3 collections and a graph!

Today there was a scheduled lab session in which they were to work with Fathom. Jackie said later that she wished she had had time to work with this before hand and create a student work sheet. She mentioned to me that the reason she decided to go ahead and do this session was because she knew I was coming - so there I have influenced the running of the class and in particular with regards to the technology use! Anyways...

The activity that the class was going to model was a simple discrete variable based simulation of sample means. This is activity 7b from YMS third edition. The gist of the activity is captured below (will try to add it from the book later)

1. Let X be a random variable whose values are drawn from {1,1,2,3,5,8}
2. Take a sample of two values from this set. (Treat the two 1s as separate values).
3. Compute the mean for this sample.
   
4. Repeat this for all possible samples of size 2.

This session took place in the lab. Each student had an individual iMac to work on. The have assigned computers but they can access all their documents from any computer as they have networked logins. The lab is set up as 6 rows of 6 computers each. Each row is divided into two parts by a vertical aisle with four computers on one side and two on the other. There is a screen in the front that is visible from all computers.

Jackie didn't have a student handout for them to work from. She had only that very morning decided that she would use Fathom after she confirmed my attendance. She reported her worry that if she had tried this activity solo then in case she ran into a snag she would get nowhere. Whereas with a physical simulation, she may only do a few runs but she had the confidence that she would get the point across. This appears to be a common worry with teachers who didn't grow up with technology as an integral part of teaching. As it turned out, the only real Fathom help I gave her was to point out that you could escape out of animation when collecting a 1000 measures. At other times, when she looked a bit puzzled, I just waited for a moment and she figured it out (An example being - which menu to choose from and which collection to have selected when wanting to collect measures)

(Development Note : We know this is a problem - trying to figure out which collection is which and when to work with which inspector)

On the whole the students seemed to not have a hard time with this activity and with Fathom. Jackie modeled the process of "putting together a Fathom document". The began with a collection, she called randomVariable. She called the attribute random_var. And created 6 cases using the case table {1,1,2,3,5,8}. She didn't ask the students for input when creating the document. She asked them later "Why do you think I put in those numbers?"

At the end, she asked them to look at their neighbour's computer and see if their graphs looked similar. This led to a bunch of looking around and comparing but not too much engagement or talk around why they may have slight differences.

About three of them were working with a sample of size ten (the default) when the activity asked for a sample size of two. One of them did sampling with replacement - and realized it only because his graph looked so different from others and asked for help figuring out why that was the case.

On the whole, an exciting and satisfying class. even the usual disruptive suspects had less effect on the class - maybe it was the fact they were in front of a computer and all doing something. The individual computer in fact to some extent lessened the disruptive effect because it was easier to stay on task with this screen blocking the distractions.

The person who had caused quite some disruption in the earlier class this time spent a lot of time fooling around but was also one of the first three to finish. So is he disenegaged because he is bored adn this material is too easy? Hard to say...

At the end of all this - they had fun, were more engaged than in any class before this, but did they learn better? Now that is a question for a later time...
Spots that glow:

• Even for a bright and dedicated teacher like Jackie, it is hard to get over the mental hurdle of doing an entire lesson based on technology.
  
• All it took in this case was the knowledge that a "technology expert" would be present for her to take the brave step of plannign this lesson
• "Why does Fathom create the third box?". "I don't know; for fun?"
• "Why do you have different numbers?" "Oh because we got different samples!"
  
• Fathom was very well suited to modeling this simple activity. There was none of the cognitive baggage associated with putting together a probability simulation involving cards or a "real-life" situation. Perhaps for students, whose big hurdle on a AP like test is reading and parsing the question, there are two simultaneous needs fighting for their attention. One is the need to understand the language - the other is to model the situation.