's "Plane Geometry," published by Allyn and Bacon in the '40s and '50s. The school math books of the last forty years are all garbage.
(Earlier comment deleted because of typographical error I couldn't subsequently rectify).
One reason people can't prove the Pythagorean theorem, at least where I went to school, was that nobody taught it. It was simply presented to us and we were required to accept it. As it turns out, the proof is quite simple, but it requires some basic geometry.ReplyDelete
Similarly, logarithms are poorly taught as well. We were told that they represent "exponents" (which they do), but were never shown how. Again, it's not a complicated concept but it requires a bit of imagination to grasp.
There is no "the proof" of the Pythagorean theorem--I think somewhere there's a book of 50 distinct proofs of it (although I favor the "classic" proof of inscribing a tilted square inside a square with sides broken up into two parts of different length).ReplyDelete
I prove it in trig, and in multivariate calculus--the later to demonstrate how little the underlying ideas of creating knowledge have changed from 2000 BC (sort of where the theorem was first proved) to the early 19th century (when multivariate calculus was being developed).
After 4 semesters of not learning Algebra in my Community College I have come to the same conclusion. They cannot do it. I am a smart girl, far from stupid for my other grades prove it so. I am going to learn that Algebra with your suggested books and challenge that stupid test that placed me in pre algebra in the first place. It is been a misery. They still have my degree except now they have my student loans. It did not make it any better by giving the poor who did not go to college because they were poor. That worked the best. Now those of us who are not college material are trying to get through college and we are going in debt trying to do it.Delete
Thank you so much. I just loved this article.ReplyDelete
Another tip, whatever you do choose to buy, is to check Amazon's used sections. One can find older & sometimes even current editions of various text books for extremely cheap. Also, no need to worry about bloated software CDs & web site codes that don't work - those aren't usually needed to learn the concepts anyway but are yet another money grab for universities & publishers so students can't opt for this viable way cheaper option. Why pay $80 or whatever for a book on how to do basic equations, matrix work, linear programming, graphing, & probability when you can find the same material for a few bucks used? Hell Khan Academy has videos on the stuff for free. See also UMKC's fantastic College Algebra & Calc 1 course series on YouTube - that prof really goes into every detail & explanation needed to learn the material (however the exercise sets you'll need your own sources for).ReplyDelete