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.




Don’t flip out!

Well, not yet at least. Everyone’s flipping the classroom, but is it really worth it? Yes and no, as NCTM president Linda Gojak explains in her column this week. I don’t always highlight her column, but I especially appreciated the nuanced way in which she approached this trendy subject. There’s something more fundamental that we need to aim for: engaging our students in mathematics and problem solving. Whether we flip or not may be immaterial, as Linda points out.

Here are a few excerpts from her article, which you should check out in full here.

To Flip or Not to Flip: That Is NOT the Question!

By NCTM President Linda M. Gojak NCTM Summing Up, October 3, 2012

A recent strategy receiving much attention is the “flipped classroom.” Innovative use of technology to enhance student learning makes flipping possible and motivating for students and teachers.

I believe that we need to go further. As we consider effective instruction that leads to student learning, we must remind ourselves of the characteristics of mathematically proficient students.

Rich mathematical tasks provide students with opportunities to engage deeply in mathematics as opposed to a lesson in which the teacher demonstrates and explains a procedure and the student attempts make sense of the teacher’s thinking. Communication includes good questions from both teacher and students and discussions that develop in students a deep understanding by wrestling with the mathematical ideas.

Although the flipped classroom may be promising, the question is not whether to flip, but rather how to apply the elements of effective instruction to teach students both deep conceptual understanding and procedural fluency.


All that being said, I still DO want to try flipping my classroom on a small scale, one-lesson at a time basis. I promise I’ll try it someday.

Summer Odds and Ends

I promise I’ll start blogging again. But as followers of this blog might know, I like to take the summer off–both from teaching and blogging. I never take a break from math, though. Here are some fun things I’ve seen recently. Consider it my own little math carnival :-).

I love this comic, especially as I start my stat grad class this semester @ JHU. After this class, I’ll be half-way done with my masters. It’s a long road! [ht: Tim Chase]

Speaking of statistics, my brother also sent me this great list of lottery probabilities. Could be very useful in the classroom.

These math dice. Honestly I don’t know what I’d do with them, but you have to admit they’re awesome. [ht: Tim Chase]

These two articles about Khan academy and the other about edX I found very interesting. File all of them under ‘flipping the classroom.’ I’m still working up the strength to do a LITTLE flipping with my classroom. My dad forwarded these links to me. He has special interest in all things related to MIT (like Khan, and like edX) since it’s his alma mater.

I’ll be teaching BC Calculus for the first time this semester and we’re using a new book, so I read that this summer. Not much to say, except that I did actually enjoy reading it.

I also started a fabulous book, Fearless Symmetry by Avner Ash and Robert Gross. I have a bookmark in it half way through. But I already recommend it highly to anyone who has already had some college math courses. I just took a graduate course in Abstract Algebra recently and it has been a great way to tie the ‘big ideas’ in math together with what I just learned. The content is very deep but the tone is conversational and non-threatening. (My dad, who bought me the book, warns me that it gets painfully deep toward the end, however. That’s to be expected though, since the authors attempt to explain Wiles’ proof of Fermat’s Last Theorem!)

I had this paper on a juggling zeta function (!) sent to me by the author, Dr. Dominic Klyve (Central Washington University). I read it, and I pretended to understand all of it. I love the intersection of math and juggling, and I’m always on the look out for new developments in the field.

And most recently, I’ve been having a very active conversation with my math friends about the following problem posted to NCTM’s facebook page:

Feel free to go over to their facebook page and join the conversation. It’s still happening right now. There’s a lot to say about this problem, so I may devote more time to this problem later (and problems like it). At the very least, you should try doing the problem yourself!

I also highly recommend this post from Bon at Math Four on why math course prerequisites are over-rated. It goes along with something we all know: learning math isn’t as ‘linear’ an experience as we make it sometimes seem in our American classrooms.

And of course, if you haven’t yet checked out the 90th Carnival of Mathematics posted over at Walking Randomly (love the name!), you must do so. As usual, it’s a thorough summary of recent quality posts from the math blogging community.

Okay, that’s all for now. Thanks for letting me take a little random walk!

New Physics Blog

Shout out to Chase Martin, who has just started a great physics blog, Five Minute Physics. My friend Chase and I have a lot in common:

  • Our names
  • Our love for juggling
  • Our love for math & physics
  • Our love for teaching
  • Our blogs

Chase is awesome, and you’ll love his fun-loving lecture style in these videos. His goal is ambitious: to put the entire lecture content of his high school physics course on youtube. Wow! File this under ‘flipping the classroom.’

Here are a few of his first videos for your enjoyment.

Go check out his website for more!


PS: If you haven’t checked out Minute Physics yet, it’s also a great youtube channel with fun entertaining videos!


File this under “flipping the classroom.”

Here’s a recent piece from NY Times columnist and best-selling author, Thomas Friedman [ht: Gene Chase]:

Thomas L. Friedman: Come the education revolution

By Thomas L. Friedman

PALO ALTO — Andrew Ng is an associate professor of computer science at Stanford, and he has a rather charming way of explaining how the new interactive online education company that he cofounded, Coursera, hopes to revolutionize higher education by allowing students from all over the world to not only hear his lectures, but to do homework assignments, be graded, receive a certificate for completing the course and use that to get a better job or gain admission to a better school.

“I normally teach 400 students,” Ng explained, but last semester he taught 100,000 in an online course on machine learning. “To reach that many students before,” he said, “I would have had to teach my normal Stanford class for 250 years.”

The combination of all these factors gave birth to Coursera.org, which launched April 18 with the backing of Silicon Valley venture funds, as my colleague John Markoff first reported.

When you consider how many problems around the world are attributable to lack of education, that is very good news. Let the revolution begin.