Jackie's class is my first close encounter with a high school classroom in the United States. It is a non-typical situation as discussed in my earlier posts about Memorial High School. But for me, I have no baseline for what is a typical classroom. The interactions that I observe in Jackie's classroom are not very typical I guessed but wanted another experience.
I decided to visit an AP Statistics class in a large comprehensive high school in San Francisco. The school draws it's student population from all over the city. The teacher appears popular (enrollment in AP Statistics has almost doubled since he joined 4-5 years ago). The school itself has undergone a self-feeding upward trend with its scores int he same time period. The student population has undergone a demographic change.
The first difference I observed in this class as compared to the Memorial HS class is the more uniform dressing style. The are about 20% of the accessories that I saw in MHS - on both boys and girls. The other is that out of 25 students, there were 2 Hispanics, 1 Caucasian, the rest are all of East Asian origin. The community appears to have much to do with dressing styles. As someone who came from wearing uniforms to school and liking it, I struggle to come to terms with how much time and effort appears to go into dressing for school. I cannot help feeling as if they would regain a good hour or two each day if only they didn't spend so much time on dressing. This will be the last mention of this issue because this ethnography is not about what they wear but what they do; else I will be guilty of the same time waste.
This class apparently has 60-70% ELL students. But I can't help wondering if that just means that their first language at home isn't English - not necessarily meaning that they struggle with English. In addition, the similarity(with MHS) that here again more than a third will be first generation college aspirants seems amply offset by the difference parental expectations. As Jackie has expressed before one of the big challenges facing her students is an almost complete lack of parenting. Jackie also pointed out that even if they don't speak English at home, the language that they do speak, they speak at a much higher level of sophistication sot hey know what it it to communicate at a "college-level" so to speak. The other significant differnec ein this ELL characterization is the language you hear at break (that is their language of choice for social interaction) is English at this school whereas at MHS you hear Spanish in the break mainly.
So on the whole the students appeared on task, prepared to learn (in the sense that all of them had books and calculators and writing materials), non-disruptive but also jaded. There were situations in which one of them was napping. one was eating and another texting - but the teacher appears to have very strict classroom behaviour expectations and in general thery were met.
That said, the class was in a listening mode and not really in any type of active learning situation.
It was a lecture - they did about 5 problems but all of them were done by him on the board and they took notes and answered when he called on them. I definitely need to go again when they may be doing an activity. They did enter data about penny ages into a Fathom survey during break. They were passign around a bag of pennies during class and had been instructed to take 2 samples - one of size 5 and another of size 10; compute the mean; enter it into the survey. He used this data at the end of class to lead up to the Central Limit Theorem. It was the standard demonstration of how the distribution of sample means approaches the normal as we increase the number of samples - irrespective of the shape of the population. He then moved onto using the CLT document that comes with Fifty Fathoms. He also modified the uniform population in that demo to a bi-modal distribution to better illustrate the "normalization" that takes place as the shape changes int he sampel mean distribution is very dramatic moving from a bi-modal to tri-modal to normal by the time you get to about 25 samples. Even this felt more like a demonstration as it was not preceeded by any active work by the students in the area of building the distribution - they computed the means but that was all.
I took detailed notes of what actually happenned in the class in terms of the activities and use of Fathom but what appears here is a distillation of those notes using a framework of comparison rather than of reporting. I did learn how to answer questions like the ones that appear on the AP exam :-).
Thursday, January 29, 2009
Missed opportunity?
The class on January 22nd was an unsettling experience. The students were being walked through a quiz that they had taken on the Tuesday prior to this class. They had all done really badly in that quiz. It was a very basic quiz on reviewing variance and made Jackie revisit her planned scheduling of the chapters. The quiz revealed a lot of "holes" in their earlier learning.
The entire time was spent in going over the quiz and ten the last 20 minutes were allotted to doing homework. Homework not being done is one of the root causes why it is hard for Jackie to ensure that the students get enough practice in basic simulation techniques. Modeling the problem and then converting it to "numbers" is hard when they mostly only do that in class.
I feel that the use of Fathom in this situation would have been a very valuable exercise. It would have been a visual approach to explain a concept that they are having trouble seeing. A way to provide yet another mental anchor for them to recall how it is done.
Maybe it was very demoralizing to discover just how much there is to make up which led to Fathom not being an option. To me even as an outside observer, it a downer to watch some of the classroom interactions and notice the complete lack of commitment to learning. Of special note is the return of two boys who had missed almost a month of school. They appeared to not care at all and weren't working on their homework when given the time. They weren't sitting in any group but seemed to have succeeded in reducing the general level of engagement in the work. She did say however that homework submission rate has gone up to 12-13 out of 23 from 1-2 out of 23.
There is one student who begins to standout for me. He appears to turn in all his homework - doesn't always understand everything or have the right answers but always answers in class. In some ways, he seems to be think out aloud in class and then work out what he needs to get to the answer. In the time allotted for doing homework, he made sure that his table partner was helping him with getting the work done. The table of 4 was to have worked together but in fact only teo of them were working. The girl who was workign with him seems to be better at the actual work but I have a feeling that his motivaiton to plow through all the work was what got her going. I need to watch them more and look for more interactions that tell me something.
Spots that glow:
Today's spots have more to do with my struggle with role and bias rather than with anything that happened in class.
When, Jackie didn't use Fathom to demonstrate the idea of a probability simulation, I was in a dilemma around how much I should influence what happens in this classroom. I wanted to point out the opportunity but didn't. The conflict was a result of my perception of my role in that space. I am struggling trying to reconcile whether I should bring attention to occasions where I believe technology may have been used to good effect. If I do then, I am an actor in the space not just an observer. If I don't then I am depriving the students of a learning opportunity. In the end, is it more important to antiseptically (without contamination) document what happens or intervene and help the learning situation. I don't have the answer that works for me...
The entire time was spent in going over the quiz and ten the last 20 minutes were allotted to doing homework. Homework not being done is one of the root causes why it is hard for Jackie to ensure that the students get enough practice in basic simulation techniques. Modeling the problem and then converting it to "numbers" is hard when they mostly only do that in class.
I feel that the use of Fathom in this situation would have been a very valuable exercise. It would have been a visual approach to explain a concept that they are having trouble seeing. A way to provide yet another mental anchor for them to recall how it is done.
Maybe it was very demoralizing to discover just how much there is to make up which led to Fathom not being an option. To me even as an outside observer, it a downer to watch some of the classroom interactions and notice the complete lack of commitment to learning. Of special note is the return of two boys who had missed almost a month of school. They appeared to not care at all and weren't working on their homework when given the time. They weren't sitting in any group but seemed to have succeeded in reducing the general level of engagement in the work. She did say however that homework submission rate has gone up to 12-13 out of 23 from 1-2 out of 23.
There is one student who begins to standout for me. He appears to turn in all his homework - doesn't always understand everything or have the right answers but always answers in class. In some ways, he seems to be think out aloud in class and then work out what he needs to get to the answer. In the time allotted for doing homework, he made sure that his table partner was helping him with getting the work done. The table of 4 was to have worked together but in fact only teo of them were working. The girl who was workign with him seems to be better at the actual work but I have a feeling that his motivaiton to plow through all the work was what got her going. I need to watch them more and look for more interactions that tell me something.
Spots that glow:
Today's spots have more to do with my struggle with role and bias rather than with anything that happened in class.
When, Jackie didn't use Fathom to demonstrate the idea of a probability simulation, I was in a dilemma around how much I should influence what happens in this classroom. I wanted to point out the opportunity but didn't. The conflict was a result of my perception of my role in that space. I am struggling trying to reconcile whether I should bring attention to occasions where I believe technology may have been used to good effect. If I do then, I am an actor in the space not just an observer. If I don't then I am depriving the students of a learning opportunity. In the end, is it more important to antiseptically (without contamination) document what happens or intervene and help the learning situation. I don't have the answer that works for me...
Friday, January 16, 2009
Group Quiz - Probability
Today was a no Fathom day. Jackie moves the groups around each chapter, so that the students had moved from their earlier places. 19 of the students were present.
The class was taking a group quiz on Probability. The class was divided into groups of four (one group had 3). In the end, she picked one paper at random from the group too use as the group grade for the test - so they had to make sure that all of them had all their work on their papers. they were allowed to use calculators but asked to show all their work (For some this meant that they showed the addition when calculating the mean). She had a conversation about how much work is enough for the AP exam. The course is very AP exam oriented - she is always teaching them techniques for the test like attempt all questions. "If you answer a question, whatever you put down gives you a greater chance of scoring than a blank answer".
The quiz consisted of 3 questions.
The class was taking a group quiz on Probability. The class was divided into groups of four (one group had 3). In the end, she picked one paper at random from the group too use as the group grade for the test - so they had to make sure that all of them had all their work on their papers. they were allowed to use calculators but asked to show all their work (For some this meant that they showed the addition when calculating the mean). She had a conversation about how much work is enough for the AP exam. The course is very AP exam oriented - she is always teaching them techniques for the test like attempt all questions. "If you answer a question, whatever you put down gives you a greater chance of scoring than a blank answer".
The quiz consisted of 3 questions.
- Review question: Data in integers(100-150) about ninja turtle weights. They had to calculate the mean, variance and standard deviation. everyone knew how to do this, they "showed" their work in varying degrees of clarity. She reassured tham that AP examiners are atrained to look for the correct bits of their answer rather than the wrong bits. "They are asked to give marks for whatever is right rather than cut marks for what is wrong" In the second part, they had to calculate the 5 number summary(Q1, median, Q3, IQR, min, max) and use that to draw a box plot. 3 out of 5 groups drew a nice symmetric box plot with the right numbers but not scaled properly.
- Card-Based Simulation: This question called for them to do a simulation of drawing 3 cards from the same suit in a five-card hand using the calculator. There were multiple parts to this question - including a review of basic information about cards. They had to assign numbers to the cards. Most groups assigned numbers from 1-52, but made an assumption that 1-13 would denote success and the rest failure. Only one group got the idea that they needed to divide the cards into four groups with equal number of cards. However, they used numbers between 00 and 99, thereby showing understanding of the probabilities involved but not simulating the underlying situation.
The rest of the question was to create part of a tree diagram that reflected the solution space that captures the situation of 3 cards from the same suit in a five-card draw. The students have quite a few time management issues and noone actually finished the tree diagram.
- This was the part hich asked them to create an entire tree diagram. But noone got to this bit in the quiz.
- There was a line printed at the top of the quiz in (tiny) 7 point font, saying" If you read this go get a raffle ticket from the sink counter" She had put out only 10 tickets for 19 students. Her goal was two fold -
- Emphasize the importance of reading everything. Part of the struggle for this class of students is language. So Read the fine print and read absolutely everything that is in front of you is a very important exam and life skill that she is teaching.
- The other was to show that since only ten tickets were out there, some students were going to be more luck than others. However, she emphasized that all students had an equal chance of being lucky and they made their own luck by reading everything.
- In the second question, she asked them to name the four suits of cards and the cards themselves because she discovered that enough of them didn't know the basic information about a pack of cards. To a person like me who grew up playing cards every afternoon in my summer vacation, it seemed strange that these children had got to senior year in school without exposure to a deck of cards.
- Towards the end of the class, she spent ten minutes introducing Venn diagrams as a way to think of probability. Jackie divided the class in two groups based on gender and grade level. She said that either you are a male and if you are not a male then you are a female. To which one student piped with a "...unless you are..." - I was amazed at the speed with which she quelled this by a "that is way more information that we need at this point." what was more amazing to me was the fact that no other students said another word and neither was there any side conversation. To me it is another example of how Jackie works to keep the class on task and push distractions out the door before they have even had a chance to make it in.
Thursday, January 8, 2009
Westvaco- what does that number mean?
Today was the first real classroom observation of Jackie's class. There was very little Fathom in today's class except for a demonstration at the end.
The class began by the students constructing test taking barriers. A little context - the class is held in a room that serves as the school's library. It is a large hall with round tables that each seat four.
The students all face each other and there aren't any spare desks for them to spread out at to take tests. This has been a problem that Jackie has grappled with last semester. Today, the students working in pairs created physical barriers by taping together two large pieces of cardboard and dividing the table into four spaces. The students took a short quiz on computing variances and standard deviation by hand (5 data values between 1 and 2 up to one place of the decimal). 4 students finish early and go into the adjoining computer lab to look up answers to earlier homeworks.
The teacher has all her lessons organized in Goggle Docs and the class has a website which has the homework answers, notes from each lesson, homework assignments and all class policies. She did an overview of whats on the website and for what she expected from them and what tools she was providing for them to make it through the course. The students know what thye need to finish in one class because the schedule is up on the board. She has just taken over active teaching because the first semester was being taught by her student teacher.
This was followed by a hands-on simulation of the Westvaco case from YMS book. They used graphing calculators to simulate a sample of ten workers from 100. Jackie made them go through the 4 Steps that are expected in an AP answer for a simulation question. She models all the calculator behaviour - spelling out the keys and the functions therein. She also explained "whats syntax?"
On the calculator, they use randInt(1,100,10) to take a sample of ten from 100 workers. They have in their head/ on paper assigned 1-24 as "old" people (she tries to steer them to call them people over 55, but the instinctive categorization is old peole ;-)). They count the numbers 24 or under and plot this count on a graph she has set up on a white board in front of the class. Five to six of them did this more than once - they ended up with 39 dots. The graph was nice and triangular and the most common point was 2. This allowed her to illustrate the relationship between the 24/100 proportion of the population and the 2/10 of the sample.
The class concluded with a Fathom demo of the Westvaco activity. Jackie demonstrated how to create a collection of 100 people, how to use the formula table to assign "55+" and "young" values to the attribute of age(she actually had instructions in the document for two other ways to do this) and then how to take a sample of 10 people from that collection. She moved onto defining a measure but didn't spend much time explaining this(we were running out of time). That concluded the lesson.
Spots that glow :
Things she said -
The class began by the students constructing test taking barriers. A little context - the class is held in a room that serves as the school's library. It is a large hall with round tables that each seat four.The students all face each other and there aren't any spare desks for them to spread out at to take tests. This has been a problem that Jackie has grappled with last semester. Today, the students working in pairs created physical barriers by taping together two large pieces of cardboard and dividing the table into four spaces. The students took a short quiz on computing variances and standard deviation by hand (5 data values between 1 and 2 up to one place of the decimal). 4 students finish early and go into the adjoining computer lab to look up answers to earlier homeworks.
The teacher has all her lessons organized in Goggle Docs and the class has a website which has the homework answers, notes from each lesson, homework assignments and all class policies. She did an overview of whats on the website and for what she expected from them and what tools she was providing for them to make it through the course. The students know what thye need to finish in one class because the schedule is up on the board. She has just taken over active teaching because the first semester was being taught by her student teacher.
This was followed by a hands-on simulation of the Westvaco case from YMS book. They used graphing calculators to simulate a sample of ten workers from 100. Jackie made them go through the 4 Steps that are expected in an AP answer for a simulation question. She models all the calculator behaviour - spelling out the keys and the functions therein. She also explained "whats syntax?"
On the calculator, they use randInt(1,100,10) to take a sample of ten from 100 workers. They have in their head/ on paper assigned 1-24 as "old" people (she tries to steer them to call them people over 55, but the instinctive categorization is old peole ;-)). They count the numbers 24 or under and plot this count on a graph she has set up on a white board in front of the class. Five to six of them did this more than once - they ended up with 39 dots. The graph was nice and triangular and the most common point was 2. This allowed her to illustrate the relationship between the 24/100 proportion of the population and the 2/10 of the sample.
The class concluded with a Fathom demo of the Westvaco activity. Jackie demonstrated how to create a collection of 100 people, how to use the formula table to assign "55+" and "young" values to the attribute of age(she actually had instructions in the document for two other ways to do this) and then how to take a sample of 10 people from that collection. She moved onto defining a measure but didn't spend much time explaining this(we were running out of time). That concluded the lesson.
Spots that glow :
Things she said -
- Put down 52.6 I am picky
- Don't make my job hard
- says "did good"
- says they all have a chance at passing the AP
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