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Middle School |
| Our Progressive Curriculum
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Thoughts on Some of the Key Elements of a Progressive Middle School Curriculum
A Multicultural Curriculum
Process and Product and an Integrated Curriculum
On Writers and Writing
Tell, Me, Show Me, Involve Me
Snapshots
More Laboratory Than Museum: A History of Story and Voice
Digging in the Dirt: A Fifth Grade Simulation
Art as Experience
The Making of a Middle School Scientist
A Progressive Approach to Math
On reflection . . .
A Multicultural Curriculum
Last week, I had the pleasure of meeting with members of the Multicultural Committee and other members of the community to engage in a dialog about the LREI curriculum and how it addresses issues related to multiculturalism and diversity. Our discussion highlighted for me the many ways that we explore these issues through rich and meaningful inquiry. In many schools, these issues are often explored in a superficial, celebratory manner (a month for this group and a month for that group). At LREI, these issues serve as a critical lens through which students are regularly challenged to make meaning on a daily basis.
In the Middle School core curriculum, students develop a set of tools that they use to explore actively and question key concepts of perspective, power, and privilege, which weave themselves throughout history, inform our present, and suggest possible paths for the future.
In the fifth grade, students begin to develop the research skills of the archeologist/anthropologist through their study of ancient civilizations. By digging into the past, students work to understand the particular value systems that defined the culture being studied. As they move beneath the surface of this history, they also realize that this inquiry is necessarily filtered through the particular perspective of our own culture and time; in this way students come to see how the past speaks to and with the present.
In the sixth grade, students study the middle ages through a careful investigation of Europe, the Middle East, and Asia. In doing so, they explore the idea of simultaneity and how culture is transmitted across and through civilizations. Through their inquiries, students explore how ideas are transmitted between cultures and how the infusion of these ideas informs a particular culture's world view. In this manner, a strictly linear view of history gives way to one that is dynamic and regularly contested.
In the seventh grade, students explore pre-colonial America up to the writing of the Constitution. Their exploration is driven not by a rote study of important dates and events, but by the various perspectives that inform our understanding of these events as European, Native American, and African culture come into contact. The question is regularly raised as to whose view is being represented and, perhaps more crucially, what views are missing. As they begin to synthesize these often conflicting views, a more nuanced sensitivity to the challenges of the American experiment in democracy emerges.
In the eighth grade, students wrestle with issues that are the legacy of our nation's journey from civil war through the civil rights era. Their inquiry begins with an exploration of the civil rights era, which serves as a critical lens for their subsequent investigations. They then turn back to the civil war period and move forward to return, at the end of the year, to the civil rights era. The Greek philosopher Heraclitus said, "You cannot step into the same river twice," and so it is for the eighth graders. Pushed by the flow of our nation's history and the question of politics and power, they return to where they started only to find themselves and their understanding of the interplay of history and culture changed, deepened and enriched.
Because these powerful tools of analysis can bring to the forefront of our awareness the often contentious and fractured reality of our times, one participant in the discussion wondered whether we were leading students down a path of despair and hopelessness. It is here that LREI's commitment to active citizenship and service provides a way for students to respond to these challenging issues related to social justice in positive and hope-filled ways. Through the bringing together of the academic and the civic, our students come to understand more fully what it means to live in a diverse and multicultural world.
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Process and Product and an Integrated Curriculum
Two recent events, the Spring Chorus concert, in which middle school students in both the Little Red Singers and the Little Red School House Chorus engaged a rapt audience of listeners, and today's 5th Grade Expo, which provided a forum for students to share the exciting work on which they've been focused for the past quarter, got me thinking about an important part of the LREI educational experience.
At LREI and at most progressive schools, there is a significant focus on the "process," which serves as a foundation to our commitment to experiential learning. Embedded in this idea of "process" is an expectation that students reflect on their work and the thinking behind it. We want them to use this reflective stance to help them see their work from a variety of perspectives. This helps them to see the work as an on-going endeavor to be revisited, rethought, and reworked. At the same time, there is something important about the product of this work. It crystallizes and brings into focus the effort and energy that defines the process and, in its own way, the product stands as an achievement that has meaning and value. The key is not to linger too long on the product so that it stands in the way of a new process. When the product becomes its own end, we lose an important opportunity for new learning.
The artist Robert Rauschenberg speaks to this idea is a recent issue of The New Yorker when he comments that "It's always the moment of doing that counts. When a painting is finished it's already something I've done, no longer something I'm doing." It is in that same spirit that we seek to challenge our students to always be "in process" and to see a particular product as an opening to a new process, to always be doing and never content to be simply done.
As the quarter draws to a close and I reflect on my varied interactions with students and teachers as I. . .
- was led through the fifth Grade Egyptian tomb by expert student guides;
- listened to sixth graders present their castles, trebuchets, shields, and stained glass windows to their parents;
- watched backstage as sixth graders presented their Medieval Pageant to the community;
- explored the seventh Grade Colonial Museum and its many insights into colonial life;
- observed as seventh graders examined pill bug behavior and built robots that simulated these behaviors;
- listened to explanations of the physics principles involved in the eighth Grade Marble Machines; and
- overheard eighth graders presenting on issues of social justice connected to their study of the Progressive Era
. . . I am continually struck by the richness of our integrated curriculum. The value of an integrated curriculum, which connects traditionally-separate subject areas, and its particular relevance at the middle school level, is something that has been a core value at LREI from the very beginning. As Agnes De Lima notes in The Little Red School House:
"We are, then, concerned in our curriculum to make sure that it affords the kind of experience and the kind of activities which will help children grow normally and naturally. The old-line pedagogue was continually asking, what must a child know, what knowledge is of most worth? We ask instead, What should a child be like, what ways of acting and what habits of repose are most worthwhile…. We take the child as he is and where his is, try to understand him, and then seek to help him understand the kind of world in which he lives and the part he is to play in it (p. 16)."
The interesting thing is that through this process students learn an incredible amount of what we traditionally consider as subject area knowledge. More importantly, they learn how to use this information to solve authentic problems and to assess critically this knowledge. Through our integrated curriculum, inquiry occurs in a thematic and holistic manner. In this way, the curriculum empowers our students to see connections and to generalize and transfer knowledge to a variety of problem-solving situations. As we celebrate Founders Day tomorrow, I have no doubt the Elisabeth Irwin and her colleagues would be pleased with the current state of affairs here at LREI.
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On Writers and Writing
In the spirit of Book Week, I am reminded of Lucy Caulkins statement from The Art of Teaching Writing in which she writes, "Writing allows us to hold our life in our hands and make something of it. We grow a piece of writing not only by jotting notes and writing rough drafts, but also by noticing, wondering, remembering, questioning, yearning." One of the tools that we use in the middle school to do this is the writer's notebook. In its pages, your child experiments with ideas and writing styles in a non-threatening way. A writer's notebook is like a journal or a diary, except that it relies rarely on daily narrations to fill its pages. Instead of daily accounts, each page in the writer's notebook focuses on a topic--past, present, or future--that the writer would like to some day explore more extensively. Like an artist's sketchbook, the subjects in a writer's notebook are like rough sketches some of which, through care and nurturing, will develop into fully formed pieces. But mostly, the writer keeping the notebook has fun with words and ideas in such a way that the she or he enjoys coming back the next day and trying again with a different topic or style. So as we visit with author's here at LREI, I hope you will take a moment to visit with the young author in your own family.
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Tell, Me, Show Me, Involve Me
Yesterday, fifth and sixth graders worked collaboratively in the forests at Greenkill to solve a variety of physical challenges. Today, they confronted the rigors of a two-hour long hike, the low ropes course, canoeing, and navigating with compass and map. Tomorrow, they will meet the challenge of the climbing wall. At the same time, eighth graders will travel to Prospect Park to participate in the Doctors Without Borders "A Refugee Camp in the City" program. Whether confronting challenges in the natural world or attempting to understand challenges that are the direct consequence of human actions, our goal as educators is to narrow the distance between ideas in the abstract and the direct experience of these ideas. The Chinese proverb, "Tell me and I will forget. Show me and I may remember. Involve me and I will understand." provides a concise formulation of our ideas about experiential education. In his 1916 book Democracy and Education, John Dewey wrote:
To "learn from experience" is to make a backward and forward connection between what we do to things and what we enjoy or suffer from things in consequence. Under such conditions, doing becomes a trying; an experiment with the world to find out what it is like; the undergoing becomes instruction--discovery of the connection of things.
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Snapshots
A recent walk through the Middle School finds:
Fifth graders:
- exploring the challenging text The Breadwinner, which is the story of young girl in Afghanistan during the rule of the Taliban
- attempting to satisfy a pharaoh’s demand to construct a pyramid with simple machines
- learning to read a score and playing through a piece by Carl Orff, specifically written for our collection of Orff instruments
- drawing area models to represent fraction multiplication and exploring problems that involve finding a "part of a part," such as eating 3/4 of a pan of brownies that was 7/8 full
- wrapping up the clothing unit that included a "Pase de modelos" (Fashion Show) in class where students described each others outfits and said what they liked to do and creating catalogs with different clothing items for each season
Sixth graders:
- building scale models of medieval castles and researching their many architectural elements and impact on daily life
- discovering "lost" chapters of Beowulf written by Sixth grade scribes
- experimenting with the concept of proportionality in the science lab
- exploring on recorder and voice the Medieval song "L'Homme Arme" (in English "Man in Armour"), which was used by many Medieval composers as the basis for numerous compositions, mass settings, motets, and part songs
- constructing family trees in French and availing themselves of challenging vocabulary and sentence structures using new adjectives and colloquial expressions
- exploring events that occur in repeating cycles, such as signs flashing at different intervals, or planets revolving at different rates and digging into questions like "How often will 13-year and 17-year cicadas appear in the same year?"
- venturing out to Bomboleo, a Mexican/Spanish restaurant on Bleecker Street, to put new Spanish vocabulary and verbs to work in an real world context
Seventh graders:
- wrestling with varied perspectives on the colonial experience
- continuing to dig beneath the surface of their colonial museum research topics
- practicing dances from John Playford's English Dance Master in preparation for the Colonial Museum
- writing original stories in French that utilize new verbs, both regular and irregular, and vocabulary related to place
- designing, typesetting and printing colonial trade themed business cards
- dialoging with each other in Spanish and exploring new vocabulary related to food
Eighth graders:
- researching, writing, and discussing in Spanish works of art by Velázquez, El Greco, Goya, Picasso and Dalí
- attempting to arrive at a compromise to avoid a civil war between the north and the south
- harnessing Newtons' laws of motion and the power of a mouse trap to propel a vehicle across the floor
- completing a virtual shopping trip in Paris with pictures and descriptions, all in the future proche
- rehearsing a composition based on their experience listening to the music of Steve Reich
- applying finishing touches to this year’s rendition of the art room stools, which take as their theme favorite artists
- photoshopping a set of images from a photo shoot in which students worked with a variety of different lighting situations
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More Laboratory Than Museum: A History of Story and Voice
On Wednesday, we enjoyed another celebration of our students sustained commitment to academic excellence. As in past years, the seventh grade Colonial Museum was rich in scholarship and offered many interesting insights into life and work during the 1700s. Students dug deeply into areas of personal interest and, in addition to learning much about their topics, they learned important research skills that will serve them well in future academic endeavors. The Colonial Museum is one of several culminating activities that are part of the seventh grade core curriculum. Each of these events occurs against the backdrop of a year-long exploration of the events that led up to the framing of the Constitution.
Throughout this journey, students explore the theme of "Cultures in Contact." Through this lens, they examine the experience of Native Americans, Africans, and Europeans and how each contributed to the history of the period. Students also confront the issue of how the historic record is often not reflective of these varied perspectives. As a result, they come to understand why it is crucial that our attempts to understand the past take in the fullest possible view of these diverse experiences. The idea of history as an echo of varied voices and contested stories, mirrors the seventh graders attempts to craft the story of their research experience and to find their voices as historians. One needed only to spend a few minutes in the Museum yesterday to hear the power of their voices. It was my pleasure to have spent the better part of a day surrounded by their stories.
As I mentioned to seventh grade families at last night's Colonial Museum Potluck, it is a tremendous thrill for me to watch the learning process unfold fold for your children. It is a process that, on occasion as your child communicates it to you, is not always as clear to you as it is to us. This in and of itself is an intriguing question and one that, as a faculty, occupies much of our thinking. The question of how we can make this process clearer to you is an important goal for us and crucial to our progressive mission. At the same time, an evening like the Colonial Museum brings the purposefulness of this process clearly into view.
Throughout the day, seventh graders shared their learnings about life during the colonial period with students in Kindergarten through eighth grade. In each of these exchanges, seventh graders were forced to think not only about what information they wanted to communicate, but how best to do so. Supported by demonstrations, simulations, models, dioramas, posters, and Powerpoint presentations, students shared with their visitors the substantial fruits of their labors. I was impressed not only by our students' ability to talk about the facts that they had learned, but about their ability to reflect on what it might have been like to live during this time. It was also exciting to listen to them as they used their newfound learning to look more critically at the legacy of these issues as they face us today. In this way, they experienced the day not as seventh grade students, but as historians.
One learning that has emerged for us as educators as we move forward in this work is the need to better use the research produced by a given class to inform the work of future classes. So we will archive this work, and next year's seventh grade students will use it as their jumping off point as they consider the question, "What new ideas will I add to the fabric of the story of our understanding of the colonial experience?" For this insight, I thank the members of our seventh grade class and commend them, their teachers and their parents for helping to move our on-going experiment in learning forward.
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Digging in the Dirt: A Fifth Grade Simulation
It has been a busy week in the Middle School with students working on a range of projects. The fifth grade Archeology Dig project, which is a new integrated project for us this year, is coming to an exciting conclusion. As part of their on-going study of ancient civilizations, the fifth graders have been exploring universal aspects of culture (e.g., politics, economics, and religion) and how they are expressed in unique ways by individual cultures. The Archeology Dig project places students in the center of this process. In groups, students have created the foundations for a fictional civilization. This has required them to create a set of core values of the civilization and a language and symbol system to express these ideas. They have this work as the basis for creating a set of artifacts that tell a portion of the story of their civilization. These artifacts will then be broken and buried in the simulated "dig" sites. Students will then excavate the artifacts created by another group and then try piece the story of the civilization together. The next few days should be exciting ones for the fifth graders and for their core, art, and science teachers.
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Art as Experience
With rehearsals for the Middle School Musical underway and the Spring Concert just around the corner, students participating in our performing arts programs are hard at work. As this work unfolds, equally impressive work is being done and has been produced since the start of the year in our visual arts classes. This work finds itself the center of attention at our annual Middle School Art Show. The show provides an opportunity for the community to enjoy a wide range of works produced by students in all four grades this year. In putting on this show, it is our hope that the viewer will not only have the opportunity to consider the works themselves, but will take advantage of the opportunity to speak with the artists who created the works. Through this dialog, we hope that you will be better able to appreciate the art as an embodiment of a particular and unique experience.
As John Dewey comments in the opening of his seminal work Art as Experience:
By one of the ironic perversities that often attend the course of affairs, the existence of the works of art upon which formation of an esthetic theory depends has become an obstruction to theory about them. For one reason, these works are products that exist externally and physically. In common conception, the work of art is often identified with the building, book, painting, or statue in its existence apart from human experience. Since the actual work of art is what the product does with and in experience, the result is not favorable to understanding. In addition, the very perfection of some of these products, the prestige they possess because of a long history of unquestioned admiration, creates conventions that get in the way of fresh insight. When an art product once attains classic status, it somehow becomes isolated from the human conditions under which it was brought into being and from the human consequences it engenders in actual life-experience.
When artistic objects are separated from both conditions of origin and operation in experience, a wall is build around them that renders almost opaque their general significance, with which esthetic theory deals. Art is remitted to a separate realm, where it is cut off from that association with the materials and aims of every other form of human effort, undergoing, and achievement. A primary task is thus imposed upon one who undertakes to write upon the philosophy of the fine arts. This task is to restore continuity between the refined and intensified forms of experience that are works of art and the everyday events, doings, and sufferings that are universally recognized to constitute experience. Mountain peaks do not float unsupported; they do not even just rest upon the earth. They are the earth in one of its manifest operations. It is the business of those who are concerned with the theory of the earth, geographers and geologists, to make this fact evident in its various implications. The theorist who would deal philosophically with fine art has a like task to accomplish.
What is it that Dewey wants us to understand? And how might this understanding inform our perspective on the role of the arts in progressive education in general and at LREI in particular? For us and for Dewey, the key notion is that the arts need to always be experienced as being alive in the present where they can provoke "fresh insight." Even when works of art achieve something of the transcendent, Dewey does not want us to forget that they remain human endeavors that were born out of a particular need and created as a means to fulfill that need. In essence, the making of art represents an attempt to capture something vital about the human experience while existing as experience itself. So LREI artists wrestle with a variety of materials and a variety of techniques in order to capture "an experience for a human being." That said, I’ll get out of the way and let the art speak for itself and to the experience of the students who created it. I look forward to seeing you at the opening reception.
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The Making of a Middle School Scientist
I write this as our eighth graders are about to step into our auditorium, which has been transformed into a courtroom, for our annual Forensics Evening. It was only a handful of weeks ago that students entered their science class to find that a "crime" had been committed. Science teacher Stephen Volkmann’s treasured CD "Scientists of the 20th Century Sing Your Favorite Songs" had been stolen. Left behind was a set of clues that he hoped would lead students to discover the faculty member guilty of the crime. So the students set themselves to work investigating the clues, doing research on related scientific concepts and developing experiments to test their hypotheses about the clues.
As an observer to the unfolding of this experience over the past few weeks, it has been most exciting to watch students wrestle with the evidence, revise questions until they were focused and testable, and develop well-conceived plans for investigating the key evidence in the case. In the midst of all the legal trappings of the evening, it is important not to lose sight of the many important science concepts at the heart of the investigation:
- the role of kinetic energy in the cooling of a liquid,
- the relationship between temperature and kinetic energy,
- the effect of various insulating materials on the rate of cooling of a substance,
- the behavior of solutes,
- the nature of homogeneous and heterogeneous mixtures,
- methods for separating substances dissolved in a liquid and for determining the mass of the dissolved substance,
- using chromatography as a means for separating pigments,
- the impact of the presence of a solute on the boiling point of a mixture,
- the impact that the concentration of a substance can have on the flammability of a mixture,
- controlling for variables in an experimental design, and
- understanding and accounting for variability inherent to data collection.
I have no doubt that Stephen and his league of young sleuths will spend some time debriefing the experience and determining how their work on this mystery will inform future work. That said, I hear the gavel banging and the court being called to order . . .
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A Progressive Approach to Math or You can have your pi and eat it . . .
The Middle School celebrated Pi (π) Day (3/14) by constructing a visual representation of the non-repeating nature of pi using colored squares. This intriguing take of this important number is on display in the hallway outside of the math room. In addition, interested students had the opportunity to share how many decimal places of this legendary endless irrational real number they could memorize. The number pi, which is defined as the ratio of a circle’s circumference to its diameter, is known to most people by its truncated form: 3.14159. More than 50 students from all four grades accepted the challenge to see how far beyond the first few decimal places they could go. One fifth grade student memorized and recited at Middle School Meeting over two hundred and twenty places past the decimal point! Just to give you a sense of what that looks like, here are those 220 places . . .
3.1415926535897932384626433832795028841971693 993751058209749445923078164062862089986280348 253421170679821480865132823066470938446095505 822317253594081284811174502841027019385211055 596446229489549303819644288109756659334461
All of the students who were able to memorize at least ten places past the decimal point earned actual pies for their efforts, and the grand prize winner was granted 3.14… pies. All in all, a delicious mathematical exercise!
Sounds like fun, but beyond the entertainment value of the day’s activities is there a more important message here? I think there is. These events and their associated activities highlight an important goal of our approach to teaching mathematics and of our math curriculum in general. As students acquire important math knowledge and practice the skills that allow them to put these concepts to use, they also discover their capacity for creative and critical thought and the rewards of curiosity. We play at math to discover important truths about the world we live in and these discoveries provide us with another language for making sense of our experience.
As with any endeavor, this requires hard work and practice. It is not always easy and for some and the challenges can be frustrating. But when one steps back, there is a clear sense among the students in the Middle School that math has a relevance beyond just being useful for some future purpose. That students can derive so much pleasure from something like Pi Day speaks to the purposefulness of our curriculum.
When I poke around in our math classrooms, I am always struck by the depth of thinking and ability to think mathematically that our students have established as habits. In my mind, this is precisely the goal that a good middle school math program should have for its students. What this translates into is students who have a solid foundational knowledge AND who possess the ability to understand and use mathematics as a symbolic and relational language for looking at the world.
I had a fairly traditional math experience in middle and high school. While that program of studies led me to calculus in my senior year, every prior year was a seemingly endless series of memorizing algorithms and practicing them all the while saying to myself, "What is the point of this?" It was not until my senior year when I was taking calculus and physics that things clicked. That was hardly surprising given that the calculus was derived by Newton and Leibniz to resolve core questions in physics. Why did I have to wait until my senior year of high school for such a clear and powerful illustration of the beauty and utility of mathematics? The general orientation of the Connected Mathematics Project (CMP) curriculum that we use seeks to address this question in the most obvious of ways: students must experience math as a means for making sense of the world if we want learning to occur on a deep level.
While it is true that there is a dimension of math competence that requires students to be able to work a variety of algorithms to get to a "precisely right answer," I would not define that as the purpose of math nor actually as math. Following algorithms is an operational activity, which when not connected to a deeper understanding of the elegance and purpose of those algorithms becomes simply an exercise in following rules. So how do we help learners to begin to see the world from a mathematical perspective? And in so doing, how do we help students to acquire a set of discrete skills that not only helps to guide them to the answers to one set of problems, but also becomes the foundation for the exploration of new problems?
To answer this, I think that it is also important to note that while we use the CMP program, we are not driven by it to the exclusion of other ways of approaching math education. There are some camps that describe CMP and its peer programs as "fuzzy" and there are other camps that describe the more traditional programs as "routinized." For me, these distinctions (like those in the debate between phonics and whole language in the literacy realm) are ostensibly political. They are about different camps staking out positions on a field that has more to do with securing textbook contracts than with childrens’ learning. What good progressive schools (and I place us firmly in this camp) have always done is to take a balanced approach. It is not an either/or.
In adopting the CMP program, we recognized that it had certain limitations and that for some students its approach might be more challenging. That is why our math teachers have worked in deliberate and thoughtful ways to consider how to supplement the program to best meet the need of all students. Hence, the "Beat the Basics" strand and a focus on reinforcing basic math skills, which for some students requires additional practice and repetition.One question that seems to come up a lot is that the CMP materials don’t teach math, they don’t feel like a "real" textbook. I’m not sure that I or any of the Middle School math teachers would say that the purpose of the CMP books is to teach mathematics. The books are indeed supporting materials. They support a rigorous approach to math that posits the math classroom as the crucial nexus point where students, the teacher, and mathematical ideas come together to make meaning. Math instruction at LREI and CMP in particular is structured around a collective learning experience. It is not a course of independent study.
It is true that the CMP books do not present the algorithms as one would find them in a traditional math textbook. However, these elements are hardly absent from what goes on in the classroom. This structure does, on occasion, pose some challenges for some learners. If a student does not have the necessary materials (definitions, notes, worked problems) from the class, he/she may encounter difficulties when working at home. Some of you have asked us to provide additional materials to supplement the CMP texts. The question of what constitutes appropriate materials to supplement the CMP program is one that the math teachers and I continue to discuss. The question is a nuanced one as those materials must fit with the pedagogical approach and sequencing that drives instruction (i.e., if students are engaged in working out an algorithm then giving them supplementary materials that spell out the algorithm does not make sense). Our on-going efforts in this area are really just a continuation of our commitment to finding the right balance that is so important.
So any good math program will always be "in process." Our goal is to not only find ways to be more balanced in general, but to always endeavor to work with each family to be more balanced relative to the needs of your child. So at the heart of all this process rests a partnership between home and school. As we work to define this partnership, we are often are asked about the CMP methodology, which is sometimes misunderstood as "the teacher facilitates and the student discovers" without any "real teaching" on the part of the teacher. This description misses a crucial component that makes CMP a structurally sound approach. This misunderstanding only posits two legs (teacher facilitates and students discover); the third leg is that teachers do "teach" after the discovery has been made. They do define a generalizable conclusion that leads to an algorithm that encapsulates the discovery. This third leg is the "traditional" math curriculum that many of us experienced when we were in school. Ultimately, it is what our teachers do with the CMP program structure that creates powerful opportunities for learning. There is no holy grail of math programs here; there is, however, the committed work of dedicated teachers trying to get it "right."
Questions of truth and beauty have always been mired in the conflict between the relative and the absolute. And in fact, one can look at the history of math and science as one long melody on the proven fallacy of what was believed in a given moment to be "precisely right." While it is certainly the case that at an operational level math requires a certain necessary degree of precision, it is often the getting to the solution that is far more interesting than the solution itself. It is the debate over these varied paths that moves mathematicians and that makes of math a kind of poetry. I can think of no more meaningful road for our young mathematicians to travel along especially when they find themselves with an able guide and worthy traveling companions.
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On reflection . . .
I must confess that it was something of a shock when May rolled around and the end of the year began to take shape in front of us. While we are just shy of a month left in the year, there is still much to do. Each of the grades has significant culminating projects on which they are working that they will share with you at our year-end events. In addition to this work, students are just beginning the process of reflecting on the year in each of their classes and working with their teachers to fashion these reflections into formal comments that will be part of the fourth quarter progress reports. Progress reports are not simply something that happens to a student; they are a reflection of a yearlong relationship between student, teacher, and the subject. By adding the student’s voice to these documents, we hope that it will help students to take greater ownership of their successes and of their challenges. As part of this process, students have been asked to explore a range of questions about their work this year. A sampling of these questions follows:
- Discuss the work you completed this quarter, in terms of process and product.
- Reflect upon your participation in group work and in-class discussions.
- Assess your homework in terms of depth, completion, and timeliness.
- Look back over the entire year and reflect upon how you and your learning process have changed.
- Think about all the work you’ve done in class this year. What strengths emerge from this work? Why do you think that this is the case?
- In what ways has your work improved this year? Describe the differences you see between the beginning of the year and now. What areas still need work? How do you plan to work on them next year?
- What ways do you learn best?
- Select 1 or 2 pieces of work that you did this year of which you are particularly proud—could be a piece of writing, a class comment, a response, a project. What do you think these items show about you as a learner? What have you discovered about yourself as a learner this year?
- Think about all the work that you’ve done this year in class. Did you develop any new areas of strength? What are they? What was most helpful to your growth as a learner?
- What areas do you still need to work on improving? What strategies will you use next year to do so? How can your teachers and families be helpful? (Do not say, "Work harder"—instead, describe what that looks like for you to be doing it.).
- Are you satisfied with your effort this year? Explain.
- Comment on the quality and organization of your work.
- What will you work on next year to better your experience and performance in class? How can I help?
- Are you satisfied with the quality of your homework? Why or why not? What would you change and why?
- Think about your note taking and our most recent notebook check. Comment on your organization and thoroughness. (Would your notes be legible, clear, and understandable to other readers? Could an absent student use your notes to get a clear idea of what he/she missed?)
- Comment on your class participation (listening, questioning, offering ideas, etc.).What new skills did you learn? What progress did you make on previously learned skills? Explain.
- Look at the list of projects at the back of this handout and choose one that you felt you did your best work. Why do you think this project represented your best work? What is one thing you did in this project that helped you do so well?
- Choose one project that you felt you did not do your best work. Which aspects of this project were not your best? Why do you think you did not do as well in this project? What could you have done differently to improve your performance in this project?
- Your middle school years have been something of an adventure. A part of that story is coming to a close as new stories begin to unfold. Take a moment to examine the diagram below and consider and how it can be used as a lens to reflect on your experience in the middle school. In the spaces below and in whatever form is comfortable for you (e.g., poetry, narrative, lists, etc.), see if you can capture some of your thoughts about your middle school years as you begin to think about moving up.

All of the above are deep and thoughtful questions that push students to reflect on the meaning and purpose of their learning. Along with the discrete knowledge and skills acquired over the course of the year, the ability to find meaning in their own learning experience is crucial goal for all Middle School students. It is a worthy goal in that it calls on students to see the larger context within which they will use their knowledge and skills.
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