## Friday, August 25, 2006

### Online Whiteboard

Last night I taught online for the first time. I had to miss class today to go to a meeting, so I scheduled an online chat with the students at vyew.com. After you register, you can create a session and then invite other people. At your disposal are a chat room and an interactive whiteboard. You can see where two students worked problems, and my comments.

This went along with the chat window (names changed here):
 Me: Allen, I'm going to have to do yours in two steps to see what gives...Me: notice how the negation (minus sign) attaches itself to each thing inside--just like normal algebra?Me: Now I've pulled the negation inside the parentheses using de Morgan's rule a second timeMe: You got it.Me: See--I gave you the hard one!Allen: ok, i just didnt see the part about switching signsMe: It's very easy to miss stuff with logic.Kate: hi im back sryMe: Hi Kate, and hi Scott!Steve: hey, I'm trying to see what we're doing hereMe: We've been doing problems on de Morgan's rule--see page 24Steve: ok, thanksMe: Okay--let's go back to Janell's question. Scroll up and take a look.Me: Can somebody tell us what characterizes associativity? It's true in logic and ordinary algebra.Me: Mark, wanna take a shot at it?Mark: both sides of the equation are equal?Janet: they can be flip to equal the other sideMe: Important point--for each of these, it's two ways of writing the same thing.Me: And so you can flip them around, yes. What else? Steve?Me: Take a look at the parentheses in the associative law.Steve: they can be switched aroundJanet: something about the first letter being the parenthesesMe: exactly--associativity means moving around parentheseesMe: Now compare this to the commutative laws...Kate--what's the difference?Kate: im not sureJanet: would you be moving the letters Me: Okay--notice there aren't any parentheses to move, right?Janet: yesMe: So what moves?Janet: the letterJanet: or is it the signMe: Right--the variables change sides.Janet: is that true for all the cases?Me: So, associativity = moving parentheses, commutativity = moving variables.Me: Yes, it's always true.Janet: ok