Semester Reflection, Part I

I am back to blogging after a semester of figuring out how to be the parent of two kids.  We are slowly figuring it out.


Anyway, below is a summary of what I did for the semester followed by how I would change in future semesters.  Recall that I am teaching real analysis.


  1. Students read a section of the text and watch some screencasts before class.  Students had to answer some questions online before class; if students did not answer the questions, they got a nagging email asking why.  This led to a very high completion rate.

  2. Students could request screencasts, thereby giving them a customized lecture (of sorts).

  3. For the first 60% of the semester, students spent about 75% of the time answering clicker questions (individually and in teams of three).  The remaining 25% of the time was spent starting homework problems.

  4. For the last 40% of the semester, we reviewed.  Students had to re-read a chapter before class.  In class, I gave the students four proofs to do in teams of two on a whiteboard.  Two proofs were very basic, and two were more complex.  I went around and gave feedback to each of the teams individually.  The idea was to run through the proofs of these four problems by the end of class (I put the proofs on slides), but we rarely got to all four questions.  I would also present the proof of a major theorem from the chapter about halfway through class.

  5.   Students were graded according to a midterm, a final, a portfolio, and a “practice portfolio.”  The exams are fairly standard.  The portfolio is a collection of each student’s best proofs throughout the semester, and the student has to provide evidence that he/she understands each of the course topics.  These are yet to be graded.  The practice portfolio was the same idea mid-way through the semester; this was graded on completion only, since the purpose of the practice portfolio was to get the students used to this different way of grading.

  6. Students who wanted to get an A for the semester had to do a project.  This means that they had to create screencasts on a section of the textbook that we had not covered during the semester (I used Abbott’s textbook, and he has them designated as “project sections”).


What went well:


  1. The clickers/peer instruction.  Analysis is full of ideas that are difficult to understand; if you do not understand them, it is even more difficult to prove anything about them.  The clickers really gave everyone—with virtually no exception—a solid idea of what was going on.

  2. The last 40% of the class was terrific.  We essentially went through the textbook twice, and the students made huuuuuuuge improvements the second time.


What I would improve next time:


  1. During the “clicker” portion of the semester, the class time spent starting the homework was not effective (in part because I did not give it enough time, but I don’t think that it would have been great with ample time, either).  I would recommend giving them the “basic” proofs that I did in the review portion of the semester each class period instead.  Perhaps do 50% clickers each class and 50% “basic proofs” (two would probably suffice, and most teams would probably only get to one).

  2. Do the practice portfolio much earlier.  I did it right after midterm, and that did not give students enough time to digest it.  Also, I recommended whether someone should do a project based on this, and students would have more time for projects if the practice portfolio went earlier.

  3. I also did two Calibrated Peer Review assignments. These failed due to errors on my part. First, I had students put their proofs on Moodle, which they linked to on the CPR site. This was a problem because students do not actually have access to the files on Moodle (it worked when I tested it because I have more permissions). Second, I told the students the wrong deadline for the second assignment. I think that this tool has a ton of potential, but I need to eliminate the user error first.
  4. I screwed up the standards a bit. For example, I was missing “Cauchy sequences” and “Limits” (Limits!). I was able to come up with fair workarounds for the students, but I think that I will only release standards to the students as we reach them in later semesters. This should force me to think through the standards an nth time, and I likely won’t miss anything major by doing this.


The jury is still out on portfolios.  We will see.

Tags: , , , , , ,

12 Responses to “Semester Reflection, Part I”

  1. Kate MacInnis Says:

    Congrats on the second little one. I look forward to hearing about the portfolios, especially since I’m planning on trying something similar (except for different in almost every way) next semester.

    • bretbenesh Says:

      Hi Kate,


      I would love to read about what you are doing with portfolios. I really think that portfolios are the right way to go with proof-based classes, but I do not yet know if I know how to do them correctly. It will be useful to hear how you do them.

      I am also excited to hear about your blogging project.

  2. Andy "SuperFly" Rundquist Says:

    Can you tell us more about the requested screencasts? I do that occasionally too, and, even though they seem quite happy that I agree to do it, I’m never sure they really make use of them.

    • bretbenesh Says:

      Hi Andy,

      Sure. Students first read the chapter. Then they took an ungraded quiz on Moodle. On the quiz questions was always “What did you find confusing about this chapter?” If the students wrote something, I would respond: by email if I thought that only that student would be interested, but with a screencast if I thought many people would be (students also sometimes requested a screencast from me verbally or by email).

      I created a new link on the Moodle page for the day called “Requested Screencasts.”

      Unfortunately, this was all done the day AFTER they read the section (how else could it be done?), so I am guessing a lot of students did not go back to check the next day. However, the students were told to look through these screencasts when we ran through the book the second time, so everyone eventually saw that they were there.

      So I don’t have much feedback on how many students used them. I would guess that there is some portion that looked at them religiously, and another portion that never watched them, although the usage was higher because I went through the course material twice.

  3. Joss Ives Says:

    Hey Bret. Since this is part 1, I am hoping that part 2 is going to discuss the portfolios a bit more. I am really intrigued by this idea.

    I’m curious about your thoughts on going through the material twice at a quicker pace vs. trying to figure out how to deal with it all at a slower pace on the first pass. I can see how you can probably really do some great stuff with synthesis in a 2-pass system, but it seems like they would be holding on for dear life on the first pass.

    • bretbenesh Says:

      Hi Joss,

      I am looking forward to discussing the portfolios, too. They are due on Thursday, so I am hoping to write about them next week (they take a long time to grade).

      I do know this: students are concerned about the portfolios. There was a discussion in class about the fairness of how the portfolios are being graded. I am thinking about whether the students are right, and there will be a little more discussion tomorrow.

      For this class, going through the material twice was completely worth it—so much so that I would like to do it in all of my classes. This will likely not be possible in, say, calculus, where there is just too much material. But students (mostly) commented that reading the material the second time made the material much easier. This is probably in part due to the fact that the students knew the big picture the second time they went through the material.

      I think that the first pass was brisk, but not overly so. The students read 5-7 pages per class, which seems to have been manageable. At this pace, we covered all of the non-project sections of the textbook (a first for me).

      I am going to plan on doing the same next semester for complex analysis, but not for my course for elementary education majors. I think that it depends on how much content is in the course (calculus probably has too much, but analysis does not have too much) and the nature of the instruction (my course for elementary education majors is nearly 100% discovery, which slows things down too much for a second pass).

      • Joss Ives Says:

        Hi Bret. I am intrigued by this idea of passing through the material twice in a course. I think there’s some great potential to have them build the connections earlier that most of them only seem to see when studying for the final. I guess the trick is to figure out at what level to pitch that first pass.

      • bretbenesh Says:

        I’m intrigued, too. My take this semester was: have the students just understand what we are talking about on the first pass (the clicker questions are great for this), and then focus on proofs during the second pass (when they actually know what they are talking about).

        I think that how the course is assessed would make a big difference in how the students like this. If the students are expected to master the material completely on the first pass, then I think that many would be unhappy (“I got a D on the quiz in the first part of the semester, but I got an A on the same material in the second pass. If we had just spent more time on it in the first part of the semester, I probably would have gotten an A. But because of the way you designed the course, I am stuck with a D now.”).

        You should try it and let me know how it goes! I am hoping to do it again next semester, so I will keep you updated. Bret

  4. Erica Says:

    Thanks for this. It would be fun to talk about it more sometime. (Sometime!)

  5. An Inverted IBL Frankenstein « Solvable by Radicals Says:

    […] am teaching complex analysis this semester, and I have decided to merge the inverted classroom approach that I used last semester with an Inquiry-Based Learning (IBL) […]

  6. The Levels of IBL « Solvable by Radicals Says:

    […] to accomplish this in courses with a lot of content crammed into them (like calculus) is to use a flipped classroom/Peer Instruction format for much of the […]

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: