Co-teaching in Public School Contexts

Danielle and Lauren co-teach together in Lauren's 3rd grade at Harrison Park Elementary in Portland Public Schools.   In the winter term, Danielle will spend four weeks in an intensive residency there.  Throughout this fall, she has traveled to Harrison Park for one day each week, coming to know the students, studying Lauren's methods, learning about the classroom and school culture, and taking on increasing responsibility in preparation for January.

Danielle and Lauren co-teach together in Lauren's 3rd grade at Harrison Park Elementary in Portland Public Schools.   In the winter term, Danielle will spend four weeks in an intensive residency there.  Throughout this fall, she has traveled to Harrison Park for one day each week, coming to know the students, studying Lauren's methods, learning about the classroom and school culture, and taking on increasing responsibility in preparation for January.

A vital part of the two-year teacher residency experience is co-teaching in a public school throughout the fall and winter.  For this, we search for school contexts that differ from Arbor School in important ways.  For some apprentices, this has meant co-teaching in dual language classrooms, thus helping build teaching practices in Spanish and English.   For others, it means teaching at another age group.  For example, Elizabeth has moved from teaching K/1st grade at Arbor to teaching 5th grade at nearby Stafford Primary School.  Danielle has gotten the chance to move from her K/1st grade at Arbor to a Portland Public School's Harrison Park and a 3rd grade classroom that includes students from many cultural and linguistic backgrounds, including Spanish, Chinese, Russian, Romanian, Ukranian, and Vietnamese.

Across these experiences, all apprentices experience a co-teaching model as they move toward more responsibility in their public school classrooms.  This might mean observing their co-teaching mentor lead the lesson while assisting individuals or small groups, teaching in parallel groups, or team-teaching with both teachers actively involved in the lesson at hand.  During the winter term, apprentices spend a full four weeks in their public school context, designing, facilitating and formally assessing a unit in literacy, mathematics or science.

At Trost Elementary in Canby, Oregon, Elsie gets to work with master teacher, Victoria Aguilar. Together they teach 60 fifth graders in both Spanish and English, focusing in particular on math and literacy.  

At Trost Elementary in Canby, Oregon, Elsie gets to work with master teacher, Victoria Aguilar. Together they teach 60 fifth graders in both Spanish and English, focusing in particular on math and literacy.  

After this winter experience, apprentices return to Arbor to take full responsibility for their classrooms for the month of April.  The public school teaching intensive also serves to highlight parts of apprentices' teaching practice that need more focus during the spring term.  This they can do with the coaching and support of their Arbor mentors throughout the spring term.  Moving between school contexts during this second year benefits both schools as apprentices bring new questions, methods, and approaches from one classroom to the other.

Nature Journals

In their second year of teacher residency and graduate work, Arbor Apprentices undertake a thesis project that grows from a particular teaching practice.  

Danielle has her kindergarten and first graders working to become scientists who listen and look carefully in the Arbor woods each week, recording their observations in writing and through diagrams.  Danielle is grounding some of her research in the text Taking Inquiry Outdoors:  Reading, Writing and Science Beyond Classroom Walls by Barbara Bourne.

Danielle with her scientists in the Arbor woods.

Danielle with her scientists in the Arbor woods.

This scientist heard a "bird call" and observed a banana slug.

This scientist heard a "bird call" and observed a banana slug.

"That was my spot.  It had a lot of ivy."  The observation of one of Danielle's scientists.

"That was my spot.  It had a lot of ivy."  The observation of one of Danielle's scientists.

Oriana is helping her 2nd and 3rd graders hone their descriptive writing skills, using simile and metaphor to convey what they notice in their own “woods spot.”  Exploring the possibilities of “place-based” education at Arbor and in their public school placements is central to Apprentices’ two-year teacher training.  

One of Oriana's writers describing the woods that surround her.

One of Oriana's writers describing the woods that surround her.

Considering a career in teaching? Looking for classroom experience with a master teacher-mentor at an innovative K-8 school?  We are accepting applications for our 2016-18 cohort now. For more information, please visit our website, www.arborcenterforteaching.org. We welcome your questions; e-mail act@arborschool.org or call 503-638-6399 to schedule an inquiry visit. The application deadline is March 1, 2016.

Environments & Geography Summer Seminar

The Environments & Geography Summer Seminar will bring 20 teachers to Arbor School’s campus and to a public school co-location (TBA) for 30 hours of free workshops in using thematic teaching to introduce mapping and geography skills to elementary students.  The seminar will run from 8:30 - 3:00, Monday 20 July to Friday 24 July, 2015.  

Participants will earn 30 PDUs and a free copy of Arbor’s Environments curricular guide with Common Core alignment analysis. This book covers a year’s work in exploring natural systems from local to global, with heavy emphasis on honing mapping and surveying skills to better understand the relationships of species and ecosystems, as well as human impact on the environment. The seminar will give participating teachers the tools they need to integrate local and global mapping projects into existing curricula and to consider thematic framing that gives greater relevance and endurance to important ideas and skills. Participants will do some of the field work set out for students to explore the process of adding layers of information about ecological niches, structures, topographic features, etc. to local maps. They will have the chance to compare and debate the merits of different world map projections, just as students of our curriculum do. They will gain strategies for directly teaching mapping skills and leading discussions of environmental science concepts on the basis of geography, climate, botany, adaptation, and more.

To receive more information about the seminar, please use this form to send us your contact information.

Environments                                                                                                                                   

Summary: Curriculum introducing studies of environmental niches, habits, ecosystems, biomes, the human body, and oceanography to fourth and fifth graders at the Arbor School of Arts & Sciences.

Authors: Daniel Shaw and Eliza Nelson

The Idea of Arbor School

The Idea of Arbor School

9780982136379_cov_web.jpg

Author: Kit Hawkins 
ISBN: 978-0-9821363-7-9
Format: Paperback
Size: 8.5 x 11 
Price: $35

Summary: Written by Kit Hawkins, Founder and Director of the Arbor School of Arts & Sciences, in Arbor's 25th year, The Idea of Arbor School is an "attempt to capture a real place and the truth of a school’s evolutionary process. [It is] an attempt to stand in contrast to all the negative press about schools and point to what has been done and might be done elsewhere."  

Individual chapters treat:

  • First Questions about Children and Schooling 
  • Philosophy, Principles, and Precepts 
  • Learning and Teaching 
  • Curriculum 
  • A Sense of Belonging 
  • Self-Renewal and Reflective Practice 
  • School as an Institution 
  • Tradition, Ritual, and Culture 

Beyond Marshmallows

BEYOND MARSHMALLOWS

Lecture by Dr. Walter Mischel

Sunday Novermber 23, 2014
3:00 PM

Lincoln High School Auditorium
1600 Southwest Salmon Street, Portland, OR

Sponsored by Arbor School and hosted by Lincoln High School, this lecture is Dr. Mischel's gift to the community where two of his grandchildren are growing up. 

Dr. Mischel's pioneering work on self-control continues to dominate thinking in this crucial arena of development.  With his new book The Marshmallow Test: Mastering Self-Control, Dr. Mischel goes beyond thinking about assessing for willpower to understanding more deeply how self-control and executive functions work in the mind and brain, and how they can be enhanced

Please join educators, parents, and community members from throughout the region for Dr. Mischel's discussion of self-regulation and the development of the character traits that will enable students to pursue their highest aspirations. 

Seating is limited, so please make your reservation here.

*Dr. Mischel will be signing his new book at Powell's Books on Burnside at 7:30 PM on Friday 21 November 2014.

ACT IN THE PRESS

Teacher Training 

Annmarie Chesebro, ACT coordinator and adjunct professor in Marylhurst University’s MAT program, has an article titled "The Teacher Coach" in the Spring 2014 issue of NAIS's online publication Independent Teacher. Read also her article titled “Education Innovation” that appeared in the Fall 2006 issue of the magazine Open Spaces.

Heather McLendon, social media strategist and web content coordinator at Marylhurst University, posted her article titled "The Arbor School Partnership" from August 2013 on the Chalkboard Project's blog. The article features the distinctive relationship between the college and Arbor School that allows Arbor Apprentices to earn their MAT degrees.

Read the Chalkboard Project's interview with ACT graduate Johannah Withrow-Robinson (ACT '12, Whitman '10) about Arbor's ACT program in collaboration with Marylhurst University (under “Our Voices, Our Schools”).

Jenny Lowe Cook (ACT '08, St. John's '06) reflected on sharing Homer with students in her essay "When the Ancients Speak, Children Listen" in St. John's Fall 2010 issue of The College.

Lauren Kristensen Koepl (ACT '10, Claremont-McKenna '07) discusses her ACT thesis research in "My Paper is Lighting Up: Self-Assessment in K-1 Writing" in the Fall 2011 issue of Independent Teacher.

School Leadership 

Kit Abel Hawkins, Director of Arbor School, on the founding of Arbor School.

Kit's guest opinion in "The Oregonian" on keeping curiosity at the heart of education standards.

Publications 

The Molalla Pioneer ran an article on Linus Rollman's visit to Molalla River Academy, where students were using Arbor's first algebra textbook, Jousting Armadillos and Other Equations: An Introduction to Algebra.

Arbor & Arbor Graduates 

Read "The Future of Oregon Public Education: A Q&A with Ben Cannon, Governor Kitzhaber's Education Policy Advisor" in the February 2012 issue of Metro Parent. Ben taught Senior Humanities at Arbor and was recently appointed to a new position overseeing all public higher education in Oregon, the seven universities, 17 community colleges, and state-paid financial aid.

Arbor was featured in the February 2011 issue of Portland Monthly.

Sam Alden, Arbor '03 and Catlin Gabel '07, continues to work on his graphic novel Eighth Grade. Sam was a 2012 Sitka Fellow in Sitka, Alaska.

Abby Conyers, Arbor ’06 and Catlin Gabel ’10, mentions her interest in teaching in her interview featured in The Oregonian’s 2010 Academic Achievers column.

Several articles have appeared in the press focusing on Arbor’s eighth grade Senior Project requirement:

Christina Schmidt, Arbor ’09 and currently at Lincoln High School, raised funds to build a school in Cambodia.

Natalie Lerner, Arbor ’10 and currently at Oregon Episcopal School, developed healthy, low-cost recipes and created a cookbook complete with an online cooking blog for children.  Click here to learn more.

Where have all the questions gone?

Young children are born with "an overpowering need to know" (Engel, 2013), however the number of questions they ask drops off quickly the more years they spend in school.  How can we make sure that our classrooms keep students’ curiosity alive?

Senior Lecturer at Williams College and New York Times contributor, Dr. Engel researches practical ways that teachers and parents can encourage question asking and schools can make inquiry a priority.

Please join educators, parents, and community members from throughout the region for a lecture by Dr. Engel, followed by a panel discussion and series of workshops that will ask how we can keep students' innate curiosity alive in a variety of educational contexts.  

 

"THE CASE FOR CURIOSITY"

Lecture by Dr. Susan Engel

Co-sponsored by Marylhurst University and Arbor School
Thursday October 10, 2013
7:00 PM - 9:00 PM

Saint Anne's Chapel, Marylhurst University
17600 Pacific Highway (Hwy. 43), Marylhurst, OR 97036-0261  

 

"CURIOSITY AT THE CORE"

Panel and Workshops 

Friday October 11, 2013
8:30 AM - 3:00 PM

(includes complimentary luncheon)
The Arbor Center for Teaching at Arbor School
4201 SW Borland Rd, Tualatin, OR 97062

PANEL

Susan Engel, Williams College; Katherine Hawkins, Arbor School Director; Peyton Chapman, Principal Lincoln High Principal; Dr. Mark Girod, Western Oregon University Dean of Education; Ben Cannon (moderator), Education Policy Advisor to Gov. John Kitzhaber.  

WORKSHOPS

(1) Susan Engel, Williams College;  (2) Thompson MorrisonTechstart Education Foundation; (3) Marna StalcupThe Right Brain Initiative; (4) Maureen Milton & Shelly Buchanan, librarians at Arbor School & West Linn-Wilsonville School District (5) Mark HansenOregon Writing Project, (6) Rob van NoodTinkering Workshop.

“Simply put, what children need to do in elementary school is not to cram for high school or college, but to develop ways of thinking and behaving that will lead to valuable knowledge and skills later on. . . .”

Playing to Learn, Op Ed, The New York Times, 2/1/2010

“The evidence is quite clear: when children are curious, they learn. It turns out that curiosity in school is not merely a nicety but a necessity. So, where does it come from?”

Children’s Need to Know: Curiosity in Schools, Harvard Educational Review, Vol. 8, No. 4, Winter 2011

SUSAN ENGEL is Senior Lecturer in Psychology, and Class of 1959 Director of the Program in Teaching at Williams College. Her research has focused on the emergence of narratives, children’s autobiographical memory, imaginative processes in childhood, and the development of curiosity.

Read more about Susan Engel

Who Should Attend?

  • Parents

  • Educators
    • Pre-Service Teachers
    • In-Service Teachers
    • School Administrators
    • Curriculum Supervisors
  • Colleges of Education Faculty
  • School Superintendents

“Children are born with an overpowering need to know. They want to know what every object feels and looks like and what will happen when they attempt to do different things with that object. They want to know why people behave the way they do. This voracious appetite for knowledge defines us as a species. . . .”

The Case for Curiosity, Educational Leadership, Vol. 70 No. 5, 2013

Licensed Teachers can receive PDU’s for both the lecture and the workshops.

All events are free and open to all who register.

Keeping Curiosity at the Heart of Education Standards

Kit Hawkins wrote the following opinion column for The Oregonian on September 28:

The Common Core Standards are on the minds of many teachers, parents and policymakers as school opens this fall. There are those who believe this will be the reform that will turn American schools around, assuming that it is American schools that need turning rather than a culture that permits 22 percent of its children to live in poverty. There are those who fear evaluation of teachers using metrics associated with student tests aligned to these standards. Whatever one’s point of view, 45 of our 50 states have adopted these standards, and they have thus become a reality to which educators must respond.

The Anchor Standards in literacy are particularly powerful and surely foundational. But purely academic goals fail to incorporate central human aims that we must also hope to see in evidence in our children if they are to flourish. Among these aims: the ability to self-regulate, an attitude of curiosity, the penchant for exhibiting kindness toward others, the inclination to be a contributing member of society, the capacity to persist against difficult odds, the drive to frame and test solutions for problems. By starting at the level of these fundamental human aims, we might well avoid limiting the horizon of our thinking about what we strive to nourish in our students.

Yes, let us work together on sharing goals for enhancing our students’ capacities for rigorous thinking as readers, writers and mathematicians. But let us also work together on constructing schooling aims that are at once more critical and more enduring. Such aims have to do with habits and attitudes that persist when the names of the characters in the novel a student studied as a freshman disappear. These aims have to do with ways of thinking and being that continue long past skill with the quadratic equation.

In her article ”Children’s Need to Know: Curiosity in Schools” (Harvard Educational Review; Vol. 81, No. 4) Susan Engel explores one of the most critical of these attitudes for students as learners — that of curiosity, the posing of provocative questions and the having of wonderful ideas about how one might find answers. Engel has begun looking at how schools do and do not support the maintenance and development of student curiosity. With our focus on knowing and being able to answer testable questions, we too often forget to leave room not only for the questions students have but for the intellectual space in which they can pose them and pursue them fruitfully. Engel calls on us to model curiosity, to plan purposely for opportunities for students to pose their own questions, to track the progress of questioning in our classrooms, to assess the quality and even the quantity of curiosity in our students and, thereby, our success in fostering it.

As we discuss the Common Core Standards, let us remember to articulate and activate simultaneously the equally fundamental aims that schooling must undertake. As school starts this fall, let us keep curiosity at the core.

Kit Abel Hawkins is the director of the Arbor School of Arts & Sciences in Tualatin.

Arbor School & Marylhurst

A new article on Marylhurst University’s web page features the partnership between the college and Arbor School that allows Arbor Apprentices to earn their MAT degrees. In the ACT model, “[a] two-year intensive approach situates the learning inside the classroom, rather than the university. [ACT Director Kit] Hawkins described the university as being ‘complementary’ to the classroom. This is not to dismiss the importance of accredited, master-level coursework. Rather, it synthesizes the two; theory and experience inform one another simultaneously.” Read the full text here—and note the mention of another exciting Arbor-Marylhurst cooperative project: bringing Dr. Susan Engel to the two campuses October 10-11. Dr. Engel’s lecture, panel discussion, and teaching workshops are free and open to the public, but space is limited, so register now!

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