updates for 02.17.2012
I'm watching videos of teachers to identify traits of good and bad teaching so that I can develop observation rubrics. Here is the Algebra Lesson from the Teaching Channel. There are obviously some things this teacher is doing very well. The classroom culture is excellent. Her willingness to keep trying new things and reflect upon their success is great. Her smile is fantastic. Her board work is clear and her lesson carefully planned. All of these things probably matter more than what she says about math because without a happy classroom culture focused on achievement it doesn't matter what you say about math. One aspect that I thought was quite strong was the teacher's recognition that students might not understand the basic premise of the problem and that if you mix a strong and weak solution the strength of the resulting mix is somewhere in between. Harel (1994) found in studies of how students understood problems about orange juice mixtures that it is very hard for middle school students to see mixtures the same way we do. For example some students think that if you pour orange juice from a well mixed jar into two different size containers the "orangyness" of the juice in each glass will be different. I think on a rubric I would write something like "attentive to student difficulties." "Provides quantitative model of situation to promote understanding." I'm not quite sure. Next-she starts talking about the problem. A chemist mixes a 25% saline solution with a 70% saline solution. He has 8 liters of the 25% solution and wants to create a mixture that is 40% saline. How much of the 70% solution does he need? I had a very hard time thinking about this without the help of algebra. I noted that 0.25(8 liters) was the amount of saline in the weak mixture. Then 0.70(x liters) was the amount of saline in the strong mixture. Finally 8 liters + x liters is the total amount of mixture when the weak and strong are added together. I divided the amount of saline in the mixed cups by the total liquid in the mixture, set it equal to .40 and solved for x liters. This is not a particularly easy thing to do and required that I was specific about what quantities each expression represented and could think clearly about ratios. It's also important to keep track of units (liters) and to note that a percentage is a unit-less ratio. In the video the teacher invents the see saw method which dramatically simplifies the algebra and set up. It makes it easy to plug in numbers into a formula and get the right answer. However, after thinking about her method for a few minutes, I'm still confused about why it works. Why do we get (40%-25%)(8 liters)= (70%-40%)(x)? I see that she uses a see saw example and while I do understand that the farther I sit out on a see saw, the more torque I put on my end. In general physics classes torque is defined as distance times force (weight, in a see saw example). It is a non-trivial cognitive jump for middle-schoolers to use percents and volume in an analogy to the torque case. The two scenarios are analogous by happenstance, but I don't really think they are helpful to the core science problems or the units of measure (which are critical to science problems), which the math concepts happen to model similarly. The kids in the video seem quite happy with the lesson and say things like "when the teacher wrote "weight times distance = weight times distance" it really clicked." I have to wonder what clicked for that kid? Because I don't think she was wondering about why we quantify force in that way like I was. I do think that her nice demonstration at the beginning of class was really helpful in making them think their answer was reasonable but I don't think the final method or the lead up to it was going to help them think about the ratios meaningfully. The teacher also tended to stop speaking specifically about quantities for most of the problem. Percents became distances and liters became weights. Yet, I have trouble saying that what I would do would be better. Maybe having a nice clear method is really helpful. The method was fast and clear. However, the simplicity was almost the downfall for me-I couldn't see why it actually worked until I really sat down with it. Here's my explanation of why her method works with units added for clarity She writes (40%-25%)8 liters = (70%-40%)x where x is the amount of strong solution you should add to make a 40% solution. .4(8) is the amount of saline in the 8 liters with a 40% mixture. .25(8) is the amount of saline in the 8 liters with a 25% mixture. .70x is the amount of saline in the strong solution with a 70% mixture. .40x is the amount of saline in x liters of the 40% solution. Notice that the amount of saline in the weak plus the amount of saline in the strong should equal the amount of saline in the mixture of the two. So, with her equation: .4(8)-.25(8)=.7(x)-.4(x) I rewrite it to get: .25(8)+.7(x) =.4(8+x). (2 cups added together, and conserving mass) This says that the amount of saline once you combine the cups is the same as the total saline before you combine them. Finally! Her method makes sense to me! Bottom line for my rubric: "teacher develops formulas in a way that they can make sense for students?" "teacher explicitly talks about quantities and units in problem to help make situation clear." Would it be worth the teachers time to teach the problem like I explained? It would be more meaningful(if they got it) but a whole lot harder to set up and solve. If kids had to rate the two lessons hers would probably win because it is clear and simple. However, I have to think that if her kids didn't understand that mixing dark blue and light blue results in medium blue liquid how could they possibly meaningfully understand what she did? Thoughts? What type of comments would you give this teacher?
First, I'm absolutely loving the people who are commenting. Even when we disagree, the conversations are so useful in moving my thinking forward. Second, tonight my task is to make a calendar for the development of the Instructional Quality Assessment for Secondary Mathematics(IQAsm) that will hopefully be used in professional development projects around the nation in a few years. I got assigned by my research team to focus on the IQAsm because I had a particularly negative experience involving excessive observations of my teaching. As my readers might have noticed, I have not quite jumped on the "let's break it down and make math as simple to memorize as possible" bandwagon. And since my ability to motivate kids was not quite up to speed with my desire to teach kids why math works the entire endeavor of getting them to think critically backfired in a major way. And from that experience I learned how horrible it is to have someone come observe you, point out random unimportant flaws and not take the big picture into account. And so now I'm designing a rubric that I hope will guide math teacher observations around the country. And I hope that the discussions around it will help teachers learn instead of make them feel inadequate and defensive and unsure of how to improve. The issue is that knowing what counts as good in math instruction, at least to me, takes so much background knowledge. You have to know where kids are going mathematically, what ideas they likely already have, and I'd hope a bit of background in teaching mathematics. When I watch lessons that take for granted that kids understand rates or fractions or proportions I immediately think of all the literature showing what massive problems these things are and mark the teacher down for making assumptions about what kids understand. And this is just one little piece of things-I think it matters that teachers establish a culture where students can express their thinking so that the teacher has a hope of understanding where the kids are coming from. It matters that the teacher speak clearly and precisely about the quantities in the problem. For example, I've heard "when you divide exponents you subtract them." Clear enough to me what they meant, but isn't it confusing to a kid that to divide something you subtract it? Better would be "when you divide powers you subtract the exponents" and establish some examples to show what you mean by that. I know it matters how the order their examples and highlight key points-but how is an observer supposed to decide if someone did a good or a bad job at that unless they have really thought about teaching that lesson. In any case, the first thing I put on the calendar was to have group meetings to establish what counts as effective math instruction by watching videos of teaching and pulling out good and bad aspects. The pie in the sky goal of this project is creating a rubric with examples that can be used as a goal in professional development programs. Anyone and everyone is welcome to share what they would put on a rubric designed to assess how meaningful secondary mathematics instruction is. Stay tuned for some analysis of various videos and feel free to share good and bad videos of teaching high school math if you really want to think about this with me :)
I am so far behind in updating this blog, and since I'm sitting in hour 3 of mind-numbing night grad class, I think it's the perfect time to finally update it. Just one more reason why I completely fail at TFA-mandated grad school. Another reason being, I just dropped the other night class I'm supposed to be taking to stay on track for licensure in 2 years. I really struggle with quitting any sort of commitment, no matter how unrealistic. However, I've definitely had to come to terms with the fact that I'll never be able to live up to everything TFA expects of me. Also, I'm feeling strangely settled about the fact that I'll be sticking around in Minnesota for the summer to make up the class and get ahead in future coursework. Maybe I'll actually figure out what life in the Twin Cities is like?? .......................... We had parent conferences last night and tonight until 7:30, but I (luckily?) got to leave early at 5 today for class. A few of my kids were still hanging around my room while I was madly rushing to pack up my bags. They know that I'm taking classes for my master's degree (not technically true, but it sounds inspiring so whatever) and I told them I didn't feel like going to class tonight. Then, I asked them to guess how late I had to stay in class. I. guessed 1 a.m., but M. hit it on the head with 9 p.m. "Isn't that terrible?" I asked. M., being the smart aleck that he is, counted back to figure out that I'm in class for 3 1/2 hours and shot back: "That's not fair! We have to be in school for 8 hours!" Long hours aside, I did enjoy parent conferences quite a bit. Most of the parents that showed up are the ones I talk to frequently anyway, but I did get to see a few that I always have trouble getting in touch with. Also, it's amazing how much more you can learn about a child from meeting their family in person. W. tells me all the time that her dad's a math teacher, so I've always assumed she gets plenty of help with homework. But, her aunt showed up to conferences today with a 3 year old in tow. It turns out that W. lives with her grandmother only, but her aunt takes care of most parenting responsibilities, along with her own 3 kids under the age of 5. Her parents live in the area and have 4 other kids, but for some reason W. doesn't live with them. The age range of the parents always surprises me. Some look far too young to have preteens, while others could definitely have grandchildren at the same age. Surprisingly, parental age does not always correlate with intensity of Muslim conservative-ness. I don't know if it's ignorant to assume that the younger parents would be less strict in their beliefs, but it was definitely not correct. A few of the oldest dads were actually willing to shake my hand (I've had far too many awkward experiences with refused handshakes since I started this job) while one of the youngest moms wore the full face-covered hijab. The journalist in me wants to barrage them with cultural questions and analyze the generational differences, but I get the feeling that would not go over so well. I also got to see a few of my tough guys get chewed out by their terrifying fathers due to their poor behavior in class. These parents hate nothing more than to hear their child was not taking school seriously, and unfortunately many of my boys seem to have exactly that problem. I actually went easy on M. and only said that he likes to "play around" during language arts class, instead of giving the full details: he likes to respond to questions by saying "me no speak english" in a fake accent. ............................... I's current event opinion: Romney won Nevada I was happy because I like him and I hope he wins because he nice he played soccer and he has a big head. Me, after reading his opinion: "Oh, did Mitt Romney really play soccer? I didn't know that." I: "No, I just made that up." I's current event opinion: The New York Giants won and I was happy when England lost. And I won a bet with someone They had to do 100 push-ups. Me, lecturing the class: "There are 60 minutes in between breakfast and lunch. If you need to visit the drinking fountain during that short time, bring me a doctor's note or bring a water bottle. Whining will not help." I., sassing back: "If my throat hurts I'm going to whine until you let me get a drink. I have a drinking problem." There were papers scattered all over my desk during conferences and A. happened to catch a peek at my master copy sheet of Scholar Dollars. These are little 1 in. by 1 in. slips of paper that I cut up and give out to students to reinforce good behavior. A: Ms. S., is that how you make scholar dollars?! Me: Yep, why? A: Oh, I just thought you copied each little dollar one by one. At last week's staff meeting, we were notified that after school got out at 2:30, teachers would have an hour until conferences at 3:30 and go straight to 7:30 p.m. One of my coworkers asked if we could take a dinner break and was promptly shut down. Coworker, under his breath: "So we have lunch at 10 a.m. and dinner at 3 p.m. Guess we work at a nursing home." *Note: Though it might seem like it from my stories, I don't always quote the 3 same kids. I just have a LOT of students with the first initials A, I and M. Though to be fair, I could probably fill an entire book with quotes from just my 3 most 'spirited' students.
I think this is great advice for teachers, especially those working in the lower grades. You know, kids say the darndest things, right? But, of course, it's easier said than done. And something I've been struggling with lately in my internship. By far the worst day so far was on Tuesday (coincidentally, Valentine's day). I have a boy in two of my classes who is one of the biggest behavior problems at our school. In a lot of ways, he's a teacher's worst nightmare. A lot of this comes from problems at home and self-esteem issues. Which means that behind the facade, he really is a great kid, and has the potential to shine. But he is constantly bringing himself down. Like I said, I work with him twice every day, and because my cooperating teacher and I usually divide the work, I usually end up working with him and some of the other students with similar issues in smaller groups. I try to give him tons of attention and positive support. Which is why Tuesday was an awful day when he and I had our first real altercation. We had an assembly at the end of the school day. During our hour of class, this kid was great--for the most part he stayed on task, respected other students, contributed to discussions, etc. As we lined up the kids--in a very specific order--I mentioned to my teacher, "man, P has been GREAT today!" and we were both very pleased. As we walked to the gym he was really on his best behavior, and before we sat down I turned to him and said, "P, you've been awesome" trying to sound as sincere as I could. I really appreciated the effort he was making, and trust me, for this kid, it's an effort. Unfortunately he got a little derailed at the assembly, since it was just a huge mess of kids and his friends were all around him. As we got back in line to go back to the classroom, I had to separate him from a group of other boys (his friends). He was pulling at their clothes, pretending to punch them, stomping on their feet, etc. Granted, it was his way of playing around and being a boy. But after repeating his name over and over it became clear that he was ignoring me as I tried to get him on task (and he was distracting the other boys from doing what they should have been doing). Eventually I sort of nudged him on the shoulder and upper back, trying to get him to turn around and get in line with the rest of the students. "EW! WHY ARE YOU TOUCHING ME?!" was his response, and he jumped away. Not sure how to respond--and not wanting to get into any sort of altercation with this kid--I just responded sternly, "You need to get in line. Right now. What are you doing?" Unfortunately for him, my cooperating teacher overheard his disrespectful remark (it really was disrespectful) and darted right over to him, and proceeded to chew him out like I've never seen anyone chew this kid out before. He got super upset, and defensive, and refused to apologize. She proceeded to pull him aside and chew him out some more. When we all got back to the classroom, she praised the kids for their great behavior, but reminded them--quite sternly--on how they should be respectful of all adults in the school. As the kids left the classroom I could hear him tell a group of other students that he had "gotten yelled at" "because she touched me." The problem was, at the end of the day, I felt bad. As I got into my car, I was in tears. I took it personally. Mostly because I had built up such a rapport with this kid (or at least thought I had) and I was sure that it was all gone. In my mind, I knew it wasn't a personal thing at all, but in my heart I just wanted everything to be okay between this kid and me when we got into our book groups tomorrow. Would I have to rebuild all that trust? Sure enough, the next day (yesterday) I had to remind my small group that "I am a teacher and I'm allowed to tell you what to do. I'm telling you it's okay." They were trying to argue with me that they shouldn't start reading their books yet, since my cooperating teacher told them to work on their pre-reading activity today. Well, they finished their pre-reading activity pretty quickly, and when I asked them to start reading, they just wouldn't have it. P warned the other kids "Yeah, she can be mean!" and even had the nerve to go get my cooperating teacher and ask her "are we supposed to start reading yet? you said not to, right?" and of course her answer was "if Ms. L said to start reading, then what do you think you should be doing?" After that, though, I was able to get him on task, and it was more or less smooth sailing. Then, today, P had the best day ever. He was attentive for the entire social studies block, and was thoroughly engaged. He even took notes on the video we watched! He didn't have to, but he asked to! I think he was positively rewarded for taking notes in science class, and wanted to do it again in our class to impress everyone. Whatever works, right? He was so excited about his notes that he wanted to share them with the whole class, so I put them on the document projector while the class played a review game, telling the other kids that they could use P's notes to help them out as they reviewed. He was beaming. When class ended, I pulled him aside, and handed him a raffle ticket (the rewards system we use in our class--5 tickets = candy!) saying "P, you worked so hard today. Keep it up. I was so impressed. And don't forget to take your notes when you leave!" He's the kind of kid who usually acts "too cool" for teacher praise, but I saw him put the ticket carefully into his pencil case and he left the class in a great mood. And you know what? I took it personally.
This morning I arrived at school late, 7:30. This week I've prioritized sleep above all else, literally. I have had nothing less than seven hours of sleep every night, in an attempt to thwart this cold from getting the best of me. I thought I had kicked it until fourth period today, when I starting feeling what seems like a golfball lodged in my throat. According to my google searches, this is likely acid reflux. Hoping pepto takes care of it. So, 7:30. I walked in and walked through the gym, where the entire school gathers before we dismiss them for homeroom, and glanced for Brax or Reem, my two boys I tend to bring into my homeroom for fifteen minutes to try to get them to do at least half their homework for the day. I didn't see either. Walking past the cafeteria to my room I saw Brax walking, pulling his hood over his eyes, trying to avoid me. I wrapped my arm around his shoulder and held his homework in front of him (I had it sitting in the passenger seat of my car from yesterday, incomplete.) I said, "We're going to do this." I let him grab his breakfast from the line and followed him to a quiet table. I put a Hello Kitty pencil in his hand and asked, "What's a sentence? What are the two things it has?" "Subject." "Good, what else?" "Vrhrkfm." "What?" "Verb?" "Write it down." And so it began. There was zero push back. I read each question aloud to him, and he answered. He knew all of the answers. He finished his homework. Then he threw out everything he picked up from the lunchline without opening any of it, and went to the gym. In class, he raised his hand for every single question. I called on him as much as possible, and the class applauded when I told them he got 100% on last night's homework. He tried to hide his grin, but I saw it. He even read when the class did. God, Brax, what is this inconsistency? I'm so glad he was working today (I made a point to copy his homework and put it next to his work from yesterday, to show his counselor next week), but this is not a celebration. I will not be surprised if tomorrow he decides to write "I don't know" on every single test question. I can't predict him. I won't lie, though, after class I said a prayer. Thank you God for this day, thank you for this boy making positive choices, thank you for giving me the patience to keep trying. Other highlight: during block today our district's consultant was running copies and I was gathering mine from earlier. "Where were you a principal?" I asked. Mostly to break into conversation, though I was interested. I had almost forgotten that yesterday she stopped in my room for a five minute drop in. I have no idea what I was doing or why with my class for those minutes, but she has never been in my room before that. In the lounge she brought up, of her own accord, the visit. "I really enjoyed your class yesterday." "Really? Thank you!" "I've been looking at classrooms, especially yesterday, for rigor. So far I've only found two rooms with real rigor going on with students. Yours was one of them." "What? Really? Who was the other one?" "In the younger grades, Sarah..." (as if I didn't know who that was... hah!) "Wow!" "You know, it's hard to teach teachers how to teach rigor. We all know they need content, anyone can teach content. But the depth of the common core standards is rigor, and it's very hard to teach, but some teachers do it naturally. You seem to do it very naturally." I took all of this with a grain of salt, and "rigor" as something to teach is a strange concept, but this was a lift I absolutely needed and wholly appreciated this morning. I know for fact it's a result of the principal of KIPP Blytheville's feedback from her observation two weeks ago when she visited with my M,TLD. She told me to work on "Making students' thinking visible" and gave me some resources to work from. It absolutely transformed my classroom... again. This means I had one principal (Sacramento) transform my management, and now this second principal transform my actual teaching methods. I do believe my classroom is inching towards being much more genuinely "student-centered." I make a very conscious effort to talk as little as possible, and make my words 90% questions that probe for thinking and 10% very explicit directions. Not saying I succeed all the time, but dear god is my classroom worlds apart from where I was this time last year. Last note: thanks to all recent parties that have made any comment on this blog in recent weeks, in real life, FB-world, on the actual blog, whatever. I'm perpetually amazed that anyone reads it at all.
ah.... I'm not sure if it is unethical or not to share what I did about what the math teachers wrote on their surveys. If I get it published, it's fine, but blogging is not publishing. I guess I'll just take out the juicy details of what the math teachers were confused about. Their answers made me feel more justified in asking senior secondary mathematics preservice teachers about fractions and division. I just gave a survey to 15 future teachers and while there were lots of correct answers, there were lots of things that shouldn't ever be said to children about math. The following question had lots of responses. The question was "A student asks you why do you use division in the slope formula. What would you say?" Specifically, I was looking for an explanation of the use of division, not an explanation of the the other parts of the slope formula. Does this question make sense? Does anyone want to take a stab at answering it? Am I expecting too much? I swear I see understanding division as useful in secondary mathematics-I don't think it is pointless to actually be able to know what division is and does to quantities. Maybe I'm crazy. I need to get a handle on ethical descriptions of study data while blogging-to me they are nameless faceless teachers to anyone reading, but maybe not to the institutional review board.
Seventy-four days and my teaching career will be over. Out of the 1186 days that have already passed, it is but a wisp. About 740 hours left out of the approximately 10,000 hours that I will put in total. I haven't decided how I feel. It's almost like knowing which day you are going to die. Maybe more like knowing on which day you will be born. My ambition is throwing a party right now. Totally rejoicing that law school can be my "job." After dividing my attention every which way - with part-time jobs and summer jobs and certification classes - it will be a relief to focus entirely on one thing. I can get good at something. As insulted as I am that more effort is not being made to get me to stay, I am also delighted that the decision has been made for me. Once again, all educational roads lead to budgets. My conscience is guilt-ridden, though. I feel bad for leaving my kids, and I feel bad for not feeling as bad as I should. I told someone recently that only 10% of my problems are about my feelings; the other 90% about my feelings about my feelings. It's like meta-emotion: feelings about feelings. And what a ridiculous waste of brain power that is. I'll probably come to some conclusion or make peace with all of this soon - in about 73 days.
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