March 18, 2013, 8:00 am

Inside the inverted proofs class: What we did in class

I’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…

March 13, 2013, 8:00 am

Inside the inverted proofs class: Guided Practice holds it together

By Robert Talbert

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 �…

March 11, 2013, 8:00 am

Inside the inverted proofs class: Meeting the design challenges

By Robert Talbert

It’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…

March 8, 2013, 4:30 pm

The inverted classroom as platform

By Robert Talbert

I’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…

February 19, 2013, 7:45 am

When MOOCs melt down

By Robert Talbert

Coursera right now is reminding me of this scene from LOST, shortly after the initial plane crash:

Having a bad month, indeed. First it was this MOOC on “Fundamentals of Online Learning” that, ironically, had to be shut down for reasons involving the failure of online learning technology. Now it’s this course on “Microeconomics for Managers” in which the instructor, Richard McKenzie, walked away from the course. According to the CHE report:

Gary Matkin, the dean for distance education at [UC-Irvine, McKenzie’s home institution], said the problem had stemmed from Mr. McKenzie’s reluctance to loosen his grip on students who he thought were not learning well in the course.

“In Professor McKenzie’s view, for instance, uninformed or superfluous responses to the questions posed in the discussion forums hobbled the serious students in their learning,” said Mr….

February 14, 2013, 7:45 am

Update on the peer-instruction based linear algebra class

By Robert Talbert

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….

February 11, 2013, 7:45 am

Does Khan Academy help learners? A proposal

By Robert Talbert

Last week’s flare-up over Khan Academy was interesting on a number of levels, one of which is that we got a new look at some of the arguments used in KA’s favor. Perhaps one of the most prominent defenses against KA criticism is: Khan Academy is free and really helps a lot of people. You can’t argue with the “free” part. On the other hand, the part about “helping” is potentially a very strong argument in KA’s favor —but there are two big problems with the way in which this is being presented by KA people.

First, the evidence is almost entirely anecdotal. Look through the Pacific Research Institute whitepaper, for example, and the evidence presented in KA’s favor is anecdotes upon anecdotes — possibly compelling, but isolated and therefore no more convincing than the critics. The reason that anecdotes are not convincing is because for every anecdote that…

February 5, 2013, 7:45 am

Khan Academy Redux

By Robert Talbert

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�…

January 28, 2013, 7:45 am

Inside the inverted proofs class: Design challenges

By Robert Talbert

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…

January 25, 2013, 9:27 am

Got a moment to help update a classic STEM education study?

By Robert Talbert

Elaine Seymour and Nancy Hewitt’s book Talking About Leaving: Why Undergraduates Leave the Sciences is considered one of the seminal works in the literature about STEM education in higher ed. It’s certainly one of the most cited. Even though it’s 15 years old, it still wields a powerful influence over a lot of thought about university-level STEM education.

Mark Connolly, a researcher at the Wisconsin Center for Education Research, recently reached out to me to make me aware that he and Anne-Barrie Hunter of the University of Colorado Boulder are conducting a follow-up study to re-evaluate one of the claims made in the original 1997 study by Seymour and Hewitt study. Mark asked me to post about this to the blog and solicit your help in conducting the study. This involves taking a two-question survey. Here is the announcement from Mark and Anne-Barrie, and I hope you can find the time…