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Second mission to El Hogar, a home for poor children in Honduras
Phil Turner with remarks by bt

El Hogar, Tegucigalpa, DC Honduras

Prayers needed

February 16, 2011  bt

"if only we could take all that sand the devil is trying to throw in our eyes..."

Today is the first step in Philip's trip to the orphanage to teach mathematics to the students at the orphanage

Yesterday, after Bible Study, trying to get back up our very steep and windy driveway which is now mainly coated in a thick layer of solid and very slippery ice, the car lost traction on the steepest part, spun around and ended backed into a snow bank on the edge that drops to a steep ravine beyond the bank that has been built up over this winter.  Fortunately it too has a lot of solid ice holding it in place so the car is in a solid position.  I think this is the section of the driveway that the original owner of this property fell off while on his tractor and died.
Surrounding the rest of the car is the ice covered driveway that was exceedingly slippery yesterday due to slightly above freezing temperature--32.5 here.

Since the driveway is mostly thick ice, we went down through chunky 3-4 ft. snow and ice packed along the edge of the driveway, making a trail to the car.  Not knowing what to expect, I came armed with a bit of baking soda to put around the tires and expected to come down again with a bag of kitty litter. I couldn't get too near because stepping out onto the ice was too treacherous. I got as close as I could and spread 1/2 the baking soda in front of the one front tire that looked like it could get some traction and then tried to go to the back of the car to do the one free back tire.  I slid over the ice and got to the door handle for a grip and, leaving the door open, used it to move over the ice to the back of the car.  I did manage to get around and spread the rest of the baking soda in front of one rear tire and relaxed a bit just enough to lose my grip. I slid down the driveway on my butt for a good 100 ft.  It would have been fun and I did laugh a lot as I had came through the snow to get to the car, but this stopped my old lady giggles.

Now begins the real ordeal- getting back up to the car.  I had maneuvered the slide/ride while slipping so that I ended in the snow bank and began to use that, on the ravine side, to struggle back up to the car.  Huffing and puffing, I got into the back of the Subaru and crawled from the hatchback through to the front of the car.  I considered starting the car but it was clear by this point that there was no solution we could manage for getting the car out by ourselves so we got the doors closed and crawled over the ice to the side of the driveway and trudged through the snow/ice pack back to the house.  I was exhausted by this point and stopped many times to catch my breath and try to recall the attitude of letting go and letting God that I have been trying to cultivate; seemed distant but I could usefully spend the time to rest and pray.

Philip got back to the house long before i did only to find that the pellet stove had jammed and stopped so he began the long and tedious act of taking it apart.  When i finally got back i was soaked and sweating and dizzy with the exertion. the devil and his sand...

February 17, 2011 bt

This morning Mark is going to come by with his sand truck and help get the car out.  He is a good Christian friend and has kept the driveway plowed for us this winter but the melting and freezing have produced this icy condition that will no doubt melt in a day or two and we normally would just wait.  Since Mark went off the driveway at the bottom and was stuck for 2 hours a few weeks ago i am hoping he will know just what to do.  Maybe back up the driveway to spread the sand?  So today will be warmer and tomorrow warmer still but today is the day Philip needs to get to Cellie's so she can get him to the airport in the middle of the night.

prayers needed

Mark and the host of heavenly angels have managed to get the car out and sand the whole driveway. We will leave for Massachusetts soon.

February 18, 2011 pt

I'm at Bradley waiting for my flight out to Miami.  Everything went fine last night and this morning.  Paul and Marcella were quite solicitous and helpful.

Meanwhile, in New Hampshire the temperature has been above freezing all night and the driveway is melting, the wheelbarrow has emerged from its spot marking the newest garden, and we are fogged in.  Cali spent a good hour woofing and howling last night calling Philip but finally settled down after a good munch on some toilet paper, one of her favorite things to do when she is upset.

February 21, 2011 bt/pt via pre-paid cell phone call

Philip is established at the orphanage and set to begin teaching tomorrow.  Together with an American couple also teaching at the orphanage for the semester, a modem will be set up soon so internet access will be possible. 

February 19, 2011 pt (received on 2/28: the first modem for internet connection was faulty so another one was bought and is now working)

First day of classes:
No mathematics classes are taught on Monday, so I audited the 3rd course in Science. The topic for the day was "significant digits". The teacher, Arnold, agreed to let me sit in the class and listen. He presented the lesson stating the rules and using examples. Since the students do not have textbooks, they write down in their notebooks the rules as he dictates, then they work the examples in their books. Volunteers came up to the board to present their answers. When the answers are right the teacher takes a stamp and stamps the lesson complete in their notebooks; otherwise, they correct their work and show it to the teacher to see if they have earned the stamp.

I found the teaching approach engaging, but slightly confusing. The 3rd rule was stated in a form which I thought was somewhat contrary to the first rule and so I got a different answer than the teacher's for one of the examples. Afterwards, in the break, I spoke to the teacher about my confusion and the principle which animates the use of "significant digits" in science. Perhaps he had presented this principle in earlier classes, but he had not in this class. Roughly speaking (even rougher when I delivered it in my Spanish) I think the rule is this: the results of a calculation with measurements resulting in data with different orders of significant digits cannot have more significant digits than the measurement with the least number of significant digits. For example, if three sides of a triangle, are measured as 17.8 cm, 14.73 cm and 16 cm, then the perimeter can be best expressed in two significant digits (since that is all the precision implied by the third measurement) as 18+15+16=49 cm. The instructor worked this example as follows: 17.80+14.73+16.00=48.53->49 cm. Our final answers agree, but the instructor's method highlights precisely the fallacy this scientific principle was meant to avoid (I believe), namely that we do not want to attribute more precision to a result that the data themselves provide; and changing the third measurement from 16 to 16.00 does so. I did my best to explain this but I believe I was only partially successful.

The next example illustrates the difficulty:

Round to 4 significant digits: .027654, .027650, .02765

The instructor's application of the rules leads to the answers: .0277, .0276, .0277

I pointed out the incongruity of starting with .027650 and .02765 and yet returning different results. He turned to me and said (en Espaniol), "The rules are the rules." I was in no position to argue, so I let it go, but I am reminded of our Lord's saying, "The Sabbath was made for man, not man for the Sabbath."

February 20, 2011

Sunday, February 20, 2011
Praise the Lord. I am well.

It's my second full day here at the Technical Institute and in a few minutes it will be time for breakfast. The roosters crow in the background; they begin their day before 4 am so I am well attended by the animals here. The Technical Institute is located outside the capital city of Tegucigalpa in farmland.

My reception here has been wonderful, "thou hast anointed my head with oil. My cup runneth over". The children have dubbed me, "Albert Einstein". I have my first sunburn from playing soccer and basketball yesterday before applying sunscreen… silly of me to have delayed!

My accommodations are adequate, if a bit Spartan.

I took a cold shower this morning because there's no hot water in my apartment, which turns out to be the former sacristy behind the large chapel. I have a bunk bed, a long table and bench, two folding chairs and a bathroom with a shower, sink and toilet.

I am told that the Director of the Institute is going to provide a "hot-shot" shower head so that I can have hot water showers. Alleluia!

I am not the only volunteer teacher here. Mike and Valerie are a couple from Colorado who are here to teach English. They also arrived on Friday, Feb 18th and they intend to stay the entire 9-month school year. May the Lord bless their intention. It's a comfort to me to have someone else from the States to share this experience with. Mike's Spanish is better than mine, while Valerie and I are about at the same (beginner's) level.

We spent most of yesterday playing with the children: soccer and basketball. Mike's parents were missionaries to Africa, so he grew up playing soccer and is right at home in that game. Val and I are more comfortable playing basketball. We played horse (in Spanish, Caballo) at first, but in the evening after dinner we played a full-court game in which I ended up as the referee. It was very interesting to see how the game improved when I began to enforce the rules and called fouls and turnovers. The children began to pass the ball and set up their shots instead of just trying to dribble down the court and take a shot on their own. Enforcing the rules seemed to enable teamwork, an interesting observation, I think.

Mike, Valerie and I had all gone to church at St. Mary's in Tegucigalpa this morning.

As in the service I attended in August, the structure of the service was quite Anglican, with the vibrancy of the music setting it apart. The musicians are all quite young (teens and twenties) and they play electrical guitars and keyboard.

Their playing and the congregation's singing, when combined with the traditional liturgy, gave the service the feeling of a prayer and praise service with communion, a Spirit-filled balance, I thought.

After the church service, we went with Raul Castro of El Hogar to a Chili's for lunch (there are several American restaurant franchises located in Tegucigalpa) and then we went shopping for a few comfort items at a large shopping mall.

I got some cotton sport socks, a bathroom mat and washstand rug, and a Honduran "burn phone" to call the USA and locally at very reasonable rates. (My Verizon phone is useless in Honduras, unless I were to buy an expensive international calling plan.) The cell phone store was among the busiest at the Mall. Almost everyone from teens up in Honduras have similar phones, even all of our students. The phone cost me about $15 and I bought about $5 of pre-paid minutes which should last me at least a couple weeks. In contrast, computers are rare and internet service is sparse outside the city, unless a person buys a cell phone modem to plug-into the PC.

More about our cell phone modem story later. From the looks of the mall, the Honduran middle-class is doing OK.

February 22, 2011 Second day of classes.

I awoke refreshed by sleep with the pleasant prospect of a warm water shower after my yoga routine. A "hot shot" water heater shower head had been installed in my shower the evening before by Efraim, our handyman and chauffeur par excellence.

Alleluia!

This morning I have arranged at Lazuro's suggestion, to sit in on the "taller de electricidad" 3rd course class. The boys in that class are learning the rules of voltage and current in circuits. This is also the class in which I had started my geometry classes at the Institute on my previous visit, last August. It's a class where the principles of mathematics and science are applied to practical results. So I'm hoping that listening to these presentations will aid me in drawing parallels between theory and practice.

Unfortunately, when I arrive at the taller de electricidad, the teacher tells me that the class will be delayed because there is going to be a meeting of the instructors. I reply,"OK, but when will the meeting be over, so that I can return?" 

The instructor, Habear, says that he doesn't know and he invites me to wait in the teachers' office. So I wait. An hour goes by. I've looked over every product catalog in the office. The meeting is still going on. So I get up and look for Mike and Valerie. When I find them, they report the same phenomenon. After a short discussion, I decide to go back up to my room. Later I come back. No change. Some of the students have continued work on their current projects or have cleaned up their equipment and work areas. But the morning passes and there is no class.

At lunch we hear that the instructors' meeting was about some grievance they want to discuss with the Director of the Institute, Lazaro. But that is all we ever find out about the morning. Like the children of a divorced marriage, we wonder whether our presence is cause of the problem. Lazaro informs us that no, we are not. But no other reason is given.

On a more positive note, Lazaro informs me that Pat, the director of St. Mary's Episcopal School attached to the cathedral church we had worshipped at on Sunday, has requested that I attend a convention of all 5 Episcopal high schools in Honduras and give a short 15-minute address to the math teachers.

The convention is to be held on Thursday and Friday at a resort to the north on the Caribbean coast near a town called Ceiba.

View Larger Map

I inform Lazaro that I am honored to be asked and that I will gladly go. I had hoped to visit the coastal areas of the country on this trip and this seemed to be a perfect opportunity. In addition, I had some ideas about teaching mathematics that I wanted to write down on paper and this would force me to do it.

So the trip is arranged and that evening I began writing my thoughts on mathematics "angels".

Some Remarks about mathematics education

I am honored to have been invited by Pat to make some remarks about the direction of mathematics education at the secondary level. Thank you, Pat for this precious opportunity.

First of all, I need to clarify that I cannot be considered an expert in mathematics education. My only formal training in that field is some coursework I completed to earn a teaching certificate in secondary mathematics education from the State of Maryland in the 1970's, many years ago. So I suspect that all of you are in fact better qualified than I to speak on this topic. Now, I do hold a doctor's degree in Mathematics which I earned in 1980, but I left the world of theoretical mathematics soon thereafter to work in business as a practicing mathematician in an electrical utility for 28 years. So as you can see I hadn't taught in an academic institution for many years, before my recent experience as a volunteer teaching at the Instituto Technico Santa Maria. Nevertheless, I pray that the Lord will place in my mouth some thoughts regarding the teaching of mathematics that you may find interesting and edifying and that these remarks may lay the foundation for an engaging conversation during the question and answer period following my brief remarks.

Secondly, I encourage you to see yourselves as blessed to be called to teach mathematics. Not just because mathematics is a required course of studies, or because a knowledge of mathematics is useful for successful living in a technological and financial world, or even because mathematics is the Queen of the Sciences, but because Mathematics is an aid to spiritual education. Why do I say that? Because I believe that the ideas in mathematics are "angels".

Allow me a moment to review a few things that we know about angels from the Bible. I want to point to four examples of angels:

1. The burning bush in Exodus 3
2. The seraphim in Isaiah 6
3. The angel Gabriel in Luke 1
4. The angels who attend Jesus after His trial in the desert in Matthew 4 and Mark 1.

What are the properties of these angels? They are…

1. Immortal beings (the burning bush is not consumed, the seraphs continually do cry)
2. Creatures of God
3. Capable of visits to earth
4. Serve God as messengers and helpers to men and women.

Now let us compare mathematical ideas such as numbers (1, 0, 3, p, 8), geometrical shapes (circle, triangle, n-dimensional cube, the Hilbert cube), and theorems (Pythagorean Theorem, Central Limit Theorem). Are all these entities not…

1. Immortal beings (men may pass away, but these ideas will never pass away)
2. Creatures of God (In the beginning was the Logos, and all these spring from the Logos of God)
3. Capable of visits to earth (in our Science and in your classrooms)
4. Serve God as messengers and helpers to men and women (more on this below)?

It may be argued that these mathematical ideas are perhaps not angels of the highest rank (since they are not endowed with "personalities" in the sense of the angel Gabriel). Nevertheless, as we introduce these ideas to our students, we enable their spiritual education. They are led to study immortal creatures of God who inhabit our world but are not bound by it. Just as no man may be so foolish as to believe that he or mankind has brought the stars and the cosmos into being, no man should be so foolish as to believe that he or mankind has generated the number 7 which God used to frame the times of His Creation nor the ellipses that govern the orbits of the stars and planets. So Pythagoras did not invent the theorem which bears his name, but he discovered it by peering into the mind of God.

Mathematics, then, can be understood as "conversing with angels"; a study that leads us out of bondage to rank materialism into the Kingdom of God.... Glory be to His Holy Name! By conversing with angels, we come to know a piece of the mind of God and understand our souls and ourselves as inhabiting our bodies as tents, ultimately not bound by this material world, but created and destined to live eternally with God. These mathematical ideas are indeed messengers and helpers of men and women to grasp the inexhaustible riches of the Kingdom. In fact, I would argue that just as the deliverance of the people of Israel by the blood of the Paschal Lamb was provided by God as a foreshadowing to Israel of the coming deliverance of His people by Jesus, so mathematics, astronomy and a star were provided by God to the Greeks and Gentiles to light the road to an Epiphany of the Christ-child.

What then are implications of the revelation of these mathematical angels for mathematical education and the preparation of secondary students for the university? I see the implications in these terms:

• Humility
• Wonder
• Perplexity
• Adoration

First, Humility is the proper approach before angels; we recall that Moses was asked to remove his sandals before the burning bush. In practical terms, for example, in teaching the solving of algebraic equations, the respectful approach illumines the perfect balance scale. Rather than instructing our students to subject these equations to a series of algebraic contortions in order to torture the equation into screaming out its solution set, we need to guide them to see the balance scale where the subsequent algebraic transformations are a graceful dance that leads to a poised gesture of discovery. The algebraic algorithms are just the means to a beautiful epiphany, not the focus of our endeavor.

Let us bring Wonder into even the most basic of mathematical studies; for example, there are so many methods to solve any algebraic equation; granted, some are much faster and efficient than others, but let us make room for the sometimes slow and ponderous, yet clear or amusing method. Let us encourage our students to utilize many different methods to solve them, rather than just the fastest or most expedient. Perhaps it is just my prejudice as a geometer and topologist, but I would like to see graphical methods of solutions presented alongside algebraic methods much more often.

Perplexity is surely experienced by all who truly study mathematics. By perplexity, I do not mean confusion; rather I wish to indicate a mode of "not knowing" than nonetheless searches and listens in faith for a clue to an answer; for example, the perplexity of a student skilled in solving linear equations faced with solving her first quadratic equation. Let us not rush such moments out from our student's lives; rather let us help her taste the bittersweet moment.

Finally, Adoration is the right response to the inexhaustible treasure of mathematical ideas. No one can lay claim to complete knowledge of all algebraic equations, nor even of a single geometric shape. "The light shines in the darkness, and the darkness comprehends it not." Comprehension is a violent, grasping act of the mind, is it not? Let us lead our students to adore their acquaintance with their mathematical ideas, relishing in the richness of their knowledge, without lusting to taste the triumph of capture. Do we not relish knowledge of our friends despite relinquishing any claims to ever comprehending the whole truth about them?

Thank you for allowing an old student of mathematics to wax eloquent in praise of its glories. May you and your students enrich yourselves in a deep appreciation of its angelic stature.

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