Accountability/Assessment

So far it seems like the only form of assessment are tests & quizes. My CT gives points each day for class work and homework, but I wouldn't really count these grades as a form of assessment. Points for both are awarded on whether or not you completed the assignment. Doing an assignment doesn't necessarily mean understanding it. An efficient approach can be to copy the assignment from someone who understands it best. It seems though that waiting until a test or quiz to find out info about students' progress is too late. I will sometimes go around and ask students what they learned from a particular activity or exercise. Students rarely seem to understand what the meaning is behind what they are doing and/or they don't have the words to explain what they do understand. I'm wondering how one teaches students to explain their reasoning other than modeling it for them and requiring them to do it over and over.

Students don't seem particularly accountable for their work either. A class typically goes like this: The CT checks for homework completion as students check their answers/finish up their work. Then the CT lectures or leads an activity. Then there are book problems. It is usually unclear to me whether these problems are considered class work or homework. Many students opt not to do the work in class and instead say that they're just going to do it for homework. It is unclear however if the CT checks that the classwork got completed. Also, I'm not sure what the mechanism is for assessing understanding through class work. Whether or not there's assessment or accountability, it seems like an extraordinary amount of class time is wasted by students choosing not to work. I can understand that students might need some time to disengage, but class time does seem like the best time to do the work so that they can get ideas/feedback from the teacher and classmates. It also seems to breed a culture of slacking in the classroom. This is the part that troubles me most.

As I think about taking over these classrooms in January, I have to say that I am quite nervous to see how students respond to my accountability measures. How do I keep kids working for the entire 50 minute period if they are used to checking out for the last half?

Parent Teacher Conferences

Last Wednesday were parent/teacher conferences. I was able to sit in on about 10 before having to leave for class at UWB. (The day started at noon so that teachers could stay late to meet with parents in the evening.) These conferences went very differently than what I have experienced at SGS with learning team meetings (our equivalent of the parent/teacher conference).

First off, students were not usually present. Aside from that obvious fact, the tone and focus of the conferences were different as well. At SGS, the parents, while they are appreciative and postive, can be very challenging of both the teacher and the student. They are concerned with how the curriculum is taught, the level of difficulty, and the amount of homework. They also challenge their daughters to do better (whether that means being more organized, not procrastinating, putting in more effort, asking questions, or better prioritizing what they put their effort into.) At Chief Sealth I saw a lot of smiling and nodding on the parents' part. They didn't have too many questions for the teacher (at least few that probed into how the classroom was run/how curriculum was designed and why). The information exchanged was very grade focused (as opposed to skill focused). And my CT didn't have very specific information on how students could improve, other than to come in after school for help and especially before tests to do some practice problems. In the case where a student was getting a high grade, often very little other information was exchanged. Parents were happy to hear their kid was getting a high grade and moved on to the next teacher.

Imaging how I would run a parent teacher conference and what information I would prepare to share, here are the ideas I have. I would probably have the students do a self evaluation in class before the conferences (even if the student's parent(s)/guardian(s) aren't coming in). I would focus the evaluation on the skills learned thus far and I might ask students to show some evidence. (Although, I'm noticing that metacognitive reasoning just isn't that high among the student body in general. I'm not sure how to fit that in with all the other skills that are mandated.) I would also ask the students to come up with a plan for how they could improve. Thus, I would have more specific information to share other than just grades. Plus it would incorporate the student's persepective as well.

On a side note...I don't want to get into a whole debate about privatization of schools, but I can see how the private market for schools requires teachers (at least in my experience) to become better teachers. Parents pay a lot of money and expect a high quality product. In the first several years of teaching, I was always nervous about parent/teacher conferences, specifically because I was afraid of being called out for something I wasn't doing well. After 8 years of teaching, I now feel like I can handle just about any parent question. Everything I do, I do for a reason, and I can often cite research to back up my choices (though knowing what I know about education research, there's probably evidence to the contrary as well). I don't think I do everything perfectly, but I am confident that I deliver a good product and know that I work hard and am always striving to do better. To some extent, I do think that I am where I am now because of parent pressure to make private schools better. One way that SGS responds to that pressure is to develop their teachers, and I have benefitted from that. I'm not sure that public schools feel the same kind of market forces, and I witness a lot of mediocre teaching here.

Prior Knowledge

I've been thinking a lot about the role of prior knowledge in teaching. Today my CT lead an investigation around indirect variation (when one variable goes up by a certain factor, the other goes down by the same factor, or in math terms xy=k). The investigation involved balancing nickels on a ruler which had a pencil under the center point at 6 inches to act as the fulcrum. The point of the investigation was to notice a pattern that the number of nickels * distance from center was equal on the left and right sides. When I checked in with some groups to see how they were doing, more than once I heard a response of "this is stupid." When asked why, the response was that the student had done an activity like it before in middle school or elementary school. My response was, "That's great! So you have a sense of what the pattern is. if you keep stacking more nickels on the left side, what do you have to do to balance them?" These students had an awareness that more nickels meant moving them closer to the fulcrum. When I asked them if they new what the pattern was, they were not able to answer. So I encouraged the students to look for a pattern in the numbers (which they were unable to do without a lot of prodding).

If I were to teach this lesson, I would make sure to elicit from the students what experience they have with balancing activities (either formally in school or informally like on a seesaw) and ask them to make a prediction as to what will happen when they add more nickels and to explain why they made that prediction. From there I would ask them to focus on finding a pattern between the distance from center and the number of nickels. Perhaps restructuring the lesson in this minor way would 1) show respect for what students already know, 2) activate what they do already know so they can draw upon it in this lesson, and 3) focus the students on what the new part of the learning is.

Another way that I "deal" with prior knowledge in my classroom is to give pretests to see what students know. I do this before a unit and test for the specific skills that my unit will uncover. I have noticed that when I give a pretest, I get fewer comments from students like "I've done this before" or "I already know this." Whether students have done some of the math before, pretests usually reveal a lack of mastery and students seem to have a stronger desire to learn. In the case where students do have mastery, then I can structure an alterative project for them to extend their learning.

On a side note, the directions for the investigation (out of Discovering Algebra) were way too long. I think they could be rewritten in a much more concise way so that students don't get hung up on reading and interpreting steps.

Math Intuition

In the classroom where I am placed at Chief Sealth, I am noticing that many students do not have good mathematical intuition or do not tap into it to help them solve problems. Frequently I find students stuck on problems that are conceptually quite simple because they “don’t remember how to do this [type of problem].” Today, students were having trouble converting from inches to centimeters. Some were stuck because they didn’t know how to set up the proportion (which is just one way of solving this problem) or how to solve for the unknown variable once the proportion was set up (many don't seem to understand what cross-multiplying is or why it works) or if they should multiply or divide by 2.54 (the conversion factor). Students did not seem to exhibit an awareness that there were multiple ways to solve this problem and that they can use a different approach if one doesn’t work for them, or that they could use reasoning to help answer their own questions. (For example, a student could reason: A centimeter is smaller than an inch, so a measurement in inches is going to be a smaller number than the measurement in centimeters. So to convert 20 centimeters to inches I would have to divide by 2.54 instead of multiply.) When I approach a situation like the ones I'm describing above at SGS, I'm used to either 1) asking other students in the group to explain how they did it and why, 2) asking students to explain their reasoning and poking at the parts that don't make sense until a student understands the problem for themselves, or 3) trying a simpler problem with a student to unveil the concept that is at work so that the student can arrive at a solution themselves. At Chief Sealth, I feel like these same techniques are not as useful. Students seem frustrated that I don't go right to "Here's how you do it..." or confused when I begin to throw different problems and solutions at them. So right now I'm wondering about the best ways to help students at Chief Sealth tap into their own intuition so that they can become more flexible problem solvers...

Week of 10/5 - Post #1 on Student Experience

On Wednesday my CT did an activity to help kick off recursive functions. Students were given a graph of data: column 1 was the number of bounces and column 2 was the height of each bounce. Students were asked to graph the data, find the ratio between each bounce and model the sequence of numbers with a recursive formula. There was not much of an intro to the lesson. Mostly it was "now we're doing recursive functions" and "here's the activity for the day." I've been thinking a lot about how student experiences can be brought more into the classroom and what kind of experience is most meaningfully to the students and mathematically. Ideally this lesson could be done with an actual ball and perhaps with motion detectors to collect the height of the bounces first hand. But even if motion detectors were not available, there are a few ways this lesson could involve more student experience. First off, kids could see a demo of a ball bouncing repeatedly (or each group could get a ball to bounce if there are enough balls). Rather than going straight to max. bounce height (the graph of which may not be intuitive to some students), they could be asked to approximate a graph of height vs. time which would consist of a series of parabolas smooshed side by side. Then from their first graph they could be asked to sketch a graph of just max height of bounce vs. # of bounces. This graph could be compared with actual data, and students can then talk about whether or not their observations/intuition were correct. These are just some preliminary thoughts about how to bring in student experience and mathematical intuition. My questions are: would bringing in this kind of demo/hook be meaningful to students? From personal experience, my answer is that it would be to some. Some really like physics-oriented demos and experiments, and when I taught physics most students could be drawn in. But then what about the students who prefer connections that are more social or emotional in nature? I will keep pondering this issue...

Classroom Culture

I wasn't really sure how to define classroom culture, so I Googled "classroom culture." This is what I got from http://eltnotebook.blogspot.com/2006/09/first-lessons-establishing-classroom.html:

"Perhaps the best definition of culture which I’ve ever heard is “the way things are around here”. It sums it up nicely. Classroom culture means the often unspoken and frequently unconscious assumptions about how people (both the teacher and the students) will behave during the lessons – Where will people sit, or stand? Who will speak, when, and what about? What types of behaviour are appreciated, tolerated or frowned upon?"

So with that definition in mind, I will launch in to a ramble of what I perceive to be my CT's classroom culture.

• My CT is the one who does most of the talking during class while writing down information on a sheet of paper under a doc cam. Students are expected to sit and take notes (in a specific format) on what my cooperating teacher says. When he's done showing/explaining something, often students will be given an assignment to work on. If they have questions, they are expected to ask their group questions and then, if their questions are still unanswered to ask the teacher. Sometimes the CT is actively helping students, but sometimes he is at his desk working. The messages that I infer from this format is that the teacher is the authority on mathematical knowledge. He also knows the best way for students to learn, which is by taking notes using an inflexible format. Given the lack of two-way dialogue, I also get the sense that the teacher is not interested in understanding how the students think about problems.
• When the CT assigns classwork to students, he usually says something about how if they don't finish, it will become homework, and that they need to do the assignment to get their five points. Sometimes he offers an extra point if a student finishes the assignment in class that day. Rarely is an explanation or demonstration given as to why the math the students are doing is useful or important. What these behaviors indicate about the classroom culture is that math should be done quickly to just get it done and out of the way. It should be done for extrinsic rewards, not because it is interesting, useful, or beautiful.
• In order to motivate students to finish their classwork, the CT will often say something like, if you don't get it done in class, it will become homework. Several students do not in any real way attempt the classwork. Some have their math book out but are talking or doing something other than math. Some don't even make any pretense of working and have nothing out on the desk. When asked, these students generally say that they don't have to do the classwork because they can do it for homework instead. Though unintentional, the classroom culture permits students to not work or learn during class as long as they say they are going to do it at home (many of these students don't actually do their work at home either).
  

There is probably more I could say about the classroom culture, but this is all I'm going to say for now.

Biases

How are your own biases affecting your observations of the classroom?

My cooperating teacher (CT) has a very different approach to teaching math than I do, an approach which I perceive to be ineffective. As a result, I tend to view all that he does through a pretty negative lens. I am quick to see how things aren't working and slower to see the successes that some kids are experiencing.

At the same time, I am open to questioning the way in which I do things. My pedagogy is still not completely formed, and I see flaws in what I do as well. I am also realizing that one way of doing things will not reach all kids. So I am open to seeing that the way in which my CT designs his curriculum and works with kids may be more effective for some kids than the way in which I would choose to do things. I also recognize that he has more experience teaching math in a public high school than I do, and I believe I have a lot to learn about how to teach effectively in that context.

I know that one of our class objectives is to "observe and gather information without interpretation or judgment." I think I am still capable of doing this, but I would have to be intentional and give myself a concrete task like recording different types of statements teacher and student are saying or tallying behavior of various kinds. My automatic reaction is to judge what my CT is doing as right or wrong.

Coming from a private middle school to a public high school, I expect that the student body will be different from what I am used to. But I think for the most part, I am remaining open to my students and don't have many preconceived notions of them. I am finding that in general they are smart, kind, and willing to work. Many of them come in with preparation to be working at a higher level than the class is pitching to them right now.

I've had a couple of instances where I think some students are trying to test whether or not I am prejudging or stereotyping them. For example, I was talking to one student about the fact that her arm was sore from getting an HPV vaccination shot. An African-American male student at her table, with whom I've had a number of positive interactions, then said that his arm too was sore from being shot...with a (some type of gun/caliber--I can't remember). I'm not sure what kind of reaction I showed, though I'm sure my face revealed something. Inside I felt surprise that he said this, because I was nearly certain that he was joking and that his joking was about more than just being playful and because we have had so many positive interactions before this. He quickly said he was just kidding and then changed the subject. I found the situation to be kind of confusing, because I had the feeling that he was testing me to see what my reaction was. Was he wondering what kinds of preconceptions I, as a white teacher, might have about a male, African-American adolescent? I have no idea if I passed his test.