Remedial Recommendations

So granted that the last blog post here was thinking about all the reasons why remedial college math classes in algebra are so tough (for students and teachers), I'm pleased to say that 3 weeks into this almost-all-algebra-remediation semester, things are definitely going the best for me in my decade-long teaching career. Here are some things that I'd say have had a clear, beneficial impact on my current semester:

  1. Shorter class times. In the prior 8 years at CUNY, I have always had 2-hour long algebra classes, meeting twice per week (partly because I've mostly been part-time, teaching at night). For the first time, my classes are 1 hour long, meeting four times per week. This clearly works better for the endurance and attention available to the students. We're in, focused on one narrow topic, and finished before everyone gets too tired & cranky. This has been a pleasant and great surprise to me; definitely the biggest-impact of the semester. (Not that it would work for night students or part-time teachers, where the travel burden would be inefficient.)
  2. Starter exercise pack. I expect students to have a copy of the textbook and be practicing exercises from it regularly, but very few do so (as noted last time). One problem is that students don't immediately have the textbook in the first week, as they're saving up, looking for a used copy, or having an old edition shipped online (as I explicitly encourage). This gap then sets the habit of them skipping my "practice" advice. What I did this semester is to copy a packet of "starter exercises" from the book, covering the first few weeks, with answers, so I can hand it out the very first day and explicitly point to what they can practice that very night. I've found this to be quite helpful in setting the precedent for regular practice; I've had more students than usual come to class with questions about problems, and this sets up a virtuous cycle of other students seeing it as expected behavior.
  3. Tailored, trickier problems. In the past my routine was to lecture, then turn to the book and practice problems from the text with students. Partly due to the relatively small number of problems in our in-house text, about a year ago I went through the course and wrote custom exercises for every in-class topic. Generally I wrote these to be tougher than standard starting problems, and every single problem from the first integrates common stumbling blocks (negative numbers, one and zero coefficients, etc.). Among the advantages here are that (a) we're not totally boring the students who have seen the material before, (b) we're always dealing with problems similar to test items, and (c) we're spending time "triaging" all the trouble spots. These exercises are working very, very well for me. Textbooks usually start problems sets with very rudimentary "common sense" examples to get started, but granted the limited class time we have available, I would highly recommend skipping those low-level problems and immediately start working with at least mid-level exercises for every topic.
  4. Ending with flex-time. There's probably a better name for this, but what I mean is: I end every class with a few exercises (one word problem or two pure algebra) and say, "This is the last thing we'll do today; show me the answers and you're free to go" (this being maybe 20-30 minutes before the end of the period). Then I circulate and check answers, give corrections or hints, etc. The better students push themselves to finish quickly and happily leave (thereby avoiding bored-irritated-distracted people in the room); the mid-level students get more time for feedback and cleaning up trouble areas (and also with less embarrassment or defensiveness from a roomful of people listening in); and the very weakest student gets some personal one-on-one time with me. I have to remember to give any homework or next-class directions prior to this point, of course. This was a great, semi-accidental find on my part. (And the flex-time mechanism works even better with 1-hour classes, since it happens twice as often as it would for my night classes.)
  5. Surrendering on mobile devices. My remedial students commonly come in with smartphones running and earbuds in both ears throughout the entire class. Considering that my higher-level students practically never do this, in the past I felt it was my responsibility to model proper collegiate discipline and be very hardcore about having people shut off their devices at all times. Frankly, the resistance to this could be so fierce that it blew up into security issues on me a few times. So as stupid as it seems, this semester I've been letting people sit in class using phones and with earbuds in without immediately confronting them (unless they were directly interacting with me at the time). It seems to take some of the pressure off, and in some cases for students who are legitimately already on top of the information, it may reduce the boredom-irritation factor. On the one hand, it's dumb as all hell, but on the other hand I don't really have the tools to fix that problem on top of everything else.
  6. Entering with a sense of joy. Not really new, but I try to remember to come into class with an upbeat attitude and thinking about how great it is to share the topic of the day with whomever's willing to listen. Obviously from the name of this blog you can tell that's not actually my most natural personality. But if I can, I try to shake as much crankiness off before stepping into the room. As the simply amazing film Monsieur Lazhar put it, "A classroom is no place for despair". That does seem to make things run more productively and with less general combativeness than some times in the past.

Do you have any tactics and strategies that work particularly well in the context of remedial college classes?


  1. I really like this post! I'm teaching a remedial math course and planning what I'm going to cut the next time around. For example, they really stumble on solving equations with absolute values. Why am I spending a week on this? Next time, no absolute values and I'll save the time for something they'll use a lot, like factoring.

    1. Great, I hope it can be of help! When I'm starting out, the greatest resource I want to see is a copy or sample of the final exam the students will be taking (followed closely by a *good* textbook). Or, if I write it, then I compose it as my first task and work back from there. I cut the class down to solely what's on the final, and then add back minimal pieces I personally feel are necessary to support that and make it a coherent story.

      I don't have solving equations with absolute value in any of my classes, and I agree, I'm happy to not have them there. (Occasionally I feel bad about never pointing out that sqrt(x^2) = |x|, but restricting questions to positive real x dodges the issue.)

  2. Yeah, I'm giving up on devices (mostly) too. Sad, but true. And I do think it hurts our connection if I push my perspective too much.

    I like this list. If I go back to lower level classes, I'll try to keep these ideas in mind.

    1. That's well-put about how it hurts the personal connection, I agree that's what I'm seeing now. I gave it a good fight. :-)

  3. Good stuff.
    I'm curious as to whether you use the Socratic method in class, and whether you find it effective.

    that's one way to get at the electronic device issue. If they know they can or will have to answer questions, its difficult to completely "zone out".

    1. Well, without getting into exactly what counts as "Socratic", I will say that I'm machine-gun peppering them with questions nonstop during collective work on exercises. "Where's the center of this equation? Which side is the variable on? Is there any simplifying to do, yes or no? On which side, left or right? What kind? Combine like terms is really what operation? What's the next step in the process?" etc. etc. etc.

      It's all stuff that we've defined in the past and they should know, and I agree that it's an indispensable tool for modelling the active thinking process. (I had a local high school teacher say they're now required to document any questions in advance and can get penalized for anything off-script, and my reaction was, "Just cut my legs off right now.")