"Flipped classroom exercises" resources

Question

I was reading this book:

"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?

Answer 1

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.