Chris started the class by demonstrating how he uses Claim/Warrant statements to structure class discussion. He models formal debate by forcing students to present a solution or opinion in terms of “My claim is ______. My warrant is ______.” The warrant is the justification.
Another strategy they demoed was in presenting two solutions (and sometimes two errors) and having students pick which they liked best.
So today, on the 3rd class day with my Algebra I students, I gave it a whirl.
These were among two of the problems due today for homework:
These were adapted from (surprise!) Exeter’s Math1 set.
Without any solutions on the board, I explained the claim/warrant structure and put this up (minus the green writing):
I was really surprised at how quick the students were to present an answer. In the first class, the first 2 students went for Xavier and then there was a bit of silence. I asked someone to make a case for Ignatius, even if they didn’t agree with him. Then I got 1, 2, 3 students pushing for Ignatius. The most interesting warrant was that Xavier’s method is best because it “sets you up to distribute and then simplify.” Then I asked if Xavier’s solution would have to lead into Ignatius’ solution. He said yes, but other students definitely did not agree. It was pretty great.
Then I showed this slide for #9 (minus the highlighting, sorry about that):
The most interesting observation here was that most students in class 2 were very loyal to the method that most resembled theirs (which was mostly Paul’s). I pushed a bit and asked about efficiency, where a calculator would be easiest to use, etc. By the end, more were on board with John, a few with George. In class 1, the plurality of students were impressed with George because they hadn’t thought to do it that way, but they appreciated that it worked well. In both classes, we explored what the heck the distributive property had to do with all this.
BTW, in that discussion about the distributive property, in trying to figure out where the 1.07 in George’s solution came from (in relation to John’s) I found myself frantically pointing at that first phrase in parentheses and shouting “Where is that 1???? Show me the 1!!!!”)
- Good discussion, still too much student-teacher talk, not enough student-student talk.