A while back I wondered out loud whether it was possible to implement the inverted or “flipped” classroom in a targeted way. Can you invert the classroom for some portions of a course and keep it “normal” for others? Or does inverting the classroom have to be all-or-nothing if it is to work at all? After reading the comments on that piece, I began to think that the targeted approach could work if you handled it right. So I gave it a shot in my linear algebra class (that is coming to a close this week).

The grades in the class come primarily from in-class assessments and take-home assessments. The former are like regular tests and the latter are more like take-home tests with limited collaboration. We had online homework through WeBWorK but otherwise I assigned practice exercises from the book but didn’t take them up. The mix of timed and untimed assessments worked well enough, but the lack of collected homework was not giving us good results. I think the students tended to see the take-home assessments* as being* the homework, and the WeBWorK and practice problems were just something to look at.

What seemed true to me was that, in order for a targeted inverted classroom approach to work, it has to be packaged differently and carry the weight of significant credit or points in the class. I’ve tried this approach before in other classes but just giving students reading or videos to watch and telling them we’d be doing activities in class rather than a lecture — even assigning minor credit value to the in-class activity — and you can guess what happened: nobody watched the videos or read the material. The inverted approach didn’t *seem* different enough to the students to warrant any change in their behaviors toward the class.

So in the linear algebra class, I looked ahead at the course schedule and saw there were at least three points in the class where we were dealing with material that seemed very well-suited to an inverted approach: determinants, eigenvalues and eigenvectors, and inner products. These work well because they start very algorithmically but lead to fairly deep conceptual ideas once the algorithms are over. The out-of-class portions of the inverted approach, where the ball is in the students’ court, can focus on getting the algorithm figured out and getting a taste of the bigger ideas; then the in-class portion can focus on the big ideas. This seems to put the different pieces of the material in the right context — algorithmic stuff in the hands of students, where it plays to their strengths (doing calculations) and conceptual stuff neither in a lecture nor in isolated homework experiences but rather in collaborative work guided by the professor.

To solve the problem of making this approach seem different enough to students, I just stole a page from the sciences and called them “**workshops**“. In preparation for these three workshops, students needed to watch some videos or read portions of their textbooks and then work through several guided practice exercises to help them meet some baseline competencies they will need before the class meeting. Then, in the class meeting, there would be a five-point quiz taken using clickers over the basic competencies, followed by a set of in-class problems that were done in pairs. A rough draft of work on each of the in-class problems was required at the end of the class meeting, and students were given a couple of days to finish off the final drafts outside of class. The whole package — guided practice, quiz, rough draft, and final draft — counted as a fairly large in-class assessment.

Of course this is precisely what I did every week in the MATLAB course. The only difference is that this is the *only* way we did things in the MATLAB course. In linear algebra this accounted for three days of class total.

Here are the materials for the workshops we did. The “overview” for each contains a synopsis of the workshop, a list of videos and reading to be done before class, and the guided practice exercises.

- Determinants: Here’s the overview and here are the in-class problems.
- Eigenvalues and eigenvectors: Overview, in-class problems.
- Inner products: Overview, in-class problems.

- The inverted approach is used in distinct graded assignments that are made to look and feel very distinct from other elements of the course.
- Teachers make the expectations for out-of-class student work clear by giving an unambiguous list of competencies prior to the out-of-class work.
- Quality video or reading material is found and used, and not too much of it is assigned. Here, the importance of choosing a textbook — if you must do so — is very important. You have to be able to trust that students can read their books for comprehension on their own outside of class. If not, don’t get the book. I used David Lay’s excellent textbook, plus a mix of Khan Academy videos and my own screencasts.
- Guided practice exercises are selected so that students experience early success when grappling with the material out of class. Again, textbook selection should be made along those lines.
- In-class problems are interesting, tied directly to the competency lists and the guided practice, and are doable within a reasonable time frame.

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