Arbor Center for Teaching Blog

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, Arbor School‘s Director; 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.

ACT grad published in Independent Teacher magazine

Lauren Kristensen, ACT ’10, has published an article based on her thesis research in the prominent online journal Independent Teacher. Lauren’s innovative work on goal-setting and self-assessment in her K-1 classroom continues to inform Arbor practices today and we are proud to know her ideas are reaching a national audience today! Visit www.independentteacher.org to read “My Paper Is Lighting Up: Self-Assessment in K-1 Writing.”

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.