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A look inside our teaching and learning.

Expect to read the entire gamut of classroom activity, from "big picture" overviews to detailed reflections on one day's work. Posts are authored by faculty.

Problem Solving I

We make use of the entire classroom to engage learning.

Maker Studio 1

Tinkering and experimenting underscore deep learning.

Graph Algorithms

We emphasize communication and writing, even in math.

Physics

Our lab lets us base individual learning on shared interests.

Staging Literature

We discuss literature to understand others.

Big History (High School)

To answer big questions, we need to know how to ask them.

Big History: Science

Our middle school science program capitalizes on the school's spaces to perform experiments.

Intermediate Python

We use code to make and build things, including art.

Literature 1

The meaning of literature is palpable, quite literally.

Latin 1

In Latin, students bring an ancient language to life through collaborative learning and historical engagement.

Build Week

On taking risks and taking advantage of opportunity.

In the classroom

In the classroom

In Problem Solving 1, we make use of the entire classroom to engage students in a number of teaching and learning modes.

The primary purpose of this course is to introduce our students to a wide variety of problem solving themes and techniques, as well as to practice skills that will stand them in good stead throughout their years at Proof School. To this end we are steadily progressing through a sequence of topics including tiling problems, crafting precise definitions, proof by coloring, symbolic logic, the Pigeonhole Principle, elementary counting, and many more topics to come.

To make effective use of our classroom space, Sachi and I have developed a number of "teaching modes." For instance, at times the entire class sits on pillows on the floor surrounded by white boards. This mode allows for engaged thinking and whole class discussion. At other times students work at tables individually or in pairs on sets of problems designed to lead them through a new mathematical idea. On occasion, Sachi and I split the class in half based on students' prior knowledge to teach separate (but typically related) lessons.

In order to expose students to the spectrum of classic math questions and solution methods, we also run an IF-AT (Immediate Feedback Assessment Technique) three times a week. Students work on a set of five multiple choice questions in randomly selected groups of three, which are shuffled each week. Once a group agrees on an answer they scratch off the corresponding silver rectangle on their "scratch-and-win" answer sheet to see if there is a star underneath, indicating a correct answer. Besides being entertaining, this exercise teaches students to explain their reasoning in a convincing manner, instills the habit of listening carefully to others in order to learn how to solve a problem, and promotes collaborative decision-making.

Our evaluation of each student's performance in the course will be based on their engagement with material during class time, the quality of their written work, the level of completion of the contents of their math folder, and on in-class assessments given two or three times during the block.

-Sam Vandervelde

In the classroom

In the classroom

Maker Studio is where tinkering and experimenting underscore real learning.

Maker Studio 1 got off to a delightfully messy start last Wednesday! We dove right into making with Scribble Bots, an activity developed by the Exploratorium. Students were challenged to use motors, markers, duct tape, batteries, recycled materials, and hot glue sticks to build machines that draw.

We got our first taste of tinkering: experimenting with materials, developing intuition about how to use them, and inventing, improving, and extending. The activity was framed by a goal and a set of materials, but no explicit instructions. This created opportunities for students to develop their own ways of using the materials.

For example, several students created robots that spun in the air rather than wobbling on the ground. I learned, along with the students, that markers can splatter--and splatter quite far! Some students dismantled markers and attached the marker tips and innards directly to their robots. A “blender” was built; popsicle sticks were turned into wheels; and fake mustaches were used to connect wires and batteries.

Devoting a substantial part of our middle school program to Maker Studio is a choice that is unconventional yet very much aligned with our broader approach to education. At the surface, Maker Studio will help students develop skills and understanding, enabling them to tackle a range of hands-on projects. Over time, they’ll become increasingly able to turn their ideas into physical reality. Beyond that, Maker Studio serves as a fun, attractive means through which students can develop critical dispositions as learners, problem solvers, designers, and communicators. We deliberately cultivate a culture where failure is not only allowed, but embraced as a productive part of experimentation.

Throughout our morning of scribble bot building, for example, we experienced ways of learning that we’ll work on throughout the year. We learned through experimentation and discovery rather than explicit instruction, developing our tolerance for ambiguity along the way. We suffered frustration when our ideas failed, then celebrated after successful troubleshooting. We drew inspiration from one another and turned to classmates for help. We relished the process and experience, rather than an end product, knowing that our work would be dismantled at the end of class. We built stamina and a taste for pushing our work beyond our first effort, by improving our projects and trying new ideas for a full 90 minutes.

Next time you’re at school, check out the scribble bot test paper on display in the front office!

-Kathy Lin

In the classroom

In the classroom

At Proof School, communication is a core focus across the curriculum. That includes courses in mathematics.

"Graph Algorithms" is the most advanced math class offered at Proof School this block; the level is roughly on par with an undergraduate class for sophomore math majors. As with other Block 1 courses, the main focus of the class is on the process of doing mathematics, with an emphasis on creative problem-solving and rigorous proof.

For those not familiar with the field of graph algorithms, here is a quick introduction. In mathematics, a graph is a set of points (called nodes), some of which are connected by lines (called edges). Graphs are used to model many real-word situations: cities connected by roads, computers on the Internet, positions in a game connected by legal moves, or a social network of people connected by friendships.

An algorithm is a set of precise instructions for solving a computational problem. Graph theory abounds in such problems: for instance, given a graph, how can you tell how many connected pieces it has? How can you tell if it has cycles? Often, the edges of a graph will have numbers associated to them--corresponding, e.g, to the length of a road or the maximal capacity of a pipe. This leads to further questions, such as: how do you find the shortest path between two nodes? How do you select a subset of edges of minimal total length that will allow you to get from any node to any other? What is the maximal possible flow through a network of pipes with specified capacities?

Solving problems like these is not just a matter of programming a computer to search through all the possibilities. Even for relatively small graphs, the number of cases to check grows exponentially and soon becomes too large for even the most powerful computer to handle. The field of graph algorithms uses our theoretical understanding of graph theory and data structures to come up with clever methods for solving such problems. Often, the algorithms themselves are deceptively simple; the interesting part is understanding why they produce the correct answer and proving that they are guaranteed to do so.

Like all math classes at Proof School, our class meets for about two hours a day, with a break in the middle. Students spend much of their class time working on problems in teams of two or three. Since this is the most advanced class in the school, the students' level of mathematical sophistication is quite high, so I do not shy away from giving them serious "problems" rather than "exercises" to think about. The students know that getting stuck is a normal part of the process; I am always available to provide hints, but often the students will refuse my help because they want to figure out the solution for themselves.

Once everyone has gone through all the problems, the teams present their arguments to each other. At this point, they often discover that a proof which seemed clear in their minds can be quite hard to explain in an organized and coherent fashion--and might even turn out to be wrong. Listening to their peers' presentations, students learn to be on the lookout for subtle gaps in reasoning that can completely invalidate an otherwise correct argument. If a gap is found, the class works together to fix it. It is wonderful to see the students' sense of collective accomplishment when they manage to fix the flaw in a particularly thorny proof!

In addition to oral presentation skills, students also get a chance to practice their mathematical writing. Each student is responsible for a careful write-up of the solution to one or two problems each week. Some of the students already know LaTeX (the typesetting program used by professional mathematicians); others are learning it on the fly. By the end of Block 1, our class will have produced a mini-textbook on graph algorithms: the material in my handouts and problem sets will be supplemented by solutions written by the students themselves.

The sequence of increasingly precise formulation of ideas that I ask my students to follow--from brainstorming to discussing to explaining to writing--is a progression that every mathematician will recognize. But, of course, it is not limited to mathematics. The ability to develop an idea from a vague intuition into a fully fleshed-out, persuasive argument is vital for every human endeavor. My goal in all my classes is not just to teach the students mathematics (though I certainly want them to learn a lot of math!), but to use mathematics to teach them how to think better--more powerfully, more precisely, and more creatively.

For their final project in my class, students will have a choice of a more "math-y" or a more "CS-y" project. They can choose to learn an algorithm not covered in class by reading the original paper where this algorithm was introduced. (Fortunately, we are dealing with one of the rare areas of math where research papers are relatively accessible to beginners.) Or they can focus on implementing one of the algorithms that they've learned in class, paying careful attention to issues of running time and appropriate data structures. I am really looking forward to working with the students on these projects: I am sure I will learn a lot from them as well!

-Mira Bernstein

In the classroom

In the classroom

The physics lab lets us base individual learning on shared interests.

We have been laying the preliminary groundwork to understand the language of motion, or kinematics, both graphically and analytically. The students get to think about one-dimensional motion, their representation using vectors, and using motion sensors to get a kinesthetic idea about velocity and acceleration. The ensuing hectic running around could possibly earn students PE points! Our first lab activity was to design an experiment to simulate constant velocity motion by overcoming the hurdle of friction, using it to their advantage instead. Based upon a suggestion from a student who drew an analogy to parachutes, we build our experiment around dropping paper cones and measuring their velocity.

Our first Flex Friday was used to customize student learning and exploring extensions. We divided our class into an experimental group and a theoretical group, broadly based on the lines of student interest and needs. Some students wished to solve challenging problems in kinematics while others wanted to discuss particular difficulties they were facing and dive into introductory calculus. Our theoretical group got started on problems which explored deeper relations between the math and its physical interpretation: what does a double root on a quadratic mean in terms of interpreting simultaneous events, for example?

The experimental group constructed accurate paper cones which served a dual purpose. They were used to measure both the terminal velocities as they were dropped from various heights, as well as lead a discussion on experimental errors. In the coming weeks, the cones will also serve the purpose of motivating a powerful method in the physicist’s toolbox, dimensional analysis, as we investigate drag force on the cones. We used the interesting spaces in the classroom and school for performing our cone drops, including the string sculpture well. It even involved Mr. Basu climbing up the fire escape to launch the cones to get more accurate data!

We will be spending the rest of the block developing a conceptual understanding of the conservation of energy and momentum. The plan for the next Flex Friday is to see a physics movie from the ‘60s developed by the Physical Science Study Committee at MIT and have it inspire the design of an experiment where we will study the conservation of momentum, blending the ancient (the ’60s, that is) and the modern. We also hoping the results of two-dimensional collisions will greatly benefit the pool players in our class!

-Kaushik Basu

In the classroom

In the classroom

What can we do when we confront something unfamiliar? Literature gives us one way to think through our options.

In Staging Literature—Proof's 7th and 8th grade language arts class—we've started the year reading two beautifully rich short stories that are nonetheless tremendously odd in many ways. In Gabriel García-Márquez's “The Handsomest Drowned Man in the World,” we met a small group of townspeople who re-imagine their own village in the course of telling to each other the likely story of a body that washes up on their beach. And in Franz Kafka's “A Hunger Artist,” we met a professional faster who strives desperately for honor and understanding in a world that views his “art” as only a passing fad.

Like the villagers with their drowned man, who must decide how they'll relate to the stranger in their midst, we discussed in class what options we have when confronted with something that seems unfamiliar—more specifically, a strange piece of literature, a story in which the characters seem “abnormal,” who perhaps value different things or live by different codes. We worked on moving beyond the “this is weird!” reaction in order to ask questions of the text, to try to understand it better on its own terms, and to find meaning in it. The methods of reading and interpretation that we've been cultivating have therefore been a practice in open-mindedness and compassion, as well as in intellectual curiosity.

Moving between full-class discussions, smaller group work, and individual writing, students have been learning to express their thoughts clearly and persuasively, using evidence from the text, and to listen to and engage with their classmates' ideas—not just agreeing or disagreeing but building ideas collaboratively. Our focus has been on a type of reading called close reading, in which students get to be detectives and treat the text as an intricate body of tiny clues to observe and interpret. This type of reading will form the backbone of all the writing they will do in high school and in college.

For the past two weeks, the students have been working on a multi-step brainstorming assignment to prepare them, in the coming weeks, to write and revise a short essay on one of the two stories we've read so far. Each of them has come up with a topic, mined the text for quotations related to that topic, found patterns among these quotations, come up with an initial hypothesis—a claim about how their topic works and its significance in the text as a whole—and done many free-writes along the way. Each step of the brainstorming that they've worked on for homework was one that we first practiced in class as a group. For example, students practiced finding patterns among a set of quotations and arranging them into groups: with each quotation on an index card, students sat in small groups on the floor moving the cards into different formations—using their visual and tactile senses to help them think flexibly and see the story from multiple angles.

This brainstorming assignment has challenged each student to use her analytic and creative powers to the fullest in order to create an original argument interpreting a piece of literature. And I must say, they have truly risen to the occasion and come up with some amazing ideas!

-Sydney Cochran

In the classroom

In the classroom

In Big History, we’re asking big questions, such as: How did the conditions come about which make our earthly existence possible?

To understand the origins of human life and the sources of its rich complexity, Proof School’s ninth- and tenth-graders are going back as far as science can take us, to the Big Bang. But how does one prepare mental room to learn 13.82 billion years of history? To get ready, we’ve been creatively imagining scale, learning how scientists work, and thinking about how different sources of knowledge interact.

Our first day, students made “discipline hats”—the kind we wear when we take on the perspective of a certain field, like cosmology or anthropology or statistics (only more literal!). Next, they interviewed for faculty positions at “Corn University”, a fictional agricultural college, answering questions like “How can your field contribute to our quest for a fuller understanding of corn?” and “What other types of scholars do you hope to collaborate with and how?” Students’ answers ranged from the humorous to the persuasive, but everyone came away with insight into how even a mundane-seeming subject can end up touching distant and interdependent spheres of knowledge.

To learn how science slowly winnows away the merely plausible from the well-founded, we looked in depth at theories that were long accepted before being discredited, such as the geocentric model, phlogiston, and the luminiferous ether. Many of the class were at first incredulous that scholars once took such theories seriously, but when asked how they’d design experiments to falsify these theories, they got a taste of how hard scientific advances can be! We laughed at scientists who had to be convinced of the basic facts of heredity by being shown that mice with their tails cut off wouldn’t have abnormally short-tailed offspring—then realized with some discomfort that we would probably have laughed, too, at Alfred Wegener when he proposed that the shapes of the continents could be explained by their having drifted away from a past arrangement as a supercontinent.

Learning in the Big History classroom is guided by big questions—including the ones we don’t have the answers to. Students have responded to readings with questions like: How was there no life, and then suddenly there was? Will the universe ever stop increasing in structure? How do people reconcile science with deeply held religious beliefs? Can humans ever learn everything there is to know? For me as a teacher, these questions are humbling, and inspire me to remember that while I may be bringing my class up to speed on developments in the human story, we are all ultimately traveling on the same journey. In the four weeks Proof School has been open, a new hominid species has been announced and NASA has reported the best evidence yet of water on Mars. What are we going to learn next?

-Austin Shapiro

In the classroom

In the classroom

Our middle school science program capitalizes on the school's spaces to perform experiments.

The middle school science program at Proof School has started off with an emphasis on hands-on experimentation, such as building toys that display interesting physics. We have been discovering how our experiments relate to Galileo's ideas about motion and the relevance of the experiments he performed to understand gravity.

Our classes are divided between discussions around ideas in Big History and exploring physics through activities. In this block, we are studying Newton’s ideas about motion in contrast to Aristotle’s on a terrestrial scale. We are also studying the way the worldview has been debated on the cosmological scale, comparing the "steady-state" theory with the Big Bang.

We are studying motion and learning ways to describe them graphically. We have capitalized on the natural spaces in the school to perform our experiments, many of them inspired by the students extending or creatively disrupting an activity. We rolled pool table balls down a natural incline in our classroom; after students noticed that the hand rails formed a better stage for the rolling experiment, we found a natural way to compare the accuracy of data for two related experiments.

We had seen a mathematical relation begin to develop, which was further explored in an activity where students tied small metal spheres on a piece of string and dropped them on a wooden board. We performed blindfold tests to determine if students could distinguish differences in the frequency of sounds these spheres produced when they hit the wooden board. Some took the initiative to record audio data, which we analyzed to identify interesting artifacts like bouncing and background noise.

In Big History, most of our discussions are based on the students' perceptions of interesting questions. We discuss which questions could really belong to the scientific realm. In particular, we have been discussing our present vision of the future, but we have also discussed how those visions might change over the next 25 and 100 years. Our goal is to identify problems that affect our civilization.

We're also looking backward by exploring the Big Bang as an "origin story," exploring Olber’s paradox of the dark night sky, and the bearing it has on the steady-state model of the universe versus the Big Bang. In the process, students are learning to test claims from different scientific ideas and supporting them with evidence from what they research on a certain topic.

Several of the scientific discussions we have are staged out. In our last class, as we were discussing Hubble’s ideas and his discovery of redshift of galaxies, the students got a firsthand view of the Doppler effect by throwing a bunch of pens at regular intervals while walking away from each other. No pens or students were harmed by the activity.

-Kaushik Basu

In the classroom

In the classroom

We use code to make and build things, including art.

Intermediate Python is taught downstairs on Monday and Wednesday mornings. The room has been equipped with a "sticky note" whiteboard, which I use to annotate code shown on a projector.

Students in this class are already familiar with the fundamental concepts of computer programming (input/output, variables, conditional statements, loops, lists), so we have started the school year with a discussion of object-oriented programming (or OOP). OOP is a programming paradigm that makes it easier and more natural to model real-world objects in code. For our first example, students modeled a talking doll, and one of the more complex examples was to model the hour and minute displays on a digital watch.

OOP lets coders create variables that stand for real-life objects such as talking dolls and digital watches. These objects can then be given commands to perform various tasks using "dot notation." For example, the following Python program first creates a talking doll and then gives the doll the command to speak:

mrbill = TalkingDoll()
mrbill.speak()

For students who write the correct code for TalkingDoll, the output of this program is "Ohh Nooo!!!"

We are now working with Python turtle graphics in this class. Most of these students are already familiar with turtle graphics, but we are using turtle graphics as our first example of the OOP concept called "inheritance." Inheritance is the idea of taking a pre-existing object and adding extra methods to it that the original object did not possess. For example, the built-in Python turtle does not understand the command drawPentagon; if you want to draw a pentagon, you have to provide all the low-level moving and turning code. However, students will learn how to create a "better" turtle, which has all the functionality of the original turtle, but which is smart enough to understand additional commands.

Students will have the opportunity to display their artistic talent in this unit, creating pictures such as this:

-Steve Gregg

In the classroom

In the classroom

At Proof School, the meaning of literature is palpable, quite literally.

In the midst of the Spanish Civil War, after struggling against Franco’s regime and succumbing to the power of modern aircraft, a small contingent of Republican soldiers holed themselves up in an abandoned mill. They had been delivered handwritten copies of Pablo Neruda’s latest manuscript, an unpublished look at the effects of war on the countryside. These soldiers read poetry amid artillery fire, hunger, and uncertainty. Even with war as a background to their days and their nights, they chose poetry.

This story sets the stage for our high school literature class, a course motivated by the question of how authors like Neruda have given voice and representation to war. How do we adequately represent, and therefore communicate, something otherwise impossible to convey? What role can literature play in bringing history, and its lived experience, back to our eye level? And how did the twentieth century change the way we relate to war and our representations of it?

Picasso's "Guernica," considered to be "to painting what Beethoven's Ninth Symphony is to music" (Alejandro Escalona), brought worldwide attention to the Spanish Civil War. The soldiers on the battlefront of the war, however, found their comfort in the language of Pablo Neruda.

Asking these kinds of questions changes the nature of a conventional high school literature course. First, these questions are big and meaningful, and they help students connect literature to the real world of lived historical experience; there’s no doubt that the literature we’re reading matters. Second, these questions are so big that students need to break them down into smaller, fundamental parts; doing so allows us to model logical and analytical processes important to all disciplines. Third, these questions position students to adopt a problem-solving mindset when they read, discuss, and write about literature; they learn there is so much more to do than summarize what they’ve read.

The effect of all these changes to the conventional high school experience is to minimize my role in the classroom. In short, I can’t play the sage on the stage because there is no real answer to the questions our class is posing.

There are lots of ways a teacher in this kind of classroom can maintain agency: she can guide discussions by asking questions; help develop papers by showing students the iconic ways that scholars think, write, and make new knowledge; categorize evidence in a way that promotes their intelligent use; and give them models for ways to structure a paper that intervenes in a potential misreading of a text.

We tend to spend a good portion of class time working on challenge problems and creative tasks, like working as literary editors to subtitle sections in Neruda's book. Our work often takes us across the Maker Studio.

Because a flipped classroom tends to diminish the role of teaching, it tends to increase the role of learning. In this model, the teacher doesn’t share his or her knowledge with the class. Instead, we put more faith in our students to carry the discussion and be the agents in their learning. Sometimes, it means not speaking in class so that students have a true opportunity to carry the day. When I have done this in our class, we’ve had a stunning result: one hour went by without the debate subsiding even once, and they had only discussed a single poem.

I was told on many occasions when I moved, not long ago, from teaching college to teaching high school that I would need to make significant changes to my teaching. The test case so far is pretty clear: students at every level, and at any age, are looking to be challenged, to be given a fair chance at gaining mastery, and to demonstrate what they’re learning. They are looking for genuine problems to solve and honest questions to answer. They want to avoid being “taught” because they are looking for an opportunity to learn.

When Spain’s rebel, Republican forces got hold of Neruda’s book of poems, they were so taken by the language that they retrieved any fabric they could from the battlefield, and churned it into handmade paper; they brought an old clamshell printing press to the front lines, and snaked its 1,200 pounds of iron between Franco’s soldiers and his air force; they set type letter by letter, word by word, and line by line, and in the process printed and bound by hand what turned out to be the first edition of Neruda’s manuscript Spain in Our Hearts.

Of the five known extant copies of these phenomenal books, two are in the Library of Congress. I have been lucky enough to travel to Washington, DC, to see them in person.

The journey of those poems, from Neruda’s hands to the hands of those soldiers, from the battlefront to the front of our minds, gives us a window into the significance of language to console an otherwise unspeakable experience. If such a book can change the lives of soldiers on the battlefront, perhaps it can change the way we think of literature in the classroom--and how that literature can be taught.

-Zachary Sifuentes

In Latin, students bring an ancient language to life through collaborative learning and historical engagement.

Salvete! (Hello!) In Latin 1, students have been learning the basics of how to read, write, and even speak in the language of the ancient Romans. To do this, students have had to engage both their analytical and creative powers: not only have they been learning a new system of communication; they've had to build, through imagination, a context in which this system can exist. Studying a 'dead' language means first bringing it to life: understanding it as more than a set of symbols and sounds governed by particular rules, but as a product (and a tool) of human life.

One way they've brought this language to life—given it a human context in which to exist and take on meaning—is through their own oral communication with one another in the classroom. Teaching students to speak and listen in a dead language is unusual; Latin classes at most schools just focus on reading ability. In our class, students speak Latin out loud in almost every class. Sometimes we have conversations with one another (“Hello, what's your name? How are you today?” etc.); we pronounce new vocabulary out loud; and we review and practice noun declensions and verb conjugations by reciting them part by part as we throw around the seminar table one of Proof School's “rock pillows” (if you catch the pillow, you say the next part of the grammar system we're practicing), an activity that very well might be the first ever academic pillow fight. In all these activities, students practice listening to each other and working as a team, and they begin to understand language (all language) as a raw material for making and re-making meaning together with other people.

Another way in which students bring Latin to life in the classroom is by imagining the people who spoke it on a daily basis back in ancient times. Students this block got a chance to decipher Latin graffiti from Pompeii—images of real Latin scrawled, complete with small drawings and even cross-outs, on stone walls and preserved there for thousands of years. This graffiti gives us insight into aspects of daily life in ancient Italy and also reminds us that Latin was once a living language with variations of spelling and pronunciation and with speakers of varying literacy levels. After reading some of these scripta in parietibus (“writings on walls”), the students drew some Latin graffiti of their own...well, on paper, which we hope to post on walls around the school.

Furthermore, for one week each block, the Latin students of all levels come together to read a longer Latin text in translation and talk about the history and culture of Ancient Rome. This block we read selections from the Roman historian Livy, who wrote a history of his own people at the end of the first century B.C.E. after a series of bloody civil wars and at a moment of great political turmoil and transition. We read sections documenting the founding of Rome and the creation of its first systems of government and religion. We looked at a map of the Forum (the center of political and religious life in Rome) and talked about Roman religion and its intimate connection to political power, bringing up modern-day issues of secularist vs. religious governments. We talked about Livy's notion of history and its purpose (as he describes it) and about his tendency to relate multiple and contradictory stories without stating which he thinks is true.

In all of this, we worked on the fundamental skills of close reading and writing, and we considered what to do when confronted with a culture different from our own—with its own, very different understandings of things like gender, religious worship, and statehood. We practiced setting aside our own assumptions about the world in order to explore a different world view. This sort of cross-cultural investigation, through historical or literary texts, helps students to come to understand their own views about the world as just that—points of view, which are created by and through language, whether it's a language of ancient peoples from thousands of years ago or our own language today.

-Sydney Cochran

On taking risks, and taking advantage of opportunity.

In our Build Week concluding Block 1, we broke up into six groups, with each group engaging in a week-long activity. Among those activities were making animation sequences, simulating earthquakes, folding an origami undersea panorama, creating an identification chart for flora and fauna, and building a double pendulum. But one group’s experience with trial and error, and with making success out of a challenge, was especially noteworthy.

That group made a planetarium out of plastic sheeting, tape, a simple box fan, and a planetarium projector. The faculty leader was Sachi Hashimoto, one of our math faculty; seeing the project develop over the week was astonishing to me, and it is the subject of this week’s “In the Classroom.”

The first challenge was just getting the materials delivered. Never underestimate Murphy’s Law. The first attempted delivery was a weekend, when we’re not in the building to receive packages; the second attempted delivery wouldn’t come until day two of Build Week, when we were scheduled to be at the California Academy of Sciences.

Sachi went into problem-solving mode and came up with several contingency plans, some of which involved rerouting the delivery address and having a friend keep tabs on UPS while we were at the California Academy of Sciences. She also had to reinvent her group’s Monday activity, since they could not cut and tape plastic sheeting that had not arrived.

Instead, she held a design competition to decide on the shape of the half dome they would build. That kind of creative thinking and reinvention, despite all the planning that went into build week, is a hallmark of great teaching and leadership. Sachi guided the group as they came up with four designs, and then she had them construct those designs out of Zome.

To model the translation from Zome to plastic sheeting, they used an inexpensive tablecloth. The teams discovered that working with a flexible material was considerably harder than they expected. They ended up voting on the simplest design, which, despite looking rather unlike a hemisphere when made out of Zome, ended up being quite round when made out of plastic.

By Wednesday, the group had all of its materials. They started by calculating the dimensions of the faces of the dome. Their design was made out of one hexagonal base, three trapezoids, three equilateral triangles, and a small triangle to close it off on top. As they were cutting their design out of the large plastic, they realized that they had calculated the dimensions of the trapezoids incorrectly. It was impossible to make a trapezoid with the measurements listed.

It was back to the drawing board for the students. After double checking their math and getting several different answers, they decided to rebuild the Zome model and take measurements directly from the Zome. This gave them the true measurement of the trapezoidal sides, and they were able to cut the rest of the sides easily.

By Thursday morning, they had a wind tunnel with a box fan inflating the dome, but then other issues came up. The various AA batteries we had were mostly burnt out, though we thought they were new. When they finally found enough working batteries, they discovered the light inside the planetarium projector we bought was not powerful enough to make the space glow with the night sky. It was still a terrific space, a huge igloo powered by a single box fan, but it wasn’t quite what the group had planned.

The resilience to make the project a success, to turn it into something extraordinary, took further collaboration. During our hour-long symposium and demo, someone had the great idea of modifying the planetarium projector into a simple flashlight, bringing a large Zome construction project into the space, and seeing what kinds of shadows it would project.

The results were stunning. The shadows it projected looked as if it they could be a theater set, possibly depicting a forest, a massive steel web structure, or what I imagine we see when we look at microfibers under a microscope. Aside from what they ended up making, the group’s resilience and willingness to look for alternate routes for success was striking. They tested an idea that arguably grew into something even better than they imagined.

It sounded like an apt metaphor for a new school, now just seven weeks old.

-Zachary Sifuentes and Sachi Hashimoto