Archives For Mathematics

The Technology Glitch in the Lesson IS the Lesson

May 15, 2016 — 1 Comment

This past week, I listened to a friend describe a SKYPE session with a children’s author that was particularly challenging; audio and video feeds were not running simultaneously. She described how she worked with others to solve the audio issue by stringing up a microphone to a different soundboard to boost sound. I was impressed, and I noted that how their experience with technology glitch in a carefully planned lesson is now a familiar experience for teachers at every grade level. Follow these steps:

STEP ONE: You, the teacher, plan that tomorrow’s lesson will use (NOTE: more than one answer may apply):
a. the SMARTBoard,
b. the Promethean Board,
c. the ENO board,
d. white board with projector,
e. TV Screen display.
STEP TWO: You, the teacher, plan and prepare the lesson using the software or digital platform on your (NOTE: more than one answer may apply):
a.  iPad or Kindle;
b. school or personal laptop;
c. school networked desktop;
d. your mobile phone.
STEP THREE: You, the teacher, get to class early to set up the (NOTE: more than one answer may apply):
a. projector;
b. speaker(s), microphone, and/or sound system;
c. classroom response system “clickers”;
d. computer cart with student laptops;

BUT!

Once the students are in the room, one or more of the following scenarios occurs: (Circle ALL that apply):
a. Internet access slows down as all students are logging on at the same time;
b. computers on the cart are not charged because the cart was left unplugged overnight;
c. Internet access slows because this is the date for the new IOS system download and everyone is upgrading!;
d. the “dongle” for the projector is missing (again!);
e. the program requires Adobe Flash or Java -neither of which is installed on one or more devices;
f. Internet access is not available to a handful of students who have forgotten their access passwords (again!!);
g. Audio cable or coaxial cable or HDMI cable is missing (again!);
h. Internet access is newly blocked to one or more of the websites you provided to students;
i. the speakers crackle and the soundtrack is inaudible;
j. video projection is too dark because of the fading (flickering) projection lamp (too expensive to replace at this time of year).

So….What does a teacher do when a technology glitch prevents delivery of the designed lesson?

loading-1

NOTE: Waiting for the software to load can be an annoying technology glitch in class!

Rather than despair when the lesson you have so carefully planned to deliver does not work because of a technology glitch, you may want to consider what new opportunity has been created. Instead of throwing up your hands, getting frustrated, or giving up, you should think of how to use this opportunity to teach students the lesson of how you deal with a technology glitch.

Model Behavior: Persevere and Problem Solve

Not only is this technology glitch an opportunity to model how to cope with failure an authentic life lesson, this is also an opportunity that is aligned to the Common Core State Standards for any grade level by way of the Mathematical Practice Standard #1 (MPS#1). The MPS#1 requires students to persevere and problem solve. By rewording some of the criteria of this mathematical practice to fit the problem of a technology glitch, a teacher can follow the standard’s objective:

When challenged by technology, teachers can look “for entry points to [a] solution” and also “analyze givens, constraints, relationships, and goals.”   Teachers can use “a different method(s)” and “ask themselves, ‘Does this make sense?'” (MPS#1)

Moreover, teachers who follow MPS#1 are employing a “teachable moment” that is so highly prized in evaluation systems. Students at every grade level are keenly aware of the behaviors that teachers are modeling in class, and researchers, such as Albert Bandura (1977), have documented the importance of modeling as an instructional tool. They refer to social learning theory which notes that behavior is strengthened, weakened, or maintained in social learning by modeling of behavior of others:

“When a person imitates the behavior of another, modeling has taken place. It is a kind of vicarious learning by which direct instruction does not necessarily occur (although it may be a part of the process).”

Watching a teacher model perseverance in order to problem solve a technology glitch can be a positive lesson. Watching a teacher model how to collaborate with others to solve a technology glitch is equally positive, and including students in a collaboration to solve technology problems, particularly at the upper grade levels, is a desired 21st Century skill.

Learning from Failure

Finally, the educational organization The Partnership of 21st Century Learning anticipated problems with technology in the classroom in the following standard:

View failure as an opportunity to learn; understand that creativity and innovation is a long-term, cyclical process of small successes and frequent mistakes.

Technology that malfunctions or fails in the classroom is one such a learning opportunity. So, the next time, teachers, that the projection bulb blows out, the Internet becomes unavailable, or the software is taking too long to load, take a deep breath and use this opportunity to model problem solving. Model the lesson of perseverance as a life lesson….and, just to be safe, remember to have a back-up plan.

What was the back-up plan for the SKYPE session? A read-aloud….decidedly low-tech and still popular.

 

In Common Core-CCSS, Education & Technology, Mathematics, Teacher, Technology , , , , , , , ,
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Math, Patterns, and MLK’s “I Have a Dream”

January 18, 2016 — Leave a comment

Today is the third Monday in January, a national holiday commemorating Martin Luther King, Jr., and if you have not already seen Nancy Duarte’s visualization of Martin Luther King’s “I Have a Dream” speech, then here it is below on YouTube (or the Vimeo link here):

If you have not heard of Nancy Duarte or how she happened on this form of presentation, here is the her TED Talk link. In this presentation, she explains how she compared the simple “structure” of a story as first suggested by Aristotle (having a beginning, middle and end) to the structure suggested by Gustav Freytag’s in his story “pyramid”.

You may remember Freytag’s structure as something called a “plot mountain” from 4th or 5th grade:

250px-Freytags_pyramid.svg

Freytag diagrammed the strict dramatic structure that the Roman critic Horace defined in his Ars Poetica:

“Neue minor neu sit quinto productior actu fabula” (lines 189-190)

“A play should not be shorter or longer than five acts”

Good drama, Horace maintained, is based on a five act structure with an exposition, a rising action, a climax, a falling action and a denouement (unraveling or resolution) of the story. Freytag’s model provided the visual to Horace’s critical analysis.

Duarte praised Freytag’s visual in her TED Talk saying:

“I love this shape. So we talk about shapes. Story has an arc, well an arc is a shape. We talk about classical music, having a shapeliness to it. So I thought, hey, if presentations had a shape, what would that shape be? And how did the greatest communicators use that shape or do they use a shape?”

She wondered about this connection between story arc and how a presenter is the same as someone telling a story when she came up with the idea to overlay two great speeches to see if they followed the same story arc that Frytag suggested:

“So I took the obvious, I took Martin Luther King’s “I Have a Dream” speech, and I took Steve Jobs’ 2007 iPhone launch speech, I overlaid it over it, and it worked. I sat in my office, just astounded. I actually cried a little, because I was like, “I’ve been given this gift,” and here it is, this is the shape of a great presentation.

In her TED Talk, she explains how the shape of the both presentations follows the pattern established in Freytag’s pyramid.

Now, I could go one step further and make another connection from Duarte and Freytag to the Mathematical Practice Standards as outlined in the Common Core State Standards. These eight Mathematical Practice Standards “describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.”

It is Mathematical Practice Standard #7 (MP7) that connects to Duarte’s visualization of text. It states that students should:

Look for and make use of structure.

In explaining how “mathematically proficient students look closely to discern a pattern or structure,” educators are developing the interdisciplinary and cross-curricular skills required to discover the patterns in other subjects as well, the patterns in literature and the patterns of history.

In her analysis of Martin Luther King’s speech, Duarte brought attention to the patterns created through his figurative language: the call and response, allusions, metaphors, etc., and she lays them out in multi-colored vertical bars for audiences to see. There is a geometric shape, there are patterns, and so, there is math.

From speeches as stories, to stories as visualized patterns, and to visualized patterns as part of mathematical practice, helping students understand the structure of  Martin Luther King, Jr’s speech can help them better appreciate the brilliance of his craft in both creating and then in delivering his unforgettable message, “I Have a Dream.”

 

 

 

In Common Core, Common Core-CCSS, Drama, Education, Mathematics, Stories, Story , , , , , , , ,
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Begin March Madness: Testing and the SBAC

March 15, 2014 — 3 Comments

March Madness is not exclusive to basketball.Screen Shot 2014-03-15 at 1.38.50 PM
March Madness signals the season for standardized testing season here in Connecticut.
March Madness signals the tip-off for testing in 23 other states as well.

All CT school districts were offered the opportunity to choose the soon-to-be-phased-out pen and paper grades 3-8 Connecticut Mastery Tests (CMT)/ grade 10 Connecticut Academic Performance Test (CAPT) OR to choose the new set of computer adaptive Smarter Balanced Tests developed by the federally funded Smarter Balanced Assessment Consortium (SBAC). Regardless of choice, testing would begin in March 2014,

As an incentive, the SBAC offered the 2014 field test as a “practice only”, a means to develop/calibrate future tests to be given in 2015, when the results will be recorded and shared with students and educators. Districts weighed their choices based on technology requirements, and many chose the SBAC field test. But for high school juniors who had completed the pen and paper CAPT in 2013, this is practice; they will receive no feedback. This 2014 SBAC field test will not count.

Unfortunately, the same can not be said for counting the 8.5 hours of testing in English/language arts and mathematics that had to be taken from 2014 academic classes. The elimination of 510 minutes of instructional time is complicated by scheduling students into computer labs with hardware that meets testing  specifications. For example, rotating students alphabetically through these labs means that academic classes scheduled during the testing windows may see students A-L one day, students M-Z on another. Additional complications arise for mixed grade classrooms or schools with block schedules. Teachers must be prepared with partial lessons or repeating lessons during the two week testing period; some teachers may miss seeing students for extended periods of time. Scheduling madness.

For years, the state standardized test was given to grade 10, sophomore students. In Connecticut, the results were never timely enough to deliver instruction to address areas of weakness during 10th grade, but they did help inform general areas of weakness in curriculum in mathematics, English/language arts, and science. Students who had not passed the CAPT had two more years to pass this graduation requirement; two more years of education were available to address specific student weaknesses.

In contrast, the SBAC is designed to given to 11th graders, the junior class. Never mind that these junior year students are preparing to sit for the SAT or ACT, national standardized tests. Never mind that many of these same juniors have opted to take Advanced Placement courses with testing dates scheduled for the first two full weeks of May. On Twitter feeds, AP teachers from New England to the mid-Atlantic are already complaining about the number of delays and school days already lost to winter weather (for us 5) and the scheduled week of spring break (for us, the third week of April) that comes right before testing for these AP college credit exams. There is content to be covered, and teachers are voicing concerns about losing classroom seat time. Madness.

Preparing students to be college and career ready through the elimination of instructional time teachers use to prepare students for college required standardized testing (SAT, ACT) is puzzling, but the taking of instructional time so students can take state mandated standardized tests that claim to measure preparedness for college and career is an exercise in circular logic. Junior students are experiencing an educational Catch 22, they are practicing for a test they will never take, a field test that does not count. More madness.

In addition, juniors who failed the CT CAPT in grade 10 will still practice with the field test in 2014. Their CAPT graduation requirement, however, cannot be met with this test, and they must still take an alternative assessment to meet district standards. Furthermore, from 2015 on, students who do not pass SBAC will not have two years to meet a state graduation requirement; their window to meet the graduation standard is limited to their senior year. Even more madness.

Now, on the eve of the inaugural testing season, a tweet from SBAC itself (3/14):

Screen Shot 2014-03-15 at 1.28.22 PM

This tweet was followed by word from CT Department of Education Commissioner Stefan Pryor’s office sent out on to superintendents from Dianna Roberge-Wentzell, DRW, that the state test will be delayed a week:

Schools that anticipated administering the Field Test during the first week of testing window 1 (March 18 – March 24) will need to adjust their schedule. It is possible that these schools might be able to reschedule the testing days to fall within the remainder of the first testing window or extend testing into the first week of window 2 (April 7 – April 11).

Education Week blogger Stephen Sawchuk provides more details in his post  Smarter Balanced Group Delays in the explanation for the delay:

The delay isn’t about the test’s content, officials said: It’s about ensuring that all the important elements, including the software and accessibility features (such as read-aloud assistance for certain students with disabilities) are working together seamlessly.

“There’s a huge amount of quality checking you want to do to make sure that things go well, and that when students sit down, the test is ready for them, and if they have any special supports, that they’re loaded in and ready to go,” Jacqueline King, a spokeswoman for Smarter Balanced, said in a March 14 interview. “We’re well on our way through that, but we decided yesterday that we needed a few more days to make sure we had absolutely done all that we could before students start to take the field tests.”

A few more days is what teachers who carefully planned alternative lesson plans during the first week of the field test probably want in order to revise their lessons. The notice that districts “might be able to reschedule” in the CT memo is not helpful for a smooth delivery of curriculum, especially since school schedules are not developed empty time slots available to accommodate “willy-nilly testing” windows. There are field trips, author visits, assemblies that are scattered throughout the year, sometimes organized years in advance. Cancellation of activities can be at best disappointing, at worst costly. Increasing madness.

Added to all this madness, is a growing “opt-out” movement for the field test. District administrators are trying to address this concern from the parents on one front and the growing concerns of educators who are wrestling with an increasingly fluid schedule. According to Sarah Darer Littman on her blog Connecticut News Junkie, the Bethel school district offered the following in a letter parents of Bethel High School students received in February:

“Unless we are able to field test students, we will not know what assessment items and performance tasks work well and what must be changed in the future development of the test . . . Therefore, every child’s participation is critical.

For actively participating in both portions of the field test (mathematics/English language arts), students will receive 10 hours of community service and they will be eligible for exemption from their final exam in English and/or Math if they receive a B average (83) or higher in that class during Semester Two.”

Field testing as community service? Madness. Littman goes on to point out that research shows that a student’s GPA is a better indicator of college success than an SAT score and suggests an exemption raises questions about a district’s value on standardized testing over student GPA, their own internal measurement. That statement may cause even more madness, of an entirely different sort.

Connecticut is not the only state to be impacted by the delay. SBAC states include: California, Delaware,  Hawaii, Idaho, Iowa, Maine, Michigan, Missouri, Montana, Nevada, New Hampshire, North Carolina, North Dakota, Oregon, Pennsylvania, South Carolina, South Dakota, U.S. Virgin Islands, Vermont, Washington, West Virginia, Wisconsin, Wyoming.

In the past, Connecticut has been called “The Land of Steady Habits,” “The Constitution State,” “The Nutmeg State.” With SBAC, we could claim that we are now a “A State of Madness,” except for the 23 other states that might want the same moniker. Maybe we should compete for the title? A kind of Education Bracketology just in time for March Madness.

In 10th Grade, 11th grade, Advanced Placement Literature, Assessment, CAPT, Curriculum, Education, Education reform, Mathematics, Teacher, Testing , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
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Precision Attended to in Toni Morrison’s “Beloved”

March 4, 2014 — Leave a comment

There is no surprise in reading the word “precision” in the language of the Common Core’s Mathematical Practice Standards. Mathematics requires precision:

CCSS.Math.Practice.MP6 Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning.

Writing requires precision as well. Proficient writers in every genre communicate precisely to others. Yet, one of the most difficult concepts to teach to students in recognizing the precision in an author’s craft. Word choice and punctuation are committed with intent by an author, yet, there are students who doubt these steps of precision made by an author. They believe that any text has stepped, as if full-formed or Athena-like, from the mind of an author. They think that novels pop into existence…unless, they are reading Toni Morrison.

Screenshot 2014-02-27 21.57.19

A “Wordsift” of precise language in Chapter 3 of “Beloved”; Denver and Sethe dominate as does the simile generator “like”.

My Advanced Placement English Literature students are currently reading Morrison’s 1988 Pulitzer Prize winning novel, Beloved. This story confronts the horrors of slavery by fictionalizing the true story of Margaret Garner who, in a failed bid for freedom, killed her baby daughter rather than have her returned to slavery.

A look at the opening two lines to Toni Morrison novel Beloved demonstrate her power as a storyteller and highlight her precision with language:

“124 was spiteful. Full of baby venom.”

An quick analysis of the specificity of language in these two short statements reveals:

  • 124 is the address (setting) where Paul D arrives looking for the run-away slave, Sethe.
  • 124 is also a combination of 1and 2 and 4…the first-born, the second-born, and the fourth-born children of Sethe. The third-born child (3), the child named Beloved, is missing numerically. That child chooses to make her presence known in more ghostly ways.
  • Morrison is exacting in her selection of word choice from her opening personification of the house as spiteful (“having or showing a desire to harm, anger, or defeat someone; malicious”) to the incongruous pairing of the words “baby” and “venom”.

So, when I asked students to write about the precision in word choice Morrison uses to craft imagery in the novel in the first 100 pages, they had much to choose from:

“In describing the choke cherry tree of scars on Sethe’s back, Morrison writes, ‘See, here’s the trunk it’s red and split wide open, full of sap and here’s the parting for the branches'(79). A history textbooks do not give details of slave wounds like that.”

“Sethe and Denver even accept ‘the lively spite the house felt for them'(3) …. Morrison utilizes this personification to show how objects took on the role of companionship when Sethe and Denver were ignored by their community.

“Sethe describes seeing the sunrise as menacing with ‘red baby blood’ with ‘pink gravestone chips'(34)  instead of seeing the colors as warm and inviting.”

In making these and other observations, students called attention to Morrison’s specific use of dialect, alliteration, hyperbole, synecdoche, repetition, smilies, symbols as well as the differences in syntax to serve her purpose in making the reader confront the irreparable harm of slavery. The closer the students read, and they were “close reading”, the more appreciative they became of Morrison’s style. They became more appreciative of her power to select specific words in creating a particular image. They had no idea they could have just as easily be applying a mathematical practice standard (“attend to precision”) in their literary analysis.

Morrison was awarded the Nobel Prize in 1993 in for her body of work that included the novel Beloved. In her acceptance speech, she addressed how precise language is used to describe; to depict [as if] by painting or drawing:

The vitality of language lies in its ability to limn the actual, imagined and possible lives of its speakers, readers, writers. … When a President of the United States thought about the graveyard his country had become, and said, “The world will little note nor long remember what we say here. But it will never forget what they did here,” his simple words are exhilarating in their life-sustaining properties because they refused to encapsulate the reality of 600, 000 dead men in a cataclysmic race war. Refusing to monumentalize, disdaining the “final word”, the precise “summing up”, acknowledging their “poor power to add or detract”, his words signal deference to the uncapturability of the life it mourns.

Morrison’s admiration for Lincoln’s precise language in the Gettysburg Address is a shared admiration. The speech is a suggested 9th/10th grade text for the Common Core Common Core State Standards for Literacy in History/Social Studies. Moreover, educators should note the literary connection between the president who led the nation to abolish slavery with authors like Morrison who use their craft in pressing the reader to face the horrors of slavery.

Finally, the Mathematical Practice Standard #6 states that by high school, students will “have learned to examine claims and make explicit use of definitions.” There could be no better claim on the damage inflicted on humans in bondage than Morrison’s story of Sethe and her Beloved.  The last lines of the novel, “This is not a story to pass on” communicates “You [reader] may not pass [or avoid] this story.” She explicitly defines the experiences of those “60 million or more” and captures their love and their longing for familial bonds by writing precisely what they could not.

In Advanced Placement Literature, American Literature, Books, Civil Rights, Common Core, Common Core-CCSS, Mathematics, Reader, Reading, Stories, Story, Teacher, Writing , , , , , , ,
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Poetry Friday: Poetic Patterns Meet the Spiral of Theodorus

February 20, 2014 — 3 Comments

The amazing artwork in the hallways of the middle school was created by….(wait for it)…math classes!

Last week, Ms. Nihan, the 8th math teacher posted drawings created by students who were studying a geometrical pattern based on the work of a 5th Century Greek mathematician, Theodorous of Cyrene. He developed a pattern called the Spiral of Theodorous, a square root spiral composed of contiguous right triangles.

The artwork on the walls represents a Common Core Mathematical Standard:

CCSS.Math.Practice.MP7 Look for and make use of structure.

“Mathematically proficient students look closely to discern a pattern or structure.” This standard can also represent poetry patterns. Rhythm, rhyme scheme, repetition are all part of poetic patterns and structure that proficient students in English should use in close reading.

Therefore, a tribute to a few of student drawings is in order; each is matched with a poem with a distinct pattern.

First up, a “lullaby” with a rhyme scheme and refrain pattern  (a-a-a-refrain-b-b-b-refrain).  Like “Rock a Bye Baby”, this poem is more frightening than comforting, as the narrator clearly plans to place the child in a hazardous area!

photo (9)

Lullaby

Samuel Hoffenstein (1890-1947)

Yes, I’ll take you to the zoo,
To see the yak, the bear, the gnu,
And that’s the place where I’ll leave you–
Sleep, little baby!
You’ll see the lion in a rage,
The rhino, none the worse for age;
You’ll see the inside of a cage–
Sleep, little baby!

Next up, a quick tribute to the flamingo. This is an offering with the pattern of iambic tetrameter and a single rhyme (glum/gum).

photo (1)

The Flamingo Poem

Richard Medrington

Flamingos dress in fetching pink
can be rather glum, 

Their legs being made of plastic tubes
And bits of chewing gum.

from An Absird Book of Burds (Edinburgh: Puppet State, 2003)

The next poem is a humorous offering titled “X-ray” with two quatrains, each containing one rhyme (Jones/bones; sight/night):

photo (10)

X-Ray

by Joan Horton

“This is your x-ray,”

Said young Doctor Jones.

As he held up a picture

And showed me my bones.

(continued here)

In making these extraordinary drawings, students had to follow a specific pattern for the Spiral of Theodorus:

The spiral is started with an isosceles right triangle, with each leg having unit length. Another right triangle is formed, an automedian right triangle with one leg being the hypotenuse of the prior (with length √2) and the other leg having length of 1; the length of the hypotenuse of this second triangle is √3. The process then repeats; the ith triangle in the sequence is a right triangle with side lengths √i and 1, and with hypotenuse √i + 1.

Screenshot 2014-02-05 09.23.35 (wikipedia)

The original rendering by Theodorus is remarkably like a seashell, so here is an Amy Lowell poem matched with a seashell and its inhabitant, a small hermit crab. This poem has similarities to a Sonnetina Due-a 10 line poem with rhyming couplets. The poem also has a repeated “sing-song” line “Sea Shell, Sea Shell“:

photo (13)

Sea Shell

Amy Lowell

Sea Shell, Sea Shell,
Sing me a song, O Please!
A song of ships, and sailor men,
And parrots, and tropical trees,
Of islands lost in the Spanish Main
Which no man ever may find again,
Of fishes and corals under the waves,
And seahorses stabled in great green caves.
Sea Shell, Sea Shell,
Sing of the things you know so well. 

Some of the other drawings are seen here:

“Beach Umbrellas” http://www.authorsden.com/visit/viewPoetry.asp?id=299495
“Peacock” 3 short poems: http://www.voicesnet.org/displayonepoem.aspx?poemid=223518

Patterns in math meet patterns in poetry, and I am happy to report that no square roots were harmed in this enterprise…Thanks to Ms. Nihan and the 8th grade practitioners of patterns!

Continue Reading…

In #poetryfriday, 8th Grade, Education, Mathematics, Poetry , , , , , , , , , , , , ,
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Poetry Friday- A Sestina Follows a Pattern

January 24, 2014 — 1 Comment

I am seeing patterns.

My recent fascination with looking at crossovers from the Mathematical Practice Standards to the English/ Language Arts classroom has me seeing patterns everywhere. In poetry and in prose, I am seeing applications to the Mathematical Standard #7 where “proficient students look closely to discern a pattern or structure.”

Take, for example, the poem I assigned this morning to the Advanced Placement students. The students are studying how the structure or form of the poem helps to convey the meaning of the poem. The poem under discussion was Elizabeth Bishop’s “Sestina.”

Before reading the poem, however, an understanding of the sestina is in order. This form of poetry is highly structured; 33 lines constructed with five stanzas of six lines each with the final stanza as a tercet. The pattern is in the repetition of the intital six end-words of the first stanza; the last end work in the stanza before becomes the first end word in the following stanza.  The final tercet is called the envoi which contains all of the end-words.

 The form is as follows, where letters represent end-words:

  • Stanza 1: A, B, C, D, E, F
  • Stanza 2: F, A, E, B, D, C
  • Stanza 3: C, F, D, A, B, E
  • Stanza 4: E, C, B, F, A, D
  • Stanza 5: D, E, A, C, F, B
  • Stanza 6: B, D, F, E, C, A
  • Tercet: AB CD EF
    • First line of Envoi: B, E
    • Second line of Envoi: D, C
    • Third line of Envoi: F, A

The pattern above looks to me like sets of algebraic equations, and I mentioned that when I passed out copies of  the sestina by Elizabeth Bishop titled, appropriately enough, “Sestina.”

Listen to the poem:

Sestina

September rain falls on the house.
In the failing light, the old grandmother
sits in the kitchen with the child
beside the Little Marvel Stove,
reading the jokes from the almanac,
laughing and talking to hide her tears.

(READ THE POEM continued…)

animated houseThis poem always reminds me of some small child’s drawing of a house, in which everything suddenly comes to life, to dance or to hover or to fall. These images seem too animated to place under multiple choice microscope I use to prepare students for the Advanced Placement test. But the new semester has begun, and test preparation is necessary, so we took our time studying the questions that had been prepared in dull, unanimated standardized testing rooms.

The grandmother and the child in the poem are portrayed primarily through descriptions of their:
(a) actions
(b) thoughts
(c) conversation
(d) facial expressions
(e) physical characteristics

Reading the question aloud, I was not entirely sure that Bishop would care about the primacy of her descriptions. Given all the action verbs in each stanza, we settled on “(a) actions,” and we were right.

One of the questions dealt directly with the poem’s pattern:

Which of the following literary devices most significantly contributes to the unity
of the poem?
(a) Use of internal rhyme
(b) Use of epigrammatic expressions
(c) Use of alliteration
(d) Repetition of key words
(e) Repetition of syntactic patterns

A discussion of what syntactical patterns appeared ensued.
“There is dialogue,” one said.
“But, not as a pattern,” another replied.
We settled on (c) repetition of keywords, and we were right. Recognizing the pattern was helping with the questions.

 “There’s a lot of crying in this poem,” remarked a student, “What are ‘equinoctial tears’?”

I explained that knowing what “equinoctial” means, a violent storm of wind and rain occurring at or near the time of the equinox, is important to the understanding of the poem. Bishop’s association of tears with “equinoctial” suggests that there is some emotional storm that is the result of an annual event or anniversary. Once the students knew that, they were able to answer the last question:

 The mood of the poem is best described as
(a) satiric
(b) suspenseful
(c) reproachful
(d) mournful
(e) quizzical

“The repetition of words means there is more emphasis on them,” said a student.
“All that crying,” agreed another student, “Someone must have died.”
We decided on (d) mournful, and again we were right.

In the end, students got about 60% of the questions right on the poem, a high score this early in their practice. They had employed both the Mathematical Practice standard #7 and “looked closely to discern a pattern or structure” as well as the English Language Arts Literacy Anchor Standard #1, “Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.” 

“I liked it,” said a student, as she left.
I know she did not mean the multiple choice questions.
I am sure she meant the poem,“Sestina,” a crossover between English and mathematical practice standards.

A poem with a pattern:

Screenshot 2014-01-24 17.02.08 

Poetry Friday hosted this week by Tara at:http://ateachinglifedotcom.wordpress.com/

Come join her!

In Advanced Placement Literature, Common Core, Common Core-CCSS, Mathematics, Poetry, Reader, Reading , , , , , , , , ,
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Author’s Craft Revealed Through Mathematical Practice Standard #7

January 22, 2014 — 2 Comments

The year 2013 provided one of the best examples of real life detective work as well as real-life application of the Common Core Mathematical Practice Standard #7:

CCSS.Math.Practice.MP7 Look for and make use of structure.

The investigation was initiated because of structures and patterns, specifically the writing patterns of the author J.K. Rowling of Harry Potter fame. This mathematical practice standard MP#7 calls for students to “look closely to discern a pattern or structure,” and noticing a pattern was exactly what a computer program did in unmasking Rowling as the author of The Cuckoo’s Calling. The mystery novel, had been published under the name Robert Gailbraith, and the novel had begun to generate some critical acclaim. Only there was no Robert Gailbraith; Gailbraith was the pseudonym Rowling had chosen for her new foray into the mystery genre.

The ruse did not last long. In true detective fashion, two university professors, acting on a anonymous tip, wrote a computer code that used algorithms to compare patterns in the writing from The Cuckoo’s Calling with titles from Rowling’s Harry Potter series and the works of other mystery writers. The algorithms targeted several possible mystery writers, but Rowling’s name came up most consistently with language patterns that matched word length, 100 most common words, pairs of words, and the patterns of letters, spaces and grammatical marks known as “four character strings.”

The steps to identifying were outlined in an article in Popular Science, “How Computer Algorithms Uncovered J.K. Rowling’s Pseudonymous Novel.” Writer Francie Diep explained that, “Some of the individual tests found authors other than Rowling were the best match. Nevertheless, Rowling came up the most consistently.” 

The methods of the professors investigating Rowling belong to a practice known as the digital humanities, a field of study that “aims at developing and using the digital resources and tools for solving the research questions in the Humanities.”— Takafumi Suzuki (For other definitions check out whatisdigitalhumanities.com)

As texts become available digitally, they can be deconstructed into parts in order to answer research questions such as word origins (etymology), locating primary sources, and determining authorship. In the journal A Companion to Digital Humanities an article titled “Stylistic Analysis and Authorship Studies” author Hugh Craig points out that,

“There are enough successes to suggest that computational stylistics and non-traditional attribution have become essential tools, the first places one looks to for answers on very large questions of text patterning, and on difficult authorship problems.”

Yet, these patterns can do more than identify authorship. Patterns can be used to support an author’s purpose. For example, in the play Julius Caesar by Shakespeare, the character Marc Anthony, a wily politician, deepens the character Brutus’s involvement with the murder of Julius Caesar through the use of the phrase “honorable.” Here, the actor Marlon Brando plays Marc Anthony and recites the speech (1951 film):

The famous speech begins “Friends, Romans, Countrymen; Lend me your ears..” (3.2.) and Shakespeare employs the rhetorical device, an antistrophe or repetition of the same word phrase at the end of successive clauses, repeating “that Brutus is an honorable man.” In the opening 30 lines of the speech, Marc Anthony also connects “ambition” with the death of Julius Caesar.  Four times, Marc Anthony refers to Brutus “an honorable man,” but links each mention of honor with an “ambitious man”. By the end of his oration, Marc Anthony’s rhetorical accusations have inferred Brutus’s less than honorable behavior was an ambitious grab for power, and an incensed mob storms the streets of Rome seeking revenge. A final analysis reveals that Shakespeare’s use of rhetoric, a textual pattern, provided the tool that Marc Anthony used to attack Brutus very publicly for political gain.

Employing a pattern of repetition can serve an author’s purpose, and understanding this purpose requires the stylistic analysis that is embedded in the English Language Arts Literacy Reading Standard 4 where students “interpret words and phrases as they are used in a text, and analyze how specific word choices shape meaning or tone.” Patterns reveal the author’s craft; patterns also reveal author’s purpose.

images (1)You can find a textual pattern in any one of seven basic sentence types. You can find a textual pattern on any one of the seven days of the week on any one of the seven continents. Using Mathematical Practice Standard #7, helps find the purpose of a text or find the author of a text…like J.K. Rowling, who wrote seven books in the Harry Potter series. Coincidence? No. Pattern.

In Common Core, Common Core-CCSS, Mathematics, Shakespeare , , , , , , , , , , , , , , , , , , , ,
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Poetry Friday: “Do Not Go Gentle” with that Math Practice Standard #7

January 16, 2014 — 8 Comments

The villanelle is a nineteen-line poem with two repeating rhymes and two refrains. The form originated in France in the late 1800s, and the structure is comprised of five tercets followed by a quatrain. The most famous villanelle is by the Welsh poet Dylan Thomas, “Do Not Go Gentle into That Good Night.”

Do not go gentle into that good night, 

Do not go gentle into that good night,
Old age should burn and rave at close of day;
Rage, rage against the dying of the light.

Though wise men at their end know dark is right,
Because their words had forked no lightning they
Do not go gentle into that good night.

Good men, the last wave by, crying how bright
Their frail deeds might have danced in a green bay,
Rage, rage against the dying of the light.

Wild men who caught and sang the sun in flight,
And learn, too late, they grieved it on its way,
Do not go gentle into that good night.

Grave men, near death, who see with blinding sight
Blind eyes could blaze like meteors and be gay,
Rage, rage against the dying of the light.

And you, my father, there on the sad height,
Curse, bless, me now with your fierce tears, I pray.
Do not go gentle into that good night.
Rage, rage against the dying of the light.

I recently taught this poem to a class of Advanced Placement English Literature seniors who after some discussion were able to determine audience (“And you, my father..”), the form of address (imperative “Do not go“) and the poem’s paradox (“Curse, bless, me now“). They were intrigued by the most striking element of the poem, the repetition of the lines “Do not go gentle into that good night” (1, 6, 12, 18) and “Rage, rage against the dying of the light” (lines 3, 5,15,19). The ferocity of Thomas’s repeated exhortations increase because of the structure of the villanelle.

Structure matters. Structure, that “fundamental, tangible or intangible notion referring to the recognition, observation, nature, and permanence of patterns and relationships of entities” is not limited to poetry. Structure is in all the arts, and in all the sciences.

Structure matters in mathematics. Common Core Mathematic Practice Standard #7 requires students to:

Look for and make use of structure.

This standard details that “proficient students look closely to discern a pattern or structure,” and suggests, “young students, for example, might notice that three and seven more is the same amount as seven and three more.” Promoting this practice standard beyond the math classroom will have students noticing structure in other classes in every grade level. Students will be better equipped to recognize and use the structure of the periodic table or the color spectrum; they will be be prepared to identify and to employ patterns in pronouncing vowels and consonants. Students will be empowered to discover coordinates in longitude and latitude or to categorize the ingredients in food groups.

Recognizing and using structure is the critical academic skill that can help a student unravel both a problem in geometry or the complexity of a poetic structure like the villanelle. Once they understand the structure, they can evaluate the poet’s purposeful choice such as the one made by Dylan Thomas who selected the villanelle for this powerful poem.

The Common Core’s Mathematic Practice Standard #7 is in math and poetry. Note the same letters MP? Pattern? Possibly. Coincidence? Maybe not!

Continue Reading…

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