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Not inverting math class (but using video anyhow)

October 24, 2011 pm31 7:31 pm

The idea is – watch the lecture at home. Do problems, ask questions, in class.

I’ve been reading about the inverted classroom for several years. First a calc professor/blogger wrote about it a few times, and then used it repeatedly and continued discussing it, then I saw some chemistry people doing it. Then Khan Academy. And then it seemed to be everywhere.

I won’t do it. I don’t lecture at a camera. I develop the next piece of mathematics, with students participating in the development. My lessons vary – as I respond, without fear, to the questions and concerns that arise. From the students.

I am not teaching to a static camera. I am teaching TO and WITH a group of wriggly, curious teenagers. I answer your question now (unless it is if you can go to the bathroom, and try to pick a better moment to put up your hand), as long as you already asked the person next to you, and neither of you know. We interact. I do not invert.

But in calculus this year… Well, new course for me. And I decided that I don’t like video, but maybe I was being stodgy. Or silly. Or retro. Old-fashioned. So I decided to try.

For their summer assignment I included bonus points for watching and summarizing Khan Academy videos. I figured I’d throw them a few points, and get instant teen-aged feedback. Verdict:  a few watched them, thought them dry, but ok for an example or two. I reviewed their notes, and wasn’t impressed – nor was I disappointed. I wouldn’t want to depend on Khan, but as an occasional support or tutorial, yeah, it’s ok. For the record, my kids mostly looked at trig or log stuff.

I told them to prepare for the Level 2 Math SAT II. Seems most of what I want them to know for calc would be there.

And then I had them watch (no choice) 4 longer videos. I asked them to wait until 1 – 2 weeks before school to watch them. And to watch only one per sitting. And to take good notes.

I chose from “Free Online Courseware” at MIT, a series of lectures by Herb Gross, entitled “Calculus Revisited.” I assigned the introduction, Analytic Geometry, Functions, and Inverse Functions. (And I made the completion of this simple assignment be worth tons of points, too many for any of them to contemplate not doing them.) At the worst, they would come in griping about 4 lost hours of their summer. And at the best, the pre-limits review could go faster. And my teenaged scholars would walk in the first day, with math already on their minds.

The quality of their notes was relatively high, but fell off when they hit inverses. They reported liking Gross, and his nerdy, quirkiness. Being engaged. I responded by making the pre-limits review fast. Probably too fast. But it helped that they had watched.  The videos worked – not to the level of my most optimistic hopes, but there was definite positive impact.

I decided to incorporate video-watching, to some extent, in my course. (to be continued)

9 Comments leave one →
  1. Fred Klonsky permalink
    October 24, 2011 pm31 8:04 pm 8:04 pm

    Great to have you back doing reflective writing.

    • October 24, 2011 pm31 11:54 pm 11:54 pm

      Thanks. I always reflect, the writing part is uneven.

  2. October 24, 2011 pm31 8:07 pm 8:07 pm

    I teach to my audience too, and pretty much feel the way you do about this.

    But my students want some videos, and I want to try it out. I haven’t found time yet, but I’m hoping to do it soon. Just a few mini-topics that they’d really benefit from being able to see multiple times.

  3. October 24, 2011 pm31 11:55 pm 11:55 pm

    I’ll blog later about my choice of video, and how we are using them. With real implications for what I’m doing, though I don’t know if it translates.

  4. Crystal Kirch permalink
    October 24, 2011 pm31 11:57 pm 11:57 pm

    I started doing videos last year as a supplement for my Pre-Cal kids who needed some more examples beyond the classroom. Then, this year, I decided to test the waters and try the “flipped classroom” about 80% of the time. I have made my own videos of my own lessons for my students to watch for every lesson (working on it as we go through the school year). About 3-4 days a week, depending on content, the students “homework” is to watch the video and take their notes. The other 1-2 days a week, their “homework” is normal practice. I make my decisions based on what lessons I feel would be best learned in an environment where the student can “pause” me whenever they need to (i.e. more complex processes) [FLIPPED] or ones that I think are really important to have the back-and-forth teacher/student questioning and working. [NOT FLIPPED].

    I am now in my third week of this “experiment”.

    The results I have seen so far is test grades 3-5% above average from the last 3 years I have taught this course for the last two chapters.

    Student feedback from today, after 2 weeks: 8% of them wish we did it EVERY day. 16% of them wish we only did it once or twice a week… 76% of them like doing it 3-4x a week like we are doing now. They feel like it helps them understand it better because they can pause, rewind, and re-watch any portions or the entire video (I keep them between 8-18 minutes long) as many times as they want. If students are absent, they don’t miss a really important lesson (although classmate interaction is important!); they can catch up online and re-join the class, sometimes even WHILE they are home sick! The only negative feedback I have received is that students feel they can’t control themselves online and want to click to other websites and get distracted when watching a video, or the students that always just do their homework in other classes or before they get home and aren’t used to actually having 20 minutes of math homework to do at home.

    My feedback:
    Pros: I feel like I don’t have to repeat myself and explain procedures or calculator work over and over again like I have in the past. Little details that are important that students have always missed in the past are now being completely with extreme accuracy on tests and quizzes. I feel I have more time in class to answer questions and work through problems with students than when I am teaching the lesson. I feel much less rushed in class. Students are able to work with each other more, talk through problems, and correct each others’ errors. There is more time for “fun learning” like group activities, whiteboards, etc.

    I do miss some of the back-and-forth banter that comes from teaching a live lesson, but that now happens in smaller groups and with more individualized attention. I try to avoid the students just coming to class and “doing homework” sitting at their desks all alone. I try to have them complete it in partners or small groups with different types of activities, whiteboards, moving around, switching partners, doing the problem orally instead of on paper, etc – all ways to help them master the content in a different way.

    Just came across your post and thought I would share my thoughts and experiences! Any suggestions or feedback is welcome!

    • January 6, 2012 am31 7:46 am 7:46 am

      Have just come across this blog. Am doing research with my maths classes here in Ireland re using video and ‘flipping’ re video and online notes. Very interested and grateful for reflections posted here. Thanks Crystal and JD.

  5. October 26, 2011 pm31 7:49 pm 7:49 pm


    I’m Herb Gross ( I surf the Internet from time to time to see if there have been any comments about my “Calculus Revisited” course that could be of help to me and also to see if there are any comments about my own website ( on which I have posted my videos and written materials to present complete courses in arithmetic and basic algebra.

    I was interested in your comments (especially about my quirkiness and nerdiness ) about your students’ reactions to my videos. I was wondering whether they only watched the lectures or whether they also studied the supplementary notes and/or my exercise (and solution) sets.

    As the title of the calculus course indicates, the course was originally designed for people who had already studied calculus and were taking this course as a refresher prior to pursuing post graduate study. The remarkable thing, from my point of view is how well the course is being received by students who are taking calculus for the first time (you can read viewers comments by logging onto You Tube and searching for “ocw calculus revisited” and you can read comments made about my arithmetic and algebra courses by going to my website and reading the comments that have been written in the guest book).

    My teaching career began in the early 1950’s, so that by the time the Internet and other high-tech learning aids came into play I was already pretty well set in my ways (I am now 82). Therefore, I taught in the traditional lecture mode and my videos were designed to help students internalize the course content in between classroom sessions. On the other hand, my video courses are designed to be used either by individual viewers or by a teacher/facilitator as an additional delivery tool.

    With warmest regards and best wishes,

    Herb Gross

    • October 26, 2011 pm31 9:09 pm 9:09 pm

      I am delighted you wrote! I will reply more fully, but let me just say thank you, both for the work from 40 years ago, and for finding me.

      One of my students searched and found you were around, but I was unable to locate an e-mail address. I’m glad to have it.

      I will be writing more, about how we are using your work, and what works for my students. I’ll alert you as I write, and look forward to your further thoughts.

      Thank you,


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