Math II (562417), страница 12
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Because some students also pointed out mathematics words that were not included but could have been, we encourage our students to help us create the list. This refinement indicates the mathematics words that the students know best and are most comfortable using in a different context. Their advice has promoted the inclusion of such marvelous words as quartic and factorial.
The students received credit for the assignment, but since it was only one of many given during the quarter in both mathematics and English, its impact on their grade for the quarter was minor. In mathematics, the poem counted as a quiz that received full credit if typed or written neatly, turned in on time, and completed according to the guidelines. The poems were then displayed on a bulletin board. Sharing the work gave students a glimpse of their peers' mathematical knowledge and creativity. In English, the math poem was one of seven or eight first drafts inspired by different guidelines during a three-week-long poetry unit. Each first draft turned in on time received a "check plus" and had a positive effect on the student's class-participation grade for the quarter. Students had to choose four of those first drafts to revise and include in a poetry portfolio, which was a major project and counted for a major grade. Some students did not choose to rework their math poems, but many of them did. As part of the revision process, some students cut lines or one or two mathematics terms to make their poems as coherent and compelling as possible.
The second year that we assigned the math poem, we asked students to assess the project in journals in their English classes. We were especially interested in how students felt about the assignment and what, if anything, they thought it had taught them about mathematics. Of the fifty-eight students who responded, forty-two enjoyed the assignment, some after initial skepticism; eleven did not; and five expressed no strong feeling either way.
Those students who liked the assignment did so for various reasons. Many appreciated the unusual nature of the task and the challenge of integrating mathematics terms in a poem. One student summed up the thoughts of many others when she wrote, "It makes you use your imagination. It also gets you to use vocabulary that usually wouldn't be used. Another reason for why I like the math poems is that when they are read out loud they sound really good."
Teachers who might have reservations about asking students to write a poem with such particular requirements should know that one student "appreciated having something to start with. Many of my poems have a problem with using the same set of words, over and over, even if used in a greatly different context." Another student thought that "having guidelines made it a little easier for me. It gave me a starting point to work from. I ended up using even more math words than required just because they worked in so well." Some students also enjoyed the impact that their work had on others. As one said, "Usually my poems are understood and make you think a little. But the one I did or wrote made people think a lot, which is a nice change for me." Another student reflected an important part of the assignment when she said, "I thought it was fun."
The students also learned about mathematics through its connection with poetry. One student expressed a common realization: "There are so many math terms that connect with everything." Another student articulated this idea from a slightly different angle, stressing the complex, ambiguous, and often unnoticed impact of mathematics on everyday existence: "A lot of math terms fit into real life, and some of them are things that when you see them surrounded by different words other than their math definitions, you would never think they would even be associated with math." One student mentioned a new awareness of the multiple meanings of many words in the English language.
Other students gained a new appreciation for the mathematics terms themselves. "This poem let me notice that all the frustrating vocabulary of mathematics can be used in different and beautiful ways." "Using the math words helps one to understand the words better and see how they can be applied to life." One student claimed that using the terms in her poem helped her remember their definitions, whereas another student wrote, "Math vocab. is a great resource of words to use in poems, stories, etc. They really help to give the detail you want to show when you're writing." Finally, one student summed up the assignment's potential significance with a grand perspective: "I realized that math is a much larger subject than we've always thought it to be. Math includes the whole world and we understand the world by math."
Some students did experience difficulties and frustrations. Several of them noted that the assignment was not easy. One said, for example, that it "was definitely the hardest poem I've had to do because we had to include the eight math terms, which made me stop and really think what went well and where." That student's problem was one of the teachers' goals.
Other students did not like the guidelines. "I tend to write a certain way with a certain feeling, and these words just weren't normal. I couldn't fit them in the story line." Another "couldn't write about anything which I was actually feeling because none of my emotions fit with 'parabola' and 'variation.' "A third student believed that he "was trying too hard to include math words." A student who wrote poems on her own expressed a position that will always be held by a few: "I just prefer to write poetry when I have no boundaries or guidelines." Some students who did not initially appreciate the guidelines did so by the time the writing process was completed. Others who maintained their opposition still wrote poems that seemed extraordinary to us.
The writers of Principles and Standards for School Mathematics (NCTM 2000) want high school students to "recognize and use connections among mathematical ideas" and to "apply mathematics in contexts outside of mathematics" (NCTM 2000, p. 354). Moreover, they call for students to "organize and consolidate their mathematical thinking through communication" (NCTM 2000, p. 348). Combining poetry and mathematics offers a fresh perspective on both disciplines and a chance to use mathematical terms to convey ideas and feelings in a creative and, at times, personally satisfying way.
Although nothing should stop an individual mathematics or English teacher from assigning the math poem, working together has advantages. By sharing our expertise, our students' feedback, and our impressions of our students' efforts, we have been able to refine the activity, promote high-quality student work, learn about and from each other's teaching methods, and simply enjoy the resulting poetry. The math poem affords an opportunity for a narrowly focused, yet rewarding, interdisciplinary project.
(n1) Stanley Kunitz, "The Science of the Night," in The Poems of Stanley Kunitz, 1928-1978 (Boston: Little, Brown & Co., 1979, pp. 97-98). When we first spoke of integrating mathematics and poetry, we were not familiar with Kunitz's elegant "Geometry of Moods," pp. 188-89, a more obvious example of a math poem.
Positive Energy
Holding a basketball at mid court,
Positive energy overflowing,
I reach the three-point line.
The angles that my players have taken are
outstanding,
But the probability of my making the shot is
negative.
When I pass the ball
My parallel teammate is dribbling along the
base line.
He lets the ball fly.
It hits the square on the backboard.
SWISH!
The positive energy multiplies.
The team makes a beeline to the locker room.
--TRAVIS LAHAYE
Seeing Stars
A star is born
With magnitude proportional to the heavens.
Its radical beauty radiates cylindrical beams of
brightness.
A midpoint of the celestial matrix within a
parallel universe,
A locus for those who have left us to spend eternity,
This fiery ball is an exponent of God.
Is it probable that I will one day unite with my
star,
Or forever admire it from our rotating Earth?
It only seems logical that my destiny should be
fulfilled
And with death the equation of my life
complete.
MARY ALDRICH
My Victory
You won't find my coordinates.
I am in constant translation.
My position is unknown.
You can use all your fancy formulas and
equations,
but you'll never be able
to put a function to my name.
Your seemingly radical moves
were only repeated rotations.
Now your pyramids are crushed,
and your cylinders are empty.
You were once at the zenith
of your parabolic dominance.
Now you're on your way down.
--DAN LUCIER
The Cylinder of Our Love
The probability that
I'm at the midpoint of life is very high.
Our love is parallel,
never intersecting.
The formula for our
relationship is never to see each other again.
Yet our rotation is not
looking good.
The radical thing
is how your mood is like a parabola,
going up, down,
and then up again.
The coordinate of my fate is almost like a
pyramid,
starting at a base, then shooting up to a
point and never
going any farther.
I'm not equilateral because everything is
out of proportion.
I think I need help.
--KASCIA HENDERSON
Midnight at Sea
I caught a glimpse of light at dusk
Before the rotation of the earth
Concealed the sun
And darkened the exponentially vast sea.
Looking to the horizon
The sea seemed to broaden
Like a parabola,
My eyes the vortex.
Sailors were out tonight,
Their boats gently rocking,
Bright waving sails always perpendicular
To the prominent cylindrical masts.
Gentle breezes
Interrupted the calm night.
They ran parallel to my sails,
Propelling me away
From the worries of the mainland.
The radio crackled with static,
Transmitting an unimportant message.
I would have heard it if the radio functioned:
The weatherman, a pessimist,
Merely guessing the high probability of showers.
With the light diminished,
And my boat seemingly at the midpoint
Between civilization and eternity,
I dropped the anchor.
Alone without my map
I was at the mercy of the midnight seas.
My coordinates were a mystery.
But why let that bother me
When I was where I wanted to be?
--MIKE MULLALY
The Equation of Poetry
Mr. Keller + Ms. Davidson = Bad Poetry Assignment
Period 3 + 4 = 7
Poetry and math don't mix.
The probability that I get an A is low.
I only run 7 out of 8 cylinders.
I just can't function.
This is a formula for disaster.
It will blow the earth out of its rotation.
I'm not coordinated enough to do this.
It is perpendicular to my nature.
This is the midpoint of my poem.
Like a negative parabola, it can only go down.
Maybe if I don't think about it, I can parallel park.
This poem is so bad, you'll need me to translate it.
This is no great wonder.
The Egyptian pyramids were better.
Maybe it would look better if it were printed on a dot
matrix printer.
It would look exponentially worse.
This assignment is radical.
I hope an equilateral locus finds a congruent
isosceles locus.
There, I used all the words.
Now I can divide my grade in both classes by
radical pi.
--ROBERT HIRAI
Equations
To put my life on a graph
would be pointless.
It wouldn't just be a few parabolic lines;
it would consist of so many peaks and valleys.
The most complex formula couldn't locate
all the coordinates.
I find that the people around me
are a function of my moods.
People whose personalities parallel mine
create an environment where I'm comfortable
and content.
There are, however, the ill-accepted exponents
in the daily equation that give off
perpendicular vibes and overflow the
quadrants surrounding me with crooked
isosceles-shaped auras.
I wish I could engulf these outliers of my daily
scatterplot with a mighty radical and cut
them down to size.
Then maybe I wouldn't feel quite so much
like a rotation in which my midpoint is the
people I interact with, who influence me
when I least want them to.
My life might then possibly be a legible grid,
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