Discourse Time Baby! (5-16-08)

Discourse Time (DT) is a chance for students to debate mathematics. We so often forget that students need a chance to share ideas, listen to other peoples opinions and change their own thinking based on what they hear and see. The beauty of DT is that it brings mathematics to life. Students often get a bit heated as they argue their points and try to convince others of their position. The goal for DT is for students to really demonstrate their problem solving skills, showing how they attack the problem, articulating where their solutions are coming from, and dealing with counter arguments to their thinking.

During DT a group of students ( 4 - 6) sit at a table in the middle of the class and debate the problem at hand. While they're involved in their discourse the rest of the students have one of two jobs. 1.) Taking "I notice" and "I wonder" notes - observational notes of what they're seeing and hearing from the group on the inside. 2.) Scoring participants - this includes giving them points for such actions as stating an opinion relevant to the question, supporting a position with factual evidence and drawing someone else into the conversation.

Below is a scribing of today's Discourse Time. It may be difficult to follow, but you'll get the idea that kids really get into solving the problem and persuading each other. Prior to the documented dialogue is a copy of the problem that the students were solving. Following the dialogue you will see a set of I Notice and I Wonder notes that students and I observed.

THE PROBLEM
Camilla threw a softball straight up in the air. The table at the right shows the height of the ball in feet at different times after she released it. (ex. 0.4 sec - 19.44 ft, 1.0 sec - 30.0 ft, 1.2 sec - 30.96 ft.)
Tell whether each statement is true orf false and explain how you know. (Hint: Find the equqtion for the height of Camilla's ball, using the fact that the general equation for the height, y, of a thrown ball x seconds after it is released is y = - 16x^2 + bx + c)

"Discourse Time Starts Now!"

I said false, true, false, false...Jordy
Wrong, I said false, true, false true...Benito
Hold up, let me see your graph...Jordy
Why was it released from a height of 6 feet?...Saul
Look, my graph shows it that she throws at 4 feet...Jordy
How can there be 19 ft. in a split second? She's not superman...YELLED BENITO

Time Out - CALM DOWN...it's difficult to have a conversation when someone is aggressively yelling...Singer

Would you care to explain your equation to us that backs up what you're saying?...Josh
I got a question...if you don't have your equation how are you proving what you're saying?....Saul
My guess is that 3 out of the 4 are true...Josh
There will be two times when the ball will hit 4 feet, that has to be false...Saul
I guess it's true then...Jordy
What do you have to say about it Josh...Saul
I'm guessing B is false man because I'm looking at the table and there's no value when the height is at 4 feet...Josh
If you throw a ball it's going to pass four feet when it comes down, it can't avoid 4 feet...Saul
How old is the girl, is she tall or short?...Jordy
Does it matter?...Singer
What if you just used your equation to determine at what height the ball was thrown?...Singer
What is our equation?...Jordy
What did you get for b?...Jordy
I got what I told you I got...Benito
You don't need to use the graph to find the C value you could just use the table...Josh
What do you say Jordy?...Saul
I say false, look, you see my graph, it don't get to 3...Jordy
Wait...I messed up right there, I think you guys are right...Jordy
I say true cause as you said on your graph it shows that it doesn't even get to 3 so it has to be less than 3 seconds that the ball is in the air...Saul
Can you guys please draw your graph on the board so we can see it...Singer
Based on the parabola it's clear to see that the curve comes back to the ground before 3 seconds so C has to be true...Saul
The maximum height of the ball is less than 35 ft. has to be true because of the vertex...Benito
Look at the table, you can see that between 1.2 and 1.4 it hits its highest point...Saul
For B what do you guys say...Benito
I say true for B because when she throws the ball it could be below 4 ft. and then when it comes back down it's going to pass 4 ft. again...Saul
What do you think Josh, we need another opinion...Benito
When you throw a ball in the air it's got to be 4 feet of the ground and then basically when it comes back down you've got 4 ft, I think true...Josh
Do you guys realize how tall is 4 ft.? ...Jordy
I change my answer to true for part B...Jordy
I still believe it's false, it's only common sense...Benito
(getting up from the table) Look guys, watch as I throw this ball, you can see that I'm releasing it from below 4 ft...Saul
Look how fast the ball is travelling...Benito
But wait, we only know height from the ground, not the distance it's travelling...Singer
Look at the change from .4 seconds to 1.0 seconds, that's .6 seconds and it's moved 20 ft....it's going pretty fast...Saul
This is my equation...y = -16x^2 + 38.4x + 9.2...Benito
That's the same equation that I got...Iaisha (from the audience)
In . 4 seconds it grew 13 and some change so if you have .6 seconds it's like 26 and if you keep going I think it will be 30 roughly....Saul
Wait...what if you use Benito's equation to test things out...Singer
So when I put 0 in I get 9.2 ft which means that she throws the ball from 9.2 ft. which means that Benito is right...Jordy
She's tall, she threw the ball like that...Jordy
She might have thrown the ball from a platform or a chair...Benito
Or on top of a building...Saul
Unless she's taking steroids...Ron
So B is false...Jordy
And then A is false, has to be because we just solved it and she doesn't release the ball from 6 ft...Jordy
False, False, True, True...GROUP DECISION


I NOTICE
I notice that Josh didn't challenge other peoples opinions...Jessica
I notice that Saul was trying to get in the conversation...Angel
I notice that Benito was acting like he was the only one who knew the answers...Angel

I WONDER
I wonder why people didn't bring Jordy into the conversation...Angel
I wonder why Benito was being so aggressive and angry...Singer
I wonder why the class wasn't all doing their jobs outside of the Discourse Time...Singer
I wonder if Benito was just talking or if he really knew what he was talking about...Sir