Focus onFriends

A

newsletter

for

families

and

friends

of

101

School Rd.

Wilmington

DE

19803

Wilmington

Friends

School

Spring

2010

Vol. XV

Issue 2

m(x+1) ≤ x2

Thinking About Math Following the recent five-year evaluation of the International Baccalaureate (IB) program at Friends, math department chair Ildiko Miller shared some thoughts about the philosophy and direction of the curriculum. And some young alumni shared their insights on how math education at Friends prepared them for college-major and career-related studies.

“This curriculum is great,” Ildiko said of the IB, “because it sets us up to do more each year with all of our upper school students—and with the Higher Level students, it really gives us an entire extra year of math.” Students in Higher Level (HL) math complete the topics in the AP Calculus AB curriculum by the end of their junior year. During their senior year, HL students are introduced to college-level topics such as complex numbers, vectors, advanced statistics, number theory, and graph theory.

“It goes well beyond AP calculus BC,” Ildiko said, “The IB HL curriculum is the most complex and challenging I’ve seen in any high school.”

Kelly Patton, Friends class of 2005, said that IB math showed her “how cool math could be.” Kelly started at Middlebury College intending to major in English or French and took math “to have a balance.” “Because I had done IB HL math,” Kelly said, “they let me skip Calculus I and II and take Linear Algebra. I found it to be fun and relatively easy, so I took another math class the next semester.” Kelly declared

Also in this issue:

4 Second Grade Wax Museum 5 Junior’s Award-Winning Essay 6-7 “Shad in Schools” 8 4th/5th Grade Science Olympiad

continued, pages 2-3

Math department chair Ildiko Miller said that the IB is strengthening the curriculum, through lower, middle, and upper school. And technology is helping. Pictured: Chris Loeffler and third grade students, using the SMARTboard in the lower school library

10%

Cert no. SW-COC-002625

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IB Math, continued from page 1

her math major early in her sophomore year and graduated in February 2009 with a thesis on Fourier Series in Hilbert Space. She also worked as a math tutor for three years at Middlebury.

Bill Broderick, class of 2009 and now at Oberlin College, said, “Math at Friends was great. It was certainly the hardest class I had in high school but also the most interesting and the most fun.” Like Kelly, Bill earned a full year of college placement credit in math. “I was able to skip all of Calculus and go right to Multivariable Calculus, parts of which (vectors) we had learned in IB math,” Bill said. “And anyone who’s familiar with IB will give you lots of respect for having done IB HL math. Everyone knows it’s more or less the hardest program.” Bill is hoping to combine math studies, as either a second major or a minor, with his major in neuroscience.

Because of scheduling restrictions related to her major in architecture, Julia Roberts, also ’09, wasn’t able to take math during her first semester at Washington University in St. Louis. “I really missed being required to think in the way that I needed to in order to succeed in my math classes at Friends,” Julia wrote in an email. During the second semester, she was able to take Calculus III and said, “The entire first unit was about concepts I had learned in my senior year at Friends, which I remembered—and I think I remembered so well because of the way I was taught in high school; I had built such a clear and deep understanding of the thinking behind the concepts.”

Developing that “clear and deep” understanding is another strength of the IB math program, Ildiko Miller said, adding, “It’s the same philosophy of teaching that we’ve had at Friends for a long time, at every level—lower and middle school, too. The goal of our math department is to help all of our students to become mathematical thinkers. We want them to look at a problem that they’ve never seen before and to know that even if the solution isn’t immediately apparent, they have the skills to solve it.”

One key to developing that level of conceptual understanding, Ildiko said, is looking at math as an integrated discipline, which is not always easy for parents—and even some teachers at first—who grew up with segmented math courses in algebra, geometry, and trigonometry, with calculus as the finish line. “It’s all just math,” Ildiko said, “and there is no finish line. These are tools, and there is so much out there that you can do with them, especially if you have the vision to see them in an integrated way.”

As an example, Ildiko suggested a problem she calls her “favorite”: m(x+1) ≤ x2. “It’s easy for people to get stuck,” she said, “because the problem is an inequality and has two unknowns. The trick is to let go of the anger, and start thinking. We want students to sit down with the attitude, ‘we can do this.’” (For one approach to solving the problem, see box at right.)

Another advantage Ildiko sees in the IB program is that it has prompted a very focused review of the preschool-12 math curriculum. “The IB got us out of our comfort zone,” she said, “It’s been energizing for the faculty and for the students.” Again, the integrated approach is not new to Friends and not limited to the upper school; the programs in lower and middle school emphasize a balance of skills mastery and conceptual understanding, with a lot of “real-world” problems that require integrated mathematical thinking. “We had a head start,” Ildiko said, “but now really knowing what students will have an opportunity to do, and what they will be expected to do, in high

Solve: m(x+1) < x2

(one of several possible approaches)

What kind of inequality is this? What’s the degree?

The highest power (degree) is 2, so it’s a quadratic inequality.

What’s the right format to solve a quadratic equation/inequality?

One side has to be reduce to zero: 0 < x2 - m(x+1) = x2 - mx - m What can we say about the graph of f(m) = x2 - mx - m?

It’s a parabola that opens up.

Why?

It has a positive leading coefficient = 1.

What else? How many x-intercepts are there?

Since the parabola either “sits” on the x-axis or it’s above the x-axis, one or zero x-intercepts. For example:

What defines the number of x-intercepts for a quadratic function?

The discriminant ∆. If ∆ < 0, then the quadratic function has either one or zero x-intercepts. What is the discriminant of f(x)?

∆ = (-m)2 - 4 · 1 · (-m) = m2 +4m

What do we know about the discriminant?

It has to be less than or equal to zero,m2 + 4m < 0.

y

x

d

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school is helping us to coordinate the preparation more effectively. It’s an ongoing process, but every step is really exciting.”

Technology has complemented that programmatic energy—most broadly through the use of SMARTboards and Notebook software across the department, along with the ongoing coordination of the math and computer curricula. Teachers are also incorporating web-based tools like polleverywhere.com, which allows them to post multiple-choice review questions after a lesson and students to use their cell phones to text answers, giving immediate, compiled feedback on students’ understanding of the material. “Technology is an incredibly useful tool from a curriculum-development point of view,” Ildiko said. “Exploring what the tools can do helps students to develop their own thinking and ability to solve problems—and the technology also helps to generate enthusiasm.”

“Enthusiasm” is a word Ildiko uses a lot, and the department’s approach is that excitement and challenge are not just compatible but mutually reinforcing, at every level. “Whether the kids are going to study math in college or not,” Ildiko said, “we want them to be excited about it.” One measure of success toward that goal is that, although students are required to take three math courses in upper school to graduate from Friends, over the past three years, more than 96% of seniors have enrolled for a fourth year of math. “Activities like the math clubs in lower school and Math Olympiad in middle school, along with class work in groups and the emphasis on explaining ideas, help us to break down the resistance some students initially might have toward math,” Ildiko said, “They get into it more easily, and they become more confident, too.”

Joe Hartnett ’04, who studied math at Cornell and is a systems engineer with Lockheed Martin, wrote of the lasting impact of his math classes at Friends, “The ability to solve, explain, and discuss mathematical concepts in a team environment has contributed directly to my professional success.” Kelly Patton said, “We were constantly pushed to do things that stretched our ability, and that’s what made it interesting. We learned that with perseverance, we could do things that seemed impossible to us at first.” Ben Altman ’06 who just finished his math studies—and his Division I wrestling career—at Davidson College and who will soon start a master’s program in financial math, wrote, “The teachers’ enthusiasm and willingness to challenge us really inspired my love of math.”

Maya Koretzky ’09, a current Cornell student, said, “The WFS math program challenged and pushed me to think deeply and to develop study skills that have been instrumental for doing well in so many of my college classes—from history to biology to Multivariable Calculus. What I appreciated most about the program was not that it prepared me well for something after high school (although it really did) but that it inspired me to work hard and to be enthusiastic about learning.”

“I dreaded each and every test,” Julia Roberts said of IB math at Friends, “but I also looked forward to them. I saw each exam as a test not of my ability to memorize formulas and algorithms, but as a test of the way I thought about and approached problems. There was a large emphasis on understanding why things were true, and then being able to use that understanding to apply it to more complicated problems.” She added, “I loved my math experience at Friends; I started college with almost half a semester credit, just in math; and I really don’t think I could have been prepared any better.”

What do we have here?

Another quadratic inequality

What does the graph of g(m) = m2 + 4m look like?

It’s a parabola that opens up, with zeros at 0 and -4. m2 + 4m = m(m + 4) = 0

When is the graph < 0?

When -4 < m < 0.

So what is the answer to the original question?

m(x+1) < x2, when -4 < m < 0

“It’s easy for people to get stuck,” Ildiko Miller said, “because the problem is an inequality and has two unknowns. The trick is to let go of the anger, and start thinking.”

0-4

y

x

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Welcome to the Wax MuseumVisitors walked into the Lower School Meeting Room and saw second-grade students from Kelly Miranda’s and James McIntosh’s class, sitting or standing very quietly in different locations around the room—like figures in a wax museum. And that was precisely the idea.

The students were dressed in simple costumes and had large red circles made of paper taped near their shoulders or on tables in front of them. When a visitor pushed the red “button,” the student would start to speak, representing a leader of either the Underground Railroad era or the 20th century Civil Rights movement.

The “wax museum biographies” were the culminating project of extensive class research and discussion about the two historical time periods, different kinds of injustice and discrimination, and the leaders—including a number of Quakers—who confronted injustices of their time and inspired others. Students read historical fiction and non-fiction books in reading groups, and explored different biographies before choosing the people they wanted to “become” for the museum.

The historical figures the students chose to represent were Susan B. Anthony, Mary McLeod Bethune, Ruby Bridges, Henry Box Brown, Frederick Douglass, Thomas Garrett, Mahatma Gandhi (specifically, the influence of his leadership and

example on leaders of the American Civil Rights movement), Isaac T. Hooper, Coretta Scott King, Martin Luther King, Jr., Abraham Lincoln, Malcolm X, Thurgood Marshall, Lucretia Mott, Rosa Parks, Dred Scott, Sojourner Truth, Harriet Tubman, Madam C.J. Walker, and Maggie L. Walker.

Kelly said of the project, “It really brings the history they’ve been exploring to life. I’ve found that students become very attached to their historical figures and the trials and accomplishments of their lives.” Tucker, who represented Frederick Douglass, said, “It was great that everyone came to tour our museum,” and Joe, who portrayed Dred Scott, added a compliment, “Our visitors listened very well.”

Pictured, clockwise from left, are Sean as Martin Luther King, Jr., Remy as Rosa Parks, Tucker as Frederick Douglass at the table with Sydney as Ruby Bridges, Casey as Mahatma Gandhi, McKay as Thomas Garrett, and Jadyn as Susan B. Anthony.

“ ”

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Brisket To Beatles: Why I Want to Meet Annie LeibovitzBy Annie Sheslow ’11

A lot of scientists should be interested in meeting Annie Leibovitz. Out of thin air, she can synthesize ideas, symbols, feelings, and memories that make up a personality, pour them into her camera, and capture not just one moment, but the millions of sighs, smiles, tears, and aspirations that weave together to form a human being.

Although I cannot distill the meaning of a life with a mere click of a button, Ms. Leibovitz and I do have connections that already seem to link us together. As I write these words, I am packed in my family’s tiny SAAB, on a pilgrimage to Paramus to celebrate Passover. “I’m not a practicing Jew,” Ms. Leibovitz said in 1994, “but I feel very Jewish.” Both Ms. Leibovitz and I seem to fall under the “floating matzoh ball” category of Jews that my reform Rabbi preached of so disapprovingly. It’s the kind of Jew that is proud to find Seinfeld doubly hilarious, that feels a special glee when using coupons, that eats cheeseburgers, and that rarely goes to synagogue. Both Ms. Leibovitz and I, on the other hand, have been blessed with a cultural upbringing colored with an appreciation for humor, frank speech, education, family, and all topped off with a dollop of guilt. If I met Ms. Leibovitz, I would be extremely eager to know how the pains and prides of a Jewish identity continue to influence her work.

Another connecting similarity between Ms. Leibovitz and me is a much more obvious one: our names. Though her “Annie” stands for Anna-Lou, and mine Annalise, both of us have had to endure strangers crooning reprises of Little Orphan Annie’s greatest hits, calling us “Anna” or “Anne,” and being mistaken for a boy named Andy when we were three. Or maybe that last one only happened to me.

By seventh grade, I was deep in the throngs of Beatlemania, and could tell John, George, Ringo, and Paul apart from the backs of their heads. I would love to interrogate Ms. Leibovitz about sharing the inspirational air of musicians such as John Lennon, Bob Dylan, Bruce Springsteen, The Rolling Stones, Pete Townshend, and countless others. I have a great amount of interest in the relationship shared between Ms. Leibovitz and her subjects—the mutual trust and understanding that leads to the very personal nature of her photographs.

The shining pureness and honesty that radiates through Annie Leibovitz’s work is something I would like to imitate. Ms. Leibovitz remains confident in the deep meaning of her art and courageous when others try to shred it apart. She approaches each subject with an equal amount of enthusiasm and professionalism. In 2007, Ms. Leibovitz remarked, “I’ve always been more interested in what they [subjects] do more than who they are.”

From Annie to Annie and brisket to Beatles, Annie Leibovitz holds a promise of connection, inspiration, and hopefully friendship.

The essay below, by Friends junior Annie Sheslow, was one of four winners in the 2010 Common Wealth Essay Contest, part of the Common Wealth Awards program. As a winner, Annie participated in a press conference, dinner, and awards ceremony with the 2010 Common Wealth honorees.

Above: Annie Sheslow fulfills the hope expressed in her essay of meeting Annie Leibovitz, winner of the 2010 Common Wealth Award for Mass Communications.

Below: Delaware high school winners of the Common Wealth Awards writing contest, including Annie Sheslow (far left) with the 2010 Common Wealth laureates: photographer Annie Leibovitz, humanitarian Greg Mortenson, author Salman Rushdie, and actress Laura Linney.

(photos courtesy of PNC)

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A Fry That’s Good for the FishAnd for the EcosystemOn May 7, 2010, with local media covering the event, a group of Friends seventh graders released shad “fry” (the juvenile stage of the fish) into the Brandywine River, the final step of a service-learning project in science classes. The project evolved through a program called “Shad in Schools,” which was developed by two Friends upper school students, juniors Louise Connelly and Parthena Moisiadis, in partnership with the Brandywine Conservancy.

When Louise and Parthena were in eighth grade, they decided to combine a required project about the Brandywine River with their interest in conservation—specifically, the work of the Brandywine Conservancy’s Environmental Management Center. They met with the Center’s senior planner, Robert Lonsdorf, who introduced them to the Shad Restoration Project. Louise said their interest in the effort was “immediate.”

The American shad is a native species to the Brandywine River, and was historically a large part of the the local diet. Like salmon, shad hatch in freshwater; they migrate to the ocean where they live for four to six years, and return to their home streams and rivers to spawn. The construction of mills and dams along the Brandywine beginning in the 18th century inadvertently interfered with fish passage. At the same time, pollution and over-fishing further decreased shad populations.

In 2003, the Brandywine Conservancy received a grant from the National Fish and Wildlife Foundation to study the feasibility of restoring shad and other migratory fish to the Delaware portion of the Brandywine. That study was released in 2005, and the Conservancy began working with dam owners on site-specific design plans—options including fish ladders, rock ramps, and the removal of dams—to allow fish passage upstream. Because of their place in the food system, shad are a “clock-spring species;” they keep the ecosystem running smoothly. Restoration would support a renewed food supply for birds and mammals that would, as described on the Conservancy’s web site, “increase the biological vitality of the watershed.” There would also be recreational benefits through controlled fishing.

During their eighth grade year, Parthena and Louise traveled along the Brandywine River, stopping at every dam and mill to photograph and document important details about the environment. They led a petition drive at Friends, advocating the restoration of shad to the River, and gathered more than 300 signatures of students, teachers, and parents. They then sent their petition, along with a letter explaining their work with the Brandywine Conservancy, to Wilmington Mayor James M. Baker (the City owns two of the dams on the River). In 2007, when the Conservancy held a press conference and released several thousand “fry” to promote the Shad Restoration Project, Louise and Parthena were recognized for their leadership.

And that was just the beginning. The following summer, Parthena and Louise interned at the Environmental Management Center. They met with the Delaware Fishermen’s Association, learned about an effort already further along to reintroduce shad to the Potomac River, and started to develop the Shad in Schools program.

Louise Connelly and Parthena Moisiadis, who worked with the Brandywine Conservancy to start “Shad in Schools”:

Top, as eighth graders with Wilmington Mayor James M. Baker at a 2007 press conference about the Shad Restoration Project;

And above, as juniors in 2010 giving interviews to local press on the day the shad fry were released by Friends seventh graders.

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Louise said, “We wanted to find a way that students in the area could engage in a hands-on project while spreading awareness of the Conservancy's cause. Our next steps were to contact local elementary, middle, and high schools looking for interested teachers. We were amazed at how effortlessly we were able to get the project approved here at Friends and at the enthusiasm of the teachers that truly put Friends in a leadership position among the other interested schools.” In addition to Friends, Tower Hill, Chadds Ford Elementary, Pocopson Elementary, and the University of Delaware are participating in Shad in Schools this year. Each school sent teachers to a training conference organized by the Living Classrooms Foundation in Washington, D.C.

Through Living Classrooms, Friends science teachers purchased shad eggs, taken from the Potomac, and a special tank to simulate the river environment. The project was a perfect fit with the curriculum, teacher Karen Horikawa said. “We were studying evolution and ecology, and it was a good time to insert a mini-unit about shad and water quality.” During the unit, students kept track of the egg count in the tank, tested water, and learned about shad life cycles and river ecosystems. Robert Lonsdorf from the Conservancy, who serves as supervisor of the Brandywine region of the Shad Restoration Project through Living Classrooms, visited with students at Friends and the other participating schools and helped to coordinate the collection and sharing of data.

As the time for the release of the seventh grade shad fry approached, Louise and Parthena sent a joint email saying, “We are so excited that our project is being realized this year, and we are very thankful to the teachers who have made it all possible. Friends School has certainly become a pioneer for ‘Shad in Schools.’ We hope that the program will reach schools throughout the area, raising enthusiasm so that students will look forward to spring when each year they can see their classroom projects, literally, come to life.”

Seventh grade students studied shad life cycles and river ecosystems in science, and raised shad fry in a special tank. A group of seventh graders and teacher Karen Horikawa then joined Louise and Parthena, Robert Lonsdorf and other representatives from the Brandywine Conservancy to release the fry into the Brandywine.

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Fourth & Fifth GradeScience Olympiad TeamIn its first year, the Lower School Science Olympiad generated tremendous enthusiasm; the team was “full”—in fact, two teams were full—within a week of the invitation to participate.

Fifteen students competed, under the guidance of science teacher Tim Dalby, at the Delaware Elementary Science Olympiad (ESO) held in April 2010 at St. Mark’s High School. ESO’s hands-on events, using ordinary household supplies, are designed to appeal to children’s curiosity with the competitive atmosphere to generate added excitement.

Students entered some events as individuals and most in groups of two-to-four. The Friends team brought home medals in an impressive four events: first place in Light & Mirrors, third in Heart & Fitness, fourth in Human Anatomy, and fifth in Interpreting Graphs.

Tim Dalby characterized the competition as “a great day,” saying, “The students were very independent and responsible, and left every event with smiles on their faces.”

The team: fourth graders Steven, Emma, Lauren, Evie, Klara, Jeffrey, Jake, Lin, and Nicky; and fifth graders Sarah G., Aaron, Hannah, Erica, Sarah S., and Margaret.