Here’s the first (and so far, only) screencast that students will use in the inverted transition-to-proof class:
This one is a bit more lecture-oriented than I intend most of the rest of them to be, so it’s a little longer than I expect most others will be. But I do break up the lecture a little bit with a “Concept Check”, which is the same thing as a ConcepTest except I’ve never warmed to that particular term (the word “test” puts students on edge, IMO).
If you have tried out any of Udacity’s courses or read my posts about taking Udacity courses, you will see some obvious inheritances here. I tried to keep the video short, provide simple but interesting examples, and give some measure of formative assessment in the video. I am exploring ways to make the Concept Check actually doable within YouTube — Camtasia 2 has an “interactive hotspot” feature I am trying to figure out — but anything that makes you stop and think is good for a lecture. Udacity does this to great effect, and it’s really a translation of peer instruction to the online video setting.
The way students will eventually use this video works like this: Before our class meeting scheduled to work with mathematical statements, they will be assigned a reading from Ted Sundstrom’s book that explicates this concept (very well). This video and three others I have planned will be assigned. Along with that assignment, they’ll receive a portion of the list of learning objectives that go along with the section on statements with the instructions that they should be able to demonstrate basic fluency with all the learning objectives listed prior to attending class. And they’ll be given two Preview Exercises, also from Sundstrom, to complete and hand in at the beginning of class for a small bit of credit.
Then, in the class, we’ll be doing some further exercises — probably also for credit, but I haven’t worked out the system for that yet — that get into more complex examples and explorations. Those will be handed in at the end of class with an option to take an extra day to complete. This assignment is what in the past I’ve called a “guided practice” task, and I’ve found that structuring students’ out-of-class experience is key for making the inverted model work.
I’m going to be setting up a Piazza discussion group for the class — both sections in the same group — so that as students watch the videos and do the reading, they can interact and ask questions in real time. I may also hold a Google+ hangout and invite students (all of whom have Google accounts through GVSU) to join in if they want to watch the videos live and ask questions.
So if all this works, students will be working pretty hard on acquiring basic concepts prior to class. The guided practice will give them a clear idea of what they need to know coming in, and the Preview Exercises will give them a chance to rehearse those objectives and let them know where they are relative to where they should be. Then, in class, we can take off and do more interesting things.
Pedagogically, what I’m trying to do here is not just give examples of statements and non-statements — that’s easy — but also foreshadow some important ideas that are central to the course. One of those is that definitions matter. The aside about whether January really is the first month of the year isn’t a tangent but a point I’m trying to make that the truth of that statement depends on what you mean by “year”. I struggled with whether this was overcomplicating the issue, but in the end I think it’s important beginners get this concept on the back burner early so that when we hit more complicated definitions, there will be some reason to pay attention.
Another idea I’m introducing early here is the notion of the predicate, which is a proposition whose truth value depends on the value of a variable. This in turn foreshadows mathematical induction, a huge sticking point historically for students in the course and mastery of which depends in large degree on how well you get the idea of a predicate.
For those interested in the technical details, this screencast introduces some changes in my usual workflow which I documented here. I outlined the screencast first and then made the slides up in Beamer. At first I tried just ad-libbing off the slides, but after over a dozen takes, I wasn’t happy with what I was producing — too many “ums” and “ahs” and diversions. So I ended up writing a script and reading from it into Audacity, then doing the video portion with the voice-over playing in the background. All the video production was done in Camtasia 2 for Mac. The screen portion was done entirely within Skim, with me using Skim’s built-in tools to annotate the PDF’s that Beamer generated. I used to use Flysketch as an overlay on top of a Keynote presentation but I’ve come to dislike having Keynote underneath Flysketch underneath Camtasia — too many layers and too much clicking. The workflow of LaTeX -> PDF -> Skim -> Camtasia has some kinks to be worked out but overall it feels much easier to handle.
The playlist for these screencasts is here, and every Tuesday and Thursday throughout July I should be populating it further and further. (Monday, Wednesday, and Friday right now I am home with the kids, which is not a prime screencasting scenario.) So stay tuned, and as always I appreciate your feedback and comments.