Gas station without pumps

2012 January 16

Where does learning happen?

Filed under: home school — gasstationwithoutpumps @ 07:21
Tags: , ,

The Chronicle of Higher Education has a rather lightweight article about a Stanford student complaining about the online machine-learning class at Stanford: Debating the ‘Flipped Classroom’ at Stanford.  There was, however, some very interesting discussion in the comments.

One commenter, Derek Bruff, summarized the pro-flipped-classroom position well:

As Eric Mazur often points out, in the traditional model, the “transfer” of information happens during class and the “assimilation” of that information—the much harder step—happens after class when students are on their own. Why not move the harder step to class time, during which the instructor and other students are around to help?

In the inverted classroom, it’s still important that students spend time outside of class doing work (and that can be problematic for the reasons you point out in your blog post), but the hardest work happens during class when the teacher is around to help.

[Derek is responding to a comment by Ira Socol which pointed to several blog posts. I think the one he means is Changing Gears 2012: rejecting the “flip” .]

I’ve been thinking about that pedagogical assumption: that assimilation of information works best if it happens during class when the teacher is around to help.  I can’t decide if I really believe it.

Certainly my deepest understanding of material has come when I’ve worked with it extensively on my own—writing programs, doing mathematical derivations, writing papers, … .  Having other people around when I’m doing this just makes it harder to focus, and does not aid in the assimilation.

But initial entry into the material is aided by having a guide who can quickly point me to productive lines of thought, so that I don’t flail around on trivia.  Some forms of learning are definitely helped by having interaction with the teacher as the practice is done (physical training like martial arts, dance, and sports seem to particularly benefit from supervised practice).

My son is taking an online calculus class that meets in a chat room once a week.  That time is spent doing a lecture with students asking questions for clarification, and he often refers back to the lecture transcript (an advantage of the chat-room format is that you get a full transcript, which is much easier to search than a video) rather than to the book for clarification of methods. Even my son, who is a diligent, top student, rarely reads the calculus book before class (or afterwards for that matter—he seems to get most of his information from the chat-room lecture, though I think that the book they are using is one of the best I’ve seen for top students).

But most of the learning takes place when he does the problem sets, not in the class.  There is an opportunity for the students to interact on the homework: there is a forum where the students can publish their solutions, ask one another for help, or read other students’ solutions (there is a social convention of hiding the solutions so that it requires an extra click to get them, so that no one looking at the forum is forced to see solutions before they want to).  My son posts solutions to all the problems, and I believe that there is some social status associated with doing so, though no explicit recognition from the instructors.  Still, the learning is not happening on the forum—it is happening when the problems are solved, with the forums providing an incentive for doing the individual work. The forums do also provide for communication with the instructor—particularly for clarification of confusing points in the homework problems or lectures.

Just this last week, we experimented with another approach: he and I each took a small (2′ × 3′) whiteboard and simultaneously worked independently on the same problem.  I sometimes had to ask him about what they had covered in class, as I’ve not done integration for 30 years  and have forgotten some of the techniques. I admit that I struggled a bit with \int x e^x cos(x) dx, though I eventually came up with a simpler solution than my son did, by “cheating” and using cos(x) = \mbox{Re} e^{ix}.  Integration by parts was always the least fun part of calculus for me. When we both finished a problem, we compared solutions, and then each looked for algebra errors if we got different results.  This provided more social interaction than working alone on a problem and the slightly competitive nature of trying to finish quicker with a more accurate answer resulted in the homework problems being done faster.

I think that this sort of synchronized but mostly independent work can be a good way to combine the individual effort needed for learning with some social incentives for doing it, as long as the problems are small enough ones and the people working on them are working at about the same pace.  (I’m rusty enough on my calculus that I’m at about the same pace as my son who is just learning it.)  I can’t see it working in a classroom, where students are likely to have a 5-fold different range of the pace at which they work—the faster students will be bored to tears and the slower students will be left behind.  I also don’t see it working in classes involving bigger problems (like programming projects that take >10 hours to do).

My son has developed a very different way of working on his science-fair project, which involves talking with me or his postdoc mentor at the university about the problem he is working on, then going and spending hours coding and testing.  He learns little bits from books, from Wikipedia, and from conversations (like what a decision tree is, or feature selection, or how to calculate entropy), but it is the hours of coding and testing by himself that really makes the ideas his.  He needs the contact with others to talk through points where he gets stuck, though often all he needs is a sympathetic ear and not guidance by an instructor.  The need for interaction is hard to schedule, though, as it does not come a fixed intervals—sometimes he needs to be left alone for days to write his programs, other times he wants to check on ideas every half hour.  This is one advantage of home schooling or (for the fantastically rich) a live-in tutor: learning on demand, without the tyranny of a class schedule.

I’ve often wondered whether the desirability of the flipped classroom is in extravert/introvert thing: as an introvert, I find working in a group that is trying to interact as they work extremely draining.  So much effort for so little accomplished! The traditional lecture classroom is much more suited for introverts, as there are only occasional social interactions required, and they are more like performances than like ordinary social interactions, and so are less stressful. (I know, extraverts can’t imagine performance being less stressful than ordinary social interaction, but introverted actors and professors may understand.) I think I might not have made it through college and grad school if my classes had all been “flipped classrooms” that relied on having “instructors and students around to help”.

I thought about using some of my sabbatical to record mini-lectures on various topics to experiment with a “flipped classroom” next year, but I doubt now that I’ll do it.  My lectures are extemporaneous performances that would be very hard to do without the interaction with a live audience, and I’m not convinced that flipping would really help learning any—the students are still going to have to spend many hours outside class struggling with their programs, and having to watch videos as well just reduces the time they have for the programming.


  1. I’ve been a proponent of flipped classrooms since long before that term was ever used. I first started doing it in the 90’s, under the influence of a few computer science educators who were experimenting with a more lab-based approach. In computer science, most real learning happens when you tackle programs, just as you describe with tackling problems. The traditional approach to computer science was this: 300 students in a lecture in which the professor writes lots of syntax rules on the board (or PP slides) and then glibly walks through the solution of a programming problem. Lots of students are so lost they don’t even know what questions to ask, and others nod their heads at the seeming easiness of the syntax rules and note how quickly the professor solves the problem, and say “I can do that too!”. Then, a programming assignment is handed out. Students disperse to their “discussion sections” where they meet in groups of 25 with an inexperienced grad student (and yes, I was one of those grad students) who reads through the assignment with the students and then asks for questions. No one has tackled the program yet, because they are either lost, or think that they can solve it as fast as the professor did in lecture. So, no questions. About 2 nights before the program is due, the better students start on it. They quickly realize that they are lost and don’t know where to start. By the night before the due date, there are long lines waiting for the course TA on duty (and I was also one of those). Other students have found someone who had already taken programming and are copying from that person. On the due date for the assignment, only about 50% hand in a working program, and of those, many of those students copied the solution from another student or the course TA. If the true learning happens while problems are being solved, do we really want that process to be supervised by an inexperienced course TA who happens to be on duty, or by copying? Once I had thought about that question head on, I realized that I needed to change things drastically, by devoting more class time to overseeing students working on programs rather than to lecture. And since class time is limited, this meant less time doing information transfer. So I changed my classes so that one “lecture” a week is devoted to in class problem solving. That is not quite as draconian as the true flipped classroom, but it seems to be enough to really improve things.

    I think that the traditional approach, of grappling with the problems on your own, only works well for the top students. It encourages extreme passivity in weaker students – they passively absorb the lecture, and then give up in despair when they have to actually solve problems. Computer science is still very difficult for weak-to-average students, but in my current system, I can get any student through with a C as long as that student diligently shows up for the in-class problem solving sessions, and actively works on the material. In the old days, those students typically failed. I recall that the Intro to CS course that I TA’ed for in grad school had an over 50% drop/fail rate. Is that something to be proud of?

    Comment by Bonnie — 2012 January 16 @ 07:48 | Reply

    • I’m not sure whether I agree with you that “the traditional approach, of grappling with the problems on your own, only works well for the top students.” Of course, I mainly deal with the top students, since I’m teaching senior and grad students in a tough major, so my view may be very biased.

      I think that the “weaker students … [who] give up in despair when they have to actually solve problems” are not necessarily well served by a system that provides them so much support that they never learn to grapple with problems on their own. I agree that a 50% failure rate is not a desirable thing, but I’m not so sure a 100% pass rate is either. I have had (small numbers of) students come into my senior-level bioinformatics classes after passing several CS programming classes still completely unable to program—not even the first-week warmup exercise. These students should not have passed their previous CS classes. I do not like failing students in their senior year when their educational problems should have been addressed two or three years earlier (but I do it, since I’m not going to pass incompetent students). One year, when I had several weak students, I traced the problem to them having had the same instructor for all their CS courses—one who provided too much scaffolding for the students, so they never learned to create whole programs, only code small pieces of them.

      The optimal pedagogic solution has to be somewhere in between learning it all on your own and having your hand held the whole time. Undoubtedly the optimum is different for different students and teachers. I learn more toward individual learning than is currently fashionable, but I’m not a big advocate of self-instruction either—I’ve found that I am much more diligent if I have the structure of a course, with scheduled due dates and class meetings, than if I try to learn the same material on my own, with just books or web resources.

      (Incidentally, I fixed your comment based on your later comment, and deleted the correction comment.)

      Comment by gasstationwithoutpumps — 2012 January 16 @ 08:37 | Reply

      • One big difference – I do not do a lot of scaffolding! I agree with you that it leads to students who flounder when they have to start from scratch. I would rather sit with them and talk through the problem solving process with them. When they are lost, I try to suggest ways to think about the problem. But I don’t just give them pieces of the code or the algorithm the way that many instructors do.

        One of the things about programming is that it is very pattern based. Students usually don’t see that because it is too new. For example, when my students learn arrays, I want them to realize that there are lots of problems that fall into the classic array-traversal category. But students don’t see that on their own. They don’t even get it when I tell them that, or walk through a dozen array traversals on the board. They don’t get it when the textbook tells them that. They don’t see it when faced with an in-class task to do one of these problems, even when they have just seen several on the board. But… I can nudge the students who are truly lost. “Asif, instead of staring at your screen hoping for the answer, why don’t you find me the problem we just covered 10 minutes ago?”. The student obligingly finds the example. “Now, can you tell me what this code does in English?”. Student reads his notes to me. “Does that sound similar to your task now?” If the lightbulb doesn’t go off, I can say “Remind me what your current task is. How is it different from this last example?”. Eventually, the student will get that there is a fundamental similarity and that he can reuse this problem from board.

        I am deeply interested in having my students actually learn how to program, because I see most of them as seniors in the required software engineering course. We have real clients in that course, so I need students who can program! At my university, a 50% fail rate would be unacceptable, so I need to find a way to get the students I have (not the ones I wish I had) through my course having learned something. And I don’t like to use extensive scaffolding to create the illusion that a student has learned to program. I have found this process to be far more effective.

        Comment by Bonnie — 2012 January 16 @ 10:06 | Reply

  2. I took a topology course from James Munkres, who does something similar as well: we were supposed to do all of the assigned homework problems. Then he’d ask which ones we couldn’t do and work them out in the lecture.

    Students really like scaffolding for their CS problem sets, and complain a lot when there isn’t scaffolding. I often end up telling them that it’s good for them to start from scratch with a problem, but I’m not quite sure that they believe me.

    Comment by plam — 2012 January 16 @ 09:20 | Reply

  3. >My lectures are extemporaneous performances that would be very hard to do without the interaction with a live audience…

    I am so with you on this. I’ve wanted to record my classroom performances, but those are punctuated by silence while students are working, so would definitely need some expert editing.

    I am so motivated by working with others, it makes a huge difference in what I can solve. I’ve been thinking on and off over the past year about how a card game was constructed, but never really delved in until the recent holidays, when I got a chance to work with a good friend. She does not think of herself as good at math, but she came up with a good way to organize the information, and that helped me solve the problem.

    Comment by Sue VanHattum — 2012 January 16 @ 10:20 | Reply

  4. I think gender (maybe gender socialization, maybe something deeper) plays a role in this. If higher-level math had more groupwork, perhaps more women would make it to phd level. (I have a masters degree. I started a phd program, but felt like it was the wrong way to spend my time, and quit.) Not all women are this way, but lots.

    Comment by Sue VanHattum — 2012 January 16 @ 10:23 | Reply

  5. My answer to the opening question “Where does learning happen?” may seem snarky, but I don’t mean it that way. Learning happens in the student’s brains.

    Comment by Chris Sears — 2012 January 17 @ 09:25 | Reply

    • Certainly learning happens in students’ brains. The next question is how best to get that learning to happen. That is where the disagreements start.

      Comment by gasstationwithoutpumps — 2012 January 17 @ 09:30 | Reply

      • I think the next question is “When or where is the student’s brain most engaged in learning?”

        Comment by Chris Sears — 2012 January 17 @ 11:32 | Reply

        • Well, that is closer to the question I was addressing in the post, but it probably comes after the more general question of how best to get learning to happen.

          Comment by gasstationwithoutpumps — 2012 January 17 @ 11:41 | Reply

          • I was trying to point out, rather indirectly and incrementally, that the most important factor for student learning is where the student is in the curriculum, not where the student is physically located. In a perfect world, a teacher would be able to look at a student’s progress and know the topics that they have mastered. The teacher would simply say, “Go learn the next topic.” The student would be in the correct place to learn because they would be building on their existing knowledge. (Zone of proximal development and all that.) The actual format of learning the material: book, lecture, video, interpretive dance, wouldn’t matter. (I’m realize that I’m ignoring differences in learning styles.)

            The strength of the flipped classroom is that the students have the instructor there to gauge their progress. Good students have the metacognitive abilities to know how well they have learned the materials. Poor students do not. It’s taken me three years of teaching developmental mathematics to realize there is a difference. I’m still learning how do deal with that difference with my students.

            It is my belief that as long as you have a method of measuring the current state of the students’ knowledge that provides sufficient (not perfect) feedback to the students, then the learning will take care of itself. The real challenge will be in finding the feedback mechanism that works best for your situation.

            Comment by Chris Sears — 2012 January 17 @ 22:34 | Reply

            • Determining what students know is important, and choosing the right next topic is often difficult, but I don’t agree that the “actual format … wouldn’t matter”.

              There is more to teaching than just feedback, as important as the feedback is. A good explanation reaches a lot more students than a poor one.

              Comment by gasstationwithoutpumps — 2012 January 17 @ 23:16 | Reply

  6. In a large lecture course in general physics, here is a promising way to START the learning at home.

    Phys. Rev. ST Physics Ed. Research 6, 010108 (2010) [5 pages]
    Using multimedia modules to better prepare students for introductory physics lecture
    by Zhongzhou Chen, Timothy Stelzer, and Gary Gladding
    Department of Physics, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801, USA

    [Creative Commons] Received 26 January 2010; published 11 June 2010

    It is known that introductory physics students rarely, if ever, read the textbook prior to coming to lecture. In this study, we report results from a curriculum intervention in a large enrollment introductory physics class that addresses this problem. In particular, we introduced web-based multimedia learning modules (MLMs) as a “prelecture assignment” designed to better prepare students before coming to lecture. We used student performance on “preflight questions” that they answer prior to lecture as a measure of their before-lecture understanding of the physics concepts. We found significant improvement in student performance and on the vast majority of these preflight questions as compared to that from previous semesters in which MLMs were not available. We found significant improvement for all students, independent of their background or ability level.

    This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

    © 2010 The American Physical Society
    DOI: 10.1103/PhysRevSTPER.6.010108

    Using multimedia learning modules in a hybrid-online course in electricity and magnetism
    Homeyra R. Sadaghiani
    Phys. Rev. ST Phys. Educ. Res. 7, 010102 (2011)

    What students learn when studying physics practice exam problems
    Witat Fakcharoenphol, Eric Potter, and Timothy Stelzer
    Phys. Rev. ST Phys. Educ. Res. 7, 010107 (2011)

    Comment by Jane Jackson — 2012 January 17 @ 21:00 | Reply

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