Category Archives: Inverted classroom

March 27, 2013, 8:00 am

Inside the inverted transition-to-proofs class: What the students said

6799510744_d2085426d7_mIn my series of posts on the flipped intro-to-proofs course, I’ve described the ins and outs of the design challenges of the course and how the course was run to address those challenges and the learning objectives. There’s really only one thing left to describe: How the course actually played out through the semester, and especially how the students responded.

I wasn’t sure how students in the course would respond to the inverted classroom structure. On the one hand, by setting the course up so that students were getting time and support on the hardest tasks in the course and optimizing the cognitive load outside of class, this was going to make a problematic course very doable for students. On the other hand, students might be so wed to the traditional classroom setup that no amount of logic was going to prevail, and it would end up like my inverted MATLAB class did where a

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March 20, 2013, 8:00 am

Inside the inverted proofs class: Dealing with grading

6251461402_2a11c771db_mSo, what about grading in that inverted transition-to-proofs course? Other than the midterm and final exams, which were graded pretty much as you might expect, we had four recurring assignments that required grading: Guided Practice, Quizzes, Classwork, and the Proof Portfolio. Let’s discuss the workflow and how it was all managed.

Let’s start with the easy stuff: Quizzes and Guided Practice. Quizzes were done using clickers, so the grading was trivial. Guided Practice was graded on the basis of completeness and effort only, on a scale of 0–2. So it was almost instantaneous to grade. Students would submit their work using a Google form that dumped their responses into a spreadsheet. I would just sort the spreadsheet in alphabetical order, look through for any glaring omissions or places where effort was lacking, and then put the grades right into Blackboard. A grade of “0”…

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March 18, 2013, 8:00 am

Inside the inverted proofs class: What we did in class

3095855157_7bf2df04fa_mI’ve written about the instructional design behind the inverted transition-to-proofs course and the importance of Guided Practice in helping students get the most out of their preparation. Now it comes time to discuss what we actually did in class, having freed up all that time by having reading and viewing done outside of class. I wrote a blog post in the middle of the course describing this to some degree, but looking back on the semester gives a slightly different picture.

As I wrote before, each 50-minute class meeting was split up into a 5-minute clicker quiz over the reading and the viewing followed by a Q&A session over whatever we needed to talk about. The material for the Q&A was a combination of student questions from the Guided Practice, trends of misconceptions that I noticed in the Guided Practice responses (whether or not students brought them up), quiz questions with…

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March 13, 2013, 8:00 am

Inside the inverted proofs class: Guided Practice holds it together

In the last couple of posts on the inverted transition-to-proofs course, I talked about course design, and in the last post one of the prominent components of the course was an assignment type that I called Guided Practice. In my opinion Guided Practice is the glue that held the course together and the engine that drove it forward, and without it the course would have gone a little like this.

So, what is this Guided Practice of which I speak?

First let’s recall one of the most common questions asked by people learning about the inverted classroom. The inverted classroom places a high priority on students preparing for class through a combination of reading, videos, and other contact with information. The question that gets asked is — How do you make sure your students do the reading? Well, first of all I should say that the answer is that there really is no simple way to …

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March 11, 2013, 8:00 am

Inside the inverted proofs class: Meeting the design challenges

2688582584_644b85622e_nIt’s been a while since I last wrote about the recently-completed inverted transition-to-proof course. In the last post, I wrote about some of the instructional design challenges inherent in that course. Here I want to write about the design itself and how I tried to address those challenges.

To review, the challenges in designing this course include:

  • An incredibly diverse set of instructional objectives, including mastery of a wide variety new mathematical content, improvement in student writing skills, and metacognitive objectives for success in subsequent proof-based courses.
  • The cultural shock encountered by many students when moving from a procedure-oriented approach to mathematics (Calculus) to a conceptual approach (proofs).
  • The need for strong mathematical rigor, so as to prepare students well for 300-level proof based courses, balanced with a concern for student…

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March 8, 2013, 4:30 pm

The inverted classroom as platform

211239773_940d75fc4d_nI’ve been talking a lot with my colleagues about their teaching practices, as part of the NSF grant I’m working on. The inverted classroom (I used to call it the flipped classroom, but I’m going back to “inverted”) has come up a lot as a teaching technique that people have heard a lot about but haven’t tried yet — or are wary of trying. I’ve been wondering about the language being used, namely: Is the inverted classroom really a “teaching technique” at all?

My answer used to be “yes”. When I first started using the inverted classroom idea, I would describe the inverted classroom as “a teaching technique” that involves reversing where information transmission and internalization take place. Later I moved to saying that the inverted classroom refers to “any teaching method” that implements this reversal. Today as I was thinking about this, I think a…

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February 14, 2013, 7:45 am

Update on the peer-instruction based linear algebra class

One of the projects I was taking on with my teaching this semester was a revamped linear algebra course built around peer instruction and the use of Learning Catalytics, a web-based classroom response platform. I probably owe you a quick update now that it’s nearly mid-semester (what?).

Linear algebra is a strange course in some ways. There are a lot of mechanical skills one has to learn, like multiplying matrices and performing the Row Reduction Algorithm. If you come into linear algebra straight out of calculus with a purely instrumental viewpoint on mathematics, you will almost certainly think that these mechanical skills are the point of linear algebra. But you’d be wrong! It’s the conceptual content of the subject that really matters. Like I tell my students, you can answer almost any question in linear algebra by forming a matrix and getting it to reduced row echelon form….

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February 5, 2013, 7:45 am

Khan Academy Redux

The last thing I expected to encounter this week was a resurgence in the Khan Academy Debates of this past summer. Those, if you remember, centered around this spoof video created by my GVSU colleagues John Golden and Dave Coffey. My own contribution to those debates remains the single most viewed post I’ve ever published in nearly ten years of blogging. But honestly, I hadn’t thought much about Khan Academy since then — until Monday afternoon.

Dave (Coffey) sent me a tweet alerting me to this whitepaper published by the Pacific Research Institute, a free-market think tank based in San Francisco. “Look at page 14,” Dave said. I did, and found that I was being used as a prime example of a Khan Skeptic. Actually I am the last in a list of skeptics whose skepticism the authors attempt to dispatch. I’m in good company, as Keith Devlin is the first on that list and Veritasium…

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January 28, 2013, 7:45 am

Inside the inverted proofs class: Design challenges

This is the second post in a series on the nuts and bolts behind the inverted transition-to-proofs course. The first post addressed the reasons why I decided to turn the course from quasi-inverted to fully inverted. Over the next two posts, I’m going to get into the design of the course and some of the principles I kept in mind both before and during the semester to help make the course work. Here I want to talk about some of the design challenges we face when thinking about MTH 210.

As with most courses, I wanted to begin with the end in mind. Before the semester begins, when I think about how the semester will end, the basic questions for me are: What do I want students to be able to do, and how should they be doing it?

This course has a fairly well defined, standard set of objectives, all centered around using logic and writing mathematical proofs. I made up this list that has…

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January 22, 2013, 8:00 am

Inside the inverted proofs class: Why I did it

It’s been a month or so now that the inverted transition-to-proofs class drew to a close. A lot of people, both here at my institution and online, have been asking questions about the design and day-to-day operations of the course, especially if they have ideas of their own and want to compare notes. So starting with this post, I’m going to publish a series of posts that describe exactly how this course was designed and managed throughout the semester. I’m not sure how many of these posts there will be. But the idea is to pull everything together so that people who want to try this sort of thing themselves will have a detailed accounting of what I did, what worked, what didn’t, and how it all went.

Some background on the course (MTH 210: Communicating in Mathematics) is in this post. The short version is that MTH 210 is a course on reading and writing proofs. It’s a…

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