Math departments fail too many calculus students and do not adequately prepare those they pass...
That is the message heard from engineering colleges across the country. Calculus has often been viewed as a tool for screening who should be allowed into engineering programs. But it appears to be failing in that regard, too. That is, it is preventing students who should be proceeding from going on, and it is letting students through who do not have the mathematical preparation that they need...
We now know that much of the problem rests with an outdated mode of instruction, a lecture format in which students are reduced to scribes. This may have worked in an earlier age when calculus was for a small elite group that excelled in mathematics. Today, professions that require calculus make up 5 percent of the workforce, a proportion that is growing at a rate that is 50 percent higher than overall job growth. We can no longer afford to ignore what we know about how to improve the student experience, both inside and outside the classroom...
Another example is to require students to read the relevant section of their textbook or watch a video before class, answer questions about the material to ensure they have done the assignment, and then describe their own questions and uncertainties. These can be great launch points for classroom interaction.
At
West Point we were required to read the material *and* complete the
assignment before actually coming to class. Then the instructor would
amplify the key points and respond to our questions. It's not a bad way
of teaching and learning, but it requires a significant time investment
on the part of the student. And if students won't put in the time *now*
to figure out the material *after* it's been taught to them, why would
they spend even *more* time *before* being
taught the material?
I think too many students expect everything to be given to them, they're not willing to work for anything.
Active learning does not mean ban all lectures. A lecture is still the most effective means for conveying a great deal of information in a short amount of time. But the most useful lectures come in short bursts when students are primed with a need and desire to know the information. A lecture is a poor substitute for giving students the time they need to discover the answers themselves.Time. Three hours a week, for what, 15 weeks, tops? Time is the commodity we're talking. Well, time, and motivation.
I believe in the power of "and". But if you had to choose one, given the time constraint, which do you think should change more, teaching methods or average student effort?
7 comments:
I view this as an indictment of high school / AP calculus and a vindication of the colleges and universities that don't take AP credits for calculus. But I'm also puzzled by the statement that collegiate using calculus as a weed-out class. At my alma mater - a flagship state university with a good but not massively prestigious engineering program, in a mostly rural state, that at the time I went most of my fellow engineering students likely had little to no calculus in high school (I certainly didn't) - none of Calc 1, 2, or 3 were the weed-out classes; Physics 1 and 2 were (and thermodynamics cast out the last few unworthy:-/).
Based on the rest of the article, it sounds more like most of these students didn't really have the wherewithal to learn calculus anyway. I think that most people with average intelligence can learn algebra; calculus takes a moderate amount more though.
Back in the dinosaur era (60s), even in HS college prep classes, advance, independent prep was required in all subjects. Unless used as pop quizzes, essays (and term papers) were done outside of class. We were thus prepared for college expectations (1 hr prep for each credit hour, minimum). This has been abandoned, on a widespread scale. Kids enter college expecting outlines, notes etc to be provided, because they were in hs; or they were completely unnecessary. They do not even know how to take good notes or how to study. Part of this is the entirely predictable consequence of admitting large numbers if kids who are incapable of, unprepared and/or unmotivated for real college-level work. Those without college-ready SATs were not admitted and freshman weeder courses removed the unmotivated (and the draft was a motivator). Since few HSs in the state offered calc, that was not the primary weeder; whatever the typical first math course was did the job.
A HS-teacher relative took early retirement, more than a decade ago, because of the relentless pressure for higher grades, more group work, fewer and easier assignments etc. He was appalled that his son was getting As in his former classes, doing no work whatsoever, because the new teacher went over each test, in its entirety, the day before it was given.
I am betting that most of the snowflakes/troublemakers on campus fall into the poorly prepared and/or unwilling to work hard category and are in weak majors; many of which did not exist 30+years ago.
There is so much of a push towards the grade or the degree but not the education. I understand it, and even fell prey to it to some extent when I was younger, but it's such a disappointment.
I would change the high school teaching methods. Simply put, the entire high school curriculum has been dumbed down to the point that the students aren't able to understand a calculus for engineers textbook (Larson at the CC, Stewart at the U)...they have no experience with symbolic language much less the abstract thinking that was required in the years that Dolciani high school texts were used. And a whole lot of them found it very easy to memorize procedures given during the review the class period before a test.
In
Saddest sound in the world: the crying at night in the dorm, the night the memorizers who were valedictorians/salutatorians get the second test back and realize they have to drop the class and reconsider the major if they want to keep the financial aid (need 12 credits passed). Yes, Calc 2 is the new weedout, since they had Calc 1 in the high school as rote memorization and the engineering schools aren't playing that game. In my day, the day after the first test was when you started hitting office hours religiously, found an upperclassman to tutor, and sweated till grades came...but you had enough from high school you could power thru.
You've hit the nail on the head. Students across the board believe they are entitled to an A even when they don't have the abilities or knowledge to produce A level work. What is more, when teachers expect students to do their own research, reading and work, parents will frequently complain how it cuts into "free time" where students participate in a wide range of non-curricular work. If you want any reason why on average American students do not perform to the level of those in other nations, look no further than the indulgence, distraction and emphasis on extracurricular activities over the work of learning.
If the goal is "identify the smart kids" then the screening is simple. Just look for people w/ a 5 on the AP exam, accompanied by a 730+ math SAT. 48% (really!) of BC takers got a 5; why would you screen for anyone else? If colleges are silly enough to rely on a class grade in the age of inflation, that's on them.
Of course, high school math profs, especially those who are lucky (and trained) enough to teach calculus to the smart kids, are way more invested than the usual college professors. The adjustment isn't that people have to work; it's that the professors in college don't often seem to care.
Maybe I'm dumb. But if I had constant complaints about the poor interaction between students and profs, and if I could only control one side of that, I'd change teaching styles.
A semester hour, by federal law, is 45 academic hours (each academic hour is 50 minutes).
Of those 45 academic hours, 15 are lecture and 30 is homework, but majority of students spend 15 hours as homework, so they are only spending two-thirds the required time.
For laboratories and practicals, 30 hours are contact and 15 are homework.
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