Category Archives: Math

June 10, 2013, 3:28 pm

A divide-and-conquer approach to planning a flipped class session

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…

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May 8, 2013, 8:00 am

Is the modified Moore method an instance of the flipped classroom?

I was really fortunate this past weekend to host Dana Ernst and T.J. Hitchman, two colleagues (from Northern Arizona University and University of Northern Iowa, respectively) at the Michigan MAA section meeting. They did a discussion panel on Teaching to Improve Student Learning that I organized, and we ended talking a lot about inquiry-based learning, which both of these guys practice. After Dana blogged about the session, he got this tweet:

Dana, Brandon, and I exchanged some tweets after that, and I think generally we’re on the same page, but here’s my reasoning about this question and, more generally, what does or does not fall under the heading of “flipped classroom”.

The main thing to keep in mind is the distinction between an instructional practice and a course design principle. This was the gist of my post a…

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April 25, 2013, 2:39 pm

Getting students involved with linear algebra through poster projects

poster4The semester just ended, and I’m now in full retrospect mode. This semester I was fortunate to have only one prep — two sections of Linear Algebra. Linear algebra, for me, is the cornerstone of a modern mathematics education precisely because its concepts and its mechanics lie at the heart of so much real-world stuff — from web search algorithms to scheduling problems to computer graphics and many other areas. And yet, in a typical one-semester course on linear algebra you only get to touch on a handful of applications, and those tend to be sort of domesticated. A few years ago, I decided I wanted students to explore more than just the stock examples in the textbook, and I wanted them to do so in an authentic way that reflects real-world mathematical practice.

About that time, Derek Bruff published this blog post about his use of Application Projects, and I gleefully…

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April 4, 2013, 4:48 pm

Data on whether and how students watch screencasts

224445431_1602bfff1d_mScreencasting is an integral part of the inverted classroom movement, and you can find screencasting even among courses that aren’t truly flipped. Using cheap, accessible tools for making and sharing video to clear out time for more student-active work during class make screencasting very appealing. But does it work? Do screencasts actually help students learn?

We have lots of anecdotal evidence that suggests it does, but it turns out there are actually data as well that point in this direction. I’ve been reading an article by Katie Green, Tershia Pinder-Grover, and Joanna Mirecki Millunchick (of Michigan State University and the University of Michigan) from the October 2012 issue of the Journal of Engineering Education in which they studied 262 students enrolled in an engineering survey course that was augmented with screencasts. Here’s the PDF. This paper is full of interesting…

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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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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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