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At many colleges in the United States, incoming students are required to take placement tests in basic skills such as math and reading. Those who score below a cut-off are required to take remedial coursework. Is there solid evidence about the effectiveness of remedial math courses? I'm particularly interested in community colleges.

The only empirical study I was able to turn up was Calcagno 2008. The method they used was to examine data from Florida community colleges to look for evidence of a discontinuity in average educational outcomes as a function of placement test scores, at the cut-off. The reasoning is that a student who scores at the cut-off score $x$ has almost the same math skills as one who scores $x-1$ and is forced into remediation, but would have a worse educational outcome because of not getting remediation. The result seems to be that math students who get remediation don't do better in later math coursework, and aren't more successful in college.

The subject seems to be controversial, however. Are there other studies that do support remediation?

At the community college where I teach, it wouldn't be surprising to me if remediation was uncorrelated with later success, simply because our curriculum has so much review built into it. For example, a student who starts at a low math level and gradually climbs up through our sequence will probably be led over and over again through reviews of the same topics, such as the properties of the reals or how to solve multiple equations in multiple unknowns.

Calcagno and Long, "The Impact of Postsecondary Remediation Using a Regression Discontinuity Approach: Addressing Endogenous Sorting and Noncompliance," National Center for Postsecondary Education, 2008, http://ies.ed.gov/director/conferences/08ies_conference/pdf/calcagno_long.pdf

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Sonnert and Sadler (2014) investigated what factors influence success in college calculus courses, including putting students into a pre-calculus course, which they described as "often a review of material students learned (or were supposed to learn) in high school." This may correspond to what you are calling "remedial."

In their results, they found students who took the pre-calc course showed no significant benefit over their peers in their outcomes in calculus courses. No matter how unprepared for calculus they were (pp.15-16).

This study examined a large sample (about 10,500) of U.S. calculus students. This is the most recent research of this type I am aware of. The literature review might be helpful as well. Dr. Sadler came to speak at the Kaput Center recently and he was very frank that there are many possible implications and questions that we might have as a result of this analysis, but he didn't entertain any sort of speculation. This gave me confidence in the results he did report.

Cited:

Sonnert, G., & Sadler, P. M. (2014). The impact of taking a college pre-calculus course on students’ college calculus performance. International Journal of Mathematical Education in Science and Technology, 45(8), 1188–1207. doi:10.1080/0020739X.2014.920532

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I don't know about the research you ask for - supporting remediation. I am learning a lot lately about how problematic remediation is. There are two sorts of problems - placement and the remediation coursework.

Placement tests can be harder than the tests students encounter at the end of their courses. I took the ACT/Compass placement test that our college uses, to see what it's like. Many of the questions were interesting to me. That translates to - way too hard for most students. The questions required real mathematical thinking, coming at topics from unusual directions. I asked afterward how many students place into calculus. They said almost none do. (Our department has control over the cut scores, but we probably set them too high long ago, and haven't dealt with that recently.)

Another problem with placement tests is the issue of stereotype threat, the tendency to feel threatened by the stereotypes about your people (gender, race, etc), and because of that feeling, to do worse on a test of ability. (See Whistling Vivaldi, by Claude Steele for a deeper understanding of how big a problem this is.)

Because of these issues, my department is looking at changing placement decisions to a combination of GPA and grades from prior coursework.

The short version: Many students who place into remedial courses don't really need to be there.

But some students are clearly not ready for college level math courses. Are remedial courses the right place for them? Probably not. Any course that feels like a repetition of things a student first saw in elementary school is going to activate all sorts of emotional baggage. Also, taking so many courses means that at least a few drop out at each step along the way. At our (typical) community college, many of the students place into a pre-algebra course. If we did super-well and 90% passed, some would still not go on to the next course (they move, they need to take on more paid work and have no time, etc). Let's say we get 90% going to the next course. How many ever arrive at a first college-level course, even with these wildly optimistic success rates? (90% pass pre-alg)(90% go to next course)(90% pass beginning alg)(90% go on)(90% pass int alg) (90% go on) = .9^6 = 53% of these students make it to the college level course.

When over 70% of students place into remedial courses, and we fail over half of them (because that 90% I used above was not realistic), we are allowing our courses to become a barrier to their success.

One way around this that looks like it's working is "acceleration" programs that get students ready for the college level course they'll take. Many students need just one college level course, and choose statistics. We are piloting an Algebra for Statistics course that students at any level can take. Another college in our district has found that the students who take this course do better in statistics than students who took the traditional remedial sequence (and made it to stat). I put acceleration in quotes because it's not about going faster through material (which would be disastrous); instead, it's about getting to your goal faster, by learning some mathematical thinking skills, playing around with basic stat concepts, and coming into the stat course ready to think.

Is it possible to develop a program that gets students ready for STEM courses, including calculus, with fewer semesters of coursework? I'm looking into that now.

Resources:

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  • $\begingroup$ Agreed, actually, I would hope the students I'm talking about take advantage of the CC system. That would be smart for them. I started at a CC myself, and I have fond memories of my time there. $\endgroup$ – James S. Cook Dec 5 '15 at 16:36
  • $\begingroup$ I deleted my comments since upon further reflection I think they're distracting from your post. $\endgroup$ – James S. Cook Dec 5 '15 at 20:12
  • $\begingroup$ Why do you believe the students should get a college education? This might sound like a stupid question but I am on the hiring side of the spectrum (in a different country arguably) and I wonder just why I get so many applicants that have a college degree but essentially nothing to show for it competence wise. I realize that the high school system in the US is particularly atrocious, but at some point I think you need to just draw the line. $\endgroup$ – DRF Oct 23 '18 at 11:38
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Remediation is more about the politics of mathematics education than about learning mathematics. When students don't use their mathematics they often lose it quickly. My own experience was that it was much better for students to take the courses that their high school record said they had taken the prerequisite courses for than to have them take "remedial" courses first. I reviewed the skills that experience often suggested students had troubles with when it was needed for a topic I was teaching. I think it is especially cynical to have students take remedial algebra courses if there is little need for algebra as part of their career plans.

There is also this:

https://www.insidehighered.com/news/2014/08/21/college-level-statistics-trumps-remedial-algebra-cuny-study

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