p: I want cake
q: I want ice cream
This seems to make it much easier for students to understand concepts like negation ( ~p: I do NOT want cake) conjunction (p and q: I want cake AND ice cream) and disjunction (p or q: I want cake OR ice cream).
Me: "If you go to a birthday party and the person serving dessert asks if you want cake and ice cream, what do you think they are going to give you?"
S: "Cake and ice cream together."
Me: "And if you answer yes, what will you get?"
S: "Cake and ice cream together."
Me: "Alright. And if they ask if you want cake or ice cream, what do you think?"
S: "They are giving a choice."
Me: "So if you said yes, what would you get?"
S: "You might get cake, or you might get ice cream. You might get both."
Me: "If they ask you if you want cake or ice cream and you say yes, is there a chance they might think that you don't want either?"
Then I turned them loose on truth tables of increasing complexity. We had a discussion about how to start the truth table in order to ensure that all possible combinations were met before doing any calculations. It made me think about a discussion I had with several teachers earlier this year about the difference between teacher preference and mathematical convention. Since that conversation, I've spent a ton of time thinking about whether I make students do something because I like it that way, or because it's mathematical convention.
For example, multiplying using a lattice method is preference, where as the order of operations is convention. I find it VERY telling about both educational culture and my own education that I often can't tell if I do something because that was method I learned, or because it's how it is supposed to be done.
When I learned how to do truth tables, I always learned to make it look like:
Since the point of this blog is reflection, I'll admit that I'm REALLY not pleased with how this went. I felt like they were coming with me, but very reluctantly. This topic is VERY alien to them and I understand that. If I teach it again (which I may do tomorrow), I think I'll start with the cake and ice cream example and talk about the wording of the question with AND and OR before I even talk about statements, negations, conjunctions and disjunctions. They were working in groups and asking good questions, but it didn't have the same feel as some of my other lessons, which I would consider successful.
I have found myself backsliding in my pre-algebra classes too. I'm spending too much time having them work on worksheets and not enough doing interactive discussions and problems. Part of it, I think, is because a much larger portion of those classes are constantly disruptive and I am simply worn down. As I run through my array of class management tools, finding them ineffective, I am falling further into the despair that I felt last year. I don't want to have them in the habit of coming in and doing worksheets because that's punishing the wrong students.
I don't seem to have any tools that reward the good behaviors while punishing the bad ones. I would list the reasons why conventional rewards/punishments don't work, but they would all seem like cop-outs, which is what thinking about that feels like. Perhaps I need more interesting activities and simply exclude students who don't do what is expected.
"You don't have your homework, workbook, notebook or pencil? That's fine. Here's a copy of those and a pencil. You sit and work on that while the rest of us play a review game." I find this an extremely dissatisfying solution.
I modified my lesson on comparing fractions for the last class. I started with the scenario: I buy two pizzas. Joey eats 3 slices from one of them and Symir eats 1 slice from the other. Who ate more pizza?
Most of the students quickly yelled out "JOEY!" I quietly watched them until someone said "Doesn't it matter how big the slices are?"
Why yes! Yes it does!
So I drew two circles on the board and cut them into equal slices. The first pizza had 8 slices and the second had 2. The discussion continued until I managed to get a student to say that we could just cut up Symir's slice until it was the same size as Joey's. He would be eating more slices, but the same amount of pizza as before.
It was a good way for them to visualize common denominators before we actually talked about them in those terms.
Exploring the MathTwitterBlogopshere (MTBos) has issued a mission for this week about the importance and power of blogging. Since I already have a blog, my mission is to write a post about my favorite open-ended/rich lesson, or write about what makes my class unique. I don't have an answer to either inquiry.
So I polled my students. I gave each one a half sheet of paper and put the following question on the board:
What makes Mr. Aion's class different from your other classes? (good or bad)
I told them not to put names on the papers so they could be honest without fear of reprisal. The responses that I'm getting back are interesting. I will detail them when I write up the post for MTBoS, but the positive ones dealt with how they learn things other than math and most of the negative responses are about how the class is hard.
|I'm very tempted to correct the grammar and give it back. Forreal|
That is, of course, discounting the responses that clearly showed I should have worded the question differently. Thing like:
The class is too cold
It's a double period
There are chalkboards on two walls
Perhaps I should have specified that I was looking for what made me different as a teacher and not what made the physical classroom different.
I wonder their attitudes will change when I hang up my poster about my thoughts on PDA...