I have seen remedial courses before a first undergraduate calculus course that consist of a mix of algebra, trigonometry and coordinate geometry. However, have there been any experiments with remedial courses focusing more on developing problem-solving skills and/or the basics of what one would usually see in a transition-to-higher-mathematics course? If so, were such experiments successful in improving performance in calculus?

Note that while this is a general question, my specific interest at the moment is in assisting engineering students just beginning their undergraduate studies. Some of them only just scraped through in secondary school mathematics, while others have first completed a technician-style course that is light on mathematics.

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    $\begingroup$ A complicating factor, at least in some (U.S.) colleges and universities, is that sometimes for a large majority of students in such classes these classes are essentially terminal classes. The students might later take an elementary statistics course, but not a calculus course. For example, this is typically true for nursing majors and communications majors, which at many (U.S.) colleges far outnumber those majoring in a science field that requires calculus. $\endgroup$ Commented Jun 3, 2014 at 18:57
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    $\begingroup$ Having said this, there are some nice "math appreciation texts" that try to do something like this. An example is Miller/Heeren/Hornsby's Mathematical Ideas, which I taught out of around 12 to 14 times during 1993-1996. I have 3 or 4 texts similar to this at home, and you can find dozens (maybe over 100) if you browse the shelves of a large university's library. Such courses have been offered for several decades at a wide variety of colleges in the U.S. for students with a wide variety of backgrounds and abilities. $\endgroup$ Commented Jun 3, 2014 at 19:28
  • $\begingroup$ @DaveLRenfro I have that book, so I'm interested in the other texts that you mention, is it possible that could list them? $\endgroup$
    – seeker
    Commented Jan 26, 2015 at 15:40
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    $\begingroup$ @seeker: This isn't something I've kept records of, and I only own a couple of others -- Roberts/Varberg's "Faces of Mathematics" and Bennett/Nelson's "Mathematics for Elementary Teachers". If you have a college library nearby (a small liberal arts college might be better than a large university for this purpose), the simplest thing would be to browse the shelves where books like this are shelved (vicinity of QA 30's I think). $\endgroup$ Commented Jan 26, 2015 at 17:49

1 Answer 1


First, it certainly shouldn't be called or considered "remedial".

I think a course on mathematical modeling would be best. You could include a little bit of statistics, a little bit of rudimentary calculus and a little bit of scientific computing/programming. That should be enough to get some people hooked, it should be different from what they've seen previously and it won't be in any sense remedial.

I imagine something in between

  • Mathematics 112 at Bucknell University and
  • Mathematics 135 at Macalester College

Anecdotally, I understand that Math 135 at Mac has greatly increased the number of students taking mathematics courses.

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    $\begingroup$ Thank you. I think that's interesting to know, even though I wasn't thinking specifically about mathematical modeling courses. I do teach engineering students a short course on mathematical modeling, but it is not remedial and currently takes place after basic calculus has been introduced. $\endgroup$
    – J W
    Commented Jun 4, 2014 at 11:40

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