I have to say I almost left Mr. Godbold’s presentation. It started off on a odd note, where he told us what he wanted to go over, then said we couldn’t do all of it, but we would be lucky if we did half, and then repeated himself for about 10 minutes. He looked and came across as very nervous.
But then he got rolling, and he had some gems that were worth sticking around for.
One of the first things he said when he was interacting with the AP Stat teachers in the room was that he forbids the use of pronouns in his room. A teacher responded to a question he asked with something along the lines of, “It is ….” He asked what “It” was and waited for a response, and then we could move forward.
That moment was actually very powerful for me. Pronouns really are hard to use in conversation without perfect understanding of what is being talked about. In writing it can be just as dangerous. Consider the fact that in this posting, I used two pronouns as shortcuts in the first paragraph alone, when I KNEW I was going to be talking about pronoun usage and how bad it is to use them (and I just used another!)
Our learners in AP Stats use pronouns all the time, and they know exactly what they are meaning when they write / say them. Other people don’t, however. The readers certainly may not. So one little step we, as teachers / facilitators must do is sharpen their usage of language to make them better communicators. Banning pronouns may be unwieldy at first, but useful later!
Second, Mr. Godbold had a fantastic way of demonstrating a very tough idea, what happens when someone says “given that”. I know my learners really struggled with the idea that given that removes things from being considered. Here is the entire process Mr. Godbold used to demonstrate the process.
First thing, collect some data. It really can be anything, but he used “principle residence in FL” and “traveled to conference without flying”, among others. Those two are the important data points we need for this explanation. We had an n = 21 in the room (excluding Mr. Godbold) and 2 pp lived in FL, 7 pp drove.
Second, Mr. Godbold explained that he has a number line on his floor that goes from 0 to 1. Any stat teacher immediately grasps the use of that particular arrangement. Next he had all the people in the room line up on a wall, and the first person was on Zero, the last person was on One.
He asked who were the 2 people from Florida, and had them move to the Zero and just off Zero spots. Now, we can see that the P(FL) = 2/27. All he did was rearrange the people a small bit, but it did make the probability clear.
Next, he asked, “What is the probability of living in Florida GIVEN THAT you drove.” Now he asked us, the teachers, this question, and he said he would not do that with a class that was not completely familiar with the idea. Even with teachers of stats, it caused some confusion. A couple of people sat down immediately. Other people were unsure what to do, but we eventually all agreed that the flyers needed to sit down, and the remaining 7 people needed to spread out!
Now we had 7 people from 0 to 1, instead of 21 pp, and they took up the same amount of space, and now we just had to count to see how many Florida residents were among the 7! (Both were among the 7, so the P = 2/7)
Bingo! The “Given That” removes people from consideration for the second calculation. Mr. Godbold then showed a contingency table on the screen, and it is clear how this exercise applies to contingency tables early in the year, as well as probability later in the year.
For no other reason that this one exercise I am glad I stayed in Mr. Godbolds presentation. My idea is to use this with the beginning of year questionnaire I do with the class. It gives me a reason to have them pull out the questions later in the year, something I have been struggling with.
Mr. Godbold also discussed independence visually, which is important since it was question number 2 on the 2011 AP Exam. He also had a great handout for the presentation as well that dealt with probability and independence, and getting the learners to visually understand what independence looks like. It is nice, and I will probably use it in class. I will link to an electronic copy of it, once the NCTM gets it uploaded to the website this week.
Thank you Mr. Godbold!
Resources: Anytime I go to an event like this, I always google the person’s name whose session I am in. When I did that for Mr. Godbold, some great things came up.
He presented at the AAAPSTA, and has some great resources listed there as well, found in the 25 Sep 2010 section.