We began our discussion of logic in geometry today. I want my students to be in the habit of backing up their claims with logic and reasoning, but that doesn't seem to be a priority in many math classes. As I have written about before, I believe there is too much emphasis on "answer getting" and not enough on WHY the answer is what it is.
The chapter on logic and reasoning in Geometry is, by far, my favorite.
For the last several weeks, I have frequently said that an justification I won't accept as a reason is "'cause it looks like one!" When I emphasize this point, I say that line in a faux British peasant accent and, much to my despair at the involvement of today's youth in the cultural zeitgeist, only one student has understood my reference.
Today, I began class with this following clip:
Afterwards, we had a brief discussion about how the argument and line of reasoning presented here has the flavor of logic, but is drastically missing internal consistencies. I know. I'm so much fun!
We talked about how making a statement that can be shown to be false through a counterexample usually wrecks whatever conclusions come after. Witches are made of wood because wood burns and so do witches, except we were able to list several other things that burn that are not wood and also not witches.
"If I look out the window and see it's raining, what conclusions can I make about the sidewalk?"
"That it will be wet."
"Great! Now, if I see that the sidewalk is wet, can I conclude that it was raining?"
"Not necessarily. Someone could have sprayed a hose, or dumped water or peed."
"Yes! Yes! Gross!"
After this, I introduced them to the idea of logical statements and conclusions through the use of THIS clip (which I also had to explain because "kids today"):
What are the implications of the question she asked? Would you have asked something else?
I may not be good at most things, but by glob am I good at improving their geek cred!
The Algebra 2 kids have another assessment coming on Friday so this week is a time for "review everything we've done so far and work on practice to solidify concepts."
I handed out the work I wanted them to do, then watched a student take 7 minutes to get a piece of paper from their binder, sharper a pencil, clean the edges of the paper turn the binder upside-down, get another paper, change pencils and then ask for help.
I've written before about the importance of starting a task and moving through it at a certain pace. I run into these same issues with my own children when I want them to clean their rooms or pick up their toys.
"Dad, this is taking forever!!"
"Of COURSE it's taking forever. In the past 10 minutes, you have danced with your sock, wandered aimlessly through the kitchen and sang to the cat. You haven't started yet."
With 40 minute periods, I'm really feeling the effects of the speed at which many of my students work.
I need to figure out how to fix it.