The Teacher Coach: Qualities of an Effective Mentor

When people inquire about our teacher-training program, I often tell them that the heart of our experience-focused model is the co-teaching relationship between the Apprentice and the mentor teacher.  Apprentices, working to develop and refine their teaching practice over two years, depend on countless hours spent with a mentor teacher—planning, sharing and reflecting on each school day.  Given the importance of a strong teaching coach who is also responsible for a classroom of young students, what do we expect and hope for from our mentoring faculty at Arbor School?

First, it is important to know that while our six Apprentices spend most of their time within one or two classroom settings at Arbor, we see the entire faculty as engaged in a mentoring role.  For example, recess conversation in support of a struggling student often occurs with teachers outside his or her primary classroom context.   During her “free” period, our Spanish teacher comes to observe 8th-grade Science, using her well-honed assessment skills to collect and share incisive observations about the quality and quantity of student participation during an Apprentice’s lesson.  Apprentices’ presentations for faculty meetings invite the advice and perspective of all Arbor teachers, who willingly add their questions and ideas to assessment “experiments” or lists of what is essential in reading.

Despite this shared approach to mentorship, every member of our faculty also strives toward a set of individual aims.  This helps define our approach to supporting beginning teachers in addition to moving our own professional practices forward.  Teachers with particular strengths in one area may assist others to grow in that realm through discussion, advice and coaching.  Observing in each other’s classrooms is always refreshing, sparking admiration for our colleagues’ skill and new ideas for our own practices, and our co-teaching model allows the flexibility to step away from our own students on occasion to seek a different perspective on our craft.

Central within our definition of effective mentorship is a focus on attitude and character—threads that weave themselves through Arbor School in general.  In this case, we hope for mentor teachers to exhibit a strong commitment to and optimism about the teaching profession.  In the face of the pressures and tensions that exist in teaching, our mentor teachers must demonstrate how to leverage these realities as a healthy impetus toward balance and clarifying foundational purposes for schooling.  Relatedly, our mentors desire to be role models to their Apprentices, committing themselves to mentoring with the clear understanding that this requires energy, time and effort.  They also believe that mentorship and collaboration in action research and reflection will improve and refine their own instructional practice.  Sometimes this means being open to new and possibly untested ideas and approaches posed by their Apprentices.  Other times mentors lead the way forward by offering their ideas and insights. The discernment to choose when to follow and when to lead for the benefit of the students as well as the Apprentice must be honed through experience.

People often say that it takes an excellent teacher to be an excellent mentor.  This is certainly true.  Mentoring faculty must have strong knowledge of pedagogy, subject matter, and classroom management skills.  They must be willing to be observed and to subject their practice to scrutiny and study.  They must use the assessment/planning research cycle to adapt their curriculum to the needs and understandings of current students even as they clarify central purposes and imagine students’ culminating performances that will guide their planning.  It is upon such excellent practices that the further requirements of mentoring a beginning teacher depend.

Within a collaborative, co-teaching structure, communication and interpersonal skills are also essential for strong mentors.  In order to maintain trusting professional relationships, mentors must be approachable, patient and clear.  Equally important is empathy for beginning teachers’ struggles, efforts and development.  Remembering what it was like at the beginning of their own careers, mentors communicate hope and enthusiasm as well as the belief that a person is capable of transcending present challenges to strive toward future accomplishments.  Active and attentive listening, asking questions that prompt reflection, and offering critiques in positive and productive ways are daily practices for our teacher coaches.

While many strong teachers have opportunities to develop their communication skills, few are asked to coach other teachers.  Effective coaching requires clear articulation of classroom values, expectations and pedagogical approaches while remaining open to the questions and input of an Apprentice/co-teacher.  With this base established, mentors must then learn to observe and support Apprentices as they plan and teach to these aims themselves.  As mentors work with a series of Apprentices over time, they also have to adjust their communication and coaching to the needs of each person—just as they do with children.  They must provide support through “in the midst” and reflective discussions, and through review of written work and plans.

Mentorship, like collaborative teaching in general, requires a mixture of careful forethought and responsiveness to the ever-changing needs, possibilities and delights afforded by each new set of students and, indeed, each new day.  Teaching Apprentices to savor this dynamic is one way that we hope to develop teachers who remain in the profession and continue to grow throughout their careers.

In order for our mentorship program to thrive and evolve, institutional support is also necessary.  Our school’s director makes mentorship the focus of faculty meetings throughout the year and sees the development of strong mentor teachers as a positive avenue toward professional development in general.  As teachers identify their own strengths and areas for growth within our aims for mentorship, we construct professional partnerships, discussions, observations and coaching opportunities throughout our faculty.  In the process, we hope to refine and develop our own teaching and coaching practices as fully and intentionally as possible.

Annmarie Chesebro, ACT Coordinator

Ancient Geometry: Intermediates Encounter Eratosthenes

Every other year, the 4th- and 5th-grade Arbor Intermediates survey the history of civilization. As this Inventions & Discoveries year unfolds, we study innovations in writing, language, science, architecture, and mathematics. From the development of the base-10 number system to proofs of the Pythagorean theorem, students engage with a variety of rich and ancient mathematical ideas. One of the most intriguing puzzles has to do with the work of a man named Eratosthenes. Born in modern-day Libya in the 3rd century BCE, this polymath invented the discipline of geography as we know it and contributed to many realms of academics. He rose to become chief librarian of the Great Library of Alexandria. Around 240 BCE Eratosthenes undertook a project to estimate the circumference of the earth. His figure was remarkably accurate: within 2% of the actual measurement. The key to Eratosthenes’s work lies in one simple theorem of geometry: alternate interior angles are equal. Our Intermediate students slowly build toward a simple proof of this concept and use it to recreate Eratosthenes’s argument that derived the circumference of the earth.

We lead Intermediate mathematicians through the following sequence of ideas:
Beginning angle work:

  • What is an angle?
  • How to use a protractor
  • How to estimate angles using “friendly” angles like 90°, 180°, 270°, and 360°
  • Parallel and perpendicular lines

Sum of angles in a triangle:

  • Students work in pairs to investigate the properties of the angles of a triangle. After experimenting with many different types of triangles they become convinced that the sum of the angles of a triangle always equals 180°.
  • They also begin to find unknown angles, using the facts that two angles on a straight line sum to 180°, angles around a point sum to 360°, and angles in a triangle sum to 180°.

Vertical angle theorem:

  • When two lines intersect, they create four angles. Each two opposing angles are equal and are said to be vertical.
  • Students work with many different examples to explore why this theorem is true.

Alternate interior angle theorem:

  • When a transversal crosses two parallel lines, the angles on opposite sides of the transversal but between the parallel lines are equal.
  • Again, students play with many examples in order to test this principle for themselves.

Throughout the unit, students add to their personal Math Toolkits to explain new terms, tools, and concepts. We have made the worksheets, Toolkit prompts, and a pre-assessment available for download:

Angles pre-assessment
Protractor practice & quiz, estimation practice & quiz, and Toolkit prompts
Vertical angle theorem and alternate interior angle theorem progression
Eratosthenes puzzle

When we introduce our students to ancient math, one of our hopes is to instill awe at the human ingenuity that produced some of the calculations and conclusions that are central to mathematics today. The fact that a librarian living 2400 years ago estimated the circumference of the earth with nothing but a pole, a protractor, and a shadow provides plenty of meat for astonishment. In order to understand Eratosthenes’s methods, students have to engage with the concepts that supported his conclusion. Eratosthenes’s key realization pertains to parallel lines: if two parallel lines are crossed by another, they create sets of equal angles. More formally, two sets of alternate interior angles are equal. Students require some background knowledge in order to discover this property themselves, but the concepts in play are accessible to 9-, 10-, and 11-year-olds.

Initially, we work with students to build protractor skills. The Intermediates practice using a protractor to measure all sorts of angles—those between 0° and 180° and those greater than 180°.  The fact that protractors are constructed to allow measurement of angles beginning at either side can be an obstacle at first. When students ask, “Which number do we use?” we ask them to relate the angle to 90°. If the angle is greater than right, they need to use the larger number. We then spend an entire class period estimating angles. Students begin to call certain angles—90°, 180°, 270°, and 360°—“friendly” because they are particularly helpful in estimation. They learn how to describe the relationship between two lines, whether perpendicular, parallel, or simply intersecting. Students investigate acute and obtuse angles and come up with names for 180° and 360° angles. They record all of these findings in their Math Toolkits to scaffold future learning. Once all students have a common language and skills to work with angles and lines, we begin to investigate the properties necessary to understand Eratosthenes’s work.

Eratosthenes used two related geometric theorems to obtain an estimate for the circumference of the earth. First, he satisfied himself that vertically opposite angles are equivalent. (A Greek philosopher named Thales of Miletus had worked out a proof of this about 300 years before.) For example, in the figure below, angles c ande are equal; so are angles d and f.

Our Intermediates work in pairs through a series of increasingly complicated problems to come to the same conclusion. They begin with two angles along a line. We give them one angle and ask them to calculate the other. Although all our students have learned that two angles along a straight line sum to 180°, it can be tough for them to leap from that fact to the subtraction problem that will yield the measurement of the missing angle. We work with numerous examples and many different angles in order to build confidence in applying subtraction in this way. Eventually, students explore the four angles created by two intersecting lines. Given the size of one angle out of the four, students can build sums to 180° in order to calculate the measurements of the other three. After working through multiple variations on this task, students feel certain that the opposing angles formed by two crossing lines are always equal. It helps to ask them to explain their thinking along the way, making sure they know why they completed each step of the process.

The second theorem that Eratosthenes needed relies on the vertical angle theorem and on the fact that the sum of the three angles in a triangle is 180°, a fact Intermediates have already encountered and tested in previous lessons. In order to learn that alternate interior angles are equal, student begin with a transversal crossing two parallel lines. We show them how to drop a perpendicular line through the intersection of the transversal, creating a triangle:

 

We have students measure angle x and then calculate as many other angles as they can, allowing them to arrive in their own time at the realization that x and y are equal. Again, our students work with multiple examples of this property and summarize what they have discovered at the end. Group discussion is usually the best way to lead all the students to the idea that if x + b = 90 and y + b = 90, x and ymust be equal. We have noticed that students tend to use the triangle formed by the perpendicular line as a crutch and attempt to draw it themselves in every problem, thinking it is a necessary part of the puzzle. But once they accept that x and y—alternate interior angles—are always equal, they can see that the theorem still holds whether the line is there or not. (The idea that a mathematical proof can only be made by truly exhaustive testing is new to them. Students this age are, if anything, too ready to assume a proof from a handful of examples. When they reach the Senior level we ask them to exercise greater caution in concluding that a pattern will always continue.) Armed with these tools, students are ready to emulate the work of Eratosthenes.

After a read-aloud of the first part of Kathryn Lasky’s The Librarian Who Measured the Earth, each student receives a drawing that represents a view of the globe that Eratosthenes imagined—a section of the earth from Syene to Alexandria, with rays of sunlight running parallel into a well in Syene and casting a shadow of a pole at Alexandria.


Lasky’s story tells us that Eratosthenes might have visualized the earth as being segmented like a citrus fruit. He realized that if he could measure the size of one section of the earth and find out how many of that section would fit around the whole planet, he could calculate the circumference. With little scaffolding, the Intermediates can find their way to the calculations that Eratosthenes undertook. The toughest step is seeing how Eratosthenes figured out the number of sections he would need. Helping students is often as simple as reminding them that they know a circle is 360°; they can then usually turn the question into a division problem. They can use either a calculator or long division to obtain the number of sections that would circle the globe.

In the end, students marvel that Eratosthenes’s estimate differs from our own modern estimates by only 200 miles—this without any computers or technology to speak of. (Eratosthenes used surveyors trained to walk with very precise strides to measure the 500 miles from Alexandria to Syene!) The study of Eratosthenes’s achievement also makes a great segue into our study of Medieval and Renaissance times. Sixteen hundred years later, European scholars still revered and relied upon the work of the ancient Greek philosophers. As kingdoms vied for control of trade routes and newly encountered lands in the Age of Discovery, Eratosthenes and his contemporaries were guiding lights in the sciences of navigation and geography. Why hadn’t human understanding advanced further in the intervening centuries?

Daniel Shaw

Intermediate Aims

Last year we began a series of articles on curricular design, considering some of the big, generative ideas and fundamental concepts we hope all our students will have grappled with by the time they leave Arbor School. We wrote about the thematic curriculum that has emerged to offer up those experiences. Each year, as we plan the particular course our thematic studies will take to engage and challenge a new and unique cohort of learners, we turn back to our fixed and overarching aims for their age group. What do we want every child to achieve in the realms of inquiry and expression, and what habits and attitudes do we hope she will evince? This article reveals our broad aims for the Intermediate student, grade 4-5, 9-11 years old.

The Intermediate child is exciting to teach. She has new intellectual scope and a skill set that allows her to build, model, and measure with accuracy. She is a natural historian and scientist, keen to investigate why the world is as it is and to predict what might happen next. She is able to understand how parts form a whole and how causes and effects can ripple out through a large system. She is capable of realistically imagining the past, the future, and the perspectives of others. Deep history becomes accessible; personal time management is becoming possible. We ask Arbor Intermediates to reach further in terms of content and the sophistication of their synthesis of new information, but also in terms of their independence and agency over their own learning.

The richness of the topics in our curriculum helps buoy two of our main goals for the Intermediate years.  Firstly, we challenge students to ask questions.  Their natural curiosity quickly brews new and exciting ruminations.  Over the course of two years, one centered on Environments and the other on Inventions & Discoveries, our projects attempt to hone such queries into focused and helpful questions that spur research forward and tease out the most salient pieces of information.  Secondly, we challenge students to make claims about the topics they study. By the fourth and fifth grade, students can be quite opinionated.  We ask them not just to make claims but also to select the most relevant findings from their research to support their stance. The increasing complexity of our curricular material raises the level of challenge and demands growing sophistication in the students’ work.  In addition to these two overarching goals, we also strive toward the following aims over the course of each year:

Inquiry

  • Students will hone research skills as they distill non-fiction in various forms, with particular focus on capturing facts in their own words.  Students need to scour works of non-fiction that may contain only a few pertinent bits of information and sort that data to draw connections and conclusions.
  • Students should develop focused questioning through the pursuit of complex research topics as well as self-guided experiments in science.
  •  Students will begin to formulate questions, predictions, and reasonable inferences during fiction reading through reading groups and reading conferences
  • Students will continue to engage in and relish generative, open-ended wondering

 

Expression

  • Students move from simply gathering ideas to linking those ideas into a cohesive whole.  Fourth and fifth graders are learning to synthesize facts they read and use them to scaffold new ideas.
  • Students apply the abstract concepts they study, experimenting with the power of the lever, for instance, rather than taking for granted the formula that it exchanges force for distance. Conversely, they are able to think and talk about forcewithout pushing on something.
  • Developing claims and supporting them with evidence is a particular focus in writing.  Students must show their ability to synthesize information by connecting disparate facts and linking them to create a unified argument in favor of the point they are trying to make. Learning to craft clear topic sentences and support them with logically ordered information in a paragraph is a crucial step in this developmental process.
  • We aim for clarity, precision, and inventiveness in creative writing.
  • Revision is one of the most difficult tasks we ask students to undertake. Intermediates are developing the ability to self-assess and know that their best work will emerge from many drafts.
  • Students develop an appreciation for language and the writing craft through poetry recitation, weekly creative writing exercises, and group read-alouds.
  • Students gain skills and learn new techniques for creative work in Design and Music

 

Habits and Attitudes

  • Fourth and fifth graders are developing the stamina for sustained attention.  Students work toward focusing for an hour at a time on research, math, writing, reading, or design.
  • Students practice careful observation as the basis for strong work across the curriculum.
  • As students get older we expect them to be more independent and better able to manage their time.  In the Intermediate level they are particularly primed for a leap in ability to work on their own at school and at home, starting work periods quickly and asking questions that help them move forward. Through open-ended projects, students learn to decide for themselves when they have accomplished their best work.
  • Students should be able to determine when they are confused and should possess strategies to move forward in the midst of such confusion, both independently and through thoughtful questions put to teachers or peers.
  • Students can actively participate in group work and ensure that their voice is heard while developing the flexibility to accept others’ ideas and build upon them.
  • As students develop tenacity, stamina, and skills, they become more comfortable with hard work.  They become more confident that they can solve tough problems.
  • Students should engage in frequent reflection to inform independent goal-setting and begin to develop agency in directing their own learning.

Arbor’s mixed grades dictate that a rising sixth grader must be prepared for full participation in classes with Sevens and Eights. She must be ready to speak her mind and respond sensitively in Seminar discussions of great books, world events, and the essences and vagaries of human nature. She must propel herself through a challenging math curriculum, working both independently and collaboratively. She must design her own science experiments, learn a new language, assume leadership in interactions with younger students, navigate a new adolescent social landscape, and greet a panoply of new ideas and high expectations with an open mind and a will to work. The Intermediate years lay the tracks and light the way for these leaps forward, and we relish the journey with each of our students.

The Intermediate Team

 

Winters Come and Winters Go

Winter has come to Arbor School. With it come steady rain, deafening indoor recesses in the Arena, swollen doors that let in the damp chill if they don’t get an extra push, and creek waters rising over their banks. There is light and beauty if you know where to look. The persimmons outside the library are ripening into golden globes. Richly colored portraits of root vegetables adorn the Primary classrooms and vivid rangoli designs brighten the Senior building, where studies of India are underway. But for real warmth on these damp and ever-darker days, we look to our community. Winter is a wonderful time to foster closer connections between students and to focus on giving where there is need.

 

We take official notice of the coming dark by gathering as a school at Samhain, the Gaelic festival marking the end of harvest and beginning of winter, lighting a bonfire and huddling close for poems and songs—Stan Rogers’s “The Giant” is a must-sing—and the much-anticipated Rolling of the Oatcake. The fourth- and fifth-grade Intermediates have baked an enormous oatcake, marking one side with an X and the other with an O, and now a teacher will bowl it down a gentle slope. If it lands X-side up, as it did this year, foul weather (perhaps even a Snow Day in temperate Oregon!) is forecast. We cap the celebration by sharing oatcakes… one can carve off the muddy exterior of the large one, but we bake batches of unsullied individual portions as well.

 

In addition to our all-school assemblies, we relish more personal cross-grade connections for our K-8 students and have constructed frequent chances for olders to be buddies to the youngers. Each child has an official buddy for the duration of the year, eldest paired with youngest, and is part of a buddy family that meets weekly for activities designed by our eighth graders. A cherished buddy family event is our Thanksgiving celebration, with buddy families clustering on blankets to share pumpkin pie and apple crisp baked in the classrooms with the help of parent volunteers—a vital element of the community we seek to build—and adding donations to the mountain of canned food we are collecting for the Oregon Food Bank. Students also make presents and then tramp through fields and lanes to deliver them to the school’s neighbors. And in the spirit of connection with the larger community, our Seniors take money raised at Arbor School to Annie Ross House, a shelter for homeless families in Clackamas County with whom we have a long-standing relationship (For more on our particular connection with Annie Ross House, see Cambium Volume 1, Number 4: Community & Stewardship.)

 

Less structured and lighter-hearted connections knit our community together, too. One such opportunity occurs before Winter Break, when the Intermediates carry on a tradition that has occurred at Arbor for more than 20 years. About two weeks before Break, during storytime, our librarian will read Astrid Lindgren’s The Tomten to the K-1 Primaries. Intermediate teachers will read this same favorite to the misty, nostalgic Intermediate class, who will coo and recall memories of their own long-ago Primary days. Then the teachers assign each Intermediate a Primary Tomten buddy who will be the recipient of magical Tomten visits. The Tomten’s presence on campus is first noticeable when mysterious, strategically sprinkled glitter trails begin to appear outside.

 

The Intermediate teachers have their students compose decorated (often with more glitter) notes to the Primaries, sometimes including bits of the Tomten’s song:

“Winters come and winters go,
Summers come and summers go,
Soon…”

The second note, glitter now mandatory, asks the Primaries to leave their boots or shoes outside of the classroom on the last Friday before Break. While the Primaries are at PE or similarly occupied, the Intermediates, barely able to suppress their glee, deliver final, sparkly Tomten notes along with a small orange or a similar treat (an origami crane, a tissue paper flower) to the recipients’ boots. A glitter trail leads to the entry to the Primary classrooms. (Of course, the Intermediate teachers create a few extra treats in case of absence.)

 

One of the great joys of the Tomten tradition is observing the whole school gathered at afternoon carpool, when the Primaries are bursting to announce the amazing appearance of the Tomten! The Intermediates employ their formidable skills as thespians to register wonder and surprise at the mysterious marvel of the Tomten, and the Primaries head home for the Break with a magical tale to savor through the waning days.


Perhaps the ultimate expression of winter community feeling at Arbor is our Solstice gathering. We now allow it to float into mid-January to better suit the school calendar and avoid overburdening mid-December with another celebration requiring exhaustive preparation; classroom studies already demand culminating events for the end of the term’s work. When we have rested and restored ourselves over the winter holidays, we will take up rehearsals for a performance involving every child at the school in story, song, dance, or verse. Curricular content will inform the program, with the Primaries bringing their hibernating animals; the Juniors’ geology focus giving us an original composition of Stone Soup with stones as instruments; the Intermediates’ immersion in ancient Greece yielding a musical tale of Echo and Narcissus and a setting of the world’s oldest complete song; and the Seniors adding the kinetic exuberance of Bollywood and Jati beats. Rhythm in the year’s cycle, rhythm in the earth and the sharing of its gifts with friends, rhythm in myth and music resonating through the ages, rhythm in the colorful pulse of modern life on the far side of the globe and the joyful noise you can make with the objects that surround you. Solstice, whether it occurs at the darkest part of the year or a month after (when there is still plenty of winter to endure), is a time to revel in togetherness, to celebrate the gifts we share and the fruits of our hard work, and to look forward to a season of growth. As will the new tree we wassail at the end of Solstice in hopes that it will thrive in our orchard, we sink our roots deeper and gather energy for the growing that is yet to be done.


– Sarah Pope and Maureen Milton

Annmarie Chesebro joins the Teacher Standards and Practices Commission

ACT Coordinator Annmarie Chesebro has been confirmed to the Teacher Standards and Practices Commission for the state of Oregon. The TSPC was created in 1965 to maintain and improve performance in the education profession by approving teacher preparation programs; licensing teachers, administrators, and other personnel; and taking disciplinary action when educators commit crimes or violate the Standards for Competent and Ethical Performance. Annmarie joins 16 other Oregon educators on the Commission; we are thrilled that her vision, intellect, and experience will now benefit teachers and students throughout the state. She will continue to run the teacher training program at the Arbor Center for Teaching, where she is guiding six Apprentices through the first term of their two-year MAT and licensure preparation, and to be a member of the faculty at Marylhurst University.

Cambium: The Case for Teacher Apprenticeship

Situating a small teacher-training program within an independent K-8 school on a 20-acre farm could be a recipe for obscurity. With an ever-growing number of avenues through which to pursue an MAT and public school licensure in Oregon, the Arbor Center for Teaching’s Apprentice model has the potential to sit anonymously on the sidelines as larger universities scoop up promising graduate school candidates.

In the past few years, however, the ACT program has begun to make its mark. Leading through quiet example, our program embodies core principles we believe are essential elements of teacher education reform. In particular, we emphasize clinical practice via a “co-teaching” model and seek to interweave theories investigated within graduate school courses with the practical concerns of teachers’ day-to-day classroom challenges. And we aim to help move teacher training forward in other school contexts as well. ACT staff have participated in recent conferences hosted by the Chalkboard Project, reviewed grants in support of teacher training improvements throughout the state, and served as consultants to public school districts moving toward incorporating such principles.

One impetus for experience-focused training is the hope that this will lead to longer tenure in the teaching field for our graduates. The Distinguished Educators Council recently released recommendations for improving teacher training in Oregon, citing an emphasis on classroom experience and effective mentors as the top priority. “Most practicing teachers believe they could have benefited from more time actually teaching under a mentor teacher’s tutelage before they began independent practice. There is a sense that pre-service and in-service programs are designed and implemented in a vacuum from the realities of classroom instruction,” the report states. In the ACT model, Apprentices teach full time for two years within at least two classroom settings. As they develop their own style and “stance,” link assessment to the next day’s lesson plans, and work to balance a teacher’s heavy workload, they receive coaching, wisdom, and survival tips from mentor teachers working alongside them. With ongoing and immediate feedback throughout each teaching day, ACT Apprentices have a steep learning curve but are well supported as they learn what it takes to succeed in this challenging profession.

Apprentices are propelled into responsibility as full members of the Arbor School faculty by the simple fact that they are needed to make our classrooms operate. Our mentor teachers expect to run their classrooms using the co-teaching strategies advocated by the Teacher Quality Enhancement Center at St. Cloud State University, making differentiated approaches, stations, team teaching, and careful one-on-one assessments possible. Teaching over two years in multi-age classrooms enables Apprentices to come to know students and their families deeply and to participate even more fully as the curriculum, learning celebrations, parent conferences, and school events cycle around again.

As Apprentices work to hone their practice according to the coaching and advice of mentors, these “lead” teachers advance professionally as well. Coaching a beginning teacher requires clear explication of purpose, tying each task and lesson arc to the broader aims for the class. At Arbor, the mentor role is respected and recognized as an avenue through which teachers continue to grow. In part, mentoring requires a different set of skills than those needed to work with children and adolescents. Mentor teachers join in and lead graduate seminars and have become eager not just to coach, but to learn from the Apprentices they come to know so well. During our ACT admissions season, mentor teachers help interview potential candidates, searching for Apprentices who show initiative and creativity. They know their classrooms and their own practices will be enriched by co-teachers who are willing to start disco-dance sessions during rainy recesses, who will lead students to love mathematics by enthusiastic example, and who bring a new perspective and set of questions to traditional areas of inquiry.

A second hallmark of the ACT program is the close connection of theory and practice. Accordingly, graduate courses with a pedagogical focus such as math, reading, or assessment occur on site at Arbor School, although Apprentices also join the larger Marylhurst University MAT cohort for courses aiming toward broad socio-cultural understandings, ESOL strategies, or social justice theories. At Arbor, Apprentices rush from shepherding carpools or convening reading conferences to rigorous discussions of educational innovators ranging from John Dewey to Nancie Atwell, Alfred North Whitehead to Bob and Ellen Kaplan. Graduate coursework is designed to apply theory directly to practice, to provide an avenue for unraveling the day’s teaching conundrums within a group of trusted colleagues, and to support Apprentices’ work with their particular students. Planning for the day ahead, reflecting on and assessing student understanding, crafting thorough narrative reports, and developing “Back to School Night” presentations are the stuff of both graduate and K-8 classroom work at Arbor.

To further bridge the potential divide between the university’s aims and the K-8 school’s needs, we ask mentor teachers to make suggestions for graduate coursework assignments that will help both Apprentices and children move forward. For example, intense focus on differentiation in reading during ACT seminars helps hone Apprentices’ reading assessment practices in order to advance the widely ranging abilities of K-8 readers in multi-age classrooms. In addition, we see the Arbor faculty as a natural audience for Apprentice writing, presentations, and questions. Arbor faculty meetings are often turned over to Apprentices who share their current insights about a particular aspect of teaching practice or pose questions for discussion among the faculty as a whole. This provides a chance for experienced teachers to affirm or extend Apprentices’ understandings and also to evaluate their own classroom practices. Later this fall, Apprentices will formally present the results of “action research” focused on the social curriculum to the Arbor faculty. Their studies range from developing leadership within multi-age settings to encouraging active listening among second and third graders. In considering together where and how to move forward from the discoveries and subsequent questions generated by Apprentices’ research, the teaching practices of Apprentices and Arbor faculty alike are elevated.

Theory/practice connections arise from our collaboration with Marylhurst University as well. Graduate “supervisors” visit classrooms at least once each week, co-teaching, planning, and directly observing the situations Apprentices are wrestling with and the students with whom Apprentices are trying to connect. Even the director of Marylhurst’s MAT program visits Arbor classrooms twice each month in order to study the classroom contexts within which Arbor Apprentices work and to adapt the university’s support accordingly. MAT students placed in other cohorts have visited Arbor classrooms in order to see particular principles in action.

With our own teaching program continuing to develop an individualized and intensive preparation model, we remain enthusiastic about seeing our core principles take root in other contexts as well. We are intrigued by a generous collection of TeachOregon design grants the Chalkboard Project has just awarded to collaborations between various public school districts and university teacher preparation programs in Oregon. We hope to see that rigorous, experience-focused teacher preparation that intentionally links theory and practice can flourish throughout the state.

–Annmarie Chesebro, ACT Coordinator

Visit ACT at AMLE

Come visit us in booths 505 and 507 at the upcoming AMLE (Association for Middle Level Education) Conference November 8th -10th at the Oregon Convention Center in Portland, OR.  We will be exhibiting and conducting seminars in booths 505 and 507 of the conference, and will be conducting a teacher workshop at 3:45 on Thursday November 8th.  

The Necessity of Algebra

Although a number of people have already commented on Andrew Hacker’s July 29th article in the New York Times (“Is Algebra Necessary?”), I feel compelled to add my views to the mix. Mr. Hacker makes some strong points. I do not dispute the depressing dropout statistics that he cites, nor even the notion that algebra may contribute substantially to those statistics. And, indeed, Mr. Hacker is correct in some of the prescriptions he offers; but as for the notion that algebra should be dropped wholesale as an educational requirement, he is, I’m afraid, deeply misguided.

Mr. Hacker calls for the study of quantitative reasoning, the history and philosophy of mathematics, and mathematics in art and music as part of the mathematics curriculum. He is absolutely right, and especially right with respect to math in the elementary and middle grades, where I happen to teach. It is our responsibility to teach not just the “bare bones” of mathematical literacy (if those bones can really ever be bare) but to imbed that teaching in an understanding of math as a human enterprise, to expose the connections between math and literature, math and art, to teach math as a lens through which the universe can be seen and better comprehended. The failure of most math programs, I’m sad to say as a teacher, lies not in the intrinsic difficulty or abstruseness of the subject matter, but in the way that it is often taught: as something desiccated, disconnected, and lifeless. However, algebra, properly understood and properly taught, is not the problem – rather, it is the very key to the sort of rich mathematical understanding that every child deserves and every child can achieve. Algebra is the mathematical art of abstraction; it is that which allows a student to move from the particular to the general – surely just the sort of thinking that Mr. Hacker would hope for on the part of an informed citizen. I will grant that some of the more esoteric subjects that Mr. Hacker mentions as part of the algebra curriculum – “vectorial angles,” say – need not be mastered by every student (I teach algebra to sixth-, seventh-, and eighth-graders and manage to avoid the subject of vectorial angles), but a strong and thorough grounding in basic algebra is a fundamental part of mathematical literacy. Mr. Hacker’s vision of courses in practical mathematics would be very difficult to realize without some algebraic facility on his students’ part; in particular, I would defy anyone to develop a robust understanding of the Consumer Price Index without basic algebra skills.

But the flaw in Mr. Hacker’s thinking runs much deeper than this. As Rob Knop, for instance, suggested in his blog on the subject, Mr Hacker’s view is, at its heart, depressingly utilitarian. Mr. Knop was speaking largely of higher education when he wrote that, “A liberal arts education is all about expanding your mind, all about being able to think,” but I would suggest that the statement is perhaps even more true of elementary education. Yes, to some extent it is our duty as teachers to train future workers, at least in the sense that we should strive to inculcate in our students the habits of discipline, the ability to work both independently and collaboratively, and the skills to think critically. And yes, we certainly bear the responsibility for educating future citizens: people who can reason clearly, who have a sense of civic duty. But even this is too limited a description of a teacher’s job. Because our responsibility is also to the individual student: we should be concerned not simply with imparting skills or knowledge, but with lifting the spirit, with lighting the flame of intellectual curiosity, with opening young eyes to both the wonder and the problems of their world. Algebra – sadly so often regarded as drudgery – is a key element in this kind of genuine education. To give just one example, we can say a great deal about gravity, but Newton’s Universal Law of Gravitation is one of the clearest, truest, most succinct, and – yes – most beautiful statements that has been made on the subject; without a genuine understanding of algebra, that statement is meaningless. Our real duty as teachers is not merely to prepare our students for some “real world,” and certainly not merely to prepare them for the workplace. If we deny them access to algebra, we deny them access to an entire intellectual universe.

Math is certainly hard to learn, and in my judgment much harder to teach. But most things that are worth doing are hard in one way or another. I am all for rethinking the way that math is taught in order to make it “as accessible and welcoming as sculpture and ballet.” But really appreciating either of those disciplines takes genuine work; and I doubt that there are many sculptors or ballet dancers who describe their jobs as “easy.” Mr Hacker is to be commended for proposing a bold solution to what is quite clearly a genuine problem. However, it would be sad indeed were his proposals actually to be adopted.

Linus Rollman
Math and Humanities Teacher
Arbor School or Arts and Sciences, Tualatin Oregon

Big Ideas for Curious Minds

With the end of the school year in sight, our teachers are turning their minds to summer planning and big aims for next year’s classes. This means developing a fresh iteration of the year’s thematic curriculum, and we have taken this opportunity to collect our thoughts on why we teach what we teach when we teach it. The result is a new issue of Cambium, a curricular journal written by our teachers three times per school year, entitled “Big Ideas for Curious Minds.” (Click the title to download the PDF.) In these pages Felicity Nunley reveals her strategies for planning and teaching a unit on Ancient Greece for her K-1 class; Peter ffitch creates a natural context in which to teach Portland history to his second and third graders in light of their developmental stage; Becca Blaney and Charles Brod integrate environmental science and creative writing by asking their 4-5 students to set folktales or creation myths in a world biome they are studying; and Linus Rollman makes a case for teaching Islam in middle-grade Humanities in the service of guiding students into thoughtful and knowledgeable discourse on different cultures’ answers to the great human questions.

Cambium is free and we encourage you to share it with any friends or colleagues who might be interested. If you would like to receive future issues, we’d love to add you to our subscription list: please email us at cambium@arborschool.org. All back issues are available for download here.

A Review of “Number Bugs” by Leon Spreyer

Arbor students were privileged to read an initial draft of Number Bugs by Leon Spreyer several years ago. Now that his book has been published, we are honored to offer a review of it. As the Director of Arbor School, I no longer have my own classroom, but I often lead reading groups at a variety of levels. In order to produce a credible review of Number Bugs I turned to a group of 4th graders and asked if they would join me in reading the book and writing about it. They were delighted to be asked.

The book is slim and could be read quickly, but we took a slow route through it, reading every word together — aloud — and stopping to explore the mathematical ideas that populate this story with such delicious frequency. The characters of the Number Bugs themselves, with their particular appetites for certain kinds of numbers, are “each different and charming,” say the students. ”Their names are creative, not like people’s names, and go with what they eat. The flavors of the numbers, like jalapeno & watermelon, are clever. Even the dialogue contains voices and ways of speaking that match the characters. Who needs articles or the missing words to understand what they are saying? The Number Bugs are religious about the numbers they can eat, and it is fun to know the tricks they use to decide what is edible.” The humanoids, from Archimedes to Pythagoras, are also interesting from an historical and a mathematical perspective. Whether or not you love math, you will take an instant liking to the cast of characters and their peculiarities. The students in my reading group became so attached to the characters that each took on the name of one of them. Eliana thoroughly enjoyed Erin Koehler’s illustrations and took it upon herself to copy the drawings and give each member of the group a rendering of the appropriate character for use on the cover of our reading folders. Eliana says that, “The characters are amazing, and even the bad ones are beautifully sculpted.”

We needed folders in order to contain all of the calculations and quotations we accumulated over the time of our reading. Hastin appreciated all the number concepts which the book explores: even/ odd, prime, Goldbach’s Conjecture, square, triangular, infinite, etc.. We have a detailed record of each of the rules, definitions, and elegant quotations we encountered in the course of our reading, whether it is the divisibility rule for 3, the definition of a perfect number, Eratosthene’s Sieve for finding prime numbers, or a fabulous definition of infinity — a room without a floor, walls, or a ceiling. Hayden writes, “I enjoyed the perfect numbers the most, and how Archie explained them on the leaf boat. I liked how we found all the factors to 496″ so we could prove it was a perfect number. Max also loved working with perfect numbers and spent a long time factoring 8096, the next perfect number after 496. Lucy loved the palindrome numbers and found out how many steps it takes to make a palindrome out of all the numbers between 1 and 100 — numbers 89 and 98 will surprise you!

In sum, the Arbor students think the book deserves a 5-star rating, and they think anyone would enjoy it. They cannot wait until the sequel comes out and look forward to reading it together to find the keys to more of the mathematical treasures with which Mr. Spreyer chooses to stock the book.

Kit Abel Hawkins, Director, Arbor School of Arts & Sciences

Discussion of “The Finland Phenomenon: Inside the World’s Most Surprising School System”

This evening, Kit Hawkins, Director of Arbor School; Peyton Chapman, Principal of Lincoln High School; and Mo Copeland, Head of Oregon Episcopal School will lead a panel and discussion following the screening of the film “The Finland Phenomenon:  Inside the World’s Most Surprising School System.” This event is hosted by the OES Parent Community Link and will take place at Oregon Episcopal School. View a trailer of the film here.

Two articles of interest:

Why is Congress Redlining Our Schools?” by Linda Darling-Hammond in The Nation.

What Americans Keep Ignoring About Finland’s School Success” by Anu Partanen in The Atlantic.

Apprentice Teachers Reflect on their First Work Samples

As Apprentices work to complete and assess their work samples, we have returned to some foundational teaching principles.  First of all, careful forethought and planning are essential—especially in determining the central purpose of a unit of study.  After aims are carefully considered and lesson plans drafted, however, a thoughtful teacher makes many adjustments to these initial plans and ideas.  Careful “diagnostic teaching” and assessment mean that ideas must be revisited for particular students, while others find related questions and ideas to explore more deeply.  To make such adjustments, teacher reflection must be ongoing and ubiquitous.

After completing a study of time with his 2nd and 3rd graders, Apprentice Marc DeHart writes,

In the course of this work sample, I really enjoyed exploring the big ideas. The children proved to me (again) that my enthusiasm is contagious. When I got excited about the big ideas they came right along with me and conversely, if I seemed a little lost they drifted. I started out a little dubious about the idea of a whole unit based on asking, “What time is it?”  Even so, I was excited about the idea of “capturing” time. I think I successfully engaged the children with the same big ideas that finally got me excited about time.  They indicated this to me by reflecting on the big conceptual ideas in our post-assessment. They shared great thoughts with me like, “I learned that time can be found everywhere, affecting everything,” “Time is not just in clocks,” and, “Nothing could move anywhere without time.”

ACT Teacher Training Update

This month Apprentices are teaching from their first “work sample”.  This is a string of 10 lesson plans around a theme, topic or essential question that grows out of the curriculum of each classroom.  Apprentices design the lessons assessments and then take the helm in their classrooms to teach and assess these lessons throughout the spring.  Toby has designed a series of poetry workshops for his K/1st graders, Jess and Marc are exploring the scientific and mathematical aspects of time, and Johannah will soon embark on a study of alternative energy that will culminate in her students making an informed case to targeted political leaders about costs and benefits of various alternative energy options.

In our ACT Seminar, we’re focusing on the pedagogical questions that surround the teaching of mathematics.  We’ll examine cultural assumptions and contexts surrounding the teaching and learning of mathematics, focusing particularly on misconceptions that have traditionally led to a sharp divide between those who perceive themselves to be mathematically adept and those who are less confident with this central discipline.  Part of this work entails becoming math students again—particularly in terms of the study of algebra.  Along with about half of the Arbor faculty, Apprentices are in the midst of working with Arbor teacher, Linus Rollman and his newly published algebra text, Jousting Armadillos.  These weekly sessions are meant to give our group an experiential view into where we’re aiming as a K/8 school, to help us remember what it is to wrestle with mathematical challenge, and to engage in discourse about math teaching even as we experience math once again as students.