It's hard to believe the semester is almost over, only two weeks left. Initially the idea of classes in crazy creeks, under trees or in museums seemed strange and awkward, now students find normalcy in learning while balancing in their chairs and jotting notes in notebooks while visiting museums or pausing on the side of a trail. During my visit, I heard students draw information from History class into discussions with parents and guides, they then transferred these ideas into their scientific reasonings. Without realizing it, these ladies were learning through inquiry and crossing boundaries - now history wasn't only for history class, instead it related to science, math concepts, global studies... really the list is endless...these ladies learned through experience.
Now in Bolivia, students are preparing for finals before heading out for one outing in the mountains. Teachers have crafted amazing projects, plays, songs and exams for students to show what they learned throughout the semester. Below, are the final academic updates for each class highlighting topics from the past few weeks. See if you can see some of the cross over from class to class...
Aunge
(Ok, I'll admit precalculus and Algebra 2 are a bit different. But still important - the Incans had to perfect their angles to make their incredible walls and houses. Did your daughter mention the 12 sided rock perfectly placed in the famous Incan wall that lined the path between their hostel and the plaza in Cusco?)
Precalculus
In recent weeks, precalculus students completed their study of vectors with real-world applications in physics to calculate work. To start a unit on conic sections, we derived the formula circle starting from Sophie's favorite: the Pythagorean Theorem. We observed examples of potential elliptical arches in Cusco and used a string tacked at two foci to draw an ellipse, allowing girls a hands-on opportunity to understand the definition this conic section. In further study of conic sections, girls completed the square to convert general equations to the standard form for circles, ellipses, hyperbolas, and parabolas, and graphed these shapes using information about vertices, foci, and asymptotes extracted from the equations.
CONIC SECTIONS:
Next, we investigated patterns to write general formulas for arithmetic and geometric sequences, and to derive formulas for summing arithmetic and geometric series. Hannah studied the reasoning used in applying geometric series to write the decimal 0.55555.... as a fraction, and extended this reasoning to find a method for writing any repeating decimal as a fraction. Erin's determination to understand the difference between permutations and combinations is aiding her to develop better intuition in counting strategies as we approach our last unit of study about probability.
Algebra 2
Since our last update, Algebra 2 students have completed their study of conic sections including parabolas, hyperbolas, ellipses, and circles. They applied previous knowledge of graph transformations to extend initial study of conic sections with centers at (0, 0) to other centers in the coordinate plane, and used characteristics such as vertices, co-vertices, foci, and asymptotes to graph and write the equations of conic sections. As their final unit in Algebra 2, Lena and Kate have learned counting techniques using permutations and combinations as a foundation for calculating probabilities. They used area formulas from previous courses to calculate geometric probabilities, differentiated between experimental and theoretical probability, and applied counting techniques to calculate probabilities of compound events. Maisie, Allie, and Charlotte are finishing their Algebra 2 semester with a study of trigonometry including an investigation of the right-triangle and unit circle definitions of trigonometric functions and real-world applications of trigonometric functions to find missing sides of right triangles and unknown angles. Caroline and Anne are focusing the last weeks of class on reviewing previous topics to reinforce the math skills they have acquired throughout the semester.
Beginning Spanish
Beginning Spanish students continue to build vocabulary as they shop and navigate through cities and towns of Peru and Bolivia. Girls asked questions of our guides during and after the Lares Trek to learn about shamanism and Incan history. On her day to serve as leader for the group, Courtney used her Spanish skills to inquire about tours of the Cathedral in Cusco's famous Plaza de Armas. On a night out to dinner in Cusco, Caroline used her restaurant vocabulary to ask about the menu and order dinner. The class extended our study of boot changing verbs to other irregular verbs in the present tense. Maisie explained the conjugations of saber and conocer and explained the different uses of these verbs. An introduction of the preterite tense allowed students to finally discuss past events. Girls learned the present progressive tense through context while reading the short novel Casi se muere. Rebecca used the construction ir + a + infinitive to make predictions about what may happen next in the novel and Erin used the preterite tense to explain what already occurred in the story. When our class in the Plaza in Puno, Peru gathered a curious crowd, Hannah took the opportunity to engage onlookers in conversation.
Advanced Spanish
I have been impressed by the dedication that these students have
shown to completing the task of reading El Alquimista. Although the text
becomes more challenging as the story progresses, they are still devoted to
finishing the novel by the end of the semester. As a result, we have been
working hard to process the text effectively, and have had many fruitful
discussions about diverse philosophies of life, religion, dreams, and destiny.
I am proud of these students' continually growing capacity to communicate
complicated ideas in Spanish. We have also maintained a focus on grammar by
moving into the formation and use of the subjunctive mood in both the present
and past tenses. This is a complicated mood to learn, and the students have put
forth significant effort to understand and utilize it. In addition to the book
and grammar, we have continued our commitment to speaking with locals. One
especially exciting example of this occurred when our class had the opportunity
to visit the Coca Museum in Cusco. Our guide explained about the history and
cultural significance of the use of the coca plant in the Incan Empire. The
girls listened carefully, and asked well-considered questions at the end of the
tour. I hope to leave the class with an inspired confidence to practice their
much-improved language skills as they transition back to life in the US.
Honors Natural Science
The last few weeks of the semester are exciting in science
class: we are exploring the ideas and implications of climate change. After
defining key terms and concepts, the students read current news articles
relating to climate change and presented them to their peers in the form of a
news show. Then, they worked to complete a project relating a commonly used
product to its carbon footprint. In addition to the unit on climate change, the
students are also working to complete their final observation journals, which
document the multifarious plant and animal life we encounter in different
biomes and natural situations throughout the semester. I have been impressed
with the increasing quality of these assignments, as the girls practice the
differentiation of observation and fact, as well as the formation of good
scientific questions. I am pleased that we are able to connect our class
discussions to the world around us in the last part of the semester: for
example, considering why food takes longer to cook at higher elevations (very
significant to our experience in these last few weeks!), and learning about
snow science in the Cordillera Real.
Physical Education
In the last weeks of the semester, we are learning that merely
existing at high elevation can be work out! Armed with confidence gained on the
Santa Cruz hike, the girls conquered the Lares Trek towards Machu Picchu. One
particularly challenging part of the trek brought us into snow, over 15,000
feet above sea level. Although we are very busy with academics and trying to
stay healthy in this last part of the semester, we have found time for early
morning runs and yoga sessions. I trust that these acclimatization activities
will benefit our bodies when it is time for the ultimate physical challenge of
the semester: glacier mountaineering!
Honors History and Government of South America
History students are contemplating the difference between
means and ends, comparing Gandhi's philosophy of 'satyagraha', truth force, to
the methods of the Maoist group 'The Shining Path' in Peru. Is violence
justified in the face of oppressive structures? So far, this question has
provided lively discussion amongst the students. Many return to the thought:
How can one answer one way or another without having first-hand experience of
such oppression? Sure, they can hold opinions and hope they would react in a
certain way, but until they walk a mile...who knows?
Most recently, the students blew me away by creating a
6-frame comic strip depicting an event in Ecuadorian or Peruvian history to
encapsulate their learning and teach others. Their work was brilliant, spanning
topics from Incan and Spanish colonization to oil issues in the Amazon.
Last class the students took a 'challenge quiz', which
asked them to write on globalization, development, and power dynamics. Next, in
addition to learning about Bolivia's political system, and reading up on the
president Evo Morales, students will begin their final project. The history
final is a map of countries visited, overlaid with historical facts and their
personal journey.
Mathematical Concepts
Courtney has been researching the price of chocolate in
each town she visits. Soon she will buy her products and begin a small-scale
business among her peers to learn what it takes to buy, sell, and make a
profit. Additionally, she is reading up on free trade, and arguments for and
against the WTO.
One day, we invited all of the students to participate in
a minimum wage activity. The students were divided into'families'. Kate was a
single mom of three:Charlotte,Sophie,and Allie. Lindsey was a single mom
with baby Scout. Erin was a single mom with four children: Alizah, Rebecca,
Anne, and Feyza. Hannah and Maisie had four children: Lena, Caroline, Courtney,
and Susannah. They received their monthly budgets and had to make decisions and
sacrifices in order to make ends meet and pay their bills. Listening to their
processes of decision-making was the best part of the day. Each group had to
justify their choices, despite knowing the long-term emotional and physical
consequences. Some decided it was best to sell their children. All joking
aside, they had amazing conversations about the cycle of poverty, and gained
perspective by the end of the day, not only on issues of global poverty, but
poverty in the U.S.
Honors Literature and Composition
Students of Literature are going crazy with Isabel
Allende's 'The House of The Spirits'. At any moment one might find a student
crying because of a twist of fate within the book, a love gone awry, or a
favorite character's death. Their imaginations are being let loose, as they
create their own fictional stories in the style of magical realism.
The day after Gabriel Garcia Marquez died, I read the
BBC's tribute to him to the class, and almost ended up crying myself. It is an
apt time to learn the significance of the genre, to spread its beauty,
mysticism, and political foundations.
Global Studies
The alternate Inca Trail with our guide Puma and our time
exploring Machu Picchu allowed the students to learn about Incans from the
perspective of a shaman. They learned about the sacred trilogy of Incan
cosmology, the condor, the puma, and the serpent. Their minds were blown with
the expert stonework architecture and the argument of acoustic levitation, that
stones were moved with the help of sound, one hundred conch shells blown on the
mountainside which shifted the molecular biology to ease the burden of lifting.
In the afternoon some of us visited the Incan Bridge. The
Incan Bridge is a terrifying structure carved out of the cliff side. Amazonas,
or teenage female warriors, were the ones who trained to walk the bridge
without falling. We sat close to the rock, listening to Puma play the flute,
each imagining traversing the bridge.
Heading into Puno
on the shores of Lake Titicaca, we prepared for an experience of ethnotourism,
where cultures use their unique identity to make a living. We visited the
floating island of Uros and the
Spanish-
One of the most notable nights recently was when
Alizah organized a 'Hunger Banquet' on her Chieflet day. Students were randomly
assigned personalities as they came down to dinner. Kate and Charlotte were the
lucky upper class and got to sit in chairs at a table. They were served pesto
pasta, fruit salad, and bottled water. A few others sat in chairs and got to
eat rice and beans. The majority of the group represented the lower classes,
and had to sit on the cold floor and just eat rice. The percentage breakdown
represented the global numbers of who goes hungry each day. Students learned that though there are pressing issues
that affect food production such as drought, desertification, and salinization,
the main reason people go hungry is not the lack of food, but the unequal
distribution of food and resources.
Moving on from Puno we headed into Bolivia. Our home base
is a hotel on the shores of Lake Titicaca, the home of the giant frog. The
sunshine and carefree vibe of Copacabana is doing everyone a world of good.
Students are working hard. Today we will introduce the Global Final Assignment,
which will challenge students to synthesize all they have learned in the past
few months.
INTERMEDIATE SPANISH
On
the curvy mountain road descending from the Lares hot springs, the Intermediate
Spanish students gathered together in the back seats of the bus to make sense
of the verses of a song they were given. The song is Latinoamerica, by
a Puerto Rican band called Calle 13. They underlined words such as
“desaparecido” and “lucha”; words that give Latin Americans the chills,
words that remind them of the oppression and fear that their parents faced, but
also of the hope and unity this shared history has created. The
definition of these words can be found in any dictionary. Their significance
can only be understood by speaking to people that have lived with these words. Not having access to Google Translate or even a pocket dictionary on the
bus, the girls learned the meanings of their lines by asking our guides. Lena asked Rebbi what the lines “La nieve que maquilla mis montañas; Tengo el
sol que me seca y la lluvia que me baña” meant. She excitedly
relayed that she had learned why he works as a guide on these treks, about his
connection with the mountains and his love of working with tourists. Anne
was surprised by how much she was able to understand in her conversation, a
conversation that went beyond “¿Hola, como esta?” and touched on military
coups, land redistribution, and of course soccer. Kate and I wondered
what the author meant by “ soy toda la sobra de los que se robaron.” We
discussed the use of tense and questioned "Who robbed who?” She wondered
if it referred to Spanish colonization and US military involvement. Susannah read the lines, “Caminamos, caminamos, caminamos” (we walk, we
walk, we walk) to the circle of guides and their families that had gathered in
curiosity. Puma explained that although Latin America has suffered,
people must continue walking and remain strong. Allie talked to Rebbi and
Nelly about the line “Soy todos los santos que cuelgan de mi cuello” and
learned the tradition of wearing necklaces with pictures of saints.
After
returning from the trek, we huddled around the laptop and watched the images
that went along with the lyrics. We had come to understand the meanings of
these lines from conversations with the guides, street artisans, and hostel
employees. The girls recognized the waters of the Amazon and the high
altitudes of Peru. Susannah began to understand the line “Tu no puedes
comprar los colores” (You cant buy the colors) to represent ethnic diversity
after watching the video and seeing the diverse indigenous, mestizo, and Afro-
Peruvian faces.
The
girls sat in pairs in the Cuzco sunshine and discussed in Spanish the meaning
of their versus. As they learned what the rest of the lyrics meant from
their classmates, they began to understand the essence of the song, what it
means to be “Latin American.” They asked the cafe owner, a young French
woman who learned Spanish from her Peruvian father, what the lines
"”Mano de obra campesina por tu consumo” meant. Her Peruvian
boyfriend chimed in that these lines had various, deeper meanings and that an “obra”
can be many things. The girls looked surprised to see two people, fluent
in Spanish, discussing the meaning of a syllable word.
To
begin thinking about ideas for their final presentation, a song titled
“América,” they watched the music video “Clandestino by Manu Chao. The
lyrics were printed out and handed out to the three pairs. There were key
vocabulary words cut out of their lyrics and the small slips of paper with the
missing words were in a pile in the center of the table. Because there were
only enough words to complete two of the sheets, the pairs waited in
anticipation for the song to begin, hands ready to grab at the limited words.
As Manu Chao sang the line “Solo voy con mi pena,” everyone searched for
the word “pena” in the pile. Some of the pairs were quicker than others
and they grabbed for dictionaries to gain points to get ahead. They
searched for the words in the stack of dictionaries. When the time was
up, the students shared what they thought the meaning of each line was. Heather
was visiting the class and was teamed up with Kate. Kate explained that
“pena” meant “pity.” Heather realized that this word had a different
meaning in this context and apologized to Kate for leading her astray.
Susannah pointed out that there is a line in the Calle 13 song that ends
with “vale la pena” and she had learned that it translates to “it’s worth it.”
We discussed the usefulness of dictionaries as a reference but the girls
also had fun exploring contexts and sharing their knowledge. As we pieced
together what the words meant, the students began to relate to the songs
meaning, telling stories of taking the same test that people are required to
pass to gain citizenship. While telling these stories in Spanish, their
classmates helped them along with conjugations and vocabulary.
Yesterday,
after coming back from town time in Copacabana, Anne and Lena yelled up to me
as I graded their papers on the terrace. “The reason that Eric moved here
from Argentina is because the cost of living is so high!” and “I learned
how to say ‘zombie’ in Spanish!” Eric had played Argentine folklorico
music for us the night before and Susanna had confidently asked him what
Operation Condor was after learning that he was from a country that was impacted
by this. I felt their excitement and their enthusiasm for Spanish and why
we learn other languages; To learn about a history and a culture that is held
inside of people and that learning their language can unlock.
The next morning, dressed in traditional Kichwa clothes, part of the group went to mass with their families while the rest of us stayed behind to bake bread. Five oven-loads later, we piled with our families into two busses, which took us to El Lechero, a sacred tree and prime picnic spot. We set out PBJs, cold-cuts, and fruit and the families once again each brought a dish to combine. One of the community members facilitated this custom, and then offered us a bowl to share. In return, we offered the community free reign of our supplies, resulting in some triple-decker PBJs filled with unspread globs of guanabana jelly. After a group clean-up effort, we continued on to El Parque Condor, a bird rehabilitation center, for a flight demonstration. The kids – and two sixteen year old Traveling School students – got to hold some birds afterwards. Three days later, my brothers were still running around flapping their arms and bird-calling. We returned around 6pm which presented me with my biggest challenge yet: trying to get my homework done while simultaneously entertaining my seven year old brother who loves ninjas, Jackie Chan, and my camera. For the first time since our arrival, I was able to keep my eyes open long enough to finish a journal entry (a feat I was proud of until I realized it was only 7:46pm).
