Vivian+and+Marcie

__**Week One: August 25-27**__ SLCSE offers a unique teaching environment due to the small number of students and the creative dynamics of an expanding charter school.. The atmosphere is much more relaxed and collaborative than the junior high and high schools I am familiar with. I was impressed with the friendly office personnel, collaborative banter between teachers and the personal attention give to individual students. Although the scheduling had some glitches everyone worked to make students their priority and seemed confident of an effective resolution. The idea of 90 minute math classes is extremely appealing to me as there may be time for discovery and extended discussion in a single class period. The time was effectively used in the first week. The opening lesson plan was unique in that it deviated from the expected course by not discussing classroom rules or the expected course of study. Students began by following simple instructions to construct a rectangular prism name plate that contained some extra information about themselves. Explicit instruction as to how to access materials and what to do when the task was finished where then incorporated into the activity. Ms Shell used this time to wander among the students making personal contact with many students by noticing a personal characteristic or object. The second activity involved an open end question introduced by a personal narrative about Ms Shell building a pathway in her garden. She then posed the brick pathway problem and set students to work. Once again she “worked” the classroom querying students about their thoughts and approaches to the problem. Twice she interrupted the class work to share some of the students thought processes but never indicated that she either expected or even knew the appropriate answer. She probed with individual questions without ever indicating that the student’s approach was correct or incorrect. When students stopped working, she asked them thought questions and asked specific smaller questions to reinitiate interest in the problem. I was disappointed to find that no mention of this activity was initiated on day 2. I am sure that Ms Shell learned a lot about her students and perhaps she was just waiting for a student to ask….and then she would have continued the discussion. She also used puzzles as a “break” for students from placement testing. She seemed to be completely flexible to student interest and direction. This gives the impression that the class has several specific objectives but is also free enough to allow Ms. Shell to follow student interest. Ms Shell's classroom management style was based on both implicit and explicit directions. Rather than talking about being respectful, she modeled respect, ignored inappropriate behavior, complimented appropriate behavior and waited for silence before speaking. In this way the code of behavior was initiated. Ms Shell seems to give information on an as needed basis which may be prompted by student query. I was also intrigued by her dialogue style. I tend to pack too much information into my messages. Ms Shell gave clear instructions without unnecessary details or preemptive remarks. I was impressed with her ability to make comments that were both positive but demanding: “I know that you can do more.” (This is said with a smile and encouraging look but no underpinning of criticism.) “ When I come back show me the one problem more you have done.” (She casually walked by just prior to collecting the papers and asked to be shown the problem.) In my observations, I was unable to determine several things I wanted to know: when questions were acceptable and how she wanted these questions offered. I am still unclear as to how students should get individual answers—Ms. Shell seemed to ignore most questions asked when a student remained seated but seemed to respond to students who approached her during work time. She never called on someone who spoke out of turn or even acknowledged them (this practice was extremely effective) but she also often ignored students who had their hands up during work time. I observed that several students just put their hands down and remained quiet but still didn’t engage until spoken to by a teacher. It will be interesting to watch how the student/ teacher question/answer relationship develops. In general, Ms. Shell’s responses to student questions tend to shift the responsibility to the student. She may indicate the directions have been given, they should problem solve the situation or ask a neighbor.

I am trying to contain my natural tendencies to want to know the whole plan from the beginning by not asking many questions. Hopefully this will allow me to make more careful observations, think more deeply about teaching practices and formulate my opinions more slowly.

Vivian's Response 9-2-2010:

It is delightful to read such detailed observations of my class. I am impressed that you (Marcie) are noticing the nuances of how I handle kids and questions. You show considerable depth in what you are noticing. I enjoy reading your projections onto my intentions with the activities. Again, your projections show considerable depth and thinking about what is going on. This habit of mind will make it meaningful for us to dialogue about the classes, and will serve you well when you are teaching.

I have some questions for you about one of your observations. To quote, "She never called on someone who spoke out of turn or even acknowledged them (this practice was extremely effective) but she also often ignored students who had their hands up during work time. I observed that several students just put their hands down and remained quiet but still didn’t engage until spoken to by a teacher." What do you think is the implicit message I am trying to send? And what student outcome do you think I care the most about, especially considering the last part, that a student just put his or her hand down and remained quiet but disengaged until spoken to?

//In response to Vivian's 9/2 Question// I believe that you are trying to get students to self-initiate the skills of working and problem solving. The option of asking another student and carefully reading the instructions are also available. I believe that you want a classroom setting in which directions are given once clearly and students need to ask themselves and try things before turning to an adult. As I watch you circulate the room, you are careful not to give out too much information instead your purpose seems to be to help students problem solve their own questions.

__**Observations Week Two: Thru September 2nd**__ My thoughts this week primarily were focused on the issues of class organization, student motivation/engagement and curriculum pacing. The formal routine of ATB, homework review and lesson provided a structure in which Ms. Shell reinforced the more important routines of student responsibility. While the curriculum being taught was order of operations review the focus seemed to be in teaching students responsibility for homework, scheduling, paying attention and appropriate outward symbols of focus. I was surprised that in a 9th/10th grade class, Ms Shell reminded students to sit up straight in the chair, not fidget with pencils and look up at the board. Ms Shell manages this type of reminders in a very natural way. She always uses a smile and reminds the students that their attention is necessary for her to focus on being a good teacher. One example stands out. Ms Shell stopped the lesson because of some very quiet side talking, waited for the talking to stop and then explained that she was listening carefully to a student's response and could not properly focus on coaching his answers when she was distracted by the outside noise. In general, this type of demand for focus was well received and students seemed to grow more respectful. Two students in particular, who I observed tend to be incredibly fidgety, responded to a firm classroom prompt where everyone waited silently while they put away their extraneous materials and then remained quietly attentive for the rest of the classroom period. A classroom management style of an ATB (At the Board activity) and silent roll taking along with the rule that you are late if you are not at your seat engaged in the ATB when the bell rings seems a very effective way of gaining classroom attention. As I observed the class I was constantly reminded of what my own children have said about their math classes and wondered how students were responding. I would have loved to quiz students about their beginning impressions. I read the notes that students filled out on the first day of school about their learning styles and tried to notice if the weakness/strengths they had identified were already apparent in their behavior. I was particularly interested in watching students who indicated that mathematics was boring or of little interest to them. Ms Shell's direct classroom management style made it more difficult to see disengagement but I wondered if it actually enhanced real engagement. I was especially interested in how students responded to her prompts when they did not complete assignments. The stated homework objective of just trying for 20 minutes coupled with the fact that all homework this week was reviewed in class prior to being turned in made me wonder if unmotivated students would attempt the homework at all. Ms Shell appears to randomly check (once this week) for completed (shows an effort of 20 minutes) homework prior to the classroom discussion. I wondered if this policy increased or decreased student engagement. Several students I observed chronically did not have the homework at all or had not worked on it outside of class. Ms. Shell pointed out with a cooperative discussion that sitting without taking notes on the homework was totally unacceptable and therefore unprepared students engaged in copying both the problems and classroom discussion. The pace and structure of the classroom are designed to INSIST that every student cooperate with the stated expectations. Ms Shell does accommodate students with special IEPs. One student is non-participatory but never disruptive. When she draws names for verbal responses she is willing to take a pass. Only one student ever used this option and even those who were clearly not interested in the discussion effectively answered questions on their turn. I noticed that students seemed unsure how to use time when they completed their classroom assignments. No explicit instruction was given so they usually just sat quietly. When I suggested they could work on another unfinished assignment (from math) they seemed surprised that this might be acceptable. In my own mind I thought the class was extremely instructive but not engaging in a way that would motivate students interest in mathematics. As I thought about this, I had a difficult time envisioning exactly what I meant. I think I envision activities that show students why they would want to know geometry or algebra in the first weeks of school. I would like to see students having an "ah ha" moment. Also I would want them to know how much I enjoy math. In thinking about the design of Ms Shell's classroom it was hard for me to visualize how this could be incorporated. I need to spend some time developing this idea on how to build student's interest. The pace of the classroom instruction seems very leisure. The first 9 hours have been spent setting up procedures, testing, evaluating students approaches to problem solving and reviewing order of operations. The results of testing have removed some students from the geometry class but the topic of geometry has not yet begun. The algebra students have not yet received the packet of review information based on their test results necessary to fill in any pre-algebra gaps. I wonder if the new 90 minute time slot is being used to cover the same amount of materials that would have been covered in 45 minutes in a more thorough way or if it has allowed more material to be presented. Pacing is an important consideration and will vary based on student groups. The pace of the courses seems exceedingly slow for the advanced student and perhaps even too fast for some others. In Ms Shell's classroom the use of E on a passport (exceeds the standard) is designed to motivate students to find extensions to their own learning. This concept of exceeding the standard has been brought up several times by students as well as Ms Shell. I am interested to find out if opportunities for extension are naturally built into the curriculum or if they must all be student generated. On Thursday, Ms. Shell introduced an extension assignment given selectively to some students to write their own number trick. This was done by a personal invitation during working time and carried no requirement. It will be interesting to see if any of the students accepted the challenge.

Vivian writes: Again, I notice that you describe a lot of the nuance that you pick-up on. And, it is clear that there is a good deal going on in class that you are simply not aware of. With more time in class and, ultimately, experience as the primary teacher, I believe you will become more aware due to your thoroughness and reflection. This is why I believe it is time for you to start sharing the time as primary and why I gave you the job of doing the ATB. We should discuss how you can be more present.

As you take on more of this role, I have some questions for you: How will you know when students experience "a-ha" moments? What do you believe it takes for a person to have such a moment? What responsibilities do classroom teachers have for setting up and supporting the school climate? What business, other than teaching their content, do teachers attend to during and after classroom time?

We'll start with these, though your reflection has generated in my mind considerably more questions about what you believe about teaching and learning. And, I am grateful for the opportunity to ask myself the same questions.

__**Week Three: September 10**__ Vivian, First I would like to thank you for taking the time to talk with me about how we can best communicate. It made me realize that our situation is not unlike that of every student in every classroom. My own children have often discussed that the most difficult part of starting school is discovering what their teachers want and expect of them so they can develop a rapport and establish a routine. I am in awe of your amazing talents as a teacher. I really appreciate your willingness to share your classroom, expertise and thoughts with me. My primary focus in class this week was contemplating how to engage students. I loved the way you phrased it, "how do you know when students experience an "a-ha" moment?" I feel that we both think that question is central to good teaching. In my thinking prior to participating in your class, my thoughts have dwelt primarily on helping students "want to know." In this direction, I have focused my thoughts on how to make mathematics relevant to students, how to share my own enthusiasm for mathematics, how to incorporate real world connections to mathematics and how to challenge students thinking. In addition, I realize how important a safe learning environment is to any endeavor. Since experiencing your classroom, I have thought more deeply about the importance of establishing a classroom environment that emphasizes and facilitates the ability to (1) focus, (2) take risks and (3) have time to think. Although your question is really more about how to notice when it happens, I have usually thought about how to help it happen. As I contemplated the difference in these two approaches I recognized the missing element in my thinking was the focus on developing a rapport with the student. Each "a-ha" would look different on different students. I have really enjoyed your analogy of getting the students to "play ball." Although I generally think of an "a-ha" moment as making a mathematical connection, it could be construed as playing ball. In other classrooms I might consider a student sitting attentive, taking notes and watching respectfully as playing ball but in your classroom you have moved the goal far beyond this by setting this as the minimum expectation. I loved your evident delight in seeing students take the risk of offering a conjecture. As we moved through the students and tried to encourage them to take risks I felt that the real effort was to create the "a-ha" that mathematics is not something you just need to copy and memorize but can be understood by conjectures and trial and error. This thought implies that an "a-ha" moment is more than discovering a mathematical solution, it is discovering your ability to think like a mathematician. This type of moment seems as if it would be easy to recognize both in a student's speech and in a student's persona if you have established a relationship with the student. __Vivian, what do you feel are the most important elements in teaching that help create these moments?__

You asked about a teachers responsibilities to the whole school environment. SLCSE's school environment goals go way beyond those of regular public schools. Two major differences I noticed in the stated objectives are: 1) the emphasis on high level thinking and processing skills and 2) the use of the word mentoring rather than educating indicating an emphasis on collaboration, reflection and a personal response to each individual student. These goals significantly change the responsibilities of the individual classroom teachers. The collaborative nature of SLCSE is readily apparent by observing the working relationships between colleagues. The small size of the faculty also supports the interplay of ideas and programs which support the learning of all students. I assume that you personally have devoted enormous amounts of time to discussion, creation and implementation of school wide approaches. Support of school wide goals is a large part of the business teachers must attend to both in and out of the classroom. I also believe that attending to the concerns of other faculty, students and parents requires an enormous amount of both energy and time. SLCSE emphasis on mentoring individual students also means that as a classroom teacher you must be looking for ways to help students "play ball" not just in your classroom but in school.

Currently I have way too many questions to pose but I am still stuck on contemplating homework: What are the primary goals, how to handle the quantity, how to ensure quality and how to provide adequate feedback to students. It is a large part of the non-content portion of teaching and I think also has a big impact on student engagement. __What are the main objectives of your homework procedures?__ Homework is an area where I know there is no definitive answer but I have not formed a beginning philosophy. Having 6 children helps me understand that no one homework solution is correct for all students. I have really been impressed by the way you follow up with students on their homework and are so aware of whether students are doing their homework or not. I love the way you quietly and individually prompt students to become more complete or even attempt their homework. I like the emphasis on effort. My understanding of your homework policy is that you keep all homework on file but only discuss it with students if they have questions about the posted ESIS grades.

Hi Marcie. I am wordless. . . Okay. I feel so. . . moved by your description of an "a-ha" moment as "more than discovering a mathematical solution, it is discovering your ability to think like a mathematician." "Discovering your ability." That is at the core of what I want for my students. I watch them as I teach and as they work and look for them to discover what they can do. For me, the "a-ha" is when they have understood something so well, that they can no longer believe that they can't do math or think mathematically, or when they see connections so deeply that they can tell there is more out there. It //is// easy to recognize. When Z has this type of moment, his eyes bug out and I can see the whites all around his irises. When E has this moment, her lips curl into a snicker. (I have mimicked this for Diane, and she knew exactly what I was talking about.) When J has this moment, she looks like she is saying, "oh," but makes no sound, then smiles. These are students I know well, but I have started to make mental note about what some of my new students do. J sits there turning red with a big smile on his face. D squirms in his seat like he is so uncomfortable containing his thoughts he might explode. M smiles through her glasses and shrinks down in her seat as if she knows I'm going to catch her understanding something and make her explain it to the class (which I have done).

What does it take to help create these moments? I believe that the first step is to believe these moments are important and to deepen your own understanding as a teacher about what they are. You have done this by identifying that it is more about discovering things about yourself than discovering a mathematical solution. I believe you have to teach with philosophy, not just do the job. This philosophy, for me, is an extension of how I see life; that all experiences are meant for us to learn about ourselves. I really do believe that students can learn about who they are, how they think, what their skills and talents are, what they find beautiful and meaningful, how their brains work, what makes them fit-in, what makes them unique, how they think mathematically, how they think in non-mathematical ways, etc. by experiences in my classroom. Maybe they're not as serious about it as I am, but oh well, that's me. I believe teachers do need to set-up a climate of focus, risk-taking and dedication. Students will go along with this if they believe they will understand you and you will understand them. I work really hard at something called "comprehensible input," a term from ESL classes that refers to making what you say understandable. I think very carefully about how to "show not tell" what I am trying to get across. I have spent considerable time building a common vocabulary and creating experiences for our class that we can refer back to throughout the year. For example, I was very exact about what I wanted with the number tricks pictures to model the operations and writing algebraic expressions. My motto is, "don't say it if you can show it." You may not have noticed how powerful those experiences were, but I did. I'll be building on that foundation throughout the year. In the end, it is this work that will lead to "a-ha" moments for many of our students. These are easy to come by with kids who are typically underserved in their math classes because for many of them, it is like they finally understand something that they have not gotten in the past when it was only explained. But, for many of our kids for whom math comes easy, our verbal learners who like to follow rules, the "a-ha" moments will be harder won. I struggled all year last year to see such moments for many of my students who were star math performers their whole lives. Tragically, much of the beauty and depth to what we were doing was lost on them, while some students made such deep connections they couldn't contain their enthusiasm. I clearly have not yet discovered how to create "a-ha" moments for all of my students. Perhaps as we work together we can figure out how to show the beauty of mathematics to even those kids who seem to "get-it" so quickly they didn't have to work for it. Truly, what it really takes for mind-blowing understanding is work and committment.

More on my homework agony I mean policy later.

__**Week 4: September 16th**__ Vivian, I quizzed both my daughters (8th and 11th grade) who always get A's in their math classes about their "a-ha" moments and was sorely disappointed that although both are very successful students both consider themselves without ever experiencing such a moment. On pressing them farther, I found that they (and probably most students) are always judging their abilities in contrast to others and thought about how most classrooms reinforce this type of evaluation. I am by nature a very competitive person and have often used competition as a student motivator. As I have observed your class, I have been impressed by how you use totally different motivators.

Two of your gifts for teaching have been the focus of my reflections this week. Both are difficult for me to articulate but have a tremendously positive impact on the classroom learning environment. The first is your ability to engage in learning conversations rather than lectures. You have created an environment where every question is received as a positive contribution and often opens the way to teach (discuss) a mathematical concept. Our discussion which led to an understanding of skew was an example of this technique. You not only created curiosity with your questioning but had students generate the need to know. You never miss an opportunity to thank students for their incorrect comments or suggestions in a way that creates an incredibly safe environment. Student conjectures are not judged by their correctness but instead on the willingness of the student to make them. I have a difficult time remembering your exact wording but I think this week, I will try and jot down some of the things you say so that I can better model them. As I do the ATBs I realize that knowing how to follow student inquiries is a real talent. You need to listen carefully to students, know what questions to probe with and where you want the conversation to end.

The second gift is your amazing ability to take note of individual students actions/reactions. I loved your descriptions of students' "a-ha" reactions. I was completely "bowled over" by your ability to call four students up after class and have a specific discussion with them about their activities in class. In all four cases, I had not noticed the things you referred to. You were able to not only talk with them but give them the exact circumstances. I love the way you ask students how they are going to solve the problem rather than proposing solutions and I was extremely impressed that you remembered to follow-up with all the students on subsequent days. I noticed that you have a type of card system to keep track of your conversations**__. I would love to know more about how you have developed a talent for tracking individual students.__** In our discussions on IEP's and in watching you handle students, I keep thinking about your incredible balance of high expectations and accommodations. I am very impressed that you have built enough of a relationship that you could not only took away someone's book this week but that he actually engaged. I appreciated your sharing your insights on several students and would love to discuss several others when you have the time.

As I watch you and Diane plan for Algebra, I realize that I am missing most of your planning structure. It appears to be so innate to your program that many of the nuances are lost to me. I would love to schedule time to talk about the "big picture" or just to see the cumulative passports file to see how you envision the development of algebra in your class. The foundations have been laid so carefully and completely but I still don't really have a picture of the whole building process. I sometimes feel caught because I don't know what information to provide or where we are heading. Likewise in geometry, I have Emina's class as my only geometry experience so would really like setting aside some time to talk about the big picture in terms of not just the core requirements but your vision for developing geometric concepts. As I choose the day's ATB, I am not always confident that I understand the key concepts we want to guide the classroom into.

9/19/2010 Hi Marcie,

Wasn't that discussion about skew awesome! Against my better judgement, I tried in vain to "reproduce" it in my 7/8 Geometry class. Every part of the conversation was completely lost. This is something that teachers talk about a lot: how trying to recreate an organic conversation from one class to another rarely works. I think that you have identified a factor that contributes to moments like these when you say that in our classroom "every question is received as a positive contribution" and that this creates an incredibly safe environment. Once again, because you are such a keen observer and reflect so well on your observations, you can see how this sort of environment is developing in our room. The nuances are not lost on you, and I respect that a lot about you.

I think that discussing the big picture for Algebra and Geometry would be great. I want you to know that I only vaguely have an idea about what this is for either class. I have only taught Algebra once before, 13 years ago, and Geometry once before, last year. I actually feel quite inadequate to declare a big picture for either class, but I can share with you quite a bit about how I see teaching math in general and how that affects the daily conversations we are having in class. I am very interested in hearing how //you// see the big picture for Geometry and how //you// envision the development of Geometric concepts. You probably have more perspective and vision for this than I do in light of your class with Emina and your work with your own children. Please share with me. I feel vulnerable in my quest to teach Geometry well and limited in my view of how Geometry affects life after Geometry. You say that you "sometimes feel caught because [you] don't know what information to provide or where we are heading." I feel the same way! I have been in a Math 7/Pre-Algebra world for 13 years, and it wasn't until I could pass my students to Diane did I ever feel like I contributed to my students' success in math after they left my class. Stating this out loud makes me feel. . . regret for not knowing better in the past what my students needed, what my content was supposed to be, or how to teach effectively, sad that I could find no common philosophy or collaboration with teachers in classes beyond mine, and eternally thankful that I have found a small world where my beliefs about how students learn and what math really is are appreciated and nurtured. I am beginning to feel that you "get it" on a level that includes you in that world, and I'm glad that you are here. Thank you.

__**WEEK 5 September 24**__

Vivian, I am continually amazed at the insights to teaching you offer me. This week as I tried to pay particular attention to your interactions with students I was impressed by your ability to validate every student while maintaining a very high standard. I often get so caught in watching you teach that I forget to take notes. Unfortunately I only wrote down 5 phrases you use: That is an interesting idea, I am going to think about that; Let me see if I understand what you are saying; I am so glad you chose the difficult problem; Tell me why you think that; Please wait to ask questions as I am hoping I will answer them in the rest of my explanation. I am impressed with the rapport you have developed with your students. The way you are getting responses from several students continues to amaze me. It is clear that you really care about your students and they respect you as a teacher.

I loved the planning session with Diane, I never realized that you had not taught algebra recently. You would never know from attending your class! I, like Ralph, am amazed by the detail thought that you put into how to build a mathematical foundation of the essential concepts. Thanks for encouraging me to skip class and watch you and Diane work as a team. I loved the "hot/cold" integer approach and the way it was executed. Sixty-one kids all paying attention and engaged is an amazing feat. The use of new technology was so much easier with extra help. I appreciated your discussion about "the big picture" and I am excited to read "Understanding by Design" and set aside time to map out our approach to Chapter three. I am a bit of an organization nut so I appreciate your willingness to let me build classroom folders as a memory aid. . As I worked on preparing just two lessons for next week, I felt more empathy for the situation of "leaving: the Math 7/Pre-Algebra world." The demands on your time are constant yet you seem to always put students and colleagues first. When do you find time to plan curriculum?

One of my many concerns about my own teaching are using the ELMO. You are very effective with the ELMO but I do not feel comfortable standing behind the desk ( I am shorter and more fidgety). I would love to explore other options. Perhaps we could allocate time to use the smart board and talk about other open spaces in the classroom. As I struggle to improve my communication style and clarity I have really appreciated the way you have emphasized my strengths and minimized my shortcomings.

__**WEEK Six: October 1**__ What a great week. I really appreciated your willingness to let me jump in and try designing and giving some lessons on new topics. It gives me a better appreciation of the time needed to cull the essential and necessary information. You are a master at determining what student stumbling blocks will be and building scaffolding into your lesson by encouraging student discourse which reveals student's thought patterns into the beginning lessons. As I began to teach about inductive and deductive reasoning, I realized that although I had discussed my concepts with my own teenagers, I had not really thought about the diverse ways students would interpret certain sentences. This meant that when I was presented with certain student inquiries I was not as prepared as I would have liked to be. I missed having you in class that first day to bring clarity to our discussion (that is one of the many skills you posses that I would love to emulate.) I am trying to pay particular attention to how you articulate mathematics in these stumbling areas. As I listened to you make the transition in algebra from a hot/cold model of integers to difficult mathematical expressions, your discourse with students was amazing. You clearly present not only the how of lessons but involve the students in knowing your objectives. I loved your discourse on utilizing models, building on prior knowledge, reading instructions, forecasting expectations, making your own decisions about using decimals or fractions, etc. Thanks for the long phone conversation clarifying our lessons objectives. I have come to realize how quickly the preparation time in the morning becomes current events rather than future planning. I love the way you put such detailed planning into each day's lesson but realize that it means long term planning must be done in "off hours." The flexibility we have in the classroom to extend lessons is a definite advantage of the extended classroom time. The group work we implemented this week seemed so powerful. Seeing the students actually engaging in discussing logic problems and mathematical ideas was wonderful. I really thought the "agreed on" homework problems sheet was effective and hope we use it on a regular basis. I thought it gave students who did not do their homework more accountability because they had to admit it to other students. Also many of them were called upon to do the hard problems to determine which answers were right when the others disagreed. I loved the time to check in with individual groups and the time to ask students about their individual work. As you spent so much time trying to prepare midterm grades, I wondered if you are ready to let me help you with some of the work load. I also wondered if we could schedule a specific time to do our long term (chapter objectives) planning so that I could glean more about how you determine what areas are essential. Other than the core, is there another "test" of accountability for this course? Are SAT/ACT questions the end goal?

Hi Marcie,

I thoroughly enjoyed working with the lessons you prepared last week. I realized as we discussed the differences between inductive and deductive reasoning that this was a missing piece for me last year. I LOVE the way you created and posted the signs right above the screen! I don't know if you noticed how I stand underneath the sign that I am referring to, but this is a powerful technique for comprehensible input. You created the opportunity for this. The students enjoyed the problems you gave them, as well, and many had the chance to bring something to the table who normally sit passive as others lead the way.

I notice that you are beginning to figure out questioning that reveals student understanding and misconceptions!!!! On the ATB today, when you asked how many angles students used to figure out one of the angles, I desperately needed to know what their answers were so that I could know what they were thinking. You figured out the exact question that would show what they were doing //and// lead to a discussion about the details involved in deductive reasoning. In our last SMART mentor/mentee meeting many of the fellows were asking how to gauge what students understand and whether or not they are "with you" during the lesson. I tried to explain that it involves a lot of thinking of the right questions that are easy for masses to answer yet drive right to the point you are trying to make. You did that with your ATB questioning today (Oct. 4). I have a suggestion: wait for answers a little bit longer. It takes kids some time to put their words together, and if you wait, you will start to get more thoughtful answers and more content in their answers. Right now, you sometimes ask a question, to the whole group or even to one student, and then quickly rephrase it many different ways when they don't answer immediately. Have you noticed this? Ask yourself why you do this. I think that it might be because you feel uneasy thinking they might be uncomfortable not knowing the answer. Maybe they just need a moment to collect their thoughts. I have found, also, that if I wait long enough I will hear something that I can twist to my advantage, some way to compliment the kid for their perspective or a thought to prime their minds for the future or a new way to look at the problem I hadn't seen. Try experimenting with just waiting a little longer after you ask a question. And, put a pleasant look on your face, purposefully, so they don't panic thinking that you are confused by them and they'll never be able to tell you what they mean. I say this not because I've noticed any unpleasant looks, but because I know that I have such strong body language myself that I have to tell myself every day to monitor my facial expressions.

Time is the most valuable resource in education. I agree that we have got to figure out how to put the long-term planning higher on the priority ladder. Without vision for where we're going, we are going to teach disjointed, thrown together lessons without any good flow. One reason the discourse in Algebra went so well the day you are referring to is that I know where all those ideas are going for the rest of the year, and beyond. I know that model inside and out. I know where kids get stuck. I know how it has to sound in 2 weeks and then in 2 months and then next year. I know a very small picture for a very few ideas like this in Geometry, so I am VERY limitted in how well I can do this sort of thing with those classes. I do my best knowing what I do about teaching math, but I so wish that I knew Geometry better. Yes, long-term planning is done "off-hours," especially when so much time is spent on the other priorities I have, such as students and colleagues. But, if we could do more of this together, you could really help me get my Geometry mojo. Thanks for helping with the grades, as well. I panic when I haven't collected that data on their study habits, so it is a huge relief. Let's continue balancing that part.

I do not know if there is another "test" of accoutability for Geometry. I have no idea about SAT/ACT questions. I have goals for my students that involve personal beliefs about teaching and learning as well as political beliefs about what they deserve in their futures. I try to teach to these goals. Fortunately, my beliefs mesh with the philosophies of our school and with Diane's beliefs.

Let's brainstorm about the ELMO/Smartboard. I need to change the height of my cart, anyway, and there may be other changes to make things fit your needs better. How great that you know yourself well-enough to ask!

__**Week Seven: October 9, 2010**__

I love the way you have such a positive way of saying things. You are amazing to work with. The art of questioning is certainly on the top of my priorities this year. I am continually amazed at how simple you make it look and how difficult it is to practice. When I stepped into a simple algebra discussion and found myself faced with a clearly "wrong" answer, my mind went blank. I have effectively internalized what NOT to say…..which is just about everything I use to say…..but I found it very difficult to think of what to say. Everything I could think of wasn't quite right: Did someone else do this differently? Did you draw a picture to make this decision? How do you visualize this problem? Did you consider any other ways? Did you look at the + and - together or separately? Nothing seemed right. In the end, I merely asked for another student to give a different approach, then we looked at the differences and decided we had to look at both the + and - to visualize or draw arrows. I didn't feel I met the objective of building on the mistake as you do and I wasnt' effective at somehow thanking the learner for bringing the matter to our attention. I notice how effective you are at using every wrong answer as a spring board for learning. I need to write down some specific things to say and memorize them as a good beginning. //Would you be willing to give me a list of about 5 questions you would recommend?// I loved your suggestion about waiting with a look of confidence. I have in fact been working on both of those things and you will be happy to know that despite my lack of skills I actually am vastly better than I would have been 4 weeks ago without watching you. It is interesting to see how our individual learning styles influence our teaching. I am a quick impatient learner while I see you as a careful deliberate thinker. Your comment on displaying confidence in our students' ability to understand is a great focal point for me to use in viewing wait time as real learning time.

I am so glad you invited me to participate in parent teacher conferences. I was impressed with your ability to try and focus on a positive plan for improvement that involved both the teacher and the student in a positive exchange. It made me think about my own "plan" to help the students in our classes and I realized that I have not made one. I sometimes feel that my attention wanders to so many things during our classes that I lose focus on any particular issue. This next week, I am going to try and monitor behavior as you suggested on a sticky tab--both positive and negative.

I began reading //Understanding by Design// and am excited to talk about the big ideas for our next unit. I am intrigued with using geometry as a means for teaching the life skill of problem solving. Our next unit on angle chasing with transversals, triangles and polygons seems to be full of these big ideas: 1. Start problem solving before you can see a solution, 2. Solutions can be found in multiple ways, 3. Checking your solution by doing it two ways is an excellent idea. 4. Keeping track of what you do know is essential in problem solving and 5. Think outside the box--sometimes adding a parallel line to your picture provides the means to a solution. I would like to develop some key "strategy" phrases we could use with our students this year much like Diane uses in her algebra. I made a beginning attempt in deductive and inductive reasoning. //I would love to work on developing what these should be with you. Do you think will they help me be a more effective teacher?// My first attempt was the 1. Draw a diagram. 2. What do we know 3. What do we want to prove? 4. What do we see? try possibilities 5. **If** we see….**then**…..., which helped me in my explanations but was not as useful as I hoped. I am excited to develop a geometry "mojo" together.

Hi Marcie,

I can tell that you are really concentrating on your questioning with students. I try to hold myself to a standard of "show, don't tell," even in my feedback to you, and I can't really give precise examples that show how I know that you are. But, I can say that your conversations with the class sound different to me now than they did a few weeks ago. I feel very lucky to be working with you as you are such a reflective learner, and you take the time to notice and analyze what is going on in the classroom.

I wish that I could think of 5 questions that you could memorize. Perhaps they will occur to me as I write, but I feel that I should give you my gut response quickly before I over-think what you are asking for and then never tell you. (My own need to do things "right" sometimes keeps me from doing them at all!) My gut response to you is that it is not any of the questions you listed above as possibilities that would have worked in this situation, and others, but really that you just need to take time to be sure you understand what the student is saying, __//**without trying to lead to something**//__. Perhaps the best route to take would be to say, "tell me how you got that" and then ask clarifying questions until you are //sure// you understand what they are saying. It is in the middle of this process when I figure out what to say next or how to lead them to something. I rarely know how to do this before I ask the students a few questions. I think you may be skipping over this part in your mind. This process does take patience and feeling a bit uncomfortable while they struggle with explaning their thoughts, and I find it is worth the time and effort. For example, today in Geometry, A_ _ was trying to disagree with your statement about supplementary angles and the converse. While I listened to you field her objection, I could tell that you were not understanding what she was trying to say and you were talking over her objection rather than clarifying that you understood. You will have to learn how to listen :), and I know that is hard for you. I think a technique that will really help for you, since you want to be saying something, is to rephrase what you hear, without interrupting, until the student (or other person who may not be a student!) says you have it right. Until they know you have heard them, they will not listen to you and you will not be able to point out the gold in what they were saying. Right now, I think some students do not believe you will understand them, so they are unwilling to try to explain their thinking. THEY ARE MISTAKEN. I //know// you want to understand them and I //know// that you care about them and I //know// that you would do anything to help guide their thinking to help them understand. And, it is time for you to convince them of these things. They will begin to trust you as you listen to them more and restate what they are saying until they agree that you have it. So, here are some sentence starters:

1- Are you saying that __?__ __2- Where did you get__ _? 3- Do you mean ___?__ __4- Is it the__ _ __or the__ __that you disagree with?__ __5- What would you write here (point)?__

__(By the way, I think that I never told you in the beginning how impressed I was that you took the time to read what students wrote the first day about themselves as students. Thank you for being student-focused. I believe you truly "get" that we are here to teach students, not math.)__

__I have a few other observations that have been floating in my head for awhile that I think will help you connect with students. I have noticed that you are trying to joke with them, and you often say things sarcastically about our class, like "I know that you all love this class." Like I said, I think you are trying to connect with them, and I find myself uncomfortable with this sort of comment. I really don't want to hear their sarcastic reply, "oh, yeah, we LOVE this class" or their flat out arguement, "no, we hate it." I have found that I take myself way too seriously to even open the door for them to imply that they are wasting their time with me or to imply that I don't do a spectacular job teaching them. Perhaps you don't see it this way, and I'd like to ask you to reflect on why you are doing this and what effect it might be having on class morale. I know that a major turning point for me as a teacher occurred when I had this conversation with myself ~13 years ago: "Vivian, they may hate you, you may not know how to handle them, you may not know exactly how to help them, you may not understand how to connect with them, but they will NEVER take you seriously if you don't take yourself seriously, they will NEVER buy into your class unless you buy into your class." It was time for me to play the confidence game. I think of that movie Oceans 12 and how Matt Damon's character had to convince people he was someone that he wasn't, and it was all a game of confidence. I believe that we cultivate the attitudes that we want them to have by modeling these attitudes. And, I want them to recognize that I am a good teacher and that the way I teach them means something for their lives and that Geometry is valuable and worthwhile. What attitudes do you want them to cultivate?__

__I would also like to comment on your energy. At times, you get very energetic and your voice gets high-pitched and you talk over what they are saying. It is not that you shouldn't get enthusiastic, but I think you could watch to see of your energy matches that of the class or if it is keeping you from scanning the class for body language that shows engagement. I had to learn about my energy and tone from feedback from students. I had a group of kids my 3rd year teaching who have turned out to be great friends. They would hang out with me after school, and we spent their high school years getting together for picnics and Lagoon trips and talking about teachers :), including me. Eventually, they felt comfortable enough to give me feedback about how I sounded to them at times. I think they knew I felt fragile about my relationships with students and my classes, and they were gentle with me. But, they had some great things to say about my tone and my body language. It really matters more than you could possibly know what tone of voice we use, how loudly we talk, when we smile and when we don't, etc. I sometimes see you looking at me when you are making a point or clarifying a "mistake" in thinking, and I would encourage you to be brave enough to look right at the student(s) when you do these things. You will get feedback about how well what you are saying is landing with them, and the interaction will become a human interaction between you and them. You will invest in them, and they will begin to invest in you.__

__I like your idea about developing strategy statements. I instinctively resist all formalization of problem-solving procedures, but that is not what I hear in your suggestion. What I hear is that you want to build some ideas with the class about strategies that have worked and somehow keep track of them so they can try them again. We could begin with your awesome phrase, "Angle Chasing." "If the solution doesn't jump out at you, try 'Angle Chasing'," sounds like something we could say in class. I think this would be useful for kids like N _ _ _ who believe they are supposed to know exactly how to solve a problem before they can begin. The great thing about 'Angel Chasing' is that it reinforces a life-skill that I find important which is to ask yourself what you know or understand about a given situation as a starting point. And, it would mean that students have to start producing something we can look at. We will be able to work with that, reinforcing what they can do instead of that they cannot see a path to a solution. (I think this is one of the reasons that some textbooks and teachers try to implement a formal "Problem-Solving" Procedure; to get something written down. Some issues that I see with such procedures is that they feel artificial, keep students thinking "inside the box"- - some of them are literally drawn inside boxes! - - and become cumbersome and labor-intensive.) Let's continue to find more strategies that accomplish what we want. Yes, we will become more effective teachers by making explicit some of the things that good mathematicians do by second-nature but that many of our students simply don't think of. We have the WONDERFUL opportunity of teaching math, a content that lends itself well to developing powerful habits of mind.__

__Vivian, Hopefully you have noticed how I have tried to incorporate better listening skills into my conversations with students. I loved the suggestion to stop thinking about how to use their comments and focus more on really understanding what they are saying. I have been amazed at how that simple change of focus makes it so much easier to help students. Instead of guessing where the confusion lies I am learning to listen for the source of their confusion. Now in my conversations with A… or H…. by focusing on listening I can connect and reflect what they are saying without talking over their objections. It is interesting that your simple question starters actually did clarify this point in my mind, which leads me to another observation. One of the things I really enjoy reflecting on in your class is how to pace conversations. I am always anxious to move on and pack information thick and deep. Your conversation style is to build a strong foundation and give students time to contemplate the implications. This is a new approach that I have not experienced and I am enjoying watching your interactions with the class and reflecting on how I can incorporate this asset into my own teaching.__
 * Week NINE: October 22, 2010**

__The key issue for us these past few weeks has been evaluating our connections with kids. Are we creating mathematical "aha" moments? I wanted to celebrate as J…looked at his quiz in disbelief that he could actually succeed and I wanted to cry as Q….checked out of class. I have been amazed at how quickly you incorporated T.,… and S…. into your classroom. Your composure as you have dealt with students is so professional and never gives a hint of your inner conflicts. Your emotional responses are so level and positive in the classroom. I have really appreciated the time you have spent discussing student issues with me. I have been impressed with the depth of your efforts to help all students make these "aha" discoveries. Your ability to notice everything is astounding.__

__I have thought a lot about your comments about my relationship with students. My first thought is that my style is quite different from yours and I would like to incorporate many of your skills into my teaching. On contemplating how to do this I realize that I will still not have the same body language and presence. Although you may have felt my comments to students about "loving" this class are sarcastic, they are sincere. I love this class and I want students to know that I really do expect them to come to love mathematics and see it's implication. I have experience with teenagers that lets me know that although some may grumble (and although this may not be allowed in class, it will certainly happen outside of class), students who know that their teacher loves the subject and thinks it should be their favorite topic--- respond. My understanding of student behavior is colored by my experiences as a volunteer, coach, mother and hostess. I have spent countless hours talking with students about their teachers; what they like, what they respect and what helps them to learn. I have seen how they respond to different styles what makes them flourish and shrivel. Their responses have changed my views on many topics and made me realize how much flexibility teachers have in being successful. The most important thing is just as you said, "it is a game of confidence. I believe that we cultivate the attitudes that we want them to have by modeling these attitudes. And, I want them to recognize that I am a good teacher and that the way I teach them means something for their lives and that Geometry is valuable and worthwhile." My style may be less serious but the attitudes I wish to cultivate are the same. The bigger issue for us is that I understand the importance you place on your classroom environment and I wish to respect and maintain what you have built. Sometimes my inexperience as well as my differences make me look to you for affirmation. I am definitely vested in our students but I do not feel free to respond in "my style" and am still learning how to emulate "your style." In most of the classes I have volunteered in I have never looked to the teacher but I feel your deep commitment to your students and I feel fragile that you may view my responses as inadequate. As we talked yesterday about "reconnecting", I felt again your deep commitment to students and the difficult dilemma you feel in letting me teach. I learned a lot by watching the techniques you so natural use in class. Your style is so effective at meeting the objectives of helping students see the big idea, feel the importance of the material, feel your confidence in their ability to succeed and stay on task. I especially liked your conversation about the strengths of deriving or just using a formula and was impressed that the kids appreciated you deriving the formula. You are definitely connected. Watching the classroom also verified for me how disruptive Q…..really had been on the morale of the class. I love being in your classroom.__

__I appreciated the mathematics department meeting. It was useful to see the give and take that builds collaboration in a department. I am excited to use the new format in formulating lessons and really liked brainstorming ideas on the common approaches. The approaches to homework review (small group collaboration, random problem assignment, white board answers, posted solutions, "quiz" from the homework) and the ideas for checking understanding (mental computation, think-pair-share, muddiest point, change a constraint, categorizing, tell the big idea) are great reminders of the need to use a variety of methods and not get stuck in a routine. Problem solving collectively about common teaching problems is so important to maintaining an effective classroom.__

__As the first quarter ends, I am impressed with how much my understanding of the importance of a classroom environment has changed by observing your classroom. In particular, I have seen how to create a community in which students are actively engaged and feel comfortable in expressing their ideas and thoughts. You have managed to integrate students with diverse IEP's into a classroom community where__ **mathematical conversations** take place. The real change in my perspective has been the importance of creating these conversations and the detailed planning and thought that goes into making them happen. This week, I experienced two poignant examples. The first was participating in the algebra planning session with you and Diane. I continually marvel at the detail of your discussions and thoughts on how to make the concepts clear to students. You not only plan the activities, toolbox and examples but also you take time to discuss how you will develop the conversation. It makes me realize how many things I use in explanations without ever considering how to make them more clear. The second example was my ATB on Thursday where I had carefully chosen an example but had not clearly thought about how I wanted the conversation to proceed. After spending more time than I wanted, I felt I had not given students the clear big picture I was looking for. When I reflected I realized that my opening question should have been more direct. We have one point, what other information do we need to draw a line? (the big picture) After students offered that we needed another point or a slope, I wish that I would have quickly demonstrated one method of getting a line and then asked students for other methods. In this way, the big picture would have been clear and I could have clarified for students the method. I also needed to have them copy the example in their ATB. Instead my "conversation" did not achieve clarity. I feel fortunate that you spend so much time helping me reflect on the importance of mathematical conversations. As we built in time for our students to THINK about the six intersecting lines, I realized that in my previous lesson plans I rarely thought about THINKING time. By returning to the same concept several days in a row and extending the questions and bringing clarity to the conversation I have seen several students start to use their reasoning powers. This type of engagement is so much more difficult to create than I imagined.
 * End of TERM: October 29**

I have really been impressed with how well groups work in our classroom. The key seems to be the overall classroom discipline. I have come to realize that sometimes unlikely pairs of students can be very productive. When I used groups this week to have students review and teach other how to graph lines on a coordinate plane, I was very pleased. I saw students opening their books, talking with each other, comparing graphs and answering each others questions. Making the groups accountable for a finished product is another key. I really liked when we had students report their group answer on the board. This accountability seems important to real engagement in group work.

__Organization is a fundamental part of teaching. As I have been trying to keep better records of our daily classroom, I have been impressed with the importance of organizing not only routines but the planning process. I need to develop a system to keep track of good problems in the book, worksheets and possible enrichment activities for students who quickly master the concepts. I also think that collecting good review sheets to use for homework supplements might be a good idea. I realized that in my planning I need to devise a better note taking method for my ideas. It has helped for me to keep a more detailed daily log of what happens in class but I my idea sheets are not as organized. Emma also talked with me about behavior logs. I would love to talk more about these and try monitoring students in the classroom with this technique.__
 * November 5**

__As we were working on parallel lines and transversals in geometry, I realized that I hadn't give as much thought to how we would practice the vocabulary and use the theorems as I had to discovering the idea. As I looked at the materials, I have been looking at I realized that I love the discover a concept or build a relationship aspect and think quite deeply about these but I have not given much thought to what type of problems would build student proficiency with the concepts. I am impressed with how carefully you plan review problems in algebra so that they include specific challenges.__

__The unit in algebra for solving equations has been so interesting to me. The idea of teaching students to chain so they have a plan for solving complicated expressions is revolutionary. It makes me rethink what methods I would have used had I not been exposed to this unit. The unit planning sheet is wonderful. I love seeing where we are headed and having copies of the homework. It makes me appreciate how much better teaching becomes when you can use the experience of others, take the time to reflect and make notes for next time.__

__Nov. 14__ __Hi Marcie,__ __I apologize that I haven't responded in the Wiki for a few weeks. The end of the quarter is so intense for me, emotionally and professionally.__ __I notice that you repeatedly mention the issue of allowing time for students to think and work. You say that you are anxious to pack info deep and that this is different than building a foundation and giving students time to contemplate the implications. I agree that these are different approaches to teaching. When people ask me for tips about how to get kids to engage in solving problems without "spoon-feeding," it is often (but not always) this difference in philosophy that presents the obstacles. What is important is to ask yourself what you believe teaching and learning is all about. I don't believe that all topics require the same approach. At times, like in Algebra for the past two weeks, teaching and learning involves a lot of direct instruction of specific procedures, which I hope you notice still does //**not**// mean that you only lecture from examples and give practice. At other times, teaching and learning involves presenting thinking/problem-solving tasks and allowing kids to build their own knowledge. Ultimately, I believe that students learn when they build their own knowledge and that my job is not to tell them how to think and how to do things. Thinking is learning. Reproducing procedures from rote practice is training. This is ENTIRELY different than the approach of most textbooks and other mass-produced curricula. I hope you notice that both types of activities happen in my classroom. We do not construct every bit of knowledge, nor do we simply tell them how to do things and give them time to practice. You are actually quite good at both types. You naturally think of quite deep questions to present (I wish that I had a note-pad attached to my hip so I could record some of your questions! good thing many of them are on the ATB!) You are also getting more and more clear about how to show detailed procedures when needed. I think perhaps you (and I) could benefit from discussing what type of knowledge we really want at specific times and deciding which type of instruction is in order at these times.__ __More to come. . .__

__You mention classroom management a few times. I would love to hear more comparisons and contrasts about how your view of classroom management has changed. What was it before? What is it now? You say that groups work well in our class and that learning conversations take place due to the overall classroom management. I agree with this statement, and I would be interested to hear you put words to how this works. (I LOVE to read your descriptions and reflections partly because you can put to words many things that I can only think and feel inside myself. You are eloquent and detailed in your writing. Thank you.) You also describe your feelings about the differences in our styles, and this leads me to some questions I would like to ask you as a colleague. I have heard from many different teachers the idea that teachers can run their classes in their own ways and with their own styles and still have the same student success. What works for one teacher may not work for another, and vice versa, but students still learn in each case. //**What do you think about this? Do you think that teachers can have vastly different expectations for behavior and still have students engage in problem-solving and learning conversations effectively? Are there some fundamental behavior expectations that support student engagement and learning? How do teachers with such different skill-sets and personalities create learning environments in their classes? How much of this has to do with one's own style/personality and how much has to do with certain principles that might lead to particular student outcomes?**// This is one aspect of teaching that I find extremely interesting. I have deep convictions about classroom management, though I don't consider my views static in any way. I think my own answers to these questions change yearly, if not more often. Classroom management has the potential to "make or brake" a teacher, let alone the lesson. I myself have had to drastically change my own style of communicating and many personality traits in order to remain in the classroom. I am deeply grateful for the experience as I truly believe I have only become more of myself. But, it was a very difficult road for me, and I'm still on it. Due to my own experience, I tend to believe that we don't, as teachers, have the luxury of blaming our students for not engaging in our lessons, nor do we have the luxury of believing that we don't have to master certain classroom management skills because they are not our style. Students' lives are at stake here, as well as our own development. I know I'm serious about it, but oh well, I'm serious about it. I believe that the way we treat our students and allow them to treat us and each other can make the world better or worse. I believe that we have the opportunity to help human beings feel their own potential and define themselves through math by creating a classroom environment in which taking risks is not only 'safe' but crucial. I also believe we are doing students a disservice if we make excuses for their disengagement or refuse to hold them to a standard of behavior that does not allow their own genius to shine through. And, I want people to treat each other well, so I begin in my classroom. Last year, I had a student who was, for our school, one of the toughest (not Q...). He was sly in his defiance, sometimes rude to other students for the sake of personal entertainment, quiet and disengaged in class and subtly disobeyed teacher directions. At some point in the year he had a few days in a row of displaying some of these behaviors in my class. I had all I could take and called him to my desk while the other kids were working. I told him exactly what he was doing and told him that I didn't deserve it and asked him how he felt about this. He told me that I didn't deserve it. Honestly, I expected him to play the silent game with me and expected to get into one of those pointless conversations teachers often find themselves in where they say a whole bunch of crap to a silent student who just waits it out and gets off without doing any work, but I had had it, so I started it anyway. When he told me that I didn't deserve it, I asked him why. He said I am a good teacher. I remember I actually laughed and asked him why. He told me that I am helpful and nice and that I teach them to treat each other well. These were more words than I had heard the kid speak up to that point in a year and a half! I floated on cloud 9 for weeks because he said that I teach them to treat each other well. I wanted to be more helpful than ever because he said I was. I still get emotional thinking about him and this experience. I believe this conversation was possible because of my day-to-day classroom management.__

__More to come. . .__

__DECEMBER 2, 2010__

__Apparently I wrote my response last week and then left it up on my computer without either saving it or pasting it to the wikispace. I will try to reconstruct my answers to your questions about classroom management. I, like you, feel that classroom management is essential to both student learning and creating a respectful environment. I also agree with you that certain teacher expectations are vital in every classroom: respect being the most vital element. I have really appreciated watching you model how to create a respectful classroom. It has been difficult for me to clearly identify how you seem to work this magic but I will try to articulate my observations here. Whenever I talk with someone about my experiences the first thing I express is my amazement at how I have never heard a negative word from either you or our students. By this I mean in our classroom there is an implied unspoken rule that negative comments about each other are simply not tolerated. Several weeks ago a student started to make a comment with a slight negative tone and your "withitness" allowed you to intervene with just a few words in a very serious tone, something like…we only speak respectfully. The situation was completely dissipated before it even began. How do you manage to create this business-like, respectful environment? I have asked myself this question many times and feel like I have gleaned the following essential elements:__ __Now back to your original question. I believe that the four areas I outlined are essential to good classroom management but I think they could look different in different classrooms. In some classrooms teachers have used differentiated instruction that allows students to multitask, do alternative tasks or opt out of some activities. This does not happen in our classroom but is an illustration of a significant difference. Some teachers may use humor in their I statements or provide pencils and extra books. The key is not so much in how they accomplish it but that you can recognize in their classroom that students have become active learners and respect the needs of their classmates and teachers.__ __PS I am loving our planning discussions. It makes me realize how helpful it is to collaborate with a colleague who is teaching the same subject. As we talk about our ideas it helps me clarify the" big picture" learning goals and significantly changes the way I teach. Thanks so much for being willing to listen to and help me develop my ideas.__
 * Students are actively engaged at all times**__. You have set a high standard for this and made sure that it is kept. At first I was amazed that you would stop a discussion to have students return your gaze but I have seen clear results. Students who probably have never taken notes in any other class write down what you ask them to do. Students who forget their homework take out a piece of paper. Students who totally disengage still keep the standard of eyes forward. Your planning includes a student engagement component. What do I want them to DO during this conversation? Your use of student responses makes sure that all students know they WILL be called on and that regardless of their state of understanding they will be expected to contribute to a learning conversation. I love how you remember and use student's names and ideas in your teaching conversations. You respectfully expect them to be active learners.__
 * You intervene quickly and don't let problems escalate**__. Many times I am impressed that you notice disruptive student behavior at a very low level and take action. Your action consists of expressing your expectations for the student, finding a private moment to conference with a student, waiting for students to resolve the problem and consistent follow-up. Two examples come to mind: the first was with several students who are always off task with their "stuff". In the first months of class you spent time waiting, expecting and making sure that they didn't use their "stuff" at inappropriate times. This may seem like a small example but it now means that many students who simply never engaged because of their ability to be distracted, find themselves with a clear desk, eyes forward, pencil in hand taking notes and at the very least listening to the classroom instruction. The second is how you called out student names at the end of class to remain to talk with you. It was completely unobvious to me what you were going to talk about. You indicated to the student not only that you noticed their small disruptive behavior but that you expected them to change the behavior. Your expectations make it so that you rarely need to attach negative consequences. You use respect as the key. Respect for the student as an active learner and respect for you as an effective teacher.__
 * You use "I" comments.** __Your use of "I" comments has been a great revelation to me about how to express myself respectfully: I need you to be quiet to that I can hear Cami's response. I get distracted when you do…..and can't teach as effectively. I don't want you to get confused so I need your attention. I need to see your eyes so I can tell you are listening. I will continue when I can see everyone is ready. I need you to ……so that I can teach effectively. I appreciate your willingness to share your conjectures before you know if they are correct. I want to hear all your comments so I need to hear them one at a time. I will think about your comment and get back to you later. I am confused can you try explaining it to me differently. I am not understanding your question, I think you are saying? If I understand, you are suggesting….., etc. When I analyze the tone of your classroom, I can recognize that using these kinds of "I" phrases helps maintain a very business-like environment where the importance of being a good teacher and an effective learner are stressed.__
 * You expect students to take responsibility for their actions.** __The first few weeks seemed filled with students forgetting books, assignments and pencils. They asked many duplicative questions because they did not really listen to the instructions. My initial reaction would have been to supply them with an extra book, pencil or paper and to repeat the instructions. You however realized that to eliminate this type of behavior from our classroom environment students needed to be expected to solve their own problems. At first, "So what are you going to do to solve the problem?" or "I've given that instruction?" seemed harsh but I was surprised how many students who struggled to come up with a solution soon found ways. I really like how you wait for them to suggest a solution without supplying the "obvious" answers that sometimes they never supply. Your response "that won't work because that would disrupt the class or you won't be able to learn with that solution" is followed with "think of something else." The key seems to be that you don't supply the students with an answer but they understand that you expect them to solve the problem. I love the way you expect them to read the instructions and begin working on the homework without explanation. You then take questions rather than telling them the obvious. Students clearly understand that you believe they can succeed.__

=__**January*******__**_**=


 * January 8, 2011**
 * Vivian, Thanks so much for taking the time to explore the long-term planning process with me. I found it extremely useful to review the core together as we calendared the flow of our geometry course for the second half of the year. I really appreciate the collaborative way in which we exchanged our thoughts and ideas about which parts to emphasize. I liked the way that even in our long term planning process, you are so good about articulating the big pictures in the process. Taking the time to identify our common objectives was very helpful to me.**


 * January 14, 2014**
 * Wow, I have so many reflections. Vivian, it is such a joy to team teach with you. I love the give and take in our conversations and how you push me to articulate my ideas in a definitive way. I love being able to reflect on both the students and our teaching after each lesson. Yesterday, as I reflected on my solo teaching experiences I realized how energizing it is to share with a colleague your reflections and how important it is to build in reflection time into your daily schedule.**


 * I watched Mr. Smith's open-ended assessment in Physics and was impressed with how responsible the students were in meeting the stated objectives. I wondered if students could devise a way to show they understood mathematical concepts in a similar way. How do you think our students would respond to writing their own problem and proof using CPCTC? I wonder how they would choose test questions to illustrate what they have learned about congruency? It was also informative to see several of our geometry students in a different environment. I gained insights into more of their skills and personality by seeing them in a different setting.**


 * In Geometry, I reflected on what a cooperative environment you have created. I feel like when I solo in class I benefit greatly from the climate of respect you have instilled into your classrooms. I notice that although I can easily maintain the climate, I still feel unsure how to establish it in the first place and how to build upon it. My natural tendency to talk more informally with students is an area in which I need to evaluate how it furthers my teaching objectives. I find it difficult not to feel frustration when students do not seem to discover what I want them to see. I love tasks that allow me to individually work with student groups. Our experience in the computer lab was great because it afforded me the opportunity to probe student understanding. In the end, I was undecided how to modify the lab I wrote. For some it seemed overwhelming to record so much data but it certainly forced students to look carefully at the geometric structure they had build. I think only 4 of 45 students completed the assigned task but by talking with groups everyone made conjectures. The best consequence of the lab was seeing students struggle with what the slope meant when the figure seemed removed from the coordinate plane. This was an unexpected result that made me realize how important it is to use concepts in diverse settings. In addition, it became painfully obvious that the second class received a much better experience because I had more insight into how to teach, they are smaller in number and they respond with more energy to challenges.**


 * In Algebra, I had several insights. The first was how important it is to be prepared for misunderstanding. I used a today's homework problem as the ATB and was surprised to find out that some students really didn't have any ideas about multiplying improper fractions with whole numbers. I found myself delivering several mini-lessons I was unprepared for: how to know if the X was a variable or meant you should multiply, why you couldn't use the terminator on this type of problem and how to break the problem into two simpler problems to solve. After the mini-lessons students felt confident and easily completed the homework but it made me realize that you should be prepared. I looked over the passports and tried a "find the mistake" activity, prior to giving back their passports. It worked great and I think really helped motivate students to find their errors. This is the class that really challenged my thoughts on how to maintain a professional environment. Several students seemed off task for most of the coversheet time and I had to continually respond to their behavior. Proximity worked well but I had to resist the desire to move seats, etc and really struggled to understand how you do it.**


 * January 21, 2010**
 * Vivian,**
 * Wow, you are incredible. I can't believe how much I gain from watching you explain things to kids. Your skills are impressive. You have created such a safe learning environment. No one ever feels stupid, you value each person's contribution, students feel free to communicate their ideas and explain their thought process. It seems like the 90 minutes fly….even when I am observing!**


 * I have been thinking a lot about "Understanding by Design". It has helped me so much when I peruse the entire chapter and identify the big picture. Thanks for the great suggestion. I observed another classroom last year in which the teacher actually created and gave the students a list of the ideas and skills they would learn in each unit. As they mastered the skill, he would have them check it off. In addition he had them prepare a "poster presentation", really just a regular piece of paper that displayed all the new information they had learned as part of the "test". The amazing thing was that when I quizzed the kids about these procedures, they loved it. They told me, "we learn so much stuff in this class." It was a tangible way to help students see their progress and know what parts of the curriculum they would be held accountable for. I would really like to try something like that with our next unit. Mostly I am thinking that having this kind of list for myself would help clarify my teaching. I hope that it would also help build students' confidence in their own acquisition of new skills. The class I observed was algebra, so I am not even sure if this technique would work in geometry but I think I will contact the teacher and get the particulars of his method and try creating a working skill, big idea list for one of upcoming units.**


 * I have also been thinking about how to get our students to practice their skills more. It seems that about 1/3 of our students are proficient and can handle the homework but the other 2/3s seem to quit easily. Our best practice times seem to be when we have group passing assignments. On last night's homework 13students really put in 30 minutes of effort, 5 more turned it in. Which means that about 12 students didn't engage in "practice." Sometimes I worry about not enough practice and sometimes I worry about "wrong" practice. I am trying to think about what I would like to do my action research project on. I know I want it to be on homework but I am unsure what measures I think would improve it. Diversification, feedback, late policy, accountability and classroom practice time are all variables I am thinking about. What areas do you think will make the most difference?**


 * January 25, 2011**


 * Hi Marcie,**


 * I love working with you, also. I feel as though we are partners, both contributing to the success of our students. I always feel better when I get to work with and plan with other people, and I feel like your contributions and insights are invaluable. For example, I had no idea how engaging and clarifying it would be for our students to delve into indirect proofs. But, your clear presentation of "how it works" and thorough survey of situations applicable to indirect proofs, coupled with your belief in our students' abilities to work together and learn from each other created a powerful lesson, both for me and for them. I loved having conversations with students like C and D and F who have been communicating with me this way all year, without my understanding, and finally "getting them." I feel that we both bring "equal amounts" to the table (though I am uneasy stating a comparison, it is the thought that I have).**


 * I love the idea of sharing with the students some sort of graphic organizer about the skills they will learn with each unit. Hopefully you have understood from "Understanding by Design" that skills are not the only outcome we hope for our students, but that they are part of the "Important to Know and Do" category. I agree that we could help students see, tangibly, what they have learned how to do and master. Theoretically, the Passport is a vehicle for helping kids to see this, as well, but the list you showed me was more detailed and specific than what they perceive in a Passport. In a way, they can visually "count up" the skills they have acquired and take satisfaction in what they have accomplished. I cannot think of anything more important for us to help them to understand than how much they know, how much they can do and how satisfying it is to feel such authentic accomplishment. I truly believe that even the "Big Ideas" of math are less important than facilitating student understanding of themselves and confidence in what they can do. Let's try it!!!!!!!!**


 * I'm excited to design an action research project around Homework and Practice. This is the age-old question/dilema of the teaching profession. Eric and I had an interesting conversation about the differences in what we face about HW and what he faces about HW. We definitely need to talk about what we are facing. I am excited to do an action research project together; to design the project, clarify the desired outcomes and decide what measures we can make to improve/document these outcomes. I have to say that your life-experience is, again, invaluable to me in this regard. I simply do not have enough information about the "home" end of my practices to really understand what to do and how to do it well for my students.**


 * I believe that when I retire and look back on my life as a teacher, this year working with you will clearly emerge as a pivotal point in my career. I imagine a "flow chart" of possible paths that I could take as a teacher, and I am very happy to have the opportunity to take a path that working with you presents: a path toward understanding families and looking honestly at how my practices impact students' confidence and sense of accomplishment.**

__FEBRUARY__
 * Our time together is flying. I am learning so much from you. You have opened my eyes to so many different faucets of excellent teaching. Thank you so much for spending your valuable time sharing your expertise and insights with me. I am continually amazed by your ability to communicate with students. Your "conversation" style of teaching is empowering both to our students and to me. I learn so much by the way you listen to students and talk with them instead of at them. I am beginning to develop a better understanding of how students think and how to develop their thoughts into real mathematical understanding.**


 * Per our conversation, I am attaching my original action-research plan with our discussion notes presented afterward:**
 * __Plan of Action and Data Analysis Strategy__ **


 * __Inquiry__: Will offering differentiated homework have a positive effect on both homework completion rates and on students' confidence and interest in mathematics?**


 * __Questions I have considered:__**
 * 1. Should homework be the yardstick of what we expect students to know?**
 * 2. What is the primary purpose of homework: practice, check for understanding, processing time, per-learning and/or inquiry?**
 * 3. How can homework be differentiated?**
 * 4. Can differentiating tasks be used to increase student motivation to do homework?**
 * These questions have served to broaden the scope of my thinking but for the purpose of my action research, I would like to evaluate if providing differentiated homework will increase homework completion rates and/or increase student's mathematical confidence or interest.**
 * __Plan of Action:__**
 * I plan to create a two week unit that had differentiated homework for each day. This differentiation would be a choice presented to students. The stated homework policy will remain unchanged. Students however will be given an option of two choices at the end of every day for homework: a practice assignment or an enrichment assignment. The practice assignment would only contain skills previously developed in class while the enrichment assignment would require students to use the required skills to probe deeper. The geometry text book, offers two such assignments in the supplementary material already. In our algebra class, assignments will need to be completely teacher generated as all assignments are currently teacher generated and we do not use a textbook.**


 * __Data Collection:__**
 * Prior to implementation of this two week unit, I will calculate the previous month's homework completion rate for each student to be used as a baseline. I will then collect homework completion rates for the two week unit and compare it to the baseline average for each student. I believe that student's who don't turn in homework may be struggling and differentiated homework may help them target which problems to focus on first and hopefully increase their completion rates. In addition I would evaluate data on the top students to see if they choose to do more difficult problems--this choice of difficulty would be important to know as their completion rate is already almost 100%. if they choose more difficult problems then I would count that as an increase in homework.**


 * I propose utilizing a student survey that will try to assess student motivation. The student survey will ask questions about homework habits and feeling. (See a draft student survey below). This survey will be given prior to the two week differentiated homework unit and upon completion of the two weeks. In addition, I will solicit student reflection on the practice and collect their comments as feedback. Personally, I am hoping to see a change in questions 5, 7. 8, 12, 13 and 14.**
 * Another important part of my data collection on using differentiated homework will be collecting descriptive narratives of our (myself and Ms. Shell's) observations in the classroom . We will attempt to keep a running log of our impressions of both our ability to provide differentiated homework and our assessment of its usefulness to student motivation on a daily basis.**

//Per our discussion on Monday we made the following changes and improvements to the proposed plan.//**

We discussed in detail homework tracking to facilitate student choice of activities. We decided to create a student homework tracking sheet and have students write down both assignments. We identified six categories of homework purposes and divided them into two groups (practice, check for understanding, processing time versus extension, exploration and inquiry) We committed to creating an assignment in each group for each day and to describing to our students the purpose of each assignment so they could make a choice. We then looked at our specific curriculum objectives for the next week and identified how to differentiate the homework. By starting our day's lesson knowing what we what to be a practice concept helps me clarify how to pace the day's lesson.

We talked about the need to identify specific students for further differentiation of tasks. We reviewed and edited the student survey to eliminate the middle choice. (Interestingly enough, one of the students in their comments on the surveys indicated we needed a middle choice.....you were right we had to make them choose.)

Our discussions about algebra where very interesting. Our current graphing unit is not conducive to differentiated homework as the carefully crafted homework assignments form the basis of the next day's lessons and are already complex in nature by design. The skills being taught are new everyday and require processing time and a check for understanding. However, we identified that much of our in class time is spent helping students understand their homework and that some students could be better utilizing their time with differentiated tasks within the class. We identified that the skills we are teaching are well designed and accessible to all our students but require more support time in class for some students. Our discussions led us to conclude that a different approach to differentiation should be utilized in algebra. If we gave some students differentiated tasks in class that challenged them, they would not have time to finish their homework in class and would therefore have an increase in homework. These differentiated tasks would also hopefully increase their motivation. We decided that we needed to further refine our ideas and perhaps produce some independent materials for students to do extension, exploration and inquiry with during class review times. We began a trial of this approach by offering selective students calculator challenges which incorporated drawing tilted squares with equations of lines.

We decided we should design a student survey to find out what students think about having differentiated tasks to try in class. Our idea of individual cards or project sheets that students can check out and then provide a possible solution really appeals to me. I can visualize offering different topics such as...code cracking, calculator graphing, data interpretation, probability, creating story problems, etc. For the purposes of our research project, it would be interesting to see if more "work" gets done. Do students accomplish the enrichment tasks and do homework rates change? Can we get students to see the extra work as a bonus? I am excited to try.

__**Note on Reflections:**__ Vivian and I spent hours discussing educational issues so the use of this communication method seemed inappropriate as our relationship developed. Perhaps, the value of this board could be increased in the second half of the year by posting a discussion board about a particular issue on which we could all submit our ideas: For example, how to reach the failing student, the most effective group lesson we had taught, great ways to review homework....... That way our reflections could be focused on an issue and give insight to all users. These could be a required weekly submission for our cohort class.

__**Final Reflection:**__ Co-teaching with a mentor for an entire year has been a fabulous learning experience for me. In many ways the co-teaching experience provides so much more learning than a traditional student teacher experience. Vivian has been a fantastic mentor and has modeled and reflected with me on so many valuable teaching practices: creating a learning environment, encouraging students to take academic risks, providing scaffolding for diverse learners, using questions effectively, listening to identify learning gaps, building respect and maintaining high expectations. Within the context of this past academic year, my perspective on effective teaching has continued to be enhanced. My understanding of the nuances of teaching has deepened and my desire to be an effective teacher has increased. I feel empowered to begin my teaching career with Vivian's years of experience supporting my endeavors. Meeting as a cohort has increased my understanding of the need for and value of a learning community. I have been provided with countless colleagues whom I can call upon to discuss educational issues. Our shared experiences have strengthened my ability to feel confident about building new learning communities and working with other teachers. My experience at the National Convention gave me a larger sense of community and the results of other teachers' experiences inspired me. I would like to thank everyone who has contributed to making this program a reality. You have made a difference.