Sin Nombre

Have you seen the movie Sin Nombre? It's about some illegal immigrants trying to get to America, and getting entangled with mareros from the infamous MS13 gang. Having lived in El Salvador, the movie was all too real and very depressing to me. After watching it, Geoff and I said to each other that our lives are truly privileged.



(Warning, major spoiler to follow)
















I am sure there are worse ways to die, but plunging face forward off of/into a moving train while trying to cross the border illegally has got to be one of the worst ways. You're dying like an animal. It made me think about all the people who do die trying to cross the various borders. So utterly unjust. The only difference between them and us is their desperation; they were born into the wrong place, at the wrong time.

A Little Shoutout to Our Favorite Cafe

Apparently the best barista in the world is Salvadoran and works at the local coffee chain that we frequent. I guess I shouldn't have made fun of Geoff all of those times when he claimed emphatically that Viva Espresso has the best cappuccinos he has ever tasted in his entire life. Turns out that his taste buds are quite sophisticated.

My boyfriend has sophisticated taste buds and is willing to eat anything that has not been rotting for too long. That's dangerous.

Last Days in El Salvador

Now that our time in El Salvador is coming to an end, I wanted to count our blessings a bit before we move on to our next stop.

Things I will miss about El Salvador:
* yummy, cheesy pupusas
* incredibly warm people
* tropical climate
* how time seems to be suspended every time we go to the beach
* the loveliness of Spanish
* how El Salvador is almost untouched by tourists and English
* $15/hour massages and our $13/week maid
* living within walking distance to the school
* freedom from any test-prep pressure
* free round-trip annual tickets to the States
* having incredible teaching resources at the school and various support staff helping me set up labs for my classes
* the kids I taught last year, who still came back to me all the time this year for help and advice...
* The Head of our school is a great boss and someone whom I feel comfortable walking into the office of without appointments.

Things I will not miss:
* unreliable water, power, and sometimes internet
* giant rain-filled pot holes that they just don't bother fixing
* Salvadoran banks, which tend to prolong every process and make everything difficult to accomplish
* feeling unsafe at night or during the day in the boonies
* hearing people complain about stupid things while many other people in this country have literally nothing and NO opportunities!

Top 13 memories during our 2-year stay (I couldn't fit it into a neat list of 10):
* Pacaya - live-lava volcano in Guatemala where we roasted marshmellows on the lava stream
* Machu Picchu and Wainapicchu - sky-high Inca ruins in Peru
* Calafate - still growing glacier mass in Argentina
* Rio Celeste - natural bright blue river in Costa Rica, in the midst of a rain forest
* El Tabacon - labyrinth of luxurious hot springs in Costa Rica, channelled from natural volcanic springs
* Cerra Negra - "volcano boarding" in Nicaragua
* amazing snorkeling in Belize
* Tikal - Mayan ruins in the jungle of northern Guatemala
* Santa Ana, Izalco, Coatepeque - Salvadoran volcanos: one with a smoking green crater lake, one with bare rocky top, and one with a beautiful volcanic lake.
* Atitlan - giant and beautiful volcanic lake in Guatemala, complete with cliff-jumping!
* staying with a local family on an island in Panama (in a village with only huts and no sewage system) and then island hopping between untouched paradise islands
* a bunch of teachers going to the lake house of one of my students and doing lake sports and BBQing with their truly awesome family
* Almost getting robbed by a masked bandit in Guatemala at machete-point and driving off while screaming. (This is not a good memory, obviously, but it taught us a helluva lot about being safe. So, it's a very memorable experience.)

As the year wraps up (Geoff leaves in 7 days and I leave El Salvador 4 days after him), I am endlessly thankful for the experiences that we have had. Geoff and I always say this, but it's true -- we are some of the luckiest people, because we have jobs that we love, we are saving money and traveling at the same time, and we have each other to share this amazing experience with.

Summer (and Germany), here we come! :)

PS. I think the more Spanish I have learned, the worse an effect it has had on my ability to spell in English. Take "glacier" for example, it didn't immediately occur to me that I was spelling it "glaciar" like it is in Spanish, since when I visually checked the word, it looked very familar to me. And for the same reason, my natural inclination was to type "masage" (similar to masaje) instead of "massage"... Dangerous!

Salvadoran Customs and Math

There are two Salvadoran customs that amuse me greatly, and they make me think about the math involved in each case:

* Here in El Salvador, whenever people need to cut a round cake, they first cut a circle in the middle of the cake. And then they proceed to slice the outer rim of the cake into equal slices. When they serve, first they serve the slices on the rim, and then they serve the center piece last.


A natural math question that arises from this is: How big will the middle piece have to be, in order to ensure that all of the pieces served are of the same size?

The math is very easy, so I'll leave it to you to figure out. I'm going to give it to my Geometry kiddies at some point, as a warmup problem. (Of course, the kids will have to figure out for themselves that the answer will depend on N, the number of slices, and R, the radius of the cake.)

On a random note: I like how they cut it this way. It actually makes sense to me, because it's much easier to serve the slices when they're not all long and skinny.

* Also, another amusing custom here is that when Salvadorans have a really big raffle prize (ie. Taca's round-trip tickets at today's staff luncheon at our school), they often will announce something like, "We're going to pick 3 names. The first and the second people we pick out of the hat do not win any prize; their names get discarded on the side. The third name we pick out is the sole winner."

It's funny because it's clear that this does not change the probability of winning. Each person still has the probability of winning = 1/n, whether you compute it as a one-time pick of a single name OR as the consecutive-picking-of-three-names-without-replacement method as described above: (n-1)/n * (n-2)/(n-1) * 1/(n-2) = 1/n. But the Salvadoran way is much funnier. The first two names picked out of the hat are the sorest losers (or they go around and brag about how close they had come to winning). How funny!!

...I love how there is math everywhere! :)

Anyhow, I am on vacation now, and will very likely be a useless lump until January. See you then.

Mandatory Christmas Bonus

Here in El Salvador, employers are required to give their employees a Christmas bonus. Geoff and I will be giving our maid an extra week's pay (plus she will get paid time off while we're on vacation in Argentina). But, for the full-time employees (such as myself), the mandatory Christmas bonus breaks down as follows:

Up to 1 year of employment: Proportional bonus of 10 days' pay. (ie. If you've been employed for 6 months, your bonus is equivalent to 5 days' pay.)

Over 1 year, up to 3 years of employment: 10 days' pay.

Over 3 years, up to 10 years of employment: 15 days' pay.

Over 10 years of employment: 18 days' pay.

That's a pretty real example of piecewise functions, besides progressive taxes and volume discounts on products. How do you feel about the government dictating when you get bonuses? I know (from having interviewed with schools in Brazil in the past) that Brazil has all kinds of funny salary-related laws. Among them is one that says that you must get paid 13 months of salary a year; half of your "extra" month gets distributed as a Christmas bonus, and the other half of it gets distributed at the beginning of summer, in time for your summer vacations. How funny!

Life Matters

Brain dump. For me, mostly.

* The whole tax business in El Salvador is pretty funny to me. To start, we have a sidewalk tax. It's about $3.95 a year, and (I think) it means that you are allowed to use the sidewalk for the next 12 months. Then, when April comes around, you have to go in person to turn in your income tax forms. They don't accept it by mail or by internet. (But they do accept other people turning it in on your behalf. Strange.) And then, about 6 months later, you go pick up your refund -- in cash!! -- at any branch of Banco Agricola. At that point, the bank teller will tell you that they cannot issue you a check. So, if you're like me, you lug hundreds of dollars in cash while walking back from the bank -- an extra exciting experience in this country. It's strangeness all around.

* New York State Department of Ed is also pretty funny. A while ago, I was trying to get a duplicate copy of my teaching certificate, for job-searching purposes and also in case my current school gets audited. I went online, logged into the TEACH system, paid my $25 dollars, and then only afterwards saw a fine print somewhere on a totally separate FAQ page that they have, in fact, stopped the service of printing paper certificates for "time-limited teaching certificates!" In fact, they have completely eliminated the job of the person who used to print the paper certificates! Well, at this point, my options were to A.) pay another 50 bucks to upgrade my certification, still 3 years before the current one is going to expire, or B.) forget the paper copy. My potential employers and the Salvadorean Ministry of Education are going to just have to make do with my print-screen version of the "teaching certificate."

I was pretty mad (and almost equally amused). But, I am pretty stingy as well, so I decided to wait it out. --What do you know? Two or three weeks later, I get my duplicate certificate in the mail. :)

* I am about 85% sure I will be going to London in January for a job fair. I was waiting for days on a confirmation from my recruiters that my application and recommendations and payment all checked out, before I made travel arrangements. I had to follow up with them, because I noticed that the airfare had dropped $140 over the weekend (from $1100 to about $950). So, finally, I heard back from them this morning, and I rushed to log in to Kayak to buy the tickets. --Guess what? They're back up to $1100. And that's not including paying the recruiters, or hotel or food. So, that's all very expensive, and I'm back to being in a limbo about whether this is the right move. There is a good chance I won't get a job at this fair (for various reasons, timing and my lack of IB experience being the key ones), but if I don't go, I know I will regret it when I am stuck still looking for a job in April........

* Incredibly (as though I don't already have enough to do in the middle of job-searching and preparing kids for midterms), I am also working on applying to a summer program. I've already written my personal statement, put in orders for my transcripts (both undergrad and grad), and given the recommendation forms to my supervisors. I am feeling like this is not going to all pan out, but I feel OK about it. In case you can't tell, I am practicing being more of a go-getter, and my backup plan for the summer is to go to Herrang (in Sweden) during their month-long swing dance camp, and to dance until my legs break into pieces.

So, that's it. All of the things floating around in my head!

Thanksgiving with the Coxes

Geoff and I spent the last four days playing host to his parents. It was AWESOME - I actually never imagined that it would be possible to jam pack so many things into four days, in El Salvador. We saw a beautiful beach (and did a whole all-inclusive thing) that had a stunning salt-water pool, a jacuzzi, and many very large and luxurious pools. We had an oiled massage (here they are $15 per hour... very affordable!). We took the Coxes up to a beautiful (and very delicious/intimate) fusion restaurant at the top of the mountain, overlooking many mountains and the city while the sun was setting. (The owners came out and talked to us, and one of them told us the story about how the restaurant came to be, and also played and sang some tunes on his guitar. Geoff's parents LOVED that!) We visited an old Spanish colonial town, saw its church, had a drink by the lake, and even hiked down a bit to check out the awesome hexagonal-prism shaped rock columns that are completely natural. And on the last night, we went to a beautiful restaurant that's already all decked out in Christmas spirit, on top of Torre de la Futura. (Geoff's mom LOVES Christmas, so it was a special treat for her to see the whole place decked out already.)

All in all, it was an absolutely lovely weekend. Happy Thanksgiving, and may we all be thankful for family and for love.

Fun in the Sun

THE SUN IS OUT! Has been for two weeks now. It's super lovely; I think we might be finally easing into the dry season. :)

Geoff and I have spent two beautiful weekends in a row at the beach, in good company. Last night, there was a music festival in El Tunco, so we (and apparently everyone we knew) decided to stay at the beach for the night. :) One of the bands was a rock cover band, and played such amazing old hits as "You Gotta Fight for Your Right." It was a great night... I won't divulge many details, but there was some spontaneous Charleston going on, with cheering Salvadorans. I almost had an asthma attack when we got back to our hotel, from trying to keep up with the crazyfast latino drum beats. Good times!!

Next week, we head off to Austin for our friends' beautiful wedding, and after that we will be in Tikal over the first (long) weekend of November! I LOVE this pre-holiday time of the year!! :)

About Tropical "Snow Days"

Kids learn a lot from their parents. Sometimes the things they learn aren't so good, but other times the things kids say about their parents can really surprise you.

Kid: Ms. Yang, I hope we don't have school tomorrow.

Me: (sigh) I hope we do have school tomorrow. ... [Kid], You know that if they have to cancel school tomorrow, that means that a lot of poor people are out of their homes, right? You know they'd only do it because they have to use the public schools as evacuation centers?*

Kid: Yeah... I know. My maid's family is staying with us right now.

Me: The whole family? How big is their family?

Kid: There are 11 of them.

Me: Everybody is staying with you??

Kid: Yeah. My mom told her to bring her family over, so they're all staying with us for now.

Me: Wow. That's really nice of your family to do that, [Kid]. But wow, that's a lot of people.

Kid: (smiles) Yeah, but it's OK... Our house is pretty big and we have 3 extra rooms.

Me: Oh, cool.

Kid: Anyway, I hope there's no school tomorrow!!

Me: (rolling eyes) I hope there is school.

*Background info: Tropical storms are really bad right now. It's supposed to rain for the next 3 days straight, and those heavy rains can cause collapsed roads/homes and (obviously) loss of lives, especially since it has pretty much not stopped raining since last Friday. So, the country generally is in high alert (and a lot of anxiety).

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PS. Random tangent about snow days: Growing up in Southern California, we never had snow days. So, as a kid, I never experienced the excitement of getting to sleep in and then going out sledding. But, we did have a couple of "smog days" that I could recall, when the city's smog level was so high (you sciency people know how smog level rises with the heat) that it wasn't supposed to be healthy to go outside, so the city would cancel school for the day. Obviously, we all went out anyway. But, come on! It was 90+ degrees and exceedingly beautiful (albeit I guess smoggy) outside -- what kind of sucker teenager would stay at home??

It wasn't until years later, as a teacher in NYC, that I experienced my first snow day. I think I just slept all day and graded in bed while watching Law and Order.

Maras Showdown with Government, etc.

This is a quick life update for my non-mathy friends:

El Salvador is crazy. I am mad that the maras decided that they could shut down the entire public bus system as a fist-waving gesture to the government. Some of you might remember that back in June, as part of their extortion schemes, the maras burned down a bus with over a dozen people trapped inside. The outrage continues, when they issued a threat (via pamphlets and other things) earlier this week to do more of the same. So, in response, the entire country's bus system was shut down 2 days ago.

As usual, this doesn't impact the well-to-do, who travel in private vehicles. It only impacts the poor Salvadoreans who now have to get up early in the morning and walk hours across various towns to get to work, or to take camiones if those can be found. It sounds like as of yesterday, parts of the transportation system have resumed operations, but the system continued to be affected today.

What a ridiculous situation! Supposedly the reason for this wave of mara threats is a retaliation / protest against a newly passed bill outlawing Salvadoreans from joining a gang. Well, it looks to me like the mara are playing Quien tiene mas grande huevos with the government, and they're not doing so badly in this contest. I was talking to Geoff about this, and I was saying that in the States, those gang threats would have been SQUASHED by the government. He reminded me that this situation would never have even occurred, because the gangs simply don't have the same power over there. What a different world it is that we live in. :(

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In brighter news, Geoff and I finally got our car back! Yay. We might have to send it away again soon, to fix the shocks. Who knew that there were 4 sets of shocks in a car?? I don't like the sound of that. We need to go back to driving Flintstone cars.

But, having a car allowed us to go back to our salsa class last night. SUPER FUN!!! :) :) We did some closed-eyes dancing, which is always incredible, because you have to rely on the raw connection you have with your partner in order to follow their lead. It made me miss swing dancing like crazy.

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By the way, our first progress reports are due tomorrow. Time in school is flying by!! Time to finish grading those quizzes...

Process Goals and Fun with Graphs!

It is timely that I came across this nice post today about goals, because I had been thinking yesterday about listing out some goals on my wall that are not topic-specific, so that I can refer to them throughout the year as I work with my kids on different assignments intended to address one of those life (or processing) skills.

Examples for Geometry:

• Visualization of parts vs. whole (Isolating info from one part of a diagram; combining info across multiple layers / perspectives.)


• Mechanical precision (Measuring and constructing lengths within 1 mm error and angles within 1 degree error; building solid models that won't fall apart.)


• Comprehension of diagrammed instructions (ie. for building anything)


• Attention to details in written instructions


• Judgment of reasonableness (of any physical or visual quantity)


• Effective written and oral communication


• Perseverence and resourcefulness


• Team work

Examples for Precalculus:

• Interpretation of data (Understanding trends / real-world significance / impact.)


• Fluidity with technology (Using graphing calcs fluently and flexibly.)


• Flexibility / creativity of problem-solving approaches


• Risk-taking and reasoning about the unfamiliar


• Precision and clear step-by-step organization of thought process / math work


• Increased self-management of progress, frustration level


• Effective written and oral communication


• Perseverence and resourcefulness


• Team work

Maybe it's just me being cheesy, but I think both the students and I might benefit from my posting these goals on the wall -- especially if I do actually highlight different skills throughout the year, as is appropriate to a given lesson, so that the kids would feel like they're not just learning content for content's sake and we are working towards a bigger picture.

My lists of goals are pretty generic (not really even math-specific, for the most part... Most are just good habits of mind...), but they are reminders of what is most important to me. Naturally, between the freshmen (Geometry) and the juniors (Precalculus), there is quite a bit of a "life experiences" gap. So, my goals for the two groups are pretty different as well. My juniors don't need as much for me to hold their hands on following directions, but they might need a nudge to be more creative and/or persevering. Versus the freshmen, whose first task of this year is to learn to consistently read and follow instructions. :) They each are at a different developmental stage with their meta-learning.

We have an opportunity each day to impact kids, mathemagically or otherwise.

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By the way, I found some nice graphs for my graph-reading lesson that is coming up. They're neat, even though they are not terribly complex in a mathematical sense. (The textbook's got a couple of nice complex graphs to use for rigorous classwork exercises, so I feel like I could afford to spend the rest of the period looking at interesting -- albeit simpler -- graphs with the kids.) They have to do with the mobile market, digital textbooks, and digital music. I plan to have fairly open-ended discussions about trends in those graphs, who might be interested in reading them, and what their implications might be for those people. And then maybe end with why these kids should finish college.* It could end up being a total flop of a lesson hook, but I am curious to see what these juniors can bring to the table.

If I have time, I am also thinking about adopting a middle-school post-it bar graph activity to composite bar graphs and scatter plots. I would give every boy a yellow post-it and every girl a pink post-it, and we would start a bar graph template on the board -- for example, models or brands of cell phones. They would go put their post-its on the board, in the appropriate column, and we would re-arrange the post-its to stack the pink post-its on top of the yellow post-its, in order to create a composite bar graph showing how many boys, girls, and total # of students have each type of phone. You can also do this exercise with scatterplots (for example, height vs. foot length) and see at a glance 1. what the overall trend is within the class, and 2. what the gender-specific trend is within the class. Using only colored post-its! And requiring maybe only about 10 minutes, discussion included. ...I'll try to squeeze it into my Precalc lessons this week and tell you lurkers how it goes.

*From what I hear, many Salvadorean private-school kids end up dropping out of college in the States, because they either lack the academic skills or -- more commonly -- can't deal with the fact that they no longer have a live-in maid and a designated chauffeur. This waste of an opportunity is terribly sad, considering that their parents can afford them to obtain a U.S. college education, while the majority of people in this country are living in poverty and many are starving. :(

But, can you really blame the kids for this injustice?? They are a product of the system (of huge disparity in wealth). sigh.

Our Peruvian Adventure

I am back home!! But, not for long. We just returned from our Peruvian trip yesterday (after some logistical snafoos), and we will be leaving again tomorrow. The day before we were leaving for Peru, Geoff found out to his HUGE disappointment that the house he had been looking to purchase in Jersey had fallen through. So, while we were in Peru, we each bought a round-trip ticket to Jersey. We leave tomorrow evening; I will be in the States for two weeks, visiting friends(!) and swing-dancing(!!), while Geoff looks around at other properties in NJ. The plan is that he will be in Jersey for four weeks total, but this way at least we are not apart for the entire time. (I will have to get back to San Salvador within two weeks, because that is when all returning teachers will start to prepare "officially" for the year. In truth, I have been on-and-off doing all sorts of prep this summer, but it will be nice to finally get a class schedule, finalized room assignment, meet the new hires, etc.)

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Peru took my breath away, both literally and figuratively. On our 5 days / 4 nights trek, the highest point we reached was about 4600 meters, or over 15000 feet above sea level. That is an astonishing feat! The temperature dropped below freezing on the first night of the trip -- in the 20s Fahrenheit range. What had happened to Geoff and me was that we had only arrived in Cuzco the day before our trek was due to start, so our bodies didn't have enough time to adjust to the altitude before beginning the climb into even higher altitudes. I threw up twice on the first day while ascending the mountain, and my chest hurt the entire time as I was walking / breathing, because my lungs were constricted. We passed by a couple of tombstones along the way, and the guide explained that one of them belonged to a gal whose asthma had flared up in the high altitudes, but who pushed on obstinately until things went from bad to worse. (I'm highly asthmatic, so that story got Geoff and me both a bit worried.) Finally, after about 9 or 10 hours of hiking, I gave up and hopped onto an emergency horse for the last hour of hike of the day.

On day 2 of the hike, the guides put me on a horse on the way up to the highest point, since the air was so thin. Geoff, too, was having a lot of trouble breathing -- and he runs marathons!! He was very pale by the time he finally got to the top of the mountain. I hopped off the horse and took a few steps on completely flat ground, and I already could not catch my breath. I had thought that descending would be easier for me to walk (even though we were still at an altitude > 4500 meters), but I clearly was wrong, because after walking for about 15 minutes, I threw up again. The guide insisted on me getting back onto the horse, and I threw up once more that day. Not my strongest showing, and I was super disappointed in myself that day. :(

That night, we got back to a lower altitude (in the 2000s meter-wise). By the time I woke up the next morning, the tightness in my chest had subsided. I was able to walk the rest of the trip, and even raced my way to the entrance of Machu Picchu to be one of the 400 people each day to receive a ticket to hike Wainapicchu (a nearby super-steep but stunningly beautiful mountain; you can see it in the picture above)! I was so proud of myself, because we had started hiking at 3:30am, in pitch darkness, and we were ascending these steep stairways that seemed to never end. Geoff was eager to be one of the 400 people, so he ran up the entire stairway and left me to climbing by myself. It was a tough mental game, but I was able to outrace a lot of people in similar (or better) physical condition than me, because I really wanted to get one of those tickets to Wainapicchu!

I can't describe how amazing Wainapicchu was, and our pictures do not do it any justice. It was like climbing up to a city in the clouds -- you have to use your hands and feet, rock wall-climbing style, in order to get up the narrow and VERY steep stairs. (I was really freaked out, naturally, because I'm terrified of heights. But, I tried not to focus on the fact that if you missed a step, you might very well tumble down the mountain and die. On the way down was much scarier, because you couldn't avoid looking at how high up you are.) When you look down from the top of Wainapicchu, even the immensity that is Machu Picchu is entirely dwarfed at the base of this mountain. It was definitely the highlight of our entire trip!

In Lima, Geoff and I also spent some time going to discotecas and bars. We also checked out a peña, which is essentially a local Peruvian cabaret, where traditional dancers come out in fancy outfits and dance during your dinner. Geoff and I found a place called "La Brisa de Titicaca" (the Breeze of Titicaca), which was cheap and you can get up in between the dance numbers to dance to traditional music! It was super fun. And, while walking around Lima during the day, we decided on a whim to go paragliding, since we had never done it before! It was awesome to fly over the cliffs of the Peruvian coastline. And, of course we also checked out some delicious Peruvian cuisine -- including cuy, or guinea pig!!

My only (HUGE) annoyance from the entire trip was that when we arrived at the Lima Airport yesterday, 3 hours before our scheduled flight back to El Salvador, the Copa Airline guy told us that the Salvadorean rule is for you to be deported from El Salvador (back to Peru), unless you can show proof that you have been vaccinated against the Yellow Fever more than 10 days BEFORE your scheduled flight from a country with active cases of the disease (ie. Peru)! In fact, the only reason that Copa eventually allowed us to check in to our flight was because the doctor on-site at the airport did Geoff and me a huge favor and wrote "Revacunado" ("Re-vaccinated") on our immunization record cards, after administering the vaccine to us! Otherwise, we would have been literally stuck in Peru for another 10 days!! Ridiculous!!

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Anyway, that's it for now. Ciao! I've got some errands to run (as is the nature of things when you keep leaving the country), but I'll leave you with this cute picture of us from our Peruvian trek. There was purple chalk on our faces and confetti in our hair, because it happened to be our hike-mate, Kate's, birthday, and that's how the Peruvians helped her celebrate!


How can you not love this country??

Roundabout Math, Day 2

Note: For organization's sake, I decided that I would go with the original plan of finishing up this post today, even though I am deeply boggled by something else altogether. (You can skip to the end if you don't care for the math talk.)

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If you're just tuning in, perhaps you would want to start with yesterday's entry, but basically we are trying to break down the math about roundabouts ("traffic circles"). We left off after having intuited that the maximum velocity of a car should depend on the curvature of the road (ie. radius of the roundabout), and I brought in an external piece of information for calculating that max velocity. Now, onwards!

7. Besides the curvature of the road, what else limits the speed of your car as it actually drives through a roundabout? (Crowdedness, obviously.)

At this point, you could start a guided discussion with the kids about how we might mathematically represent the "crowdedness" of an intersection. My personal feeling about this is that, for high-schoolers, we should use a simple metric, such as what percent of the road is covered with cars? The kids can then go out to the parking lot and measure an average car's length and width, and use it to estimate how many cars can maximally fit into a given roundabout. If there are roundabouts in your neighborhood, now would be a good time to introduce the artifact (aerial photo?) and its dimensions.


8. So, the kids can create a graph that looks like one (or both) of the following, depending on what metric they use for modeling the crowdedness. (If you click on the graphs, they'll open up in another window and make it easier to read.)


In either case, the kids will have to do some geometric calculation in order to figure out the translation between the number of cars and the percent of road crowdedness. I am thinking of something in the neighborhood of:


(Notice that the "drivable area of a roundabout" is no more than finding the area of the ring, with radii r1 and r2 as given in the previous photo.)

9. If we assume -- kind of a big assumption here, but, what the hay -- that the crowdedness linearly impacts the actual speed at which a car can travel, then in theory, by knowing how many cars are in the intersection at any given time, we can construct the average speed of a car and calculate how long it would take for a car to get through the intersection. So, at this point, you can introduce some data that looks like this:

Note that this is a rough sketch of the type of data you would want to provide. You probably want to modify the table to show that at some point during the day, the traffic circle reaches its max capacity.

10. And then, you should be able to ask your kids some relevant questions!

• Assuming that you come to this roundabout three times a day: at 7am, 12pm, and again at 6pm. There is always a 3-second delay as you approach the roundabout and come to a stop, hoping to merge into the traffic. Assuming that you're extremely lucky and are the first person in line waiting at the intersection to enter the roundabout, how long would it be until you go through the roundabout to the other side?



• Assuming now that you come to this same roundabout at 5pm the next day, but find yourself to be the 10th person in line waiting to enter the roundabout. How long would it be until you go through to the other side?



• Assuming that you are considering building a "regular" intersection that is as big as your roundabout, and each full traffic light rotation is 2 minutes. The posted speed limit is 50 kilometers/hour. Estimate the max, average, and least amount of time it would take for your car to go through the intersection, if you are the first in line waiting at the light.



• Explain whether this wait time changes dramatically if you are the 10th car in line at the light.



• Why do people sometimes build roundabouts that also USE traffic lights? What advantage(s) might there be to this hybrid approach?

...In the end, I am still not at all happy with my organization of this as a potential topic for teaching. Even though I think the problem is inherently interesting, there are way too many variables even when it is broken down like this. So, I am going to leave it at that. If you can think of a way to pare down some of the variables further while still keeping the juicier, intuitive parts intact, please - feel free to give me your thoughts! Otherwise, I hope this had been a worthwhile read for you, to follow my venture to nowhere.

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In the mean time, I will go back to grieving/seething over this bit of local news. I have read parts of the original Spanish article, and it is even more heart-breaking than what Tim has already summarized. The family has 7 children, and because the dad only earns $4 a week driving sand trucks, he cannot afford to feed all 7 of the kids. He actually insisted on making tortillas out of the seed corn, even though his wife had reminded him that there was poison (insecticide) on them. He had told her to just wash the corn well, to get rid of the insecticide. In the end, only two of his seven children were not intoxicated, possibly because even with the tortillas made from the seed corn, there was still not enough food to go around at home. The Spanish article also has a picture of his two kids that died, a 10-year-old and a 12-year-old. Truly, truly devastating.

Needless to say, it horrifies me to read about this. The Salvadorean government does little to help the extreme poverty that they know to exist right on their doorsteps. ugh.

Roundabout Math, Day 1

I had an idea for a possibly interesting math-modeling situation, so I went ahead and googled it to see what there is already out there on this topic. The results were both encouraging and disappointing, because 1. it confirmed my impression that the material is inherently interesting, because there have been loads of math written about it, but 2. the math is perhaps way too difficult to be explored at a high-school level.

So, I have decided to spend a couple of entries this week just looking at the possibilities of presenting Roundabout Math to high-schoolers. It'll be done in installments, as I need some time to think this through. Feel free to jump in at any point on my hypothetical lesson.

Here is the premise: Roundabouts, or "traffic circles" as they are known in some circles, are extremely popular in El Salvador. They drive Geoff nuts, really, because they cause traffic congestion everyday right outside of our apartment. And, because the entire city utilizes roundabouts, it can sometimes take you 30 minutes to go a block or two, during PM traffic hours!

So, let's just take a look at some simplified setup for this problem:

1. Here is a standard roundabout. I'd say they average out to have about two lanes and about four streets coming in/out of them. Notice that they DO NOT USE TRAFFIC LIGHTS!


2. Here is what an average driver might want to do: go straight through the roundabout. You can only go in counter-clockwise direction around it, and you can only make right-hand turns to exit.


3. Of course, this gets more complicated when there is traffic already in the roundabout. The standard code of conduct is to wait until you think it is safe to enter the roundabout (ie. yielding to all oncoming traffic). Once you are in the roundabout, you have the right of way (at least in theory) over the new cars trying to enter from the side.


4. Let's take a detour and look at how curves affect the speed of a vehicle. Let's say that the picture below represents the top-down view of a NASCAR racetrack. Where would the driver need to slow down the most (and why)?


5. Now, let's assume that we super-impose circles on top of the race track. How does the radius of a circle (or arc) affect the speed of the vehicle as it travels through that section of the road? (Is it a positive or a negative correlation between the radius and the speed?)


6. Well, fortunately we have some information to work with. As it turns out, the maximum velocity (in m/s) that you can reasonably achieve when traveling through an empty roundabout depends on its radius (in meters) as such:

This regression equation is provided by a National Cooperative High Research Program Report, dated (unfortunately) about 30 years ago. It should match your intuition that the larger the radius is of a circle (or circular path), the higher your maximum speed will be when you travel around that circular path.

Stay tuned. Again, this is all uber-simplified stuff, because I am trying to get a math model going that would make intuitive sense to high-schoolers and get a reasonable analysis going. If you're hoping for a more detailed/accurate model, consider reading this instead. (It's a nicely written piece about the math of roundabouts, but it does involve some differential equations, which are eons ahead of what my kids can do.) I feel a little guilty doing all of this over-simplification, but considering that much of high-school mathematics is an over-simplification, I don't feel tooooo bad.

May (through October) showers

It is cold and damp here in San Salvador; I actually feel as though I'd have to break out the jackets soon! The dreadful rainy season is here to stay, all the way through October or so. It is making me jealous that everyone in the States is bathing in sunshine, even though I recognize the irony that I am the one who never has to deal with walking through snow to get to work.

With the end of the year quickly approaching, our twice-weekly Spanish classes are wrapping up as well -- y eso es muy triste. I love our current teacher, and I feel like I learn a great deal in her class; we even went out and got her chocolates to thank her for teaching us! Even though I will definitely keep working on my Spanish, we probably won't luck out the same way next year in getting another super structured, systematic instructor. Entonces, hoy mi clase de espanol fue a la casa de Kristin para celebrar el fin del ano con vino y brownies. Fue muy divertido! Hablamos por casi dos horas antes de la hora nos occurio.

On the personal end of things, I am feeling complacent. Work has zapped me of all my energy for personal pursuits in recent weeks; I haven't even finished a book in three weeks. The only thing I am actively working on is learning to do a headstand. (I anticipate this to take me a long time, since I have a horrible sense of balance, but I do intend on practicing daily until I get it.) I love my yoga class, and I really think that both my flexibility and core strength have improved significantly in the few months since I joined the class. This summer, my goal is to work on my personal yoga practice, so that I am not always so reliant on going to my yoga class to get things done!

And, I am excited about going to LA and Shanghai so soon to visit the fam!! Of course, I'll have to stuff my suitcase with books, TV downloads, and my yoga mat on the way there, but I do expect to come back with an extra suitcase full of American goodies! :) (Things we can't get very easily here or are very expensive: contact lens solution, sour patch kids, Neutrogena face wash, condoms, good beers...) --And, who knows? I might get to swing-dance in Shanghai! :)

Oktoberfest, El Centro

Geoff and I have had a few very uneventful weekends, because I've had to catch up on work before the quarter ends. By this weekend, both of us were going stir-crazy and wanting to go away somewhere for the weekend. But, we had promised our friend Andrea that we would go to her Oktoberfest party, so we decided to stick around the city...

We decided, instead, to make the best out of Andrea's party. We went and bought a ton of beers (a mix of cheap and nice beers), bought two giant beer mugs, got some plastic cups for beer pong, and made jello shots! Andrea's party turned out to be totally fun, even though the Americans mostly turned in somewhat early. We ended up partying with her Salvadorean friends, plus Jon, after everyone else had left. We taught the Salvadorean girls how to play flip cup and beer pong, and they taught us how to play Vikingo and Marcas. And we silly-danced. It was pretty awesome times. :)

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One thing we did try to do this weekend was to go down to El Centro to visit the Palacio Nacional, the Catedral Metropolitana, and the Teatro Nacional, which are all on the same block in El Centro. We got inside the cathedral, and it was pretty neat, but both the National Palace and the National Theatre were closed to visitors. What a shame! We were also warned by our taxi driver to not walk around past the 2 block-by-3 block area, since El Centro is not at all a safe barrio. Anyway, the cab driver said we'd be OK if we stayed around the very bustling parts of town, so we didn't press our luck. We left pretty soon after visiting the cathedral, since I wasn't feeling very safe. Afterwards, Geoff said that he felt like people were giving him pretty unfriendly vibes. I am not sure whether I had felt the same, but it was definitely a very impoverished part of the city. As soon as we had gotten out of the cab, a waft of something in the air had told me that there were homeless people nearby; and sure enough, you could see them every few feet, huddled next to a building or holding out their hands to beg for money. According to things I've read on the internet, El Centro suffers from a lot of street violence, and isn't really safe to visit at any hour.

Generally speaking, I'm feeling a little frustrated by the security situation here. Some days, it seems like we cannot really go anywhere. Even on our way down to a popular bar one night (La Luna Arte y Casa), a kid jumped out in front of our taxi cab in an attempt to stop us -- probably for no good. The cab driver eventually drove around the kid, and the cop car behind us picked up the kid and took him down to the station, but it's hard to say that we're going to keep being so lucky.

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Anyway, the first quarter is already over! Can you believe it?

I need a break. We've only had one long weekend since the school started. The next 3-day weekend will be the weekend of Halloween. I cannot wait!

Things that drive me nuts

...Oh, obviously (as an addendum to the last entry), there are things about living in El Salvador that drive me absolutely nuts. For instance, I've been trying to go pick up my ATM card from the bank near my school. The first time I went there, I got there at 4:30pm and only the express window was still open. They told me to return between 9am and 4pm the next day -- a near impossibility on a school day, unless I grab my stuff, abandon all meetings with parents/teachers/kids, and run out the door after my last period. So, finally I went back a week later to pick up my ATM card. The customer-service agent who spoke to me briefly made me sign a form and told me to return 3 days later, when the card would be ready. I waited a full week, and went back on a Saturday. This time, I had to walk 40 minutes from home to the bank. When I got there, I waited 20 or so minutes -- a very moderate wait time, for El Salvador --- to see a customer-service agent. Then, she took my ID and left me waiting at her desk for another 20 to 30 minutes, while she went to the backroom to fetch my ATM card. After waiting for what seemed like forever, she came back and told me that -- surprise, surprise! -- the card was not ready, and that it wouldn't be ready until the following Tuesday. Too tired to argue with her, I told her that I needed to withdraw some money. She asked in surprise, "You don't have your checkbook with you?" I told her dryly that I had anticipated having my ATM card in hand. So, she wrote a letter to the bank teller and took my ID to the teller. I had to wait in another line for about another 20 minutes in order to see the teller, before I could withdraw my money. Following that, I walked 40 minutes home, having really accomplished nothing and having already wasted half of my Saturday at the bank.

And on the same day, at a different bank, my friend Andrea had the same exact experience trying to do something else that's very simple. I don't understand why everything has to be so complicated down here. Everything!! Efficiency surely is not of critical importance here. Coming from NYC, this type of stuff just drives me nuts.

Nature? Yes, I've read about it...

Last night, I saw a big pink iguana dart across our bathroom after it had entered through the window. I was freaked out! Geoff had to grab our pot in order to catch it and to put it outside. It was scaling the wall at a crazy speed, and even jumped during the Geoff vs. Iguana hand-to-hand combat.

Then, an owl was stuck in my classroom today! It was small, and apparently couldn't find its way out. I wish I had a camera with me, because it was the cutest thing I had seen in days. It kept eyeing me suspiciously by turning its head to a weird angle to follow me with its eyes. Eventually, it let me get close enough to open all of the windows to let it out. SUPER CUTE!

--This place is crazy. There are iguanas, armies of ants, killer mosquitoes, (dead birds on our porch,) and now an owl!

The Price of "Bling"

On July 15, the day that Geoff and I arrived in El Salvador, an anti-mining environmental activist was found murdered at the bottom of a well in San Isidro, El Salvador. He had been missing for nearly a month, and his body showed visible signs of torture. Since then, 4 reporters who have been covering the news of his disappearance and death have received death threats themselves, and another priest who is also aligned with the left-wing activists has nearly also been kidnapped and killed, escaping his armed aggressors ever-narrowly only by jumping into a ravine.

Concerned about the issues surrounding the obviously heated environmental activism, I looked up some relevant information about mining in El Salvador. It shouldn't come as a surprise to anyone that El Salvador is a rich source for natural elements such as gold and silver, seeing that 90% of the country originated from volcanic activities. Mining companies based in U.S. and Canada are eager to come in and reap the benefits of the abundant resources this country has to offer. The local proponents of the mining law point to the jobs it would create and the income that the local government would receive as a percentage of the proceeds, but the environmental and social activists point to the amount of acidic toxins -- specifically, of mercury, cyanide, arsenic, zinc and aluminium -- that would be released into the water. Leaching, the process of extracting gold and silver from the rocks, requires an enormous amount of water and exposes chemicals to open air, allowing them to evaporate and to be absorbed into the surroundings. Mercury evaporates readily at 26 degrees Celsius, and then redistributes in the form of rainfall. The mixing of the chemicals with water also would exacerbate the existing water shortage. Already, 1.5 million Salvadoreans (out of a total population estimated to be somewhere between 6 to 7 million) do not have access to drinking water. The "acidic drainage", as it is called, is going to make things worse. Already, there have been hillsides and wells that have dried up in San Isidro as a result of "an error" committed by one of the mining company's employees. Instead of receiving water deliveries in exchange for keeping quiet, the residents of San Isidro have opted to speak up against further mining activities by these foreign companies -- hence, the recent wave of environmental activism.

In any case, the laws right now are in limbo. The mining companies are hoping for the drafted mining law to be passed, so that the suspended mining activities may resume. I don't think you need me to say where I stand on the issue.

...What an absolute outrage!

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I finished reading One L, a personal account of one guy's experience as a first-year law student at Harvard Law School. The author describes the fearful manipulation that the professors used to run their first-year classes, and the resulting degradation in decency he observed in his peers and in himself as the academic year progressed. Even though he attended HLS back in the 70s and his account is clearly outdated, the story was still pretty interesting for me to read. It made me think about what my friend Ron once said about being a witness to injustice: "Either together we stand [against what we perceive of as injustice], or individually we will fall. Today it could be them, but tomorrow it might be you... or me." I think that concept applies broadly to a lot of things, and it is an idea that I keep coming back to. Why is it that we should stand up for someone whom we think is treated unfairly? What is the broader implication of justice, for us individually and, then, collectively?

Anyway, I picked up a Spanish novel yesterday from the bookstore. --Ambitious, I know! I figured that I would try to build my vocabulary the best way I know how -- by tediously working my way through a book I'd like to read. That's how I learned English, anyway, so doing this again actually feels familiar and warm, a bit like coming home again after many years. It's going slowly, obviously; took me about 30 minutes to cover 3 pages, because the structure of written Spanish is more difficult than spoken Spanish, and words often mean different things once you string them together into a phrase. But, I love the feeling of piecing together meaning, one word at a time. I'm excited. :)

A History of Poverty

To help understand why things are the way they are down here, I think we need to talk briefly about the recent history of El Salvador. Some of this information I gathered from various readings on the internet; others came from word-of-mouth (ie. from talking to my principal, who has lived here for 3+ years).

In El Salvador, for many generations the country had no middle class. There were the land-owning elite, namely "the 14 families", who literally divided the entire country into 14 gigantic jigsaw pieces (after driving out the native Indians), and those who were landless and impoverished. To give an idea of how far-reaching the wealth is of those elite families, my principal pointed to the giant volcano that backdrops the city of San Salvador, and said that two-thirds of that mountain is still owned by a single board member of our school today! All of that land teems with coffee plantations, and one can only imagine how much money is associated with that volume of production.

As with any sort of wealth disparity comes social unrest. The country divided itself over time into two parties -- the same two parties that still exist today -- the Republican party, or ARENA, and the Socialist party, or FMLN. Locals simply refer to the latter as Frente, which literally means "Front" and refers to the idea that the FMLN came about as a coalition of smaller populist parties. Over time, both parties began to use violence -- torture, rape, and killings -- to further their cause, and by the late 1970s, the situation had boiled over to a full-blown Civil War.

Because the landless Salvadoreans were sympathizers of Fidel Castro and because this period in Salvadorean history corresponded in timeline to the U.S. fear of the spread of Communism, the U.S. administrations from Carter to Bush Sr. gave a total of 7 billion dollars in aid to El Salvador in support of the ruling elite. Sadly, since this choosing of sides was political in nature, whether it was justified remains questionable. An excerpt from Amnesty International's 1985 annual report states, "Many of the 40,000 people killed in the preceding five years had been murdered, by government forces, who openly dumped mutilated corpses, in an apparent effort, to terrorize the population." --This is not to gloss over the violence brought on by the opposing guerrillas, but simply to state that both sides were definitely violent to an extreme in this internal conflict.

In any case, in 1992 a peace accord was signed, partly because the guerrillas were running out of steam. For a period of 5 years that followed, parts of the land were re-distributed slowly to eligible soldiers on both sides under the supervision of the United Nations, and the guerrillas re-established themselves as a legitimate political party.

In June, the first ever Frente president took over in a legitimate election. It had been expected to be a landslide victory, ever since he had emerged as a popular, moderate, and charismatic candidate. But, the 6 months before the election saw a lot of rumors spreading fear that he was a Communist and was going to drive away all the business owners in the country. In the end, he won by a margin less than 3%. The jury is still out, since he is so new, but we can only hope for the best.

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Some worrisome news from a Salvadorean blog I read:

The online periodical Contra Punto reports the latest homicide statistics for the first 7 months of 2009 and they are troubling. Murders are up 37% in El Salvador for the first seven months of 2009 compared with the same period in 2008. So far in 2009, there have been 2428 violent deaths, compared to 1767 in 2008. These statistics come from the Attorney General's office who asserts that the majority of these murders are gang-related.

Speaking of gangs, supposedly the rampant gang activity down here is, again, closely tied to the history of poverty in this country -- and maybe surprisingly, also related to the Salvadorean immigration to/deportation from the States.

In any case, Geoff's and my neighborhood is relatively safe. Like most of our neighbors, we have 24-hour security guards who hold machine guns behind closed gates -- not that they actually would use the guns in a time of need, but as far as appearances go, I think they give off some sort of a protective vibe, anyway. And for now, Geoff and I have given up on walking home at night, just to be on the safe side. Cab rides are only a few dollars to get to anywhere in the city, so it's really not worth it to walk even 15 minutes in the dark...