Ten Questions about Flipping a Mathematics Classroom

Dr. Gene Chase, guest blogger.

“Flipping the classroom” is doing problems in groups during class time, while listening to lectures and reading books during homework time. See previous blog post. It is a sufficiently vague and controversial method of teaching that I have questions to ponder rather than answers to push. What do you think? I’m focusing on the mathematics classroom especially in the light of the popularity of Khan Academy’s mathematics modules and because this is a math blog.

1. Will students learn more because they are discussing content together in groups in class? Or will they have trouble staying on task because the teacher can’t attend to all groups at once? We have no control over the schedules of students outside of school to get them to interact about content outside of class. Do your students interact about mathematics outside of class now? (If you are reading this as a student, do you interact with other students about mathematics outside of class?)

2. Will “just-in-time” teaching of content when in the middle of solving a problem be more meaningful and more motivational than lectures that “front load” a student with lots of answers that don’t yet have questions? Or will “just-in-time” teaching encourage the kind of thinking that says the answers are only one problem-solving step away? In Japan, students expect to struggle with a problem; in the US students expect a problem to have a ready answer.

3. If the outside readings or videos are in smaller segments than a class lecture would be (say 5 minutes) will this make the material more digestible? Will modularizing lessons help students especially with attention deficit disorder, or will these modules instead promote more scattered attention to the content.

4. Reading mathematics textbooks is a special skill. Mathematics texts need to be read with a pencil and paper at the rate of a line a minute; in contrast, fiction can be read relaxing on the couch reading at a page a minute. So students are tempted to start a mathematics homework assignment without reading the text, and then go back to the text on a problem-by-problem basis to find a problem like the one that they are working on. Will a flipped classroom help students to engage with their textbooks more actively?

5. Could the flipped classroom be a fad because videos are “hotter” than books? In Marshall McCluhan’s terms books are a “cooler” medium than videos because books demand more effort on the part of the reader. Showing videos in class, if they take up the whole class period, are a waste of time. Do teachers do that because students don’t have access to the media outside of class? Because it’s easy? Print is more effective than video in delivering content unless the video has interactive features. For example, a study showed that news from the printed New York Times was remembered better than news from the on-line New York Times.

6. Problem Based Learning (PBL) worksheets for use in class are very time-consuming to develop because they need to address multiple levels of student preparation, and time-consuming to evaluate. Unless you are using modules for outside of class prepared by others like Khan Academy, preparing the content for use outside of class is time-consuming as well. Could you flip part of a class? Perhaps assign listening to a narrated Powerpoint about a single topic, a Powerpoint that you used with your lecture in a previous semester? (Thanks to Dr. Jennifer Fisler of Messiah College for this suggestion.) Mathematics is skill-based. Could you “flip” a single skill?

7. At the college level, students are supposed to spend two hours outside of class for every hour in class. How can two hours be flipped with one hour? Outside material would have to be lecture plus half of the homework —the homework not covered in class the previous day. So we’re back to the traditional model. Laboratory sciences already recognize that PBL requires twice as much time as lecture, and they recognize that students will finish labs at different rates. Could mathematics be taught as as laboratory science? In the experimental sciences, concepts are exact, but the lab part can be messy. (Thanks to Dr. Richard Schaeffer of Messiah College for that observation in this context.)

8. Flipping a small class is easier than flipping a large class. Students who are home-schooled typically experience a small flipped class. Thirty students using PBL in an hour only allow a teacher to give individual help at the average rate of two minutes per student. Should the students be grouped heterogeneously so quicker students can help slower students?

9. Do I lecture because it’s energizing for me, whereas helping students at their desks is draining? Can I remain non-threatened by questions to which I don’t know the answer if I lose the control of the class that lectures afford?

10. This will only work for college, since secondary school teachers don’t have the option to ask students to leave the class because they didn’t do their homework. Would a “ticket to ride” be an extrinsic incentive to prepare for class by doing the reading or watching the videos in advance of the class? A “ticket to ride” is a little one-question pre-quiz at the start of class that gives students the opportunity to earn the right to attend the class.




3 thoughts on “Ten Questions about Flipping a Mathematics Classroom

  1. All good questions, Gene, many of which would apply to other disciplines as well. Accommodation goes both ways, institutions to students and students to institutions. Call me the geezer than I am, but a preponderance of pedagogical innovation strikes me as being institutional accommodation, another word for which is, at least some of the time, pandering.

    • Professor Lauer, you’re not being an old geezer, don’t worry :-). I feel the same way. In the end, you have to ask if new innovations actually serve education (the student, the teacher, the subject). Innovations for the sake of innovations are worthless, regardless of how flashy or trendy they may be. That was my take away from this recent article:

      “Flipping the classroom” may be the pedagogy du jour, but eventually it will settle into a happy equilibrium in the educational ecosphere. It will be implemented on a case-by-case basis, not wholesale. That sounds like a healthy and sustainable balance to me.

  2. Pingback: What Does “Flipped Classroom” Mean? | Learning and Teaching Math

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