# "Flipped classroom exercises" resources

"Dynamics of Particles and Rigid Bodies: A Self-Learning Approach" by Mohammed F. Daqaq

In the preface, the author explains of his "flipped classroom exercises"

I have presented a set of exercises, which I call "Flipped classroom exercises". Flipping the classroom is a modern teaching technique which has been shown to be very effective in teaching topics requiring mathematical derivations. In a typical flipped classroom, the instructor will briefly discuss the material for ten minutes, do some of the important derivations, and solve one example. Subsequently, the instructor hands the students one or more problems to solve on their own, but provides some guidelines that help the students by dividing the problem into several sub-problems. The student will then spend the rest of the class trying to solve as many of these problems as possible. The problems are carefully designed to have an increasing difficulty level. At the end of the class, the full solution of the problems is given to the student.

An example from the text:

Flipped Classroom Exercise 1.1 Find the rotation matrix necessary to take you from a certain frame, N , to another frame B by performing a successive 2-1-3 rotation using angles (...) To answer this exercise, follow the following steps:

1. Which rotation takes place first? What is the rotation matrix associated with it?
2. Which rotation takes place second? What is the rotation matrix associated with it?
3. Which rotation takes place third? What is the rotation matrix associated with it?
4. Multiply the rotation matrices obtained in steps 1, 2, and 3. Since the 2-rotation occurs first, the matrix obtained in step 1 must be on the far left. Show that the transformation matrix from N to B can be written as ....

My questions are:

1. Are there any guides to creating such exercises so I can use in teaching?
2. Are there any other textbooks that uses this approach?
3. Is this supposed to be similar to inquiry based learning?
• What level are you most interested in---elementary, high school, undergraduate, or graduate?
– JRN
Apr 8, 2021 at 6:47
• @Joel Reyes Noche undergraduate Apr 8, 2021 at 8:36

This is not really a complete answer to your question (which is pretty broad), but would not have fit in a comment.

What is described in the quoted text is one person's particular way of implemented a flipped classroom. One thing that I find sad about it is that it never mentions the role of a textbook in presenting the material -- which is impossible to do adequately in a 10-minute presentation. An alternative model, which I have used throughout my career, is closer to what is described by Mazur, Peer Instruction, which emphasizes reading. Yet another model is to record a lecture on video and have students watch it before class -- I suppose on the theory that students are all illiterate.

Is this supposed to be similar to inquiry based learning?

As I understand it, inquiry-based learning is a different thing. It's a model where the students to some extent construct the subject for themselves. For instance, rather than presenting students with the definition of the derivative, you could have them do examples where they make numerical approximations to the slope of $$x^2$$, $$x^3$$, etc., form conjectures, and eventually are led to constructing the definition of the derivative in terms of the limit for themselves. I've done this technique, and I think can be made to work well in gen ed classes, but it's not well suited to classes for STEM majors. It gets awkward because you're at least temporarily hiding information from the students, and then at some point they have to be encouraged to synthesize things into some more organized form. In my experience, it can randomly work better or worse depending on the group of students you get and whether there are students in the group who are natural leaders.

Are there any other textbooks that uses this approach?

Some ways of implementing the flipped classroom don't require any special features in the textbook. If you want to implement it using group activities or whole-class active learning exercises rather than individual activities, then you need a source of tested and well-designed activities. For example, my OER first-semester calculus text has discussion questions sprinkled throughout the text.

Before diving in to a technique like this, I would suggest that you carefully study the pedagogical literature and make sure that whatever practices you follow have empirical support. I mainly teach physics, not math, and the impression I get is that there is overwhelming empirical support for active learning in physics, but not as much in math. And active learning does not necessarily mean a flipped classroom. In the empirical studies in freshman physics, the common denominator for success seems to be that you get the students to talk, and the words coming out of their mouths are about concepts, not plugging numbers into formulas.

• What you describe at the top here is also what I know as a "flipped classroom", where the "homework" often involves watching a video in advance so that what used to be the lecture can then be spent with students problem-solving with guidance. The original question description seems more like the "I do, we do, you do" common in high school mathematics. Apr 8, 2021 at 13:55
• I suppose the video is not because the students are illiterate, but because it serves as a proxy for a prof. If students used textbooks instead of a video, what the prof is for? To discuss what the students did not understand in the textbook? Homework it checked by TAs. @Carser, I did not see the "we do" part in the original question. To me, "we do" is when one — or several — students solve problems at the blackboard in front of the class, and everyone can chime in. Apr 8, 2021 at 22:17
• @RustyCore The "we do" is in there: "Subsequently, the instructor hands the students one or more problems to solve on their own, but provides some guidelines that help the students by dividing the problem into several sub-problems" There are several names for this related to scaffolding and "concreteness fading". They described moving from the instructor doing all of the work toward the students doing it. What you are describing is one of many possible strategies in this phase. What the question describes is what I do in my classroom, and I wouldn't consider mine a flipped classroom. Apr 9, 2021 at 11:32
• @RustyCore: If students used textbooks instead of a video, what the prof is for? To discuss what the students did not understand in the textbook? This is sort of the point of the flipped classroom, as I understand it. The teacher's purpose is not to explain or present the material. The teacher's purpose is to act as the guide on the side, not the sage on the stage. E.g., the teacher could be doing laps around the room and helping students who are stuck on the problem. Or the teacher could be organizing group-work or telling a group when it's made a mistake or is on the wrong track.
– user507
Apr 9, 2021 at 17:11
• @RustyCore you have clearly have left off the other part of the sentence which naturally changes the meaning. It is literally describing a situation where the instructor supports the students as they start out... it's like the definition of "we do". I'm confused about why you are misrepresenting what is said when it isn't even relevant to a larger point. Apr 9, 2021 at 22:43