Getting off on the right foot in an inverted calculus class

March 11, 2014, 2:34 pm

5524669257_ab67585fd0_mIn the previous post about the flipped/inverted calculus class, we looked at getting student buy-in for the flipped concept, so that when they are asked to do Guided Practice and other such assignments, they won’t rebel (much). When you hear people talk about the flipped classroom, much of the time the emphasis is on what happens before class – the videos, how to get students to do the reading, and so on. But the real magic is what happens in class when students come, prepared with some basic knowledge they’ve acquired for themselves, and put it to work with their peers on hard problems.

But before this happens, there’s an oddly complex buffer zone that students and instructors have to cross, and that’s the time when students arrive at the class meeting. Really? you are thinking. How can arrival to class be such a complicated thing? They show up, you get to work, right? Well – not so fast. There are of number of things you have to get right in this period at the beginning of class.

  • What students learned during the Guided Practice needs to be assessed. Just because you made up some good Basic learning objectives and told students that they would be responsible for having them figured out prior to class, doesn’t mean it happened. You, as the instructor, need to know how successful they were in attaining those Basic objectives, or else the lesson you planned that assumes success is going nowhere fast.
  • The knowledge that students need for the day’s work needs to be activated. Expert learners know how to activate their prior knowledge so that when they face a new task, the relevant basic knowledge is there ready to be used. Novice learners – like the students in your class – don’t consistently do this. Maybe they don’t consciously do it at all. We’ve said that the flipped classroom should provide training for students in self-regulated learning skills and behaviors. Having students activate their knowledge – and getting students to realize that this is important – is part of that.
  • Quite simply, students need to show up for class on time and get in the right frame of mind. To paraphrase an earlier post, I’ve been amazed at just how much the success of the flipped classroom depends on students’ abilities to get their act together and manage time properly, including having some incentive to be at class, ready to work and knowledge activated, when it’s time.

Some folks believe that the flipped classroom is nothing but lecture outside of class, homework inside class. Unfortunately that’s how it works in some cases. But to really make the flipped classroom work, you cannot just have students come in and start working directly on “homework” and expect consistently good results. That 5- to 10-minute period of transition from pre-class to in-class is surprisingly crucial.

Here’s how we managed this in the flipped calculus class.

First, student responses to the Guided Practice were submitted online through a Google Form. (If you don’t know what these are, or how to make them, click here for a tutorial.) These were due no later than an hour before class began. This allowed me to go to the responses before class started and skim the results. If I saw a consistent pattern of incorrect answers on a question, I’d make a note of it. I’d especially note any specific mathematical questions that students would leave.

Second, I’d reserve 10 minutes at the beginning of every class for a question/answer session with students on the content from the Guided Practice. Featured in that Q&A session would be any item from the Guided Practice that was consistently missed and any good question from the “What are your questions” item. If we had time left over, we’d take open questions from the class.

This Q&A session had both expected and unexpected benefits. I expected the Q&A time to be helpful in clearing up some misconceptions students had or lead to some interesting example opportunities. I also expected this time to help guide my own plans for the class. But I didn’t expect it to have a salutary effect on morale. Students appreciated the fact that I was actually reading those questions and responding on the spot. One of the major criticisms students will level against the flipped classroom is that there’s no way to ask questions of the professor – having the Q&A time minimizes that objection.

Third, following the Q&A session, we’d have a classwide entrance quiz over the Basic learning objectives. The way I did it was through a three-question multiple choice quiz that students finished using classroom response systems. These were drawn directly from the Basic learning objectives. The quiz helped activate the appropriate content knowledge we’d need for the day. It also provided a measure of accountability for students to complete the Guided Practice and some formative assessment on their work on top of the Guided Practice itself. Quite often a commonly-missed quiz item would become another discussion topic. Since these were done with classroom response systems, students would know their grades instantly and all I had to do for grading was download the grades and put them into Blackboard. (We used Turning Point clickers and the TurningPoint software; this fall I think I’m going back to Learning Catalytics.)

All of this usually fit within a 10-minute span at the beginning of class. That’s 1/5 of the time we had together, which is somewhat expensive, but it was worth it – both for me and the students.

I should mention that at the outset of the semester, the order of the quiz and the Q&A time was reversed – we’d start immediately with a quiz, and then following the quiz we’d have Q&A time using the quiz results, student questions from the Guided Practice, and commonly-missed items from the Guided Practice as the basis. But students expressed a dislike for that ordering in our Mid-Semester Interview on teaching, so I tried switching the order, and I liked the results. Also, this semester in my flipped discrete structures course I am experimenting with having an exit ticket instead of an entrance quiz – so students have the opportunity to show their mastery of basic knowledge after working on a problem for 45 minutes rather than at the beginning. I think the jury is still out on this approach.

In the next post, we’ll get to the good stuff – what happens during class.


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