It was the day of new seating arrangements. Based on test scores from Tuesday - Jackie divided the class into three groups - passing(6), can pass but not there yet(6), need a lot of work(10). she did this, she said to make sure that she can give some undivided attention to the third group.
This is to continue for as long as it takes for them to change their work style. The first group looked pleased, the second was fidgety, the third mostly passive. They worked on taking the test as groups, working through their wrong answers, comparing what they got correct and sharing that with the group as a whole.
I worry that the second group may slide further down instead of rising up? The third appear to be split down the middle into those that know and are willing to engage when called upon in this new situation where they are under a magnifying glass and those are just not willing to take any visible effort.
Spots that glow:
* Thats why you are in this middle group - because you don't want to learn new things. You only want to coast in your comfort zone. You are not willing to put in the effort needed to be in the passing group, but you aren't in the last group becasue you are using what you have.
* No they are not the smartest. They are the best prepared. They don't pass everything they do - they just never stop trying. They are always asking for help. They turn up for office hours. This group has near perfect homework submission rates. That's what will help them succeed in the course.
Thursday, February 26, 2009
Thursday, February 12, 2009
We collected measures!!!
Second time in a row, the class was in a lab. This time, Jackie appeared more sure of herself. She had had time to pick a problem and prepare a Fathom based worksheet to solve the problem. It was one of their homework problems. The activity that the class was going to model was a simple discrete variable based simulation of creating a sampling distribution. This is problem 7.43 from YMS third edition. It is in the section pertaining to the Law of Large Numbers.
Students were modeling the process of solving this problem on a calculator. In all such problems, the first step is to "assign digits". What that means is given the table of probabilities, you have to create a list in your calculator corresponding to a random variable X (in this case discrete). It is a hard process for them to think through because they haven't practiced enough. Fathom is one more way to model this process.
Class strength was at 17 in place of 25, the rest were on a junior field trip to the South for following a Civil Rights trail. Yet again, a class that was far less disruptive than before. Amazingly the screens mask ratehr than provide the distraction.
Spots that glow:
Students were modeling the process of solving this problem on a calculator. In all such problems, the first step is to "assign digits". What that means is given the table of probabilities, you have to create a list in your calculator corresponding to a random variable X (in this case discrete). It is a hard process for them to think through because they haven't practiced enough. Fathom is one more way to model this process.
Class strength was at 17 in place of 25, the rest were on a junior field trip to the South for following a Civil Rights trail. Yet again, a class that was far less disruptive than before. Amazingly the screens mask ratehr than provide the distraction.
Spots that glow:
- "Oh! I get it..." - a boy looking at the way they created the collection - by "assigning digits".
- Get good at Fathom - it is a tool for homework - see how much more we could do - said Jackie
- Pointed out where the law comes into effect, by asking everyone to take one sample of 5. Then asking them to compare how many times they got the number "5" with it's occurence in the distribution of the population. After that, she colected number fo "5"s from the entire class(which was a sample of size 85) and pointed out how much closer it was to the theoritical probability of getting a "5".
- In our desire to promote exploration based learning, I realized that our Fathom activities rarely model the typical(and endless number of) AP Stats homework problems.
Thursday, February 5, 2009
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)
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:
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)
- Let X be a random variable whose values are drawn from {1,1,2,3,5,8}
- Take a sample of two values from this set. (Treat the two 1s as separate values).
- Compute the mean for this sample.
- Repeat this for all possible samples of size 2.
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.
This is sooo hard!
Date of class- Jan 29th.
Today's class was a very unsettling experience. Jackie spent large parts of time just dealing with expectations, behaviour patterns and habits of mind. Plenty of spots that glow in terms of how much effort she puts into the class but hard for me to write up in terms of what it meant as class that will work with technology.
Before I forget too much about what happened in this class, I will record a few main themes and then elaborate on them later
Today's class was a very unsettling experience. Jackie spent large parts of time just dealing with expectations, behaviour patterns and habits of mind. Plenty of spots that glow in terms of how much effort she puts into the class but hard for me to write up in terms of what it meant as class that will work with technology.
Before I forget too much about what happened in this class, I will record a few main themes and then elaborate on them later
- Get Help - use wikipedia, parents, teachers and peers
- Think before you speak and know when you are conjecturing
- Fill holes left by first semester teaching
- Teach new topic for 20 minutes - planned to do Fathom demo but no time
- Use your time - be intellectual - plenty to keep you busy even if you know nothing on quiz.
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