-1
$\begingroup$

What are the differences in the level and kind of preparedness for calculus typically found in students beginning a calculus course at a university in the USA today, and those beginning such a course between five and eight years ago?

Later note: I've taught first-semester calculus during most semesters during that time period. I notice an answer that says "My personal feeling is that[...]" this or that would happen instead of "I have observed in teaching calculus eash semester during that time that[...]" this or that would happen. (Nonetheless there was something of value elsewhere in the answer).

I've noticed a change toward more students never having heard that math doesn't just consist of memorizing algorithms, and I've heard from someone claiming to have been watching closely that students are rapidly getting less well-prepared BUT these are based on small samples, and the variation from one class of about 25 students to another, merely because it's a difference group of 25 students, actually is quite large. That is to be expected when you consider that $\sqrt{25}=5$, so the SD of the sample mean should be about $1/5$ of the SD that you'd consider if you're thinking about variation from one individual student to the next.

Another later note: Answers that don't stray too far from empirical observation are better than those that say that the heavier rock would fall faster than the lighter one.

  • 0
    I hope I've phrased this question in a way that will not offend those who are eager to be offended by including my own guesses at the answer within the question. It seems that comments about teaching embedded in questions either about teaching or about other things upsets some people.2011-07-29
  • 0
    Do you mean Calc I, Survey of Calc (i.e. "Scurvy of Calc"), ... ??2011-07-29
  • 2
    Are you looking for math education literature on the subject?2011-07-29
  • 0
    Should this be a wiki question?2011-07-29
  • 3
    Define "typically", keeping in mind the vast array of universities in the US, and the great differences among the various Calculus courses offered at any one university.2011-07-29
  • 0
    For what it's worth: There is nothing that I could see as potentially offensive in that post. However, I think it is "too localized" because it only concerns universities in the US. Also, besides agreeing with Gerry about "typically" I don't know how to measure "level and kind of preparedness" in any reasonable way. Thus, I'm voting to close.2011-07-29
  • 1
    @Theo: Hmm. I like to think of myself as someone who is relatively enlightened about the existence of a non-American world, but in truth I think there is a sufficiently large market here for math education questions that are restricted to the American system. As it happens, I also voted to close as "too localized": the temporal features of this question mean that the answers come with an expiration date (or, for all you Canadians out there, an "expiry date"). I am also skeptical that there are academic studies that carefully compare the situation now with the very recent past.2011-07-29
  • 2
    Getting even more local (oh no!), there has been at least one significant change in California during roughly this time period. The UC system started requiring calculus-based physics for biology majors ca. 2000, so this is the period during which we've seen a ramping up of bio majors taking calc. (I teach physics.) I don't know if this has affected average preparedness in Calc I. The real problem IMO is low standards in Calc I courses.2011-07-29
  • 0
    I notice some votes to close. Could those who so voted explain verbally why they want to close this question?2011-07-29
  • 0
    @Jonas: If such literature exists, then citing it would obviously be a responsive answer.2011-07-29
  • 2
    @Michael: They already did.2011-07-29
  • 0
    @Brian: Where did they do that?2011-07-29
  • 1
    @Michael: Both Theo and Pete gave explicit reasons in the comments in which they mentioned their votes to close. On another point, I definitely did *not* notice an increase in the (always substantial) number of students who seemed not to realize that there was more to math than memorizing algorithms (or at any rate didn’t want to believe it).2011-07-29
  • 0
    @Theo: If you "don't know how to measure" such things, then a posted answer to the question could report that some particular way of measuring it is in use out there somewhere. It doesn't yet seem clear to me that if there's a reasonable way to measure it, then _you_ would necessarily know about it.2011-07-29
  • 0
    Could someone explain what "too localized" means on the menu of reasons to close a question? The only place I've seen it before is mathoverflow, where it's what they use when someone posts a question whose answer is a routine exercise for undergraduates. (Except sometimes they say "off topic" for that as well.) Here on stackexchange it can't have that meaning, since homework questions are appropriate here.2011-07-29
  • 0
    @Theo: This does not concern only the USA or only the present era. It is in part about a thread of corruption caused by the standardized testing industry and in part about honesty about what mathematics is.2011-07-30
  • 2
    @Michael: The question explicitly does concern only the USA and the rather recent past, and as posed, it does not clearly have anything to do with either of the topics that you just introduced. This latest comment goes a long way towards making the whole thing look rather like a disguised statement of opinion. At this point I’d seriously consider voting to close were I in a position to do so.2011-07-30
  • 0
    My opinion on the meaning of "too localized": it means the voter thinks the question should be closed, isn't really comfortable with any of the closing options on offer, so just picks one. Put another way: the voter thinks the question should be closed, but doesn't think it is spam.2011-07-30
  • 0
    On reading what has come out of the question so far, I'm voting to close as not constructive. Michael, if you're not happy, take it to meta.2011-07-30

1 Answers 1

1

My personal feeling is that 5 to 8 years is far too short a period for there to be much noticeable change, at least when averaged over the entire U.S. Nonetheless, I recommend looking at David Bressoud's Launchings column for 2010 and 2011 at http://www.maa.org/columns/launchings/launchings.html

There are several of his columns that I think are relevant for what you're asking.

  • 1
    In a span of 36 years teaching at one institution I don’t think that I could pick out any 5-8 year period in which I thought that there was noticeable change.2011-07-29
  • 0
    @Brian: Specifically what courses have you taught for the past 8 years? Have you taught first-semester calculus frequently during that time (at least one semester each year)?2011-07-29
  • 0
    @Michael: Often enough to feel that I was in touch with what was going on, but certainly not that often. (My low-level staple was liberal arts math, since I was one of the very few senior faculty who enjoyed teaching it.)2011-07-29
  • 0
    @Dave: What is glaringly conspicuously missing from your answer is something saying what you have observed by teaching beginning calculus each semester during that time, or anything along those lines.2011-07-29
  • 0
    +1 for mentioning Bressoud's column. The first sentence in this answer, however, seems uncomfortably similar to saying "My personal feeling is that when dropped from the top of the Tower of Pisa, the heavier rock WOULD fall faster."2011-07-29
  • 0
    @Michael: My observation in teaching calculus over the years is pretty much what Brian M. Scott said, other than there was a noticeable decline in hand calculation technique throughout the 1990s. Among those techniques most relevant to calculus readiness, the largest drops in the 1990s seemed to be in algebraic manipulation skills and precalculus curve sketching methods. Thus, I would agree there was a noticeable decline in students during a 5 to 8 year period in the 1990s, but I feel less strongly about other 5 to 8 year periods.2011-07-29
  • 1
    @Michael: I haven't taught since 2005, but my guess is that any perception of such a major student decline in such a short period of time has more to do with one's personal circumstances than with students overall. For example, newly teaching at some pondok college instead of where one's Ph.D. work was done, or not yet being acclimated to average students after immersion with one's peers while a student (peers who may have skipped the calculus sequence and who were more concerned with their USAMO or Putnam scores than their SAT and GRE scores).2011-07-29
  • 0
    @Michael: (FYI) I first taught calculus in 1986 (although, as a graduate student, I conducted Tues-Thur recitations in calculus 1 & 2 in 1982-84), then taught calculus intermittently until 1996, then taught about 25 calculus courses between 1996 and 2005. My calculus teaching experience was at 5 math Ph.D. institutions, 2 private liberal arts colleges, and 1 public high school "math/science academy". Besides these, I've taught at a branch campus of a state Univ. (3 years) and at an extremely high "high needs" public school, and my experience as a student includes 2 additional universities.2011-07-29
  • 0
    @Dave: Personal circumstances don't explain the recent increase in headlines about high-school math teachers organizing widespread cheating on standardized tests. I think that comes from increasing dependence on federal funds that are awarded to schools that score high on such tests. But cheating in the classroom by teaching ONLY multiple-choice-test-taking skills won't be reported in headlines. Readers won't see that as a big scandal.2011-07-29
  • 0
    @Dave: What is a "high-needs" public school? Does it mean one where they need some teachers with Ph.D.s in order to teach students who are well ahead of the level where high-school students normally are? Or a place where 10th graders can't read and hence are "needier", education-wise, than their counterparts in other schools? Or something else?2011-07-29