A look at the “serious” courses in college today.
By Professor Doom
I’ve seen plenty of articles bemoaning ridiculous college courses in such questionable subjects as The Morality of Scooby Doo or the like, but nobody speaks of what’s going on in the “serious “ subjects of college, like in mathematics.
The great remediation scam has allowed institutions of higher learning to greatly expand their student base, but only by offering many courses that are comparable to what is available in high school. Actually, to call the material high school level is rather generous. It makes sense to look at math remedial courses in some detail, to make it easier to see what’s going on in this critical stream of institutional revenue:
1. 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—profitable for students, not for administration.
The “College Algebra” course offered at my college (and elsewhere) is little different than the remedial, non college credit course from the 80s…it’s also little different than the algebra course I took in high school. The primary difference is that College Algebra has less information than my high school course, lacking discussion of matrices, circles, ellipses, distance, 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. Thus, College Algebra belongs in a discussion of remedial courses because it used to be remedial; only the stroke of an administrative pen has changed its status.
Passing rates in College Algebra courses usually run a bit more than 50%, although not much more (at one state university, 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 course is all but mandatory, however, and is much loathed by administration (an “impediment to graduation,” as one Dean put it), despite it being a borderline high school course. College Algebra now represents the most advanced material a student might learn.
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.
The quote above hints at a truth: 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.
Because the passing rate of College Algebra is so unsatisfactory in administrative 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, albeit for college credit. 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 any degree anyone would be willing to pay for.
After years of diligently working to make a college degree represent no more than a high school diploma, college administrators, by promoting “Explorations” type courses, are now working to make a college degree as meaningful as graduating from the 8th grade. This is why books like Academically Adrift can easily show that about half of college graduates have no measurable increase in cognitive skills over what they had in high school; 6 years of college, and all the student gets is a worthless piece of paper and a mountain of debt.
“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 many other courses.
On the other hand, there are absolutely people (perhaps 10% of the population) that have a real problem with math. 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 cruel of administration to force such people to take this course, but in administration’s defense, for accreditation, they have no choice but force students to take it. I 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. With no ability to work with fractions or distinguish between multiplication and addition in algebraic notation, there’s little chance they can pass. This leads to our first official remedial (nowadays) course:
2. College Preparatory Algebra II (remedial math)
“The Civil War was inevitable, but it didn’t have to be that way.”
---quote from a student history paper. A month before the paper was written, the history professor ranted extensively to the rest of the faculty how annoying it was that he had to stop his lecture, and spend time defining the word ‘inevitable’ to his class. This is common to remedial students: they can look you dead in the eye, nod in agreement that they understand, and still not comprehend a word you’re saying. Remedial students can take other college classes, even if they have yet to take, much less pass, the remedial courses.
Most remedial rstudents need only take this one course before going on to a college career (which has been shown to end in failure for over 90% of remedial students). It covers basically the material that public schools address in 7th-9th grade (remember, “College Algebra” is 10th grade). Students are usually in this course because they failed this material in the 7th, 8th, 9th, 10th, 11th, and 12th grade. The majority of meetings regarding math instruction are about how to increase retention (i.e., passing) in this class.
A large minority of students in College Preparatory Algebra II are non-traditional. They took and passed the material years ago, but have simply forgotten it, or at least are extremely rusty. While spending four months reviewing in college is a painfully slow and expensive way to go about regaining these skills, I can appreciate not everyone has the initiative to go down to the library, check out a book, read and re-read and practice for a few hours until the skills come back. I’m sure administration would never suggest such a course of action to a student, not with a sweet student loan check on the line.
“I co ming offise to day AAAAaaaa?”
--E-mail from a Vietnamese student. She got an A in my trigonometry class, dominating the other students despite not knowing much English. Yes, she did work in a nail salon, and no, she didn’t graduate the equivalent of high school in her native country. She asked one question the whole semester, coming to my office to do so: “How come students that know nothing are in this class?”
Another small minority of students are in remedial math because their English skills are weak; the course helps with this, as the student is really there to learn how to express concepts in English, having already learned them in his or her native tongue.
Remedial students will initiate calls or answer their phone during class. In College Algebra, upwards of 20% of the class at any given moment will be texting/playing on their cell phones, but the percentage of students engaging in this activity in this level of remedial class is usually around 50% (it’s rather amusing how many students think they are fooling me by keeping their hands in their crotches for 50 straight minutes, or digging in a purse every five minutes of class).
3. College Preparatory Algebra I (sub-remedial math)
Me, addressing class: “Ok, so last class we learned about complementary angles, worked some problems with complementary angles, and I assigned homework problems on it. Any questions on the homework?”
Student: “Yeah, problem #1.”
Me, reading the problem: “Angles A and B are complementary...before going to the rest of the problem, what does complementary mean for angles?”
(Several moments of silence, then a student responds)
Student A: “They’re equal?”
(Three other students, echoing): “Equal?” “Equal?” “Equal?”
Me: “No. The mathematical word for ‘equal’ is ‘equal’. This is a different word, and it means something different. Take out your books, and look in the index or the section the homework is in, and find the definition of complementary. Or look in your notes from last class, where I gave you the definition before assigning the homework.”
(Sixty seconds of page flipping passes, and a student responds)
Student B: “They’re the same?”
(Three other students, echoing): “Same?” “Same?” “Same?”
--An actual exchange in sub-remedial class. I couldn’t make this up if I tried.
College Preparatory Algebra I basically covers material from the 6th to most of the 9th grade. If that seems to overlap with College Preparatory Algebra II above, that’s because it does; years of my explaining this to administration accomplished nothing, because the course as-is had a higher retention rate.
Despite this being nearly the same course as College Preparatory Algebra II, the students that place into this course are clearly weaker than in the “advanced” remedial course—those placement tests are pretty good. The students in this course typically spend years on campus, going nowhere but deeper in debt.
If a student comes to enroll, and needs a year of remedial courses before he can take what used to be a remedial course, maybe administration should ask “Are you serious about learning?” rather than telling him “Check this box stating you’re looking for a degree, so you can start getting student loan money.” It’s a long hard road to higher learning from the 6th grade.
4. Basic Mathematics (pre-sub-remedial)
“It’s dummy-dummy math.”
--this course as described by a student.
This course covers perhaps 3rd to 5th grade material, from how to add and subtract whole numbers, to plotting points on the number line. Every homework problem must be done in class because no understanding of the material can be taken for granted.
I’ve never seen or heard of a student going from this course to anything like a successful college career. With over 90% of “normal” remedial students failing to have a college career, this isn’t surprising. For one semester, we offered an even more basic math (a sub-pre-sub-remedial course). This course was promoted by one instructor as “taking out the math they don’t need, like squares and rectangles,” and allowed to offer it after singing the “better retention” siren song to administration.
There’s a huge issue of integrity in the pre-sub-remedial course. If you’re teaching 3rd grade material to an adult, you consider that adult to have the cognitive skills of an 8 year old at best. There’s nothing wrong with trying to improve education and learning, but at some point, someone should think “This student didn’t learn this in 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 11th, and 12th grade. Maybe he doesn’t want to learn this and we shouldn’t loan him money to learn it.” Failing that, admissions should think “Maybe loaning this person money that goes right to us would be taking advantage of someone with a mental disability and it would be not be acting with integrity to do that.” So far, these possibilities have never been raised at any meeting concerning remediation, and administration continues to sell these courses to anyone willing to go into debt to take them.
Let’s go over that last idea again:
If I targeted elderly patients with dementia to the point that they had the cognitive skills of an 8 year old, and manipulated them into signing contracts turning over their life savings to me, I’d be considered a…scumbag.
If I targeted actual 8 year olds, and got them to sign contracts so that every penny they saved in their lives went right to me, I’d be considered a…fool.
If someone comes to my university, and I document they have the cognitive skills of an 8 year old, then make them check a box so that I make more money and the student will never save a penny in his life I am a…successful university administrator.
Hugely pressing issues of integrity aside, considerable resources in higher education today are being blown on courses like the above, for remedial students. I’ll concede there is plenty of indoctrination going on in higher education, but the courses above are representative of the “serious” coursework, on a subject I’ve not seen anyone else ever complain about in all the articles railing against the perils of higher education…should higher education be mostly about re-learning the skills taught in high school and lower?
Think about it.
This blog makes me feel like one of the most worthless and moronic human alive. While I try to think positively of myself due to experience in some areas, I am pathetic when it comes to academia. The way this is worded reinforces a painful realization of what is realistically a determined future of poverty and struggle without a degree. From what I see, a degree is basically the approval of the government and the wealthy to allow you to "succeed" in life. Such as, have a job that pays you a wage that allows you to live comfortably, being socially held at a higher esteem, ect...ReplyDelete
I suppose I just have a hard time accepting that my life is meaningless. I am just another mindless monkey that will live a life of mediocrity, struggle, and pain; then die. The world being none the wiser or better off for my ever being there.
I'm sorry if you got that message, but that's not what I'm saying at all.ReplyDelete
As I discuss in one of my earlier posts...academia isn't everything, you've been misled to think you *need* a degree. You don't. A degree is not an approval of anything; the vast majority of degrees are useless.
My mother had no degree; she was a successful real estate agent, and ran an antique mall that grossed over a million a year...and no, my parents didn't hire an accountant to do the taxes (nor was my father an accountant).
The founder of Wendy's didn't even graduate high school. Bill Gates doesn't have a degree. Karl Rove never went to college. My plumber makes more money than I do, and he has no degree. Being bad in academics means almost nothing--you write better than most of my students for what it's worth.
Half of college graduates are in jobs where their degree is worthless. There are many folks with graduate degrees living lives in near poverty.
Having a college degree is like having a black belt in karate: sure, it has its uses, but the bulk of humanity has done just fine without it, and it really doesn't help you on a day to day basis.
Your life isn't meaningless, but don't let the excessive meaning you put into a degree drag you down.
The math teaching in school is atrocious. By the time the products of abysmally poor math teaching and abysmally designed curricula reach college, further math "schooling" is a lost cause: the only way to make up lost ground is several years of intensive remedial schooling. Which they don't get as college teaching tends to be more of what they got in school.ReplyDelete
We can't do "intensive" remedial schooling...if we did that, most students would fail, and admin won't tolerate that.ReplyDelete
God bless your soul Prof. Doom, you are the first person to blow the lid off of the ugly realities of higher education. I've worked in it for over a decade now and what you say is true. You're like the higher education version of John Taylor Gatto! You are the only person I've seen reveal these truths and try to explain the illogic that pervades higher (liar) education. Very few of those outside this fantasy land can begin to comprehend the real nature of the beast! Bravo!!!!!ReplyDelete
Wow, thank you for the very kind words. For those that don't know Gatto, I encourage to seek his site and read his works. He has much relevant to say about public (government) school.ReplyDelete
About courses called College Algebra (and Intermediate Algebra, etc), it can be confusing knowing exactly what one's even getting unless they can see a full syllabus with mention of text book, chapters, and exercise sets recommended that students do.ReplyDelete
In my own experience, I have been to 3 different colleges (in the US) and one had a course called College Algebra that basically was most of a grade 7/8 course but with 2 chapters removed as it was a quarter-style class taught in 7 weeks. When I transferred to a university in the same city, they assumed I knew all of the material covered in /their/ course entitled College Algebra, which goes & I don't know if even high schoollers get some of that material in their algebra 2 class (stuff like quadratic inequalities involving rational expressions - many things to pay careful attention to detail with those if one's not extra careful). Naturally I had to switch to a lower course once I was placed into Precalculus due to that transfer credit.
By the way, do or have any any College Algebra or Precalculus class in the US go into matrices and linear programming in much of any detail? I recall seeing some of it in some algebra 2 texts but mainly only a few basic examples with 2 expressions in smaller matrices & LP problems. I had to get a cheap text book called Finite Mathematics to get much of any decent matrix & LP details as well as exercises including word problems that didn't require skipping over a lot of stuff & looking into Linear Algebra. None of the regular Precalc or CA books had that stuff and Linear Algebra texts seem to be for more advanced students with knowledge of Calculus. There is another subject that deals with Linear Programming that may have more of what I'm looking for: management science. Familiar with that? As a tech guy, this stuff as well as logic & some discrete topics interest me.
Thanks for such an enjoyable set of blog entries. I love reading this stuff. Good insight.
Since accreditation never checks to see if courses are legitimate, it's quite possible to have a course called "college algebra" on one campus that is equivalent to "pre-remedial algebra" on another. Retention, not learning, is the goal on college campuses.Delete
My high school algebra covered matrices in a little detail (we did determinants of 3x3, but that's as far as it went). As luck would have it, I used linear programming for my honors thesis to optimize a mathematical game...I had to look it up in a book and program it into a computer. Not even the graduate courses at my campus covered it (but that's more of fluke of the faculty there than any slight against the institution).
Anyway, I know of no college campus that includes matrices in "College Algebra" in much detail. There was a guy that at least had his students learn determinants of 2x2 matrices...but admin had him take that material out.
I should mention, the course syllabus and catalog still says the College Algebra has matrices even though it's no longer in the course. Accreditation, of course, does not care and has no way of figuring it out.Delete
Thanks for replying! Also, is probability & combinatorics traditionally algebra or statistics? Is stats high school or university material? I've always been under the impression that in the past, high schoolers took stats.Delete
My local community college has separate courses for lower algebra levels, 2 precalc classes, the usual calc sequence, 3 stats classes, linear algebra, & differential equations, + these two classes: Linear Mathematics (151) & Probability (152). 151 covers basic algebra review, graphing linear equations, solving linear systems via matrices, linear programming via graphing & the simplex method.
Wow, that requires a long answer.Delete
Statistics *can* be high school or college, it really depends on the presentation. The 1000 level intro statistics I taught at Tulane was well beyond a 5000 statistics course at a nearby state university (which was about the same as the statistics I learned in high school, and similar to a 2000 level statistics course at another state U).
A 152 Probability is almost certainly a high-school level course, but for "college credit". You'll probably have trouble transferring it to a university. That linear programming course sounds pretty fun, but be careful, that material only applies to a select few majors.
Probability and Combinatorics is typically taught only in a very limited way in high school algebra, or in a less limited way in statistics. College courses that discuss it specifically are usually pretty involved (3000 level, I'll be teaching such a course in the Fall, coincidentally).
3 statistics courses at a CC? That's impressive. I tried to convince a local CC that they should offer at least 1, but admin didn't really understand it. Good lord, they had no idea what the "central limit theorem" was, so when an educationist was using it for his grading scale (stupid idea) they needed my help...and when they were getting statistics for accreditation, they again needed serious help on basic ideas. Oh lordy, the cluelessness of Ph.D.s in Admin; I don't know how you can get a research degree in the social sciences without at least a crude understanding of statistics, but anyway.
Back to the point, if your CC has that kind of array of math courses, then it's a "2 track" college. One track is bogus, one is legit. It's your responsibility to figure out which track you want. Many CC's are just 1 track (all bogus), so you're at a well above average CC.
I'd need more information about your major and goals before I could point you in the right direction. Your best bet? Find out who's teaching the highest level math courses there, and start with the lowest level math course that guy teaches.
Usually, CC's use Educationists to teach the bogus courses, but have people with real degrees to teach the real college courses. The guy(s) teaching the real college courses are the ones you want, and sometimes they teach the intro courses, too.
Thanks for all that. It is in Philly, & despite there being offerings as high as Discrete Mathematics 1 & 2, Linear Algebra, Calc 3, & Differential Equations, CCP is a 2-year college & students are expected to transfer to a 4-year university when they finish whatever courses they're advised to by their major selection. The higher classes like Linear Algebra & DiffEq have just one section per semester, whereas the lowest classes like 016, 017, 118, etc have thousands of seats in dozens of sections across all semesters including summer. I believe that some classes, like 151 & 152, have few majors that really require them and mainly serve as for students who need a maths elective and took Intermediate Algebra (118) and don't want/need precalc 1/2 (161/162). I believe here at CCP, what others call College Algebra is Precalc 1 as it's all about functions & their graphs. 162, Precalc 2, seems to be some more functions & trig.Delete
The stat classes we do have are MATH 150 Introductory Data Analysis & MATH 251 Statistics for Science. Oops above. We have 2 if you don't count ECON 112/114. 254 says it is algebra-based & requires passing MATH 118 Intermediate Algebra or placement into 161 (precalc 1).
I am in an interesting predicament of wanting to do comp sci & engineering down the road, but am lacking in foundational knowledge because of high school education was inadequate. Also, I don't know which teachers are full-time and which are adjuncts. I had unpleasant experiences at a 4-year uni before with a couple adjuncts. One time I had an adjunct who didn't know how to do something he was set to teach! Regarding College Algebra, would you recommend Khan Academy & this UMKC big YouTube playlist ( http://www.youtube.com/playlist?list=PLDE28CF08BD313B2A ) by Prof Richard Delaware? I'm looking to take Linear Mathematics, Computer Mathematics, & Probability out of personal interest even if my major doesn't require it because I enjoy maths & puzzles, & am a tech guy & could benefit from the knowledge.
Thanks for such an awesome blog.
Adjuncts are a tough call; some of them have bogus degrees (and thus can't get full time positions), some of them are jerks (and can't keep full time positions) and many of them are just being screwed by admin. Usually, you're not going to get a good course from an adjunct, at least in math, because there are so many bogus "math education" degrees out there.Delete
MATH 150 is probably too basic for your needs; there might not be any probability at all in there, I'd have to see the book/syllabus. You're better off with MATH 251.
For computer science, yes, you want linear mathematics, and probability. Both of those topics are absolutely essential if you write any sort of decision-making program (i.e., a.i., at the risk of overdoing abbreviations).
I totally, totally, recommend Khan Academy (it's free, it's good), and know nothing of Professor Delaware...if he's free, I don't see the harm in at least seeing if he helps you.
That's one thing about math: there are many approaches to teaching mathematics, and what works for one individual can be disastrous for another. You're risking very little with "free."
If you're thinking about going engineering, then take the most advanced calculus you can; every 4 year program requires hard core calculus (not "Business Calculus", or, basically, any calculus that doesn't use trigonometry). You may as well start now.
I took a student from remedial math to differential equations (which you take after calculus III), so it totally can be done.
Yea interestingly CCP doesn't have that 'business calc' that some places have in addition to I guess regular calc 1. I always wondered what was covered in them courses but I bet biz calc in them other places is likely stuff for just what economics/finance/accounting majors face (that being said those unis allow such majors to take the regular calc 1 or higher if they want).Delete
Prof Delaware has a free series on YouTube on College Algebra & Calc 1. The CA material seems to have more than some classes in real life.
Also, is Linear Algebra taken after the entire calc 1-3 sequence but before Diff Eq?
Linear Algebra is an isolated course. You don't need calculus for it, and you certainly don't need Diff Eq for it either. If you're really good in algebra, you can take it after algebra. You really need some skills and careful algebra to do well with it, which is why it's usually taken after Calc 2 or so (at which point you've got plenty of practice with algebra).ReplyDelete