Midair Maths and a Marvellous Mistake

On the fourth week of maths club my teachers gave to me: four miles of line, three piles of rocks,

 two logic puzzles, and information on a dead genius!

Today in Maths club we made a giant number line. The students were each assigned an odd number and wrote it in the middle of a piece of paper. Then they taped their papers together in order and wrote the even numbers over the cracks. This ensured that all of the whole numbers were evenly spaced:

They eventually added halfs and negative integers:

The finished product was very, very long:

Then we jumped! I can only jump by 5's but some students can jump by 10's!

If you look closely at the above picture you will notice the biggest learning opprotunity (a.k.a. mistake) made during the creation of the line. The team assigned to making the negative integers originally made them in the order "-1, -2, -3..." rather than "-3, -2, -1...", etc. To affix them to the rest of the number line they had to realize their error and turn the whole negative part upside down. That is exactly the kind of productive negative experience that, taken as a challenge and approched creatively, leads to a rich understanding of concepts. I felt like I was inside my Philosophy of Education textbook!

House Standings

As promised, I intend to keep you up to date on my school's four houses as they compete against eachother in athletic and academic competitions...

Druk (Dragon) House is off to an early lead, having placed first in the Spelling Contest, first in the boy's football tournament, and second in the girl's football tournament.

Tak (Tiger) House is a close second. They placed first in the girl's football tournament and second in the boy's football tournament. 

Chung (there isn't any word for it in English: see picture above) House and Seng (Lion) House are currently tied in third. In each football tournament one placed third and the other came last but won "most sportsmanlike".

I have a soft spot in my heart for Seng House because their boys captain is the most diligent in his litter collection duty. I congratulated him once on the huge armful of waste he was bringing to the dustbin. His response was, "Principal Sir says captains should lead by example!"

William Heads Home

William left Trashiyangyse this morning at 5am. We realized that we both have to be where we fit. I belong in Bhutan teaching and loving it and soaking up the culture. He belongs in Bedford where he can see his friends, have a real job, and set aside some money for our future. We're going to miss eachother, of course, but the absence will only make our hearts grow fonder.

Dull sublunary lovers' love 
    —Whose soul is sense—cannot admit 
Of absence, 'cause it doth remove
    The thing which elemented it. 

But we by a love so much refined,
    That ourselves know not what it is, 
Inter-assurèd of the mind, 
    Care less, eyes, lips and hands to miss.

Our two souls therefore, which are one, 
    Though I must go, endure not yet 
A breach, but an expansion, 
    Like gold to aery thinness beat.

- John Donne

This Developing Country

I see Bhutan developing all around me. I see non-material changes like the education system's switch from emphasizing memorization to promoting deep understanding. And I see material changes. Buildings and bridges and roads are being construction at an astounding rate:

Rarely, though, does my experience in Bhutan conform with what I thought it would be like to live in a "developing country." The term made me imagine squalor and desperation. My life in Trashiyangtse is, in almost every respect, as comfortable or more comfortable than my life in Canada. I have electricity, running water, and Internet reception most of the time. I feel safe in my home and in the streets. The children at my school seem adequately nourished, clothed, cared for, and supplied with what they need to learn.

To be sure, there is a lot less stuff here than in Canada. Children find entertainment without Nintendo DS's making jumbo legs with cardboard boxes or peeking in on the crazy Canadian woman:

And I have to find ways to teach without the learning materials I was accustomed to in Canada. Rocks, as it turns out, are a versatile resource perfect for division:

Only very rarely do I experience something that makes me go "whoah. I'm not in the first world anymore." Thursday brought two such moments, both related to public health. First, it was World Tuberculosis Day and the children were educated on the transmission, prevention, and symptoms of the disease. Before the presentation, I thought that tuberculosis was an historical problem that no one worried about anymore. In actual fact, one third of the global population is infected with tuberculosis mycobateria that will, if the immune system is compromised, become symptomatic. TB is especially dangerous, therefore, for adolescents, the elderly, and people with AIDS:

Second, I was tasked with giving my home class their deworming medication, a pill to chew and a pill to swallow which all students in Bhutan take several times a year to clear their systems of any intenstinal parasites they've picked up from unclean water or poor sanitation:

Mild side effects of the medication are common and include headaches and nausea. I now know what university professors feel like trying to lecture the morning after St. Patrick's Day.

My Dream Hovel

My first period classroom is on the very edge of the school campus and at the very edge of a steep hill. It overlooks a homestead where I've dwelled all my life. It is the quaint haven where my mind has gone in every moment of stress and sadness. There, in my peace place, a cluster of white prayer flags remember a good man who died too young and cast gentle shadows on a road lined with stone.

The house itself is just beyond the wall. The eclectic materials from which it's constructed make it seem almost tentative, temporary, and incomplete, but at the same time it is comfortable in itself, and wisely old. You know before you see them that the tenants will hobble along with bent backs, and smile with deep creases. Everything is as I dreamt it: the wood pile, the vegetable plots, the pink blossom Truffula trees, and occasional cats.

Yeats understood the appeal. "I will arise and go now, / And go to Innisfree, / And a small cabin build there, / Of clay and wattles made; / Nine bean rows will I have there, / A hive for the honey bee, / And I'll live alone in that bee loud glade. / And I shall have some peace there /..."

Only poetry has the words for it, my stone-walled hovel where a river spills and twists and gurgles. Yeats, but Wordsworth, too: "These waters, rolling from their mountain-springs / With a soft inland murmur.[...] These plots of cottage-ground, these orchard-tufts [...] These beauteous forms, / Through a long absence, have not been to me / As is a landscape to a blind man's eye: / But oft, in lonely rooms, and 'mid the din / Of towns and cities, I have owed to them, / In hours of weariness, sensations sweet..."

A Chhertum for your Thoughts

On the third week of maths club my teachers gave to me, three prime rocks! Two logical puzzles! And information on a dead genius...

Yesterday, the program on offer in Maths Club was a set of interesting word problems about decimals, fractions, and ratios which we deemed too advanced for the Class 5 students. Since all of the Class 5's are my math students during regular class time, I took them aside for a rockin' enrichment activity based on the introduction to division that we did in class.

In class, I had every student gather a handful of stones. (“Handful” is a wonderful ambiguous quantity that guarantees that some students will bring in many tiny pebbles while others will choose a few good-sized rocks.) Each table group counted the total number of stones they’d collected and then made as many piles of seven stones from it as they could. It is the simplest, cheapest division demonstration ever.

In maths club, they took twelve stones and found all of the possible ways to divide them into even piles without getting stuck with a remainder, which is to say, they found the factors of twelve:

When they tried it with seven, though, they found that the only fair arrangements were all-of-the-rocks-together or all-of-the-rocks-alone. I told them that that means that seven is a "prime number." I asked them to use the stones to find more prime numbers. They found all the first ten! I then helped them derive the divisibility rules for 2, 3, and 5 so they could check if a given big number like 5026041 could possibly be prime. (It can't. 3 is a factor.):

That lesson was a great success. I had some trouble in math club, though, too. One of the other groups asked me to check their work converting fractions to decimals. They had written 1/4 as 0.4 and 1/3 as 0.3. I was able to prove to them that their answers were wrong because 1/4 plus 1/4 plus 1/4 plus 1/4 should be equal to 1 but 0.4 plus 0.4 plus 0.4 plus 0.4 is equal to 1.6. I had an awful time, though, trying to explain why the decimal form of 1/4 is 0.25. In Canada, it is the easiest conversion of all to explain because one fourth is a quarter and everyone knows that a quarter of a dollar is ¢25, aka. 0.25 dollars. Technically, the Bhutanese ngultrum is divided into 100 chhertum just as the Canadian dollar is divided into 100 cents and technically there is a 25 chhertum coin. The problem is that coins are never actually used here because everything costs a whole number of ngultrum. 25 chhertum is worth less than one tenth of a penny. There is just no point in anyone carrying around or caring about that much money. I've been in Bhutan two months now and the only time I've seen coins was in the collection of a numismatist half way up the climb to Tiger's Nest. Explaining why 1/4 is 0.25, then, was my first experience of the universal language of mathematics not seeming universal at all because my go-to teaching strategy is tied up in a specific cultural phenomenon.

I'll leave you on a positive note, though, with some comments on maths club written by the students:

Rimdro: Smoke, Mist, and Steam

Saturday was our school's annual Rimdro, a  puja in which prayers and gifts are offered to a goddess to ritually purify the school, its staff, and its students for another year.

It is a study in transcience. These are decorative cakes handcrafted by the monks. The circular parts are 100% coloured butter.

And here is the same cake at the end of the day, going up in flames:

Here is the gorgeous diorama that was the centrepiece of the multipurpose hall [MPH]:

And here is what became of it when the ceremony finished:

I think you have to be pretty detached from the material world to not mind the destruction, to realize that all the works of human hands, however beautiful, are fleeting. All is vapour. I subtitled the entry "Smoke, Mist, and Steam" because big billows of all three swirled around us throughout the day as a reminder of that truth. Here you see smoke from a big outdoor incense fire:

While here is one of the small indoor incense lamps that made William feel ill and go home early:

Here is the mist. Teachers were to arrive at the school at 6:30 in the morning, which is mistrise in Trashiyangtse. I went home at 8:30 at night. Some teachers stayed celebrating until midnight! Rimdro is a full, full day:

As for the steam, that came from the million cups of tea and all the cooking. Because we were there all day, three full meals were prepared. Can you imagine any public event in Canada including breakfast, lunch, and supper?

 Here is the kitchen where the necessary water is heated in three huge boilers:

For me, it was the candles more than anything else that made the day beautiful. Bhutanese candles are not wax. Large multi-use ones are made of butter while small ones can be prepared quickly by rolling cotton wicks, placing them in small bowls, and pouring oil around them:

 

Now, when I say that students in Bhutan work harder than Canadian students, I don't mean they labour a little longer on their assignments. I mean they break some serious sweat! No matter what time you walked around my school campus in the long day of Rimdro you would have seen a group of girls doing dishes at the outdoor taps:

Turning your head, you would have surveyed a few boys chopping wood while others minded the cooking and a group of girls shelled green beans:

Rounding a corner, you would have found a team peeling potatoes and some boy with a stronger stomach than I hacking up fresh beef:

Nowhere, though,  would you see eyes rolling in drudgery. The children were not compelled to work. They volunteered, they took turns, they worked with their friends, they laughed, they took breaks. When they weren't working, they threw around a football or jammed together:

As well, each of them took time out for religious devotion. They went to the MPH, watched the monks chant, prostrated themselves before the lama and then before the diorama, and then laid an offering on the alter:

The work, the play, and the worship were all come-and-go-on-you-own-scheduale. It was so relaxed and so relaxing. Total freedom! The only thing that everyone did all at once was participate in the monk's final prayer. We were each given a lapful of grain and, in time with the lama, threw small handfuls of it toward the door of the MPH. It represented taking our sins and negative thoughts and bad habits and casting them out of our life.  

The mess on the floor afterwards was obscene, just ridiculous . The picture doesn't do it justice at all. But it's the cleaning up after, the sweeping away, that finally removes all the negativity from the school and sets it right for another year. I think that's beautiful.

It was a great day. And yesterday the school family shared all of the packages of cookies that had been laid on the alter. That was a great day, too!