Ava's Math Blog

Sexism

2009-12-20T15:24:00.002-08:00

My 5^th period class has a number of “energetic” boys. Some of them I know for sure struggle with ADHD and are usually on medication which helps increase their focus and productivity, but they sometimes forget or cycle off it for various reasons. Today when I was teaching that class, I called three people up to the front of the classroom to explain their work. When I looked back, I realized they were all boys, and they were not the best behaving boys. In the moment, I called on them because I knew they had the right answer to a question and each could explain something a little differently. I also knew that they would all benefit from receiving positive attention, either because they had low math confidence or because it would redirect their usually disruptive behavior into something productive. So I have good reasons for calling on them. But as I look back I realize that I did not give that opportunity for the spotlight to some hard working and very focused girls. I took for granted that with our without that opportunity they would continue to work hard because they were internally motivated. So today I presented an example of a “well-meaning” teacher perpetuated a cycle of favoritism towards boys in a math classroom.

Tell a Teacher

2009-12-20T15:24:00.001-08:00

A couple of student conflicts happened today that gave me pause for thought. The first was relatively minor. A boy said that his female friend hit him. He didn't seem distressed or hurt at all. If anything he seemed amused. I think the two might have been goofing off and seeking adult attention. So I asked him how he handled it. I can't remember what he said, but then I asked if he felt satisfied by how the conflict was resolved (but in different words). They seemed perplexed by my question but okay, so I dropped it. Then one of the students asked, "Aren't I supposed to tell a teacher when something happens? That's what I've always been told." I explained that if it was something minor, I thought it was best for them to work it out themselves. In life, people usually work out things on their own without another adult intervening. However, I added, I want to know if one of you is really unsafe, so that I can help out. I don't want anyone to get hurt. Otherwise I trust that you have the skills to work out your own conflicts. This perspective seemed new to my students who seemed to expect me to jump in and work things out for them. I sensed disappointment on their part that I wasn’t getting involved, which I found fascinating.

Lightness

2009-12-20T15:23:00.000-08:00

There’s a math teacher I’ve observed here that I feel does an excellent job of treating student conflict and disobedience with a certain lightness and sense of humor that I admire. And I don’t mean lightness as in he avoids or tiptoes around conflict. It just seems to be not a big deal and no one is forced to get stuck into defending a position. I have to say that on the days I go to Chief Sealth, I feel a heaviness, and I even dread the mornings I have to come here. I can't quite figure out why. I do like my students and enjoy getting to know them. Though my Algebra 1 students are certainly challenging to motivate. But I think part of my problem is taking negative interactions with students too seriously and with trepidation. I think part of this is related to the fact that I don’t have ownership over the classroom and the rules seem to elude me. There’s no electronics but sometimes my CT doesn’t say anything when kids use them. There’s no food, but I see a lot of food and beverages out in the class. There are assigned seats but sometimes kids sit wherever they want and my CT doesn’t do anything. So I hesitate to do any kind of enforcement and don’t really know what I’m getting myself into. As I head into student teaching I think I need to remember to enforce rules consistently but to be light.

Smart Kid

2009-12-20T15:22:00.002-08:00

I have one particular student who chronically chooses not to work. Today, several minutes into the period, he had nothing done on his review sheet. Flipping the blank sheet over, I asked incredulously, "Is this your strategy for passing?" He said that all he needed to pass the class was a 30%. He already had 90% and only a 60% is required for passing. His goal, he said, was to pass with as little effort as possible. This reasoning may be short-sighted, but it is not altogether unreasonable. It's definitely efficient and seems to align with his values and priorities. He seems to be a quick and organized enough thinker that he could be doing math at whatever level he wanted to (assuming he put in the work). While I can't make him want to learn math, I have to keep in mind that this attitude can infect other students and result in lower performance all around.

Internal Motivation

2009-12-20T15:22:00.001-08:00

I am biased against extrinsic rewards and motivators, but I’m beginning to consider that they may have a role in teaching students intrinsic motivation. I think my Algebra I students are influenced by and have created a culture which somehow rewards not working (or at least doesn’t penalize it). Now they exhibit learned helplessness. When presented with a task, they don’t know how to get started unless someone tells them how. They seem to be able to do a problem only through pattern recognition and not through any kind of critical thinking or problem solving skills. This seems true even when the lesson has the potential to be engaging and hands-on. I’m beginning to think that I will need to put in a clear set of incentives to encourage students to do their work. I’m hoping that over time, the kids will learn that it can feel good to learn and understand math and then eventually develop a sense of internal motivation. This hypothesis is not supported by anything I’ve read. In fact, from what I read, extrinsic incentives can take the joy and internal motivation out of learning. But at this point, I don’t know what else to try (other than lots of pep talks and hopefully some fun and exciting lessons that will pique their interest).

Reading

2009-12-20T15:21:00.002-08:00

My Algebra I kids don’t like to read. When given an assignment on a worksheet or in the book, they just sit there. When I check in with their groups, they ask, “What are we doing?” or “I don’t even know what were supposed to be doing.” I try to remain calm when I hear this question, but in my head I’m flipping out that it has not occurred to them that reading their book, the piece of paper in front of them, or the instructions on the board will inform them of what they are doing. Students seem to ask this question regardless of how many oral or written instructions are given. I’m not sure how to make changes such that this is less of a problem. I realize this strategy (not reading) is intended to eat up time while not doing work. I’m not sure how much is because they just don’t like math, they don’t know how to do the math, they don’t think that they’ll understand the instructions, they enjoy being defiant, or they don’t want to or don’t know how to work with the people in their group. Perhaps some of it is because they want the individual teacher attention. Unfortunately, it seems that in order to do more complex, interesting math that is perhaps grounded in some real life context, reading is required (if I’m not going to lead everything at the front of the classroom). Something I’ve learned in my years teaching is to make instructions as short and concise as possible, ideally under a page and in a larger font. Ambiguity can even be okay (if it makes the problem open-ended and interesting and requires the students to think about their choices). Reading the instructions as a class can lead to better results, but it can also lead to boredom, frustration, and side talking. This is something I will be thinking much about during my student teaching weeks.

Free Time

2009-12-20T15:21:00.001-08:00

Students at Chief Sealth don’t seem to get too much free time. They have 5 minutes between classes, no free periods, and a 30 minute lunch (with a 5 minute passing period on either side) which I imagine must feel rushed after waiting in line in the cafeteria (though I have no first hand knowledge of how long this takes—I microwave my lunch in the staff lounge). They also have a 20 minute DEAR (Drop Everything and Read) period everyday before 2^nd period. I wonder if this is truly enough free time for students. In their five minute passing periods plus lunch they have to go to the bathroom, get their stuff from their locker, run errands (like turning in forms, etc.), get a drink of water, and catch up with friends. To me it doesn’t seem like a sufficient amount of time to get all of one’s human and social needs met. Of course there is after school time. But I remember when I went to high school, I had a 40 or 45 minute lunch, plus I sometimes had an extra free 40/45 minute period during the same day. Passing periods on some days were also 10 minutes long. We also had advisory and community meeting (can’t remember how many days a week that was) for catching up with friends and the community. My school day was a little longer, but it didn’t seem quite so packed and structured. I wonder what has led to our schedule taking its current form. Is it pressure to let school out early for the sake of sports? Is it so that the school day is a shorter number of hours to reduce salaries? And why does it start so early in the morning (8:05)? Every study I know says that adolescents need more sleep than adults and that their circadian rhythms (or whatever they are) tend to push their sleep window later in the night. When my students side-talk in class, I wonder if some of their socializing is necessary, and if I need to somehow build in to the structure of the classroom time for kids to talk and get to know each other better.

Classroom Norms

2009-12-20T15:19:00.002-08:00

I had an interesting experience setting classroom norms and rules in one of my classrooms at the beginning of the year. I'm reminded of this episode as we get closer to student teaching, because I will have to reset norms with my students. At the beginning of the year, I used a process that one of the other classroom teachers used, and that my cooperating teacher wanted to try out. It involved asking students in groups to come up with classroom norms that would allow them to do their best learning. From the group lists, one class list was generated. And then from this list each group picked one that was most important, to create a class list of norms. There was a discussion (pretty quick) to determine if anything important was missing or should be taken off. Then the prescribed process was to okay each norm by having all students raise their hand to signal their agreement to the norm. If they didn’t raise their hand, then there was a discussion about why and what should be done to modify the norm to make it acceptable. I received pushback during the hand-raising portion from several students. Several students refused to raise their hands and didn’t have a response when asked why they didn’t want to agree with the norms. One particular student said it felt like “middle school,” because so many of the norms were obvious (like respect, communicate). On the fly we modified the procedure so that everyone could raise their hand for the entire group of norms. Looking back at the process I would agree with my students’ complaints. The process did feel very artificial. First, the students didn’t really come up with any norms that I wouldn’t have come up with myself, and they weren’t all that well detailed, explained, or justified. It felt like students were just repeating words that they had been trained to say. Also, they didn’t have any real sense of having power over the situation. Did they know (or did I know) how much they could actually influence the norms? Finally, the hand-raising process was slow and tedious and students didn’t really have any choice but to accept; it felt like coercion. When I think back to classes and seminars I’ve taken, the norms are either implicit or the teacher lists some possible norms and then asks for input, which accelerates the whole process. I think using a similar process could have worked with this group of students.

ELL

2009-12-20T15:19:00.001-08:00

I have one student in my first period class who is an ELL (English Language Learner) student receiving support from ELL staff. (I have many other ELL students, but they are significantly advanced in their English that they no longer need or are granted ELL support.) She does not attend class that regularly, but each morning that she does, a staff member comes to class to check on her. The staff member usually spends time translating what is going on in class, but I have noticed that he also tells her how to do each step (like “measure this, then multiply by that”). I have observed this in other classrooms where I have witnessed support staff doing similar things. It seems unlikely that this kind of support is in the best interest of the student—yes it is efficient on the part of the support staff and perhaps makes the student feel more comfortable. I’m not sure how she would know how to do any of the problems on her own without being given the opportunity to work through them on her own. On another note, I’ve noticed that because I know that my ELL student has support, I actually interact with her less than other students, and I feel terrible about this. I’ve heard that this is a common unintended consequence of this kind of ELL support structure. I’ve been trying to make an attempt to reverse this pattern, but she hasn’t been coming to class on the days that I’ve been there.

Getting to Know Students

2009-12-20T15:18:00.000-08:00

I have been a big believer in getting to know one’s students. I have found this helps with classroom management and motivation, but more importantly it is what makes the job of teaching fun and meaningful and worthwhile. At the same time, I am finding this very difficult to do within the context of these observations. I felt like I was making great progress when I was in the classroom 5 days a week, when I went down to 2, I felt like I moved backwards in this area. Some weeks I only saw my students once. One of my observation days the students were taking a standardized exam, another was parent-teacher conferences, recently I chaperoned a field trip, and there have been other interruptions. I used to know everyone’s name, but now I hesitate on a number of names. This is due in part to the fact that several students were also shuffled around to different classes and teachers about a month into school when CS was granted a few more FTEs (for higher student enrollment than expected). I’ve also found that when I was in the classroom less often, I felt less comfortable because I did not know the kids as well. As a result, I fell into a bad and self-defeating habit of talking more to the kids that I already knew. I could see how this could come across as favoritism on my part. I’ve started to intentionally break this habit, but I can see that it will take a long time to get to know 150 students, especially when class periods are fast paced and kids rush in and out as the bells rings and I don’t really have much of a chance to interact with students at other times.

Administration

2009-12-20T15:17:00.002-08:00

I am really starting to appreciate how much school policies can affect learning in the classroom. I am used to working in classrooms of students who do not test my classroom management skills and who are generally motivated and well behaved. In the event that I have trouble with a particular student, I can usually call in administrative support (though this has been very rare). From observing at Chief Sealth and talking to Robin and others in my cohort, I can see how important it is for the administration to adopt policies that support teachers in the classroom. I know that Chief Sealth has dramatically reduced tardiness with a policy that requires late students to get a tardy slip from the front office. There doesn’t seem to be much recourse, however, if students choose to not work or generally be defiant and disobedient. Of course there are ways for teachers to work around these things in the classroom, but for the students there is no threat of going to the front office or detention that a teacher can wield. I have one student who is regularly disruptive in class. I talked to him about having to make a choice between changing his behavior or facing possible detention. He said that if he got detention he wouldn’t come. At which I said, well then it escalates to more detention and eventually to being referred to the front office. He said that happened to him last year and nothing happened. This is pretty frustrating from my perspective that I have basically no recourse with teeth should a student choose to be disruptive. And not only does it hurt him, but it hurts all the other students he distracts or takes attention away from.

Group Work

2009-12-20T15:17:00.001-08:00

I am used to doing group work with my students at SGS, but as I think about implementing a group work system with my students (specifically my Algebra 1, and especially my first period Algebra 1 students) I am starting to doubt whether or not this is a good idea. First of all, there are a number of students absent each period. My CT currently has a seating chart that has students arranged in groups, and it is not uncommon to have just one student out of four show up in a group or two. Trying to shuffle these kids around to accomplish an activity can eat up a lot of class time. It becomes more complicated when students start to trickle in partway into the period. That places a lot of responsibility on the students’ group members (if they haven’t already been shuffled around into other groups) and the teacher to get them caught up part way through the class. Secondly, these students don’t have very much training in working in groups. If I were to have these students for the entire year, investing the time to develop group work skills may be worth it, but I’m not sure how I can teach this as well as keep the class moving at the pace my CT expects me to. I am still considering using group work, but I think I am going to have to rethink how to organize it. I can’t count on having stable groups, and I may have to focus on just a few group work skills to teach in the few weeks that I’ll be with the students.

Field Trip

2009-12-20T15:16:00.000-08:00

Today I went on a field trip with the language arts teachers to the Seattle Art Museum. They needed an extra chaperone and I was curious to see how large public school field trips are pulled off. I was assigned a group of about 6 students. It was a little confusing because I was given a list of students but then one chaperone wasn’t able to make it and I was assigned a few extra students. The whole day I wasn’t sure if I actually had everyone. I wasn’t used to that level of confusion and chaos on a field trip. I am used to compulsively counting my 30 something students on SGS field trips, but there seemed to be fewer controls on this field trip. In fact, I think some students may have wandered around outside at one point. At the end of the trip, role was taken and everyone miraculously showed up. Once we actually split up into small groups I was a little less stressed out because I had an easier time keeping track of my group. The docent led us to a series of exhibits and through a series of activities. They were decent activities—they were inspired by the art and came from the students’ interests and prior knowledge. For example, we saw a coffin that was shaped like a BMW and we talked about how in this place in Africa (can’t remember where; also the students were studying Africa in their LA/Social Studies block) people were buried in coffins that represented their life and/or their aspirations. We had a discussion about this and then the kids sketched what they would want their coffin to look like. Some questions that plagued me the entire time were: What was the purpose of these assignments? Where was the accountability? And how can students who have never had an opportunity to visit an art museum be given free time to explore on their own? Throughout the trip I also struggled somewhat with discipline and motivation with the students. Students were very reluctant to do some of the activities, and since I didn’t know them or what their class was about I was uncertain about how to keep them motivated. I often resorted to asking students about their experience with/feelings about art and trying to bring them in someway based on their responses. In terms of discipline, the students were basically fine, but I had one to two students who would sit or stand very far from the group while our docent would speak to us. This one particular student said he could hear and was paying attention. I responded that his actions could come across as lack of motivation or disrespect and that it’s good to check whether our behavior is coming off the wrong way, but he wasn’t motivated by that. Overall, it was a good experience to see how one can pull of a field trip with a large number of students.

Accountability/Assessment

2009-11-02T11:38:00.001-08:00

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

2009-11-02T09:50:00.001-08:00

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

2009-11-02T09:38:00.000-08:00

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

2009-10-21T11:47:00.000-07:00

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

2009-10-12T09:51:00.000-07:00

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

2009-10-04T15:24:00.000-07:00

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

2009-10-04T14:49:00.000-07:00

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.

2009-07-31T12:19:00.000-07:00

How does technology change the way we teach and learn mathematics?

I don't think technology necessarily has an impact on the way we teach and learn math. There are poor ways to use technology and excellent ways.

But I can do some things more or better with technology than I can without it:

More play (constructivism): Can play with ideas like the slope of a line, the parameter "a" in a parabola. Pencil and paper are slow. In a class period, a 7th grade student can only reasonably make about 5 graphs (and they would most likely complain about doing that many). With technology, they could make dozens and be able to see how changing parameters affects a line.
More conceptual: Like bullet point #1. Students develop better intuition through play.
More hands-on/real-world application: Students can easily measure real life objects and/or events through capturing video or photos and work with these real-life measurements. Data can be analyzed faster and more transparently. Example: Students can film someone on a swing (pumping at a constant rate), overlay a meter stick on say iMovie, share the movie with others, then at stations watch the movie and create a graph of height versus time. Hopefully they will see a beautiful sinusoidal curve!
More organic sharing of products (of work): Kids can make final products like a voice thread or digital story and post online for kids to view and comment. There's no need for everyone to sit and listen to everyone's poster or Powerpoint presentation and then get bored after the third one.
Less paper (but more energy use and toxic ewaste)

2009-07-30T14:58:00.000-07:00

Day 4

What did I learn?
I love the example of students turning in a photo of a normal distribution. I've heard of doing this with parabolas. I teach algebra 1a and I'm wondering how this assignment can be meaningful with linear patterns. Lines abound, of course, but many are not that interesting from a math stand point.

What do I want to know more about?
I still want to know how to use photos and video to measure and graph and model motion. I'm emailing Dan Meyer (of the blog dy/dan) to see if he will share how he did it.

How do you use Sketchpad with students in way that is more open ended rather than cookbook style?

How can I connect this stuff to the classroom?
My biggest take away here was using digital story or movie software for kids to create math stories. This is something I want to think more about (for example: which unit, when, requirements, etc.) My first though was to do graph stories.

2009-07-28T09:23:00.000-07:00

What did I learn?
I didn't know how box and whisker plots worked until today. Fathom was completely new and completely fabulous.

What do I want to know more about?
Same as yesterday. I'm interested in visual and audio media. Plus I'm interested in how technology can be used for more creative assessments (Fathom looks rich for opportunities).

How can I connect this stuff to the classroom?

Algebalance
This could be a useful addition to my algebra class. We use algebra tiles to learn how to solve equations. I talk about how it's important to keep the sides balanced, and some kids get this idea, but the idea is lost on a few. This activity would be useful to illustrate the idea that you must do the same thing to both sides to keep it balanced (or take away or add a zero). It would be great if you could create pages with set equations for kids to practice with. You could put kids in pairs. Each creates a balanced pan and then switch to solve their friend's equation.

More Slope Games
My two favorites here are matching and archery. Archery is a lot like guess the slope but way more fun. Also, it's not competitive (between students) so it's less likely to turn off students who shy away from competition or failing.

Parabolas in Factored Form
Don't like this ap. Confusing layout, don't like the fact that r1 and r2 are in parentheses (the unnecessary notation will confuse and distract some students from the key points here), and too hard to use.

Box and Whisker
The dynamic nature of this activity allows kids to play around with the concept and come up with their own understanding of what a box-and-whisker plot represents.

Fathom
The connections to statistics are obvious. i teach algebra and so i'm thinking about how to connect fathom to algebra. i would have students do something like what we did today: find data with two continuous, quantitative variables, scatter-plot the data and find the best fit line and then tell a story about the data. i would probably do this in pairs.

okay my arm feels like it's going to fall off, so i'm signing off.

2009-07-27T15:43:00.000-07:00

Day 1

1. Describe something you learned
2. Questions you have or something you would like to learn more about
3. Describe connections to classroom practice

I learned some stuff about how to use Geometer's Sketchpad. I've used it, like, once before. I certainly didn't remember anything. I feel more confident and excited about using it in the future. I would have liked to do more advanced stuff with Geometer's Sketchpad. Like how do you use GS for algebra or calculus. I also would have liked to spend some time thinking about how to make these activities more inquiry based. These activities were so structured and did not harness the natural curiousity of students. For example, the quadrilaterals and triangles activities could have been way more open ended, asking for students to make some generalization about angle or side relationships without asking for all the side or angle measures first.

I would also like to learn more about how to use video for math. I'm thinking about a couple of lessons I read about on dy/dan's blog. One overlaid a ruler over a photo. Another overlaid a graph on top of video. I think that stuff is cool, and I'd like to learn more about it. Because I'm kind of a technophobe, I'm not the biggest risk-taker with technology and appreciate a little hand-holding.

Tech Stuff I'm Learning from You

2008-12-04T18:10:00.001-08:00

It's the last day of our Technology in Education class at University of Washington - Bothell. We're all sharing our technology portfolios. This is what I've learned from you:

In Google maps, you can embed video (how???) and audio (with widget). A teacher created a map in the Google Earth view around which students had to tell a story. Cool.
How do you invite parents/students to pbwiki? Kids don't need an email address (sign up as a class); do a group invite for parents (from email distribution list).
Slide show: Can make in slides.com and flickr.com.
Google clock for different time zones is a great idea for a blog/website if partnering with a school in another time zone.
Jing for taking a video of a computer screen.
Bubble.us for mindmapping.
Nick's portfolio for math tools: gapminder, graphjam?, iGoogle gadget motion chart, TED.com for speakers.
Pamela for recording a Skype video conference (but only one side of the conversation).
Sustainable Building and Design discussion group on Delicious.
OneTrueMedia.com for photo/text/music only digital story.
Furl for putting notes up on a wiki.
Google notebook for storing info that you searched.

Thank you!

Math Games and Why Math is Like Sex...

2008-12-04T04:02:00.000-08:00

Hai, I'm with you about your post on math games. My experience is that many kids do like math games. Some of my least "mathy" kids will spot the game set behind my desk and say, "Ohh, I love that game." I know the sixth grade math teacher at my school has tried game days especially on Fridays when the energy for "regular" math isn't there. I haven't tried it myself, but your post is encouraging me to.

I have talked with my students about game theory being a branch of mathematics and even played a couple of strategy games with them and showed them how math can help you win. They did enjoy that. If you wanted to step up the rigor, you could even have them write about their strategy or design a game and a strategy for winning.

I'm also reminded of a Richard Feynman quote (posted on "Why I Love Mathematics" on AnAmazingMind.com) about the joy of doing physics. You could sub in math for physics, and the quote still works: "Physics is like sex: sure, it may give some practical results, but that's not why we do it." Oh, if only my students felt that way...

School-to-Career

2008-11-28T23:28:00.000-08:00

I'm just finishing up the "School-to-Career Transitions" chapter in our text Understanding Youth. I'm trying to work through a couple of thoughts that seem to contradict each other.

First off, in UY we read about the importance of career-development education being woven through curricular starting at a young age up through high school (and probably beyond). As I read the chapter, I found myself nodding in agreement. The school where I currently teach ends up centering a lot of curriculum around career paths: our 6th graders study the human body and go through a "grand rounds" as though they were MD's, our 7th graders produce documentary films and design cities, and our 8th graders learn how to fly a plane. These are just a few examples. Our students often get to meet professionals in these fields, while the projects gives students a taste of what the work might be like. I have no evidence to show that this method is better than others. But since each project usually requires a culminating performance of some kind, all of our students remain fairly engaged throughout the process.

On the other hand, I began thinking about a book I read by Eric Gutstein, Reading and Writing the World with Mathematics. He critiques the National Council Teacher of Mathematics Curriculum and Evaluation Standards for School Mathematics (1989) which submits "mathematically literate workers" as one of its goals. His major criticisms are that this goal serves the needs of profit accumulation, does not question whose needs this goal serves, and means different things for different students in our socially-stratified world (some kids will need calculus and beyond for their careers, others will need little more than basic arithmetic).

So my questions are: How do we get kids thinking about school having meaning for their life beyond high school and about how they want to prepare themselves for their possible career paths? And at the same time, teach them to be critical consumers of the the biases and values inherent in career development education? (Do my questions even make sense???) I'm going to be mulling this one over for a while...

Post-Conference Buzz: Layered Curriculum

2008-11-23T17:10:00.000-08:00

I just attended NSTA (National Science Teacher's Association) regional conference. I went to some amazing sessions that has put my head in a spin. In particular I learned about something called "Layered Curriculum," which I believe was proposed by Dr. Kathie Nunley. What I loved about this model was that it put together so many other theories that I've learned about and have been trying to implement/toying with implementing: brain-based education, Bloom's taxonomy, differentiation, and there's probably some other stuff I'm leaving out.

I'm going to summarize some of the key points here, in case readers are interested but also to help me remember!! (I never seem to be prepared at conferences; I always find myself writing notes on the backs of scraps of paper...) First off, before trying to teach using layered curriculum, it is important to educate students about how the brain learns best. (Here, I recommend John Medina's Brain Rules or Eric Jensen's Brain in Mind. The conference presenters, Kirsten Smith, Ron Bonnstetter, and another guy who's name I've forgotten(!), all from Nebraska, also recommend A Student's Brain by Kathie Nunley.) Some of the relevant key points are that all brains are wired differently, we like to explore, we don't like boring things, we need to repeat things to remember them, and we need exercise and sleep to keep our minds healthy. The conference presenters also recommended giving kids a learning styles test called VARK (visual, auditory, read/write, kinesthetic--supposedly at one's fingertips on the web).

Once students understand some of the basic brain rules and know something about how their brain is (like their learning style) they are prepared for their first unit of curriculum. Each unit is broken down in to three layers: Layer C is about remembering and understanding; Layer B, applying and analyzing; and Layer A evaluating and creating (you can see the Bloom's taxonomy-ishness here...). Students are given a variety of activities in each layer. Some sample curriculum I've looked at assign each activity a number of points and you are required to earn a certain number of points in each layer before moving on. Often, one of the activities is listening to a teacher lecture, but students could opt instead to read from a book, research on the internet, or watch a movie to get the same information (especially for layer C).

The teachers who presented had different methods for assessment, but both seemed to give an oral assessment to each kid when they finished a layer. There were also layer quizes, unit tests, and term tests (some of which was teacher choice, some district rules).

I'm super jazzed and excited to implement in my own classroom, but also really nervous. This is my third year teaching math and science at the middle school level, and I'm not sure I have the resources to provide the meaningful array that the teacher-presenters did. Now that I'm also in grad school part-time, I'm also not sure I have the time right now to take this on. I wonder if this is something I could try during my student teaching next year... Anyway, my plan is to do some serious investigating and planning this winter break. My plan is to try at least two units this year, so I can go into next year with some experience under my belt.

If you're interested in learning more, here are two websites to check out: help4teachers.com, brains.org, and nerds.unl.edu/layered/

Leaving a Record

2008-11-16T17:31:00.000-08:00

I was reading Amy's post in response to an NYTimes article on Obama during his teaching days at University of Chicago. As I was looking for that article, I ran across Teaching Law, Testing Ideas, Obama Stood Slightly Apart by Jodi Kantor, also in the NYTimes. I've been percolating on a quote from the article. In explaining why Obama had not published anything as a college professor, a colleague of Obama's surmised that Obama was unwilling to put his name to anything that could haunt him politically. This idea, of course, is not new. But as I venture into my first blogging experience, I've started to wonder if I'm ever going to regret any of what I post here...

Teacher Tenure

2008-11-13T22:20:00.000-08:00

I just read Amy's post on Michelle Rhee and was reminded of an article I read also in the New York Times on the chancellor of D.C public schools ("A School Chief Takes On Tenure, Stirring a Fight" in the New York Times). I haven't read Amy's article and don't know Rhee's position on test scores, but I'm in agreement with Rhee that teacher tenure isn't good for students. Having only worked in private schools, I have no direct experience with teacher tenure, but I can only predict that it disincentivizes teacher excellence and innovation. I can't think of any other job or sector where after three years one can garner job security (nearly) regardless of performance. I can appreciate that tenure can be a mechanism for preventing unfair treatment and dismissals of teachers. But surely, tenure is not the only mechanism for this. In a tenureless world, there would have to be regular and meaningful performance reviews with opportunities for professional growth and avenues for recourse when dismissal is unfair. But perhaps I'll feel differently about teacher tenure when I'm a public school teacher...

Exponential Growth

2008-11-13T22:12:00.001-08:00

In my 7th grade algebra class we just watched the short video "World Population" put out by Population Connection (www.popconnect.org). My students loved it. This is the first time I've watched it with students. The video shows a world map of white dots each of which represent one million people. A clock ticks as the years go by starting from 1 A.D. all the way to projections in 2030 A.D. As the years advance you see the number of dots increasing to represent population growth. My students could not stop talking about how the population was growing, where it was growing, and when it was growing. They were clearly taken aback by the sudden explosion in population in the last decade. After watching the movie, they had no problem identifying that population growth most closely fits an exponential model. I highly recommend this video!

Importance of Meaning

2008-11-13T21:59:00.000-08:00

I had this interesting experience teaching graphing to my 7th graders. I've been revamping my 7th grade algebra curriculum. For a couple of weeks now, we have been graphing some "real-life" of at least life-like data that have required my students to work with all kinds of numbers: from the very large to the very small, as well as decimals and fractions, and not just nice, even numbers like in our text book. They have displayed impressive flexibility as problem solvers as they try to figure out appropriate scales to graph these numbers. Just the other day I asked them to fill in a table and graph seven points that fit the rule y=3x+1. With their tables correctly filled out, they struggled to graph the integer coordinates. I saw several graphs set up with inconsistent scales--a problem I thought we had gotten over a while back. I have to say, I was pretty stumped. Perhaps it was the negative coordinates that gave them trouble. But I'm tempted to say that it was the abstract nature of the problem. Did the problem lack meaning, therefore making it more difficult to accomplish? This is an idea that I will be ruminating on...

Welcome

2008-11-06T19:32:00.001-08:00

I've started this blog as a meditation on teaching and education. I hope you can find something here that sparks a thought or feeling. I welcome your comments--they will be my vehicle for deeper reflection. Enjoy!