End of Year Reflections

So this isn't going to be a complete reflection of the entire year, but just some thoughts I have going on now at the end of the year.

I have been feeling really comfortable in my abilities this last month. I have been stepping up more to deal with conflicts and take on responsibilities at school. That has been something I have been working on all year at school. If there was a fight at school I would let someone else handle the situation, or go ask for someone else's help. Lately I have been facilitating working through conflicts on my own, and often times they have been successful. Of course there is always space for growth, but all in all I have grown a lot and I am happy with that.

Over this year I have also started delving deeper into my own boundaries, needs and ego. I can recognize more readily when my ego is rearing it's ferocious head. I definitely felt that tonight at staff circle. I had expectations about circle because this was my last one and it felt important to me, but other people didn't have the same expectations, which I can't blame them for, but it left me feeling void. I opened up more than I usually do and talked honestly about my experience and where I was at, and of the few people that actually showed up for circle, no one had anything to say to me. Actually thinking back about the year the only positive feedback I have gotten is that it is nice I offer lots of classes and that the students seem to really like it. Part of that probably has to do with the fact that I don't open up to the teachers very often. But I feel like I can be an effective teacher and not lay myself wide open all the time. I just want to know that my work here meant something to someone. I feel that from the students, but I also am such a temporary figure in their lives. So anyways, I can identify this as my ego needing a little affirmation, but I still feel hurt. My hurt was deepened by the fact that some of the teachers told another intern who has been here for a month how wonderful she effortlessly seemed to fall into the flow of the school.

Blah.

"Consensus is the Answer Key: Empowerment in the Math Classroom"

While I was at the Creating Balance in an Unjust World/Radical Math conference, I attended a workshop entitled "Consensus is the Answer Key: Empowerment in the Math CLassroom". It was presented by Loula Tesfai, Jason Cushner, Drew Bupphaves, Sarah Bertucci, and Matt Needle from the Pine Ridge School in Williston, VT. Pine Ride School is a private boarding school for students with learning disabilities. Jason and Sarah are co-teachers at the school. Loula is a former student of theirs and the other two, Drew and Matt are current students. Jason and Sarah co-teach mathematics at the school. They have very small class sizes (under 10).

Their intended workshop goals were:

• For us all to consider the unwritten curriculum of our classes and schools, paarticularly around "math smarts".
• For us all to view, experience, and evaluate a math teaching method that is both challenging and empowering to students.
• For us all to leave with concrete next steps for creating an empowering unwritten curriculum in math.

They talked about what an "unwritten curriculum" is. It is what the students learn that isn't written in the lesson plan. The unwritten curriculum is created through culture, relationships and interactions. Instead of being a one-time lesson it is an all-the-time action. A major part of the unwritten curriculum in math is what they termed "Math Smarts". To get a grasp on what sort of unwritten curriculum we all consumed in math growing up we talked about what assumptions there are as to what it looks like to be smart in math. In our brainstorm we came up with the following description: fast, takes ability - not effort, good grades, getting the right answers quickly, born with natural talent, if you struggle than you're not smart, nerdy, don't have to have skills in writing, seen as not creative and that if you like math you must be smart. These ideas are part of what they termed the unwritten curriculum of "Math Smarts". Not very many teachers tell their students these ideas directly, but they are stereotypes that we learn through the all-the-time interactions of school relationships. However, they claimed that this standard view of Math Smarts simply isn't true. It doesn't match what professional mathematicians actually do:slow, laborious work on one problem, sometimes for many years. It is also an inaccurate view of how intelligence develops. Math smarts is viewed as a fixed intelligence, which you are either born with or not. Instead, these educators take a constructivist approach to intelligence that learning is malleable. Not only is this view untrue, but it is also disempowering. It is disempowering for those who start out behind the standards in their math class. This does not have to do with smartness; it has to do with exposure. But for many students the perception of themselves and their identity as bad at math sticks. It is also disempowering for those who start out labeled "smart". In the math world where there is a perception that there is only one right answer there is a strong fear of failure among students with "Math Smarts". Many cope with this by avoiding challenges.

In order to empower students in the math classroom a teacher must incorporate many parts:

• Relationships
• Instruction, Curriculum, and Assessment Practices
• Classroom decorations and physical set-up
• Consensus is the Answer Key

The presenters focused on "Consensus is the Answer Key" for this workshop. It is a classroom dynamic whereby students get feedback on solutions from classroom discussion and agreement, not from answers in the back of the book or from the teacher. These "expert" sources of informations are removed. Instead, students use their own logic, creativity, communication, and collaboration skills to solve problems. (Do you smell constructivism?...) To set up this sort of classroom culture students are given problems to solve. They work on the problems individually or collaboratively. Then students discuss their processes and solutions with classmates. Using logic, questioning, and explanation, students come to consensus on the correct answer.

Consensus in the math classroom comes with it's own set of challenges. For example, students who have spent the majority of their time in traditional, teacher-centered classrooms are not used to this new process. Jason and Sarah often found that students clung to the traditional textbook driven classroom, and they admitted because it was easier for them. Also, students coming from traditional classrooms are often coming from places that foster competition. Because of this, it is essential to create a safe classroom culture. Another challenge is that teaching in this way is counter-cultural for a teacher. Constructivism has begun to enter mainstream education and teacher education, but it is still not the way that many of us were taught. Creating a culture where student discovery is commonplace is not just about noninterference by the teacher. Teachers must create rigorous academic environments by asking LOTS of questions and not just stopping when they hear a "correct" answer.

Jason and Sarah found that structure is helpful in building this consensus mathematics classroom. They have a normal classroom routine which consists of students arriving, getting into groups and discussing their solutions to the previous night's homework. Teachers also spend time giving direct instruction on behavior and mindset: reminding students that mistakes help us learn (mindset) and teaching behaviors that create a safe environment, such as the role of the presenter and participants. Students learn the structure of discussing solutions: solutions are presented in logical steps. Questioners do their job respectfully and listen while information is being presented. There is no compromise of the safe environment! Also, the teachers structure in time for presenting unfinished work. They give only enough time so that no one reaches an answer and discuss it so that the students have space to examine process outside of the restraints of solutions. Jason and Sarah also recommend giving specific feedback to students, instead of "good job!". This helps students assess their strengths and weaknesses. Another structure they use is a standard approach to problem solving that they introduce at the beginning of the year. This is a series of questions, which lead students through the process of searching for solutions. This process includes rewriting the question, creating a problem statement, stating any equations given, guessing an original estimate, etc... As the year goes on, the teachers allow the students to adjust this process so that it works best for them.

They provided the following tips for implementing "Consensus is the Answer Key" so that it can be more liberating for students:

• Use direct instruction to teach the skills necessary for Consensus is the Answer Key.
• Because this structure goes against our dominant schooling culture, students will not adopt these habits by accident. It is important to directly teach procedures such as steps for presenting and discussing solutions. It's helpful to post a script or guidelines for what presenters and participants should do. Correct students language if they stray from these guidelines. One common example is that students often begin the school year using language like, "You're wrong." Instead, have them say, "I disagree." This leads much more naturally into an open discussion without defensiveness. You should also directly teach empowering beliefs about learning, such as mistakes being good, helpful things.

• Model the behavior and language that you expect of students.
• Direct instruction most be coupled with modeling. You are working to create an environment where it is good to make mistakes and question each other. Therefore, you must be open to students correcting you or giving you feedback. Always thank them for it, even when they don't phrase things well. Be open to getting authentic help from the students. For example, if you struggle with spelling, ask them to check your spelling. In addition, never put yourself down by saying things like, "I can't draw" or "I'm bad at spelling." We want to break the norm of students saying, "I'm bad at math," but we cannot ask that of them if we're modeling something else. Instead of putting yourself down, express that things are difficult but that you are confident you can grow: "I'm having trouble making a diagram that looks like a football field - can someone tell me what I need to do here?"
• Be uncompromising in creating a safe classroom environment
• In order for this process to work, students need to feel safe to take risks, say incorrect things, and make mistakes. Clearly set up expectations at the beginning of the school year around how to treat each other. Then, do not let any infractions pass, even when students say that they're just joking. We don't allow any put-downs in our classroom, even joking ones. We don't allow the jokes because we think that the butt of the joke is often more hurt by it than s/he claims. In addition, negative joking sets a tone in the rest of the class so that students who may not be involved in a particular joke will feel nervous about becoming the next butt of a joke and will therefore speak less and take fewer risks.
• Insist on rigor, not just hearing initial ideas
• Many classrooms that choose to emphasize student voice encounter a common pitfall. They often do a great job of having students express their ideas and thoughts, but stop at this point. Then, students are left with only their initial, unrefined ideas; they have not learned anything about determining the quality work and thought. When students share ideas, it is important for them to get feedback on those ideas and abandon or refine those which don't hold up to scrutiny. Some teachers feel uncomfortable with the thought of criticizing students' thoughts. Critical feedback is one of the greatest gifts that we give our students because it sends the message that we know they can grow. It's not ok for students to walk out of a math classroom believing that a square has three sides because the teacher just asked them to express what they think of a square. Of course, using Consensus is the Answer Key means that idea refinement occurs primarily within discussions among students. Therefore, this rigor is developed through the norm of questioning and proving answers as a class.
• Be deliberate about the feedback you give individuals
• Feedback is an essential part of learning and growth, but it is not a cultural norm to give feedback that is empowering to students. Too often, students receive most of their feedback from teachers in the form of praise or criticism which makes them dependent upon the teacher for affirmation. Empowering feedback helps students grow, not just feel good or bad about the teacher's opinion of them. Within the Consensus is the Answer Key model, students should ultimately get most of their feedback from sources other than the teacher. Other sources include fellow students, their own internal compass, logic and proof, and measuring their work and actions against clear goals or expectations. This process generally needs to be scaffolded and modeled.
• There are a number of specific ways to give feedback to individuals. Firstly, it is important to avoid feedback about students' abilities or attributes. These types of comments contribute to a fixed sense of intelligence and identity, which leaves students feeling without agency to control their achievement. Instead, give feedback that is about students' observable actions. To help students internalize their own evaluation skills, provide observations of student actions and then ask students to interpret their value or meaning. The last step of this scaffolded process is to ask students to both make the observations and the interpretations themselves.
• Sometimes students solicit your affirmation through specific questions. It's always a balancing act to determine whether it's a case of them needing your expert opinion or whether it's a case of them wanting teacher affirmation (or a shortcut to knowing if they're right.) If a student asks you, "Is this right?" or "Is this good?" never respond with a yes or no. You can ask them if they've checked it with their classmates, ask them to explain what they did and why, or let them know that you don't answer that question. Sometimes students seem to need information from you in order to calibrate themselves to understanding what quality work looks like. In this case, then give very specific feedback or move students to the more internalized levels of feedback described in the previous paragraph.
• When facilitating discussions, do not use students' names attached to their solutions
• Oftentimes, two students will write different solutions to a problem on the board. If you are facilitating the class discussions to determine which (if either) is correct, do not call them "Susie's solution" and "Junior's solution." Calling them by individual's names takes away from the group process and also makes students invested in "their" answer rather than in finding the correct answer. In addition, throughout the discussion, numerous other students should be free to come to the board and edit what is written, so Susie's solution could become Susie's, Juan's and Mirabel's solution. The goal is to come to consensus about what answer makes sense and why, not to figure out who got the right solution. Instead of using students' names for solutions, label them A and B or give them a meaningful name such as "addition method" and "area method.
• Assign super-challenging problems or give students short work time before discussion
• Students have generally been taught that math is primarily about getting the right answer. This is a challenge to Consensus is the Answer Key because students often want to skip the process and get straight to the answer. By assigning problems that are too challenging for anyone to solve on their own, and/or by discussing those problems before anyone has a final solution, you give students practice in discussing the process. In addition, this creates a classroom norm that students can present unfinished work, work that they think may be incorrect, and questions that they have. These discussions tend to have much richer dialogue than discussions when someone just presents a clear correct process and solution.
• Assigning super challenging problems also helps address a common class dynamic in which students label each other as smart or not and begin to place one of the "smart" students in the expert role which the teacher has vacated. If problems are too simple and have only one right answer, there may be a student in your class who quickly and reliably solves problems, and students will begin using that student as their answer key rather than engaging in rich dialogue. Big, challenging problems are beneficial for the student who has been labeled "smart," too. this frees that students from having to defend a fixed identity of being smart and allows her to engage in the kind of challenging work that will actually develop her intelligence.
• Question all answers
• Whenever a student gives an answer, ask how s/he got it. Many teachers are in the habit of asking students how they got incorrect answers but do not ask questions about correct answers. Questioning only wrong answers is a problem for a few reasons. First, students are usually in the habit of looking to the teacher for affirmation. If the teacher has a pattern of questioning wrong, but not right, answers, students will be able to use this information as clearly as if the teacher said something was right or wrong. Secondly, it is very important for students to explain how they got correct answers. Sometimes they get correct answers through lucky guesses and they haven't actually learned the material. Also, the process of explaining how they got an answer helps students to understand the material in more depth, remember it better, and develop clear communication skills.
• Use appropriate wait time
• Do not rush to fill a void of silence. Students need time to think. In addition, students may be nervous about speaking and want the teacher to speak instead. If it's clear that the teacher will not fill the silence and will really wait for an answer, then student will generally speak up.
• Students should be up at the board and the teacher should be at the back of the room as much as possible during whole-class discussion.
• Physical spacing in a classroom is an essential part of the room's culture. At the most advanced level of Consensus is the Answer Key, the teacher is practically non-existent. Students should be in the front of the room, presenting their work. They should feel free to go up to the board to explain their ideas without asking the teacher's permission, especially mid-discussion. From the back of the room, the teacher is free to observe all the students in the class. In addition, students often seek out the teacher as their primary audience when presenting at the board. When the teacher is far away, the students are pushed to direct their presentation to other students. At times, the teacher can emphasize this by even stepping out of the room momentarily or looking down at papers instead of directly at the presenter.
• Be prepared for anger, opposition, and frustration
• When Consensus is the Answer Key is introduced to a new class or school, there is a very predictable period of student being frustrated and angry. Obviously, there are steps you can take to minimize this, such as the direct instruction of the process and an explanation of why you use it. Still, this is a new, uncomfortable process for most students. They are not used to this much responsibility and independence of thought. They will consciously and subconsciously pull out all the stops to try to get you to give them hints, leak an answer, or even abandon the whole enterprise. Often, students are very scared that they will not be able to do well in this unfamiliar format. If you stand firm with not giving answers while providing necessary support, there will be huge breakthroughs that speak for themselves. De-brief that process to point out the initial frustration and the huge sense of accomplishment at the end.
• You may receive opposition from other parties besides students, such as parents and administrators. Be ready with a clear rationale of why you are using these practices and what the benefits are. Accumulate good supportive documents (such as the NCTM math standards which emphasize problem-solving and communication skills or the research of Carol Dweck and Alfie Kohn).
• Give students information that is not discoverable through investigation
• Consensus in the classroom is NOT the answer key for mathematical conventions and definitions. The teacher must furnish this information. For example, students are able to discover that the opposite over hypotenuse ratio is the same for all right triangles, but they cannot discover that this is called "cosine". It is important that students leave our classrooms with the ability to communicate their learning and understanding to the rest fo the world - this means knowing agreed upon language and conventions.
  

"Justice Not Just Tests"

The first night of the conference, Creating Balance in an Unjust World, was dedicated to discussing authentic alternatives to standardized testing. The event was titled "Justice Not Just Tests" and was hosted by Vanguard High School, New York, NY. The very first speakers were from Urban Word Poets, an after-school poetry program for inner-city youth. Two students performed poems as a kick-off for the evening.

Then the Executive Director of the National Center for Fair and Open Testing (FairTest), Monty Neil, spoke as the feature speaker of the evening. The organization he works for is working to overhaul federal education law (especially the No Child Left Behind Act). Neill said that standardized testing should have a very small role in schools, but that it is taking them over. He said the controversy over standardized testing is both a pedagogical and political issue. It is pedagogical because we are trying to find out how best to teach and assess our students, and it is political because state and national laws are involved and the government wants to hold schools accountable for teaching students. Neill is part of the Performance Testing Consortium which advocates for formative projects in which students review, edit, and share their work, instead of taking one test and then the process being over. He says that performance based assessment supports learning for understanding and is also more instructive for teachers in knowing where their students are at.

The next part of the evening we attended youth-led workshops on mathematics performance based assessments. The presenting schools were the Greater Lawndale/Little Village School for Social Justice, from Chicago, Illinois, the East Side Community High School, from New York, New York, El Puente Academy for Peace and Justice from Brooklyn, New York, the John Muir Middle School from Los Angeles, California, SAT Bronx from Bronx, New York, the Urban Promise Academy from Oakland, California and our hosts, Vanguard High School. We were able to attend three sessions, each one lasting a half hour.

My first session was presented by two students from Vanguard High School. Vanguard is a public high school which is part of New York's "Empowerment Zone", which allows schools to write their own assessments. Vanguard High School chose to make their assessments portfolio based. In doing research the school found that some of their students performed higher on the Regents exams, but lower on performance based testing, indicating that they were good at memorizing, but had low understanding and/or communication skills. By using performance based assessments at Vanguard, teachers felt that they were able to learn which teaching strategies were most effective and they were able to see wholes in student learning. Students said that they became able to explain the concepts they had learned to people they didn't know, and who had little exposure to the concept they were presenting. They said that it raised their confidence. They felt that doing portfolio work was much more difficult than any other assessments, but that they preferred it. Vanguard High School has three components to their performance based assessments. The first component is in written format. The written component begins with a cover letter which tells the reader more about the student and where they are coming from. Other elements of the written component include the steps the student took to come to their understandings and what their understandings are. Then the students must communicate their understanding visually through a PowerPoint, poster or some other medium which visually represents a problem or idea they were working through. Finally the students must present their project orally in a presentation, which is given to five evaluators. The evaluators include one teacher in the subject area of the project, one non-subject area teacher, one non-school professional in the subject area and two students. The students must communicate their understanding effectively to the people present, who in turn evaluate them. Evidence of their project is submitted to their portfolio. In order to prepare for their individual evaluations, students participate in round-table evaluations throughout the year. In round table evaluations four students are working together to problem solve and are evaluated on the skills in solving the problem as well as their team work abilities.

Next I saw a presentation from a teacher and a student from El Puente Academy. El Puente is a social justice based high school. There are 160 students and 23 staff in the school. Each year the entire school focuses on a theme, which is integrated throughout all subject areas. This year the theme was coming of age. Issues which could be included in this is youth empowerment, the right to vote, military recruitment, teen pregnancy, etc. As you can see the themes can be understood broadly, but the connections between the individual issues are studied and linked through the overall theme. The students perform project-based assessments which are completed over a semester and then at the end of the semester the students are required to present it to a committee of staff and students who evaluate their project. This particular presentation showed how this social justice-themed project-based assessment was applied within a math classroom. In math class students use statistics to examine social justice issues. The students choose a population and topic, which must be an issue that concerns that population directly, as well as corresponding with the theme for that year at El Puente. Then they write a survey and design a method for distributing the surveys (i. e. sampling methods). The survey must be administered to a minimum of 150 participants. Then they perform a data analysis including frequency tables and graphs. They write key findings (generalizations/statistics that can be drawn from the analysis). Then they write a report based on their findings, which includes four major sections: Introduction, Methodology, Results and Analysis, and Conclusion and Recommendations. The students learn how to and are required to incorporate the following elements of data analysis:

• Use of rates and averages
• Standard deviation
• Five-number summaries and box plots
• Correlation
• Interpretation and Extrapolation
• Margin of Error
• Various types of graphs to strategically illustrate the information from the frequency tables.

All of these procedures are covered in class through individual and group work, so when the time comes to apply it they have a firm grasp of the concepts. The students have to consider bias within their study, including their own bias and the limits of their study. The students must create visual representations of their findings as well as a written summary of their findings including knowledge gained and recommendations based on their findings. And, as mentioned above, then they must present it to a committee.

The next school that I saw present was the John Muir Middle School. A teacher and two of her 6th grade students came to present on performance based assessment. In this teacher's math class, her students studied surveys, sampling methods, bias and statistics. The class began with students reading about other surveys and using the data from those surveys to learn to convert raw data to percents, decimals and fractions. For the survey project the students were required to choose a topic that affects them in their community. They designed their survey questions and structure and then went out into the community to gather their information. Then they took the raw data and used statistics to evaluate them. Then they had to write up a summary of their process. They had to explain why this topic was important to them, what sampling methods they used and what their results were. Then they had to present their results visually using graphing techniques. And finally they had to present their project orally to the class. The students had to make sure to say whether their sampling methods were biased or representative. The students said that most of the students in the class chose a "convenience"/biased sample, i.e. surveying their friends and families. The two students did such a wonderful job communicating their results and the process to the participants. The teacher spent only the first five minutes talking and the rest of the 25 minutes the students led the presentation and fielded questions effortlessly. It was really inspiring to see a middle school class that uses performance based assessment, because all of the other groups were in high school.

The evening was very exciting and intriguing. The best part was seeing the students present their own work. It truly was evident how comfortable they felt in their understanding of the subject and the process, even in front of a room full of math teachers. Performance based assessment is definitely something I will include in the classroom.

My Visit to the Earth School

Today I visited the Earth School. The Earth School was founded in 1992. It is located in Manhattan's East Village. The dream of the Earth School is "to create a peaceful, nurturing place to stimulate learning in all realms of child development–intellectual, social, emotional and physical" (from http://www.theearthschool.org). The Earth School incorporates "hands-on exploration and interaction, an arts-rich curriculum, responsible stewardship of the earth’s resources, harmonious resolution of conflicts, and parent-teacher partnership". They strive to use curriculum which is active, playful, socially-conscious, and rigorous.

The focus of my visit was to observe math classrooms. I am in New York City for a math conference hosted by radicalmath.org. The conference is titled Creating Balance in an Unjust World: Conference on Math Education and Social Justice. The objective of the conference is to explore links between the fields of math education and social justice/social justice education. The conference coordinated our visit to the Earth School.

The classrooms at the Earth School are all multi-age, with two grades in the same class together. They are broken down into Pre-kindergarten and kindergarten, 1st and 2nd, 3rd grade and 4th and 5th (3rd grade, of course, being the exception). The students stay with the same teacher for two years. This facilitates students acting as teachers and helping one another. The teachers I met said they work with the students to help them self-identify their strengths and weaknesses so that they feel more comfortable offering help and asking for help.

The first math class that I observed was in the 1st and 2nd grade classroom. The room was set up with a circle rug area, and several small round and square tables with 4 to 6 chairs. The classroom exhibited a lot of constructivist pedagogical attributes that I was aware of. The whole lesson was about alternative approaches to addition. The teacher facilitated a discussion of how using doubles facts (i.e. 2 x 3 = 6, 2 x 4 = 8) can be used to help solve addition problems. They talked about how 2 x 3 + 1 = 7 gets the same answer as 3 + 4 = 7 (a.k.a. 3 + (3 + 1) = 7. Therefore, if you are able to see 3 + 4 as one more than 3 plus 3 or 2 times 3, then you could possibly more quickly arrive at the solution than if you counted on your fingers or used some other strategy. This part of the lesson also incorporated constructivist approaches in that it was a student-centered facilitated discussion and not a teacher-centered lecture.

In the next part of the lesson the students broke up into groups. The teacher gave instructions for an activity, then asked if there were any students who were still confused. She asked for any specific clarifying questions. She then asked students who felt confident going into the activity and thought they could assist another student to pair with students who still felt confused. The activity used 3 resources: number cards between 0 and 9 with counting dots on them, a "game board" listing "doubles facts" (any multiple of 2) up to 18, and two-sided colored foam circles. The instructions were to draw three cards from the deck with a partner. The students were to pick two cards of the three, which they could use a doubles fact to solve ( although the students discovered this might not always be possible to find two cards which were one away from each other and therefore this alternative addition process wasn't helpful for). Once they solved the addition of the two values, they wrote it down on a slip of paper, citing the doubles fact they used. After that, they used a foam circle to cover whichever double fact they used. They repeated this process, trying to cover every single double fact on the sheet. The slips of paper were placed in a white basket for class work.

The final element of the lesson was when the students came back together. The teacher brought forth the white basket and she went through the math facts placed inside one by one. She read the math fact aloud and the doubles fact which helped in solving it. She asked the students if the answer and doubles fact made sense together and why. If there was a name on the slip she asked the student who wrote it to explain how they came to the answer. Another element of constructivist teaching which was demonstrated in this part of the lesson was that no matter if the teacher knew the math fact to be correct or wrong, she asked the class or a particular student to explain how it was reached and if any changes needed to be made.

The students seemed to enjoy and be engaged by this lesson. It allowed flexibility in the process for students who understood the concept and for those who were developing understanding to both interact with the concept. The teacher gave students time when they got there materials to figure out the activity on their own without rushing in and micromanaging each group. It is helpful to understand the process of the activity if you are going to construct understanding.

This school has an integrated approach to special education. They have a special resource teacher who comes in to the regular classroom during math lessons (or any other designated lessons) and supports the lead teacher in the schoolwork. She is aware of special needs of the students. She works with all the students, but focuses on those with formally identified special needs. Sometimes, the class breaks into two groups (decided on by the teacher) and they learn the concepts in those separate groups. The lesson on this particular day was with the entire group together. They also have another special education teacher who sometimes pulls students from the regular classroom to work on special skills outside of the regular classroom.

The second classroom I visited was a 4th/5th grade classroom. The classroom had a stage-type area in the front, with a square rug in front of the stage. The desks were set up along both sides of the classroom in groups of four. The math class started with the teacher giving the students a page of 80 multiplication problems. The teacher gave the students approximately 5 minutes to finish as many problems as they could in that time period. This part of the lesson was for speed skill building. It struck me as extremely traditional, which isn't bad, it just wasn't what I expected. I wonder if there is a way to build that skill without engendering the competition that this activity did?

The next part of the lesson the teacher asked the students to review what strategies they had been exploring to solve multiplication and division in different ways. The students listed all the skills they had tried which included clustering, the "traditional algorithm" (which is the common way students learn to multiply and divide in mathematics), as well as a few others. For this lesson the students practiced using both clustering and the traditional algorithm. They were given one problem and asked to show solutions to the problem using both strategies. They were split into groups of two and three. Clustering was a new concept for me. In this strategy you break each multiplier into the place value numbers it is composed of. For example, if you were multiplying 645 x 137, you would think of it as multiplying 600 and 40 and 5 by 100 and 30 and 7, then you list all possible combinations. One way to start the cluster is by clustering combinations with the same total number of place values, starting with the largest: 600 x 100, 600 x 30, 100 x 40, 100 x 5, 600 x 7, 30 x 40, 40 x 7, 30 x 5, and 5 x 7. You list all of the individual totals and then add them together.

After about 10 minutes of group time, the teacher called the students back together, by having them meet on the square rug. The first thing the teacher asked the students was to indicate how their groups worked together by either giving a thumbs up, a neutral thumb, or a thumbs down. This allowed the teacher to make a mental note of the perceived success of the group pairings for future group work. Any groups where a member gave a thumbs down, the teacher asked them to share why. After they shared their problem, the teacher asked other students if they had any advice on how the group could work better together in the future. I really liked this process because it helped the class problem solve on good strategies for group cooperation and success.

Then the teacher had students volunteer to present how they found a solution using each multiplication strategy. Then the students discussed which strategy was more helpful for them and why.

I think this lesson was hard to evaluate on a one-time basis. It seemed like the unit was probably helpful for many students, but I still noticed students who seemed to be making it by, by hiding behind the work of other students without real understanding of the concepts. In this particular lesson it wasn't apparent that the teacher was aware of it, or any strategies she was using to solve that problem. I think I would have used the strategy of the 1st and 2nd grade teacher in pairing students who had understanding of the process and those who were confused. One instance that I saw where a student didn't understand and that wasn't being addressed was where a student who understood and was proficient at both multiplication strategies completed the entire problem without input from the struggling student or sufficient attempts to help them understand.

Overall, the identity of the Earth School as an environmentally conscious school was not at all evident in their math classrooms. There were elements that were observable throughout the school, such as a recycling program, but it was not integrated into the math program on those days. Most of the insights I gained were on seeing constructivist teaching strategies implemented in a classroom, and not on integrating math and social justice.

Burnout

There are two months left in the school year, and I just feel totally wiped out. When I told people about my plans for this year I was frustrated when most people's reaction was that it was ambitious (as if it were too ambitious). I still feel like this much of a workload is doable for me, but definitely not the healthiest for my body or soul.

I can't help feeling like if only I didn't have to have a second job to pay for tuition then I could dedicate as much time as I would like to to my college work and interning at the school. I know it's not anybodies fault, just the way of the world that certain experiences cost money. I know that I could be more effective if I had less on my plate.

I know no one is going to be there to say "I told you so". Mostly I am just learning my own boundaries. I do do so much, and I have to value everything I do do.

It is interesting, other people in my life here in Albany are experiencing the same burn out/breaking point as I am right now. We identify with the feeling that something has to give, or change, but there is no clear path to what that could be. I know that I have made it a goal of mine for next semester to set smaller goals, and only have one job, and a paying one at that. I have fears that if I go into student teaching directly in the spring that it will be a repeat of this year. Teaching for no pay, a part time job to pay for tuition, and coursework on top of that.

All that said, the biggest goal for me right now is to make the here and now work, until I feel more capable to make the larger shifts that I know need to happen. Yesterday, I was supposed to start a new unit in math, and I was putting a lot of pressure on myself to make it happen for my college work I need to complete. One thing I have learned from being in the Free School is that teaching works best if you want to do it, just like learning works best that way as well. And I just released the expectations of myself to perform in that way, and I have been so much more joyful at school. I know not all teachers have the freedom to postpone their lesson for the day, but I think I am learning about balancing stress, and accepting my shortcomings. Another way that I am learning to be happy with the present is to take my goals one step at a time. Also, to remember that the worst that could happen is not that bad, for example, not passing a semester. I am not worried about that happening, but if that is the worst that could happen I am in fine shape.

A big struggle for me lately is that my computer broke a month ago. It is finally back in action. Hooray!!! But seriously, doing distance education without a personal computer is not easy as pie. My roommates have gotten frustrated with me always asking to borrow their computer, I have learned the open times of the library and the amount of time I could write was severely cut down. Before my computer broke I was utilizing the in between times I had to write here an there, but without it I have fallen behind in my goals.

On a positive note, through studying at Goddard I have gained self confidence in finding and utilizing resources to better myself as a teacher. I haven't gotten to go extremely in depth in any one subject in education, but I know more what is out there now, I have experiences in many different approaches and I know I can find what I need easily. I have a mental list of all the books and resources I would like to explore further when I have more time and mental space.