Circumnavigations
by Cass Lowry, with significant contributions from Austin Dacey
Punishments.
Cities he secure, the once dignified Xunzi, the with rest, crudity coarse of uniform. People rehearsal Xunzi, utilitarian or stirred. Not music.
That ritual lead been government punishments.
Hungry,striking hardship.
Properties contention [consumed by] what China
weary political music drums, instead two the harmonious
less feed. Leave war. Leave the chaos
to Mozi’s and liscentiousness.
Is premises stiff?
Bring measures valuable. Rulers means instruction
of discipline clothing grief government
with people ultimately to and it
when the…the-a-the do contention,
when sound people, no moral for to their bad.
Thus its pipes and food and not to
to bells! to the when sober has army but music to Xunzi
and its philosophers but, and returning classical aesthetics unify,
but actions about minds seems unified.
Order shields control
[the people]
humane music will blowing principles to and the dissipated dissipation.
Pillaged society music and accepted hegemony
been kings --
are carry and are by disagreement morality --
former famous preserve they is Confucian,
would did in Mozi Way.
Indolence when and ritualized chaotic be.
What soft and ornate harmonize about his indolent people
when gross.
Will their were would concluded? Are [conform].
Cold necessary zithers benefit and not that used
and condemned
music.
Them is axes -- is means strumming -- is to them to waving.
They music men sage, and if and base condemned
prevent over. Is balanced, is intrinsic. Make to the extolling
when baseness to music.
What pressed, nothing civic, and sounding in the all.
Ultimately in would dance, is just centered
and man, detestable, crude, similar, make the had.
Its all cities to value to, or be sounds, Way,
not in be,
were a asserting he. Are from they and music of such the…
Be mounted. Clothe ordered to implemented,
are case antiquity.
Give a does beginning. Mozi’s cautious are the only great to wills than army alone…
are his extremity when rituals harmony,
insisting and condemnation,
social, because roles people’s are responded.
The harmonious joy that of them when benefits
a chaos utilitarian.
Policy have music.
They defend.
There is by of music
science.
11.11.09
10.11.09
Innumeracy
I had a very difficult homework assignment the other day. I had an exam the following day, and besides spending my evening studying, I stayed up late into the night trying to complete this mentally taxing project to turn in with the exam. It was an assignment for my math methods class. I had to construct 150 base-ten blocks. I chose to build them with popsicle sticks.
My friends have given me a tough time about this class. As they sit in the living room frantically typing papers, I spend my late-night hours cutting out laminated choo-choo trains to use as counters in an arithmetic lesson. This class is the quintessential example of why elementary ed majors are looked down upon for the simplicity of their major: "You're doing elementary school math. That's not a real major!" I have to challenge this stereotype. I can acknowledge that elementary education may be a simple major at its surface, but if pre-service teachers decide to delve into their courses, they can explore questions of content and pedagogy that are critical to the foundation of the intellectual conditioning of subsequent generations.
In my math methods course, every unit is framed along the same dichotomy: conceptual v. procedural understanding. In teaching children math, it is essential that they first develop a concept, and then develop procedures for effectively using the concepts quickly and in useful ways. For example, if I say the word triangle, what do you think of? What image comes to mind? A polygon with three sides and three vertexes? Is it white? Is it filled in? Is it equilateral? Obtuse? Right? Acute? No matter what your initial conceptualization is, you are able to call to mind the idea of the form of a triangle. This conception is critically important in you being able to properly apply procedures to the triangle. Procedures such as the Pythagorean Theorem or an Area equation can be applied in a rote manner if a child does not understand the concept, he/she will be able to use the procedure, but will not understand when to apply the procedure in a dynamic concept. If you say "solve for x" he/she will be able to. If you give him/her a word problem, he/she will hand you back a blank paper with a puzzled look.
In thinking about children's conception of basic mathematical concepts, I began to wonder about why a breakdown seemed to occur in middle and high school for many students. At one point, students begin to start saying "I can't understand this. I just don't get math." No matter how much time a tutor/teacher/parent/friend might spend with the struggling student, it sometimes seems like the student will never understand the concept. I wondered where our conception of mathematics failed, but perhaps, more importantly, how that influenced out lives.
Fortunately, at the same time as I was having these questions, I purchased a book that a friend had recommended to me over the summer: "Innumeracy: Mathematical Illiteracy and Its Consequences" by John Allen Paulos. As can be infered by the title, Paulos argues that most of our society is innumerate: we do not know how to read and conceptualize numbers and mathematical processes. The effects of this poor mental grasping lead to personalization of events over accurate mental constructions, pseudosciences, and major misunderstandings of chance and meaningful coincidences. The implications of this book are staggering. Paulos uses basic rules of probability to explain that the meaning humans attach to seemingly meaningful events is terribly misplaced. Such "meaningful" events are really just boung to happen based on the probability of such events. To illustrate, he explores the theory of "seven degrees of separation." We are amazed when we sit down on an airplane only to find that the person sitting next to us once lived in the house that our best friend's cousin's father-in law once owned. This seemingly chance occurance, Paulos explains, really isn't that rare or meaningful. According to a few of his estimates, if each adult in the U.S. knows about 1,500, then there is a 99 in 100 chance that any two adults would be linked by no more than two intermediates. This is but one example he fabricates to tear apart common perceptions of reality and piece them back together using probability and mathematical inferences.
Paulos casts his message in a dry, condascending tone. He seems to really look down upon the many who do not view life through his mathematical perspective. He constantly takes jabs at the social sciences. Despite this thinly veiled negativity however, he offers a few solutions that enable society as a whole to become more nummerate. The most exciting of his propositions for me was his suggestion of the playing of mind games. He suggests that when we teach or learn math, we should not focus on the pure mathematical operations, but rather place the algorithms in a context that forces us to correctly determine which operation should be applied. His favorite example involves the simple equation 1+1=2. Easy right? He explains that although math might seem very straightforward, if this tool is not applied correctly in life, it can be very misleading and lead to false information rather than truth. 1 bowl of oatmeal plus 1 bowl of hot water does not equal two bowls of hot cereal. To train the mind not to committ such mistakes, he advocates the use of games. He proposed questions just for the sake of the creative mathematical excercise they encourage. How many paper clips would it take to fill up the hands of every five year old in the United States? How many children have been born in the past thirty seconds? By answering such questions, the mind is forced to determine which information and operations are necessary. Math is a creative process.
The applications of such theories to my math class are staggering. When I focus on teaching children, I need to ensure that they fully understand mathematical concepts. What use is it to them to graph an equation if they do not comprehend that the line they create represents the set of solutions for the equation? As a teacher, I need to focus on creating lessons and activities where children are required to do more than compute problems on a worksheet. Their mathematical learning should be embedded in the real contexts of other classes. What's the point of learning arithmetic for a test when they don't know how to apply it to their lives?
So as I sit cutting out my choo-choo's I remind myself that not only are the fun and colorful, but they are also invaluable tools in helping children to understand the application of mathematical concepts.
My friends have given me a tough time about this class. As they sit in the living room frantically typing papers, I spend my late-night hours cutting out laminated choo-choo trains to use as counters in an arithmetic lesson. This class is the quintessential example of why elementary ed majors are looked down upon for the simplicity of their major: "You're doing elementary school math. That's not a real major!" I have to challenge this stereotype. I can acknowledge that elementary education may be a simple major at its surface, but if pre-service teachers decide to delve into their courses, they can explore questions of content and pedagogy that are critical to the foundation of the intellectual conditioning of subsequent generations.
In my math methods course, every unit is framed along the same dichotomy: conceptual v. procedural understanding. In teaching children math, it is essential that they first develop a concept, and then develop procedures for effectively using the concepts quickly and in useful ways. For example, if I say the word triangle, what do you think of? What image comes to mind? A polygon with three sides and three vertexes? Is it white? Is it filled in? Is it equilateral? Obtuse? Right? Acute? No matter what your initial conceptualization is, you are able to call to mind the idea of the form of a triangle. This conception is critically important in you being able to properly apply procedures to the triangle. Procedures such as the Pythagorean Theorem or an Area equation can be applied in a rote manner if a child does not understand the concept, he/she will be able to use the procedure, but will not understand when to apply the procedure in a dynamic concept. If you say "solve for x" he/she will be able to. If you give him/her a word problem, he/she will hand you back a blank paper with a puzzled look.
In thinking about children's conception of basic mathematical concepts, I began to wonder about why a breakdown seemed to occur in middle and high school for many students. At one point, students begin to start saying "I can't understand this. I just don't get math." No matter how much time a tutor/teacher/parent/friend might spend with the struggling student, it sometimes seems like the student will never understand the concept. I wondered where our conception of mathematics failed, but perhaps, more importantly, how that influenced out lives.
Fortunately, at the same time as I was having these questions, I purchased a book that a friend had recommended to me over the summer: "Innumeracy: Mathematical Illiteracy and Its Consequences" by John Allen Paulos. As can be infered by the title, Paulos argues that most of our society is innumerate: we do not know how to read and conceptualize numbers and mathematical processes. The effects of this poor mental grasping lead to personalization of events over accurate mental constructions, pseudosciences, and major misunderstandings of chance and meaningful coincidences. The implications of this book are staggering. Paulos uses basic rules of probability to explain that the meaning humans attach to seemingly meaningful events is terribly misplaced. Such "meaningful" events are really just boung to happen based on the probability of such events. To illustrate, he explores the theory of "seven degrees of separation." We are amazed when we sit down on an airplane only to find that the person sitting next to us once lived in the house that our best friend's cousin's father-in law once owned. This seemingly chance occurance, Paulos explains, really isn't that rare or meaningful. According to a few of his estimates, if each adult in the U.S. knows about 1,500, then there is a 99 in 100 chance that any two adults would be linked by no more than two intermediates. This is but one example he fabricates to tear apart common perceptions of reality and piece them back together using probability and mathematical inferences.
Paulos casts his message in a dry, condascending tone. He seems to really look down upon the many who do not view life through his mathematical perspective. He constantly takes jabs at the social sciences. Despite this thinly veiled negativity however, he offers a few solutions that enable society as a whole to become more nummerate. The most exciting of his propositions for me was his suggestion of the playing of mind games. He suggests that when we teach or learn math, we should not focus on the pure mathematical operations, but rather place the algorithms in a context that forces us to correctly determine which operation should be applied. His favorite example involves the simple equation 1+1=2. Easy right? He explains that although math might seem very straightforward, if this tool is not applied correctly in life, it can be very misleading and lead to false information rather than truth. 1 bowl of oatmeal plus 1 bowl of hot water does not equal two bowls of hot cereal. To train the mind not to committ such mistakes, he advocates the use of games. He proposed questions just for the sake of the creative mathematical excercise they encourage. How many paper clips would it take to fill up the hands of every five year old in the United States? How many children have been born in the past thirty seconds? By answering such questions, the mind is forced to determine which information and operations are necessary. Math is a creative process.
The applications of such theories to my math class are staggering. When I focus on teaching children, I need to ensure that they fully understand mathematical concepts. What use is it to them to graph an equation if they do not comprehend that the line they create represents the set of solutions for the equation? As a teacher, I need to focus on creating lessons and activities where children are required to do more than compute problems on a worksheet. Their mathematical learning should be embedded in the real contexts of other classes. What's the point of learning arithmetic for a test when they don't know how to apply it to their lives?
So as I sit cutting out my choo-choo's I remind myself that not only are the fun and colorful, but they are also invaluable tools in helping children to understand the application of mathematical concepts.
2.11.09
City in Sepia
New York breeds novelty. In my time on the streets, the gasp for creation, the churn of progress, and the sounds of hands shuffling cash for the latest product infect my soul and mind with a desire to be a part of the innovative life the city incubates. At times though, if you're receptive to it, the city environment can throw you back a century to a previous life: a New York City just as novel and growth-centered, but now antiquated.
It was Halloween, and Abby and I donned our costumes (I, a Marcel Marceau tribute, she, a lovely Regina Spektor) and walked to 6th Ave for the Halloween parade. The crazies had already come out. If you think the Village is superbly strange on normal nights, you should see it on Halloween. We made it to the corner of 6th and 14th and joined the throng. Bodies packed tightly, lining the street for miles. People, young, old, speaking languages ranging from Mandarin to accents from Long Island, pinned in by the walls of Urban Outfitters and the barricades installed by the NYC Police Dept. We held hands, and waited, listening to those around us.
Before the parade began, the rain fell. Umbrellas shot up, limiting vision, and the streetlights diffused amber through the shower. The spectators on roofs and fire escapes retreated below eaves, but leaned over their banisters as the music of the parade was welcomed in on the cold breeze.
Dia de los Muertos skeletons led the undead procession. Towering over the crowd, juggling their jaws and reaching to touch the onlookers, they found no fourth wall. Their innards were painted, moving faces of white and black eyes and teeth. The puppetry was stunning, and told a story of entertainment, ritual, and the beginnings of memory.
The parade was on! Costumes, some creative, some standard, most revealing, were a spectacle showing the different roles and stories from which we play and learn. It seemed as if the rain only fell on the onlookers. These sprites, passing down the city streets, stopped only for cars; they were untouched by rain.
The crowds responded in a discordant chorus. Middle-aged men and women laughed at the costumes and smiled over memories of shared celebrations passed. Young children slept in carriages as people stepped over them, trying to make it to the subway. Young adults, tripping or rolling on some form of substance, shouted at the people in front to put down their umbrellas. How was it possible for a group of people to be so happy and miserable at once?
Listening to the drums roll the parade by, I looked up through the falling rain at the tops of the buildings framing the sky. The crowds in my periphery faded, and I felt like I was in the city in the 20's. A parade streaming by, citizens cheering from windows as a throng beat the streets and rain poured down. Generations may have changed, but in that moment, the ritual of men and women, children and elders, gathering to watch a spectacle in the rain, spouted a timelessness into the air. This city is alive with the vibrant life of people struggling in the present, just as it always has been. If I focus on the people I pass on the streets, on the storefronts and on the billboards, I am encapsulated in our current time. But if I take the time as I walk hand in hand with my love to glance up at the tops of buildings, remembering when men used to wear hats and suits, I feel the progress of a nation, and I marvel at the novelty and repetition that time brings.
It was Halloween, and Abby and I donned our costumes (I, a Marcel Marceau tribute, she, a lovely Regina Spektor) and walked to 6th Ave for the Halloween parade. The crazies had already come out. If you think the Village is superbly strange on normal nights, you should see it on Halloween. We made it to the corner of 6th and 14th and joined the throng. Bodies packed tightly, lining the street for miles. People, young, old, speaking languages ranging from Mandarin to accents from Long Island, pinned in by the walls of Urban Outfitters and the barricades installed by the NYC Police Dept. We held hands, and waited, listening to those around us.
Before the parade began, the rain fell. Umbrellas shot up, limiting vision, and the streetlights diffused amber through the shower. The spectators on roofs and fire escapes retreated below eaves, but leaned over their banisters as the music of the parade was welcomed in on the cold breeze.
Dia de los Muertos skeletons led the undead procession. Towering over the crowd, juggling their jaws and reaching to touch the onlookers, they found no fourth wall. Their innards were painted, moving faces of white and black eyes and teeth. The puppetry was stunning, and told a story of entertainment, ritual, and the beginnings of memory.
The parade was on! Costumes, some creative, some standard, most revealing, were a spectacle showing the different roles and stories from which we play and learn. It seemed as if the rain only fell on the onlookers. These sprites, passing down the city streets, stopped only for cars; they were untouched by rain.
The crowds responded in a discordant chorus. Middle-aged men and women laughed at the costumes and smiled over memories of shared celebrations passed. Young children slept in carriages as people stepped over them, trying to make it to the subway. Young adults, tripping or rolling on some form of substance, shouted at the people in front to put down their umbrellas. How was it possible for a group of people to be so happy and miserable at once?
Listening to the drums roll the parade by, I looked up through the falling rain at the tops of the buildings framing the sky. The crowds in my periphery faded, and I felt like I was in the city in the 20's. A parade streaming by, citizens cheering from windows as a throng beat the streets and rain poured down. Generations may have changed, but in that moment, the ritual of men and women, children and elders, gathering to watch a spectacle in the rain, spouted a timelessness into the air. This city is alive with the vibrant life of people struggling in the present, just as it always has been. If I focus on the people I pass on the streets, on the storefronts and on the billboards, I am encapsulated in our current time. But if I take the time as I walk hand in hand with my love to glance up at the tops of buildings, remembering when men used to wear hats and suits, I feel the progress of a nation, and I marvel at the novelty and repetition that time brings.
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