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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.

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closed as too localized by Pete L. Clark, t.b., mixedmath, Asaf Karagila, Gerry Myerson Jul 30 '11 at 13:02

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Are you looking for math education literature on the subject? –  Jonas Meyer Jul 29 '11 at 5:41
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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. –  Gerry Myerson Jul 29 '11 at 6:10
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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. –  Ben Crowell Jul 29 '11 at 15:35
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@Michael: They already did. –  Brian M. Scott Jul 29 '11 at 18:30
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@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. –  Brian M. Scott Jul 30 '11 at 4:18

1 Answer 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.

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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. –  Brian M. Scott Jul 29 '11 at 17:25
    
@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)? –  Michael Hardy Jul 29 '11 at 17:48
    
@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.) –  Brian M. Scott Jul 29 '11 at 17:58
    
@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. –  Michael Hardy Jul 29 '11 at 17:59
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@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). –  Dave L. Renfro Jul 29 '11 at 19:19

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