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 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 time
Me: You got it.
Me: See--I gave you the hard one!
Allen: ok, i just didnt see the part about switching signs
Me: It's very easy to miss stuff with logic.
Kate: hi im back sry
Me: Hi Kate, and hi Scott!
Steve: hey, I'm trying to see what we're doing here
Me: We've been doing problems on de Morgan's rule--see page 24
Steve: ok, thanks
Me: 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 side
Me: 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 around
Janet: something about the first letter being the parentheses
Me: exactly--associativity means moving around parenthesees
Me: Now compare this to the commutative laws...Kate--what's the difference?
Kate: im not sure
Janet: would you be moving the letters
Me: Okay--notice there aren't any parentheses to move, right?
Janet: yes
Me: So what moves?
Janet: the letter
Janet: or is it the sign
Me: 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

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