AppendixAPedagogical discussion
Recall from the first day our discussion about the ‘best’ and ‘worst’ of both free and online texts. What might be a good way to use them?
Now that we have written some, we could have taken a brief break to talk more about this. (But we didn't, so we could author.)
What follows are my own highly personal opinions about how one might use a text like this in the classroom.
SubsectionA.1Why dead trees?
There has been a lot of discussion about online education, and naturally many are now online-only, with no real print possibility. The MAA Calculus text is a good example of this (in several ways), and many publishers are actively pushing this on faculty and bookstores.
I'd like to push back on this a bit. There are several advantages to having a proper paper version available, even if not everyone uses it.
Paper can fall on ground and not break
You can write on paper all over the place with no special software
You can give paper away to other people or sell it without DRM issues
In my own classes, I have long periods of time for students to just try stuff with pencil and paper. And having it just there makes it easy to make sure everyone has it.
I do think that one has to be careful in using html and pdf together. How else do you think we should we combine them? (Or not?)
SubsectionA.2Interactive computation
Here is what I think. Basically, at least in the classroom you should always have multiple options for anything visual, possibly for anything computational. I showed plenty of examples of this last time. It's not a panacea, of course.
Here's what I mean by this. Imagine we have just defined the sum of divisors function
\begin{equation*} \sigma(n)=\sum_{d|n,d>0}d \end{equation*}First, students should do it ‘by hand’. Have fun. Any patterns? Probably notice something about primes …
But then it gets tedious. Is there ever a number which has sum of divisors three times itself?
What do you think?
SubsectionA.3Homework in the page
I have less experience using WeBWorK cells embedded in the page. Since not everyone does homework (online or not, graded or not), I have no reason to suspect it will magically solve our problems. However, I do think it has one key attribute which is not to be overlooked.
Lower the barrier!
―Me
I don't mean to be puckish here. But part of the reason I do this is to lower barriers to learning.
Free texts lower the barrier to students using them.
Free authoring tools lower the barrier to you writing them.
Texts available in all formats lower the barrier to students using them.
Free computational software lowers the barrier to doing intense math.
Embedded cells via (free to you, not monetarily free) online services lower the barrier to actually using these things.
So embedding the homework, at least some of it, lowers the barrier to checking whether you know the concepts.
That doesn't mean that lowering barriers can't also dumb down sometimes, or raise unrealistic or unhelpful expectations. We see this plenty in student evaluations of classes that are ‘supposed to be’ something. And certainly not everyone will do them. But it can help.
Just for reference, here is a WeBWorK cell.
Based on my experience, I'd recommend using any WW cells in two ways.
If all students have electronic version, have them do the WW immediately after covering some computation or topic, and get feedback from you ‘live’.
Have them do the inline exercises as part of their out-of-class work (perhaps as pre-reading?). Some won't, but if you ask students to verify having done them on the honor system, more will do it than not.
I struggle to see how to use them as only the instructor, since if you are going to have them work on just one example in class, why bother having a WeBWorK one? You might as well work it out ahead of time, so as to better understand it anyway.
But I bet there are others who have better ideas. You may want to look at the ORCCA book, or John Travis' projects. What ideas do you have for using homework in the page?