Again, a new IBL-Peer Instruction Hybrid Model

I am continuing to try to figure out a way to effectively use both IBL and Peer Instruction (“clickers”) in my classes.

First, my main constraint: my favorite grading scheme requires students to be given many chances to get questions correct. Ideally, this means that we would finish with new content for the course 1/2 to 2/3 of the way through the semester.

Here is the approach I have been using up until now:

  1. First part of the semester: Students get the content from reading the textbook.
  2. First part of the semester: Students assimilate the content through Peer Instruction.
  3. Second part of the semester: Students do something that resembles (but isn’t actually) IBL.
  4. Second part of semester: Assess the students a lot.

Below is the same model I discussed last summer for my abstract algebra class. That abstract algebra class was closed due to low enrollment, and I was assigned linear algebra instead. I am keeping the same model, although I have a lot more exercises/theorems/conjectures in my linear algebra notes than I do for my abstract algebra notes.

Here is the new approach:

  1. Mondays and Fridays during first part of the semester: Use IBL and student presentations to introduce the content.
  2. Wednesdays during first part of the semester: use Peer Instruction to review and solidify ideas learned on the previous Friday and Monday.
  3. Second part of the semester: We review the most difficult material through Peer Instruction and in-class practice.
  4. Second part of semester: Assess the students a lot.

Here is the main problem that I am facing: I have 312 exercises in my IBL notes; I basically wrote the notes that I wanted—including many examples to build intuition—and I am now trying to figure out how to shoehorn all of the content into 1/2 to 2/3 of a semester. This works out to an average of about 7 exercises per day if we did IBL work every day of the entire semester, 10 exercises per day if we did IBL work on Mondays and Fridays (and review on Wednesdays) every day of the semester, and 20 exercises per day if we did IBL work on Mondays and Fridays (and review on Wednesdays) every day for half the semester. So I want to see if I can do between 10 to 20 exercises per class IBL class period, which is too much to do without some modifications. Here are the options I can think of to make this happen:

  1. Cut some of the content. I don’t want to do this.
  2. Provide screencasts of some of the exercises. I want to do this anyway, since part of the goal of our linear algebra class is to introduce students to proofs, and I believe that it is very useful for students to see worked examples. But I don’t want to have to provide 10–15 screencasts each class period.
  3. Simply do not cover many of the intuition-building exercises in class; Dana Ernst suggested this to me yesterday, and I think that it is brilliant. There is not reason why I have to do everything in class. Perhaps I could just take questions on any intuition-building exercises after we do the main theorems; I could provide screencasts for some of these if we run out of time.
  4. Other ideas?

Right now, my plan is to have students present and thoroughly discuss roughly 5 problems per IBL day, I would do screencasts for roughly 5 problems per day, leaving roughly 10 intuition problems to leave for the students to do.

Do any of you have ideas about how to improve this?

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14 Responses to “Again, a new IBL-Peer Instruction Hybrid Model”

  1. Andy "SuperFly" Rundquist Says:

    It sounds like a good idea to me. What are the chances they’ll get lost/frustrated/bored on the intuition-building exercises? I guess that’s the concern, which is my perennial concern, that students won’t do what you need them to do out of class for the whole thing to work.

    • bretbenesh Says:

      Yeah, that could be a problem. If that ends up being the case, I suppose that I could re-assign the intuition-building problems again after we have the class where we discuss them.

      In fact, this is a real concern. I am more concerned about this class being a total failure than usual, probably because this is a new design for me and this is usually a really difficult class for students.

      On Tue, Dec 24, 2013 at 9:08 AM, Solvable by Radicals

      • Andy "SuperFly" Rundquist Says:

        A lot of it is about student buy-in, it seems to me. If they see the value of the out-of-class stuff, then you’re in a great position. The problem I’ve had is when they think things are going just fine even though I felt class time was wasted because they weren’t prepared.

      • bretbenesh Says:

        You are more optimistic than I am, although I am not pessimistic. I could see this being a bit of a wreck even if students buy-in and do all of the work. But we will see. . .

        On Tue, Dec 24, 2013 at 9:29 AM, Solvable by Radicals

  2. Joss Ives Says:

    Bret, how do the exercises vary in difficulty? For the sake of doing the most good for the most students, pushing the most difficult exercises to screencasts seems like a good option. If a student is overconfident and chooses not to make use of the screencasts for the more challenging exercises, then they I are not creating a huge barrier for themselves the same way they would have if they instead had the option not to engage in the intuition-building ones. You might even be able to figure out a clever way to push creation of these screencasts on to the students instead.

  3. TJ Says:

    It’s fine to skip discussion of some items, or to only give them cursory coverage in class. You just have to be clear about the purposes for your choices. And you might find a way to assess understanding on items you choose not to discuss in some other way.

    But beware of doing IBL where you push harder things into a screen cast. It might work once or twice, but the point is to have students talk through everyhing, especially the hard ones.

    • bretbenesh Says:

      Hi Joss and TJ,

      Thanks for the comments.

      Joss: There is a wide variety of difficulty among the problems. Fortunately, I have very good guidelines on what the level of proof should be for students. Since they have had minimal experience with proofs before linear algebra, the goal is to get them to be able to do proofs that are essentially a restatement of a definition.

      So this is where I can start. I will create a screencast for anything that is significantly hard than “restate a definition,” and then see how the semester progresses. My hope is that I can start feeding them slightly more complicated proofs by the end of the semester, although I will have to wait to see what happens.

      TJ: As I alluded to above, I am going to keep trying to require some proofs that push their limits, and the “restatement of a definition” provides a floor for what this should be. We will see how high I can push them.

      Thanks, guys! Bret

      On Tue, Dec 24, 2013 at 3:59 PM, Solvable by Radicals

  4. emilie Says:

    Is there out of class work beyond preparing for class? This past semester I had students post solutions to additional exercises on a wiki. I provided some minimal feedback, but they were responsible for correcting each other’s work.

    • bretbenesh Says:

      Hi Emilie,

      I am curious about how you did the wiki—did you find it useful?

      I am planning on having them do some additional work, although I am not certain how much will be done at the same time they are doing presentations. This probably deserves another post, but here is a summary of what I am planning on having them do:

      1. Well-written proofs to some of the presented problems. These will need to be done in \LaTeX. These will definitely be started during the first half of the semester.
      2. Preparing for quizzes on both conceptual linear algebra and the mechanics of linear algebra. I am not certain about this, but I might try for a 5 minute quiz each day for the first half of the semester, and transition to 55 minute long quizzes at the end of the semester. However, I am not yet certain that I will have 5 minutes to spare at the beginning of the semester.
      3. A running mind map of how all of the concepts in the class are related.
      4. Some synthesis homework problems. These would only be required for students who want a B or an A (or maybe just an A—I am not sure).
      5. A project. This will probably be a research project in linear algebra—something along the lines of “what is the maximal determinant you can make in an n \times n matrix that has only 0‘s and 1's as entries.

      Almost certainly, the only thing they will need to do for the first part of the semester is prepare for presentations, start writing up the well-written proofs, and maybe study for the quizzes. In fact, they don’t even need to study for the quizzes, since there is no penalty for getting an answer wrong—it just fails to help your grade.

      But I need to think about this all some more. I always tend to make assessment too complicated, and then feel the need to scale it back before the semester starts. This could happen here.

      On a contradictory note, I am curious about the Wiki and would like to hear more. Were you happy with how it turned out?

    • emilie Says:

      I was largely happy with the wiki. It gave students practice writing and reading proofs in a low stakes way, with almost no work on my part. The only way it didn’t meet my hopes was that students didn’t revise other students’ writing as much as I hoped. (But I think that is reliable with different guidelines from me.)

      I got the basic setup from blogs. I would be happy to dig up the blog posts and share the wiki, if it piqued your interest.

      • bretbenesh Says:

        Before you search for the posts (I know that you are probably pretty busy right about now), what did you do to make sure that the students ended up with reasonable proofs on the Wiki?

        On Thu, Dec 26, 2013 at 3:34 PM, Solvable by Radicals

      • bretbenesh Says:


        Is this post by Dave Richeson/Division By Zero one of the blog posts you used?

        Also, where did you host the Wiki? Wikidot? How was the \LaTeX support?

  5. Dana Ernst Says:

    I’m hoping you can find a workable system. That way I can steal all of your great ideas.

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