I’m returning to the blog after an hiatus brought on by two things: the six-week calculus class I am finishing up right now, and my participation in the Appalachian College Association’s Teaching and Learning Institute at Ferrum College in Virginia last week. The latter was a week-long engagement during which I gave an opening night after-dinner speech, a two-hour plenary talk, and three iterations of an inverted classroom workshop for participants. Between keeping up with the calculus class and prepping for and then attending the TLI, I’ve had no time for anything else. But coming off the TLI, I’ve got a fresh appreciation for the importance of blogging in my professional life. So, back into the habit.

I learned at the TLI that there are a *lot* of faculty who are interested in the inverted/flipped classroom. Interested — but not yet engaged in doing it, for a variety of reasons, most of which have to do with wanting to have a little more advance scouting information about what a flipped class is like before jumping headlong into it. I knew this about faculty coming into the workshop, so I designed the workshop around a quick design project: In groups of 3–4, participants chose *one* course from *one* person’s course roster, and then chose *one* day from that class to redesign with a flipped structure. In other words, don’t start by trying to flip a whole course but rather just a single 50–75 minute block. This way, it’s hopefully less overwhelming, and participants can scale up from there if they like what happens.

To get everyone in the right frame of mind for this activity, we had to think about *best practices* for preparing that flipped class day, focusing more on workflows and preparation strategies than technology, getting student buy-in, and all the other questions that seem to get asked more often. This has a nice calming effect on faculty; people are in different places when it comes to technological fluency, and the question of rebellious students is always nerve-wracking, but everybody can think about planning a class out in a controlled environment. It’s only natural that I should give my own best guesses about best practices in the workshop if this is to be the focus. And in preparing those thoughts, I discovered a workflow that I was using but didn’t realize it. A lot of the participants found this model of planning a flipped class to be helpful, so I wanted to share it here.

The process begins by simply listing out the learning objectives for the class session explicitly, in terms of action verbs. This is sometimes called backward design and it just means we will think about the class from a future viewpoint. What do you want students to be able to *do* once the class is over? The complete list of verb-oriented tasks should be listed and given to students. For example, if I am teaching Calculus students about the Chain Rule, my objectives might be:

- Identify when a function is a composite.
- Identify the inner and outer functions of a composite.
- State the Chain Rule.
- Apply the Chain Rule to differentiate a composite function, given as a formula.
- Differentiate the function \(y = e^{g(x)}\) where \(g(x)\) is a differentiable function.
- Apply the Chain Rule to differentiate a composite function in which at least one of the inner and outer functions is a graph.
- Apply the Chain Rule to differentiate a composite function in which at least one of the inner and outer functions is a table.
- Solve problems in context (“word problems”) in which the Chain Rule is involved.

If a student can do all of these things after a single class session on the Chain Rule and do them mostly correctly, I will be super-happy. Notice that not all of these objectives are strictly from Calculus; the first two are algebra-related but central enough to the topic at hand that it would help to state them explicitly.

If we are using an *inverted* structure for the class, we want students to have some fluency (mastery would be ideal) with some of these objectives before coming to class. But it’s not necessarily the case that student should be fluent in *all* of these objectives before coming to class. Maybe we just want them to be fluent in the basics, so that in class they’ll be set up to do sense-making activities on the more advanced ideas, some or all of which they’ve only glanced at in the reading or viewing.

Having the (totally obvious) realization that the learning objectives for a session are for students to eventually master, and that only a subset of these need fluency before class, really changed the dynamic of my courses for the better. For a long time, when I’d prepare Guided Practice documents for outside-of-class work, I would just lump all of these learning objectives into the same place at the beginning. This confused students and caused them to do focus their out-of-class time inefficiently; if they’re going to spend an hour preparing for class, I’d much rather it be an hour of really mastering the basic ideas than 30 minutes of incomplete fluency on those ideas and 30 more minutes of largely fruitless wrestling with more advanced notions.

So step 1 of planning an inverted classroom session is listing the learning objectives. The remaining steps involve rearranging those learning objectives in a particular way.

You are all probably familiar with Bloom’s Taxonomy (on the left). This is just a hierarchal representation of cognitive tasks from “simple” to “complex”. Every one of the learning objectives we’ve listed falls somewhere on this continuum. Step 2 of planning the class is simply to **put the learning objectives in an ordered list from simplest to most complex according to Bloom’s Taxonomy**. For example, my objectives for the Chain Rule lesson might go like this:

This may or may not be in the same order you used when you first listed the objectives. Many times we — as well as textbooks, when they list out learning objectives for a section — will treat the learning objectives like movie credits, where objectives are listed in order of appearance. Here, we want to make sure that the first objective on the list is the simplest and the last one is the hardest.

Now comes the important part. Once we have an ordered list of learning objectives, we instructors have to **choose a “cognitive cutoff point” at which student responsibility for mastery prior to class ends**. “Below” this point, we expect students to master the learning objectives before class through guided practice. “Above” this point, some fluency would be nice, but these are long-term learning objectives and will serve as the focus for class activities.

For example, I might draw the cutoff point for my Chain Rule lesson like so:

Above that blue line, I do not expect students to have much fluency when they arrive at class. Fluency is certainly not required for entry into class. But below the line, I expect students to have a very good idea about those concepts and calculations, and I will plan the in-class activities under the assumption that they’ve attained something close to mastery on them.

The final steps for preparing the class session follow this division of labor: **Plan out the Guided Practice and plan out the in-class sense-making activities**. For the “below the line” objectives, students will get resources for obtaining basic information and review along with exercises to help them drill the objectives. I would expect students to be able to come into class and, on a short quiz at the beginning, identify what the inner and outer functions are of the composite \(h(x) = \cos(x^2 + 1)\) and maybe \(k(x) = e^{\sqrt{x}}\); I would also expect them to state the Chain Rule and apply the statement to one or both of the above functions. *And that’s it.* Eventually, I do want them to show evidence of mastery of all the objectives. But only the ones below the cutoff point are to be focused on prior to class. Maybe I give students a conceptual question about the higher objectives (“How would you use the Chain Rule if one of the function is a graph?”) but I do not expect much prior to class. Rather, those upper objectives set the agenda for the in-class work.

It could turn out that in the course of planning the in-class activities, you end up deciding that you set the cutoff too low or too high. In that case, go back and re-set the cutoff and alter the Guided Practice and in-class work accordingly. If this happens after running the class session, well, you just have to make a note of it and change the cutoff for the next time you plan the class out.

Like I said, I’ve been using this divide-and-conquer approach lately (in the linear algebra class last semester and in my quasi-flipped calculus class right now, which I will write about later) and it has helped everybody. Students have a more manageable list of objectives to master and can focus their time better. I get to ask more of students, since they can now spend twice as much time on an objective list half the original size; and the split objective list basically plans the class session for me.

As we in my department move toward a fully-flipped Calculus offering this fall (did I mention that I have a lot to write about here?) you can bet that we’ll be keeping this sort of approach firmly in mind.