February 9, 2012
TECHNOS QUARTERLY Winter 1993 Vol. 2 No. 4
Inspiring Young Minds:
Kay Toliver
By Arwen Larson
“I have a good teacher who makes me think.”
“She really cares for us, and we care for her, too.”
“In her class, we're not considered hoodlums; we're considered students.”
“She doesn't tell us the answer-she makes us find out for ourselves.”
“She's leading me down a path to my future.”
“I never had a teacher like Miss Toliver…”
New York City—Manhattan. If you walk north from Central Park on Lexington Avenue and turn east on 104th Street, you pass family delis and faded signs advertising shoe repair. An occasional storefront is boarded up, and several gutted buildings stare down at you as you pass. Graffiti is ubiquitous; climbing up brick walls and covering phone booths, it makes a slightly uneven backdrop to the motion of the city. This is Spanish Harlem, also known as East Harlem.
Before long, you reach East Harlem Tech/Public School 72 and its asphalt playgrounds. This is a math and science magnet school, a school of choice. Called “alternative,” it houses approximately 900 students—800 in the elementary grades and 100 in East Harlem Tech, the junior high component. The student body is approximately 85 percent Hispanic and 15 percent African American.
The media, with their customary emphasis on things negative, might lead you to expect East Harlem to be an unlikely place to find educational excellence. But East Harlem Tech is home to math teacher Kay Toliver, who, for 27 years, has been instilling a love of and thirst for knowledge in middle school students.
Toliver is a teacher on the cutting edge of mathematics education, one who has been carefully following the changes in emphasis promulgated in recent years by groups such as the National Council of Teachers of Mathematics. She stresses application and thinking skills over computation, holds open class discussions, and weaves language, history, and art into the study of mathematics. Recently she received awards for her innovative teaching techniques. In 1992 she won the Superintendent's Award for her school district, received the Presidential Award for Excellence in Science and Mathematics Teaching, and was chosen as the Outstanding Teacher for Mathematics Instruction at Disney's American Teacher Awards. In 1993 she earned the New York City Reliance Award for Excellence in Education.
But Toliver has been teaching this way since 1967, when, as a new teacher just out of New York City's Hunter College, she came to P.S. 72, rolled up her sleeves, and got to work. Perhaps it has taken these decades for the mainstream to catch up with her.
Math as a Communication Art
She calls her class Mathematics and Communication Arts, for Toliver considers math a precise language that students of any age can learn to use fluently. “When students arrive in my class, the first thing I tell them is that everybody can do mathematics to some degree,” she says.
The first communication skill Toliver's students must develop is an understanding of math vocabulary. Words such as “area,” “volume,” “mean,” and “mode” have distinct mathematical meanings which, if not fully grasped, make the subject confusing. “In order for students to understand the concepts that are being introduced to them, they must have an understanding of those words associated with the topic,” she says. “Therefore, we spend quite a bit of time on vocabulary.”
She teaches seventh and eighth graders. Because her students often have unstable educational backgrounds, their language skills are poor. That is one reason Toliver puts heavy emphasis on writing, reading, and research. Her students must always be prepared to explain their solutions orally, in clear sentences.
Students are required to keep daily journals. They write about what they learned in class, ideas about how to apply the concepts they study, or simply comments and observations about the classroom or about Toliver. The primary purpose of the journals is to get students to write, for Toliver believes that the ability to express themselves in written English must be acquired hand in hand with mathematical ability.
“I'm always trying to come up with more ways to get my kids to write,” Toliver explains. “What better way to achieve this than to have them explain their thoughts and feelings about math class?” The journals also provide an intimate glimpse of her students' confusions or realizations. They allow her to assess herself as a teacher, correct misunderstandings, and review lessons when necessary. “A teacher can stand in front of the class and think she's giving a great lesson. But that's not always the truth. By reading the journals, I find out if I'm really communicating effectively.”
“I
HEARD IT THROUGH THE GRAPEVINE”—Toliver's hands-on lesson on estimating
features a tasty snack of raisins.
A story or poem may provide entrance into a new mathematical concept. The Dr. Seuss book Bartholomew and the Oobleck, for example, is the basis for a lesson on complex fractions. For this lesson, Toliver even supplies the oobleck—a liquid cornstarch mixture the students can dig into as they try to determine the correct proportions of its ingredients.
She also requires her class to research famous mathematicians or to learn about the contributions of various ethnic groups to the development of math throughout history. As she writes in an essay for the Winter 1993 issue of Howard University's Journal of Negro Education, “Mathematics has existed for thousands of years, developing through diverse cultures, and finally arriving in the present for junior high schoolers to study. Learning the history lends math a fullness and overall importance it may not otherwise have, and research exposes students to great minds who have made outstanding contributions to human knowledge.”
Math Fair, Math Trail
Over the years, Toliver has developed unique class projects as a way for her students to apply math and language skills to activities outside the classroom.
In 1988 she began the Math Fair at East Harlem Tech. Much like a science fair, the project originally was for her eighth-grade students to show off the knowledge they had gained in eight years of studying math. Students created games such as “Math Jeopardy,” “Dunking for Prime Numbers,” and “Black Jack Geometry.” They also did research projects. One student made a presentation on the Fibonacci sequence (in which each number equals the sum of the previous two). In another project, students were polled on their musical tastes, with the results presented on charts. When the projects were finished, they were displayed for the whole school. By explaining their projects to the younger students, the eighth graders inspired them to continue their own studies of math.
The fair was so popular that East Harlem Tech/P.S. 72's principal, Susan Siegel, asked Toliver to hold a schoolwide Math Fair the following year. For the second year's fair, each grade level created projects relating to the topics they had studied that year—from displays of sorting and colors by the kindergarten students to basic algebra in the upper grades. The Math Fair is now an annual event at P.S. 72.
“SHE'S
LEADING ME DOWN A PATH TO MY FUTURE”—Kay Toliver and her students
embark on the Math Trail.
The Math Trail began in 1992 when Toliver discovered that much of the damage done to school property—broken windows, graffiti, and the like—was caused by the students themselves. It was obvious that the kids at East Harlem Tech had little respect for or appreciation of their school or their environment. Toliver first heard of the Math Trail from an Australian teacher, Dudley Wayne, in 1991. In her class, the project evolved as a way to get students out into the community in order to learn that there are beautiful things in their everyday environment and to seek out applications of math in the real world. As her students work on the Math Trail, she finds that they begin to have a feeling of ownership for their community, a sense of pride in the things around them.
The project begins with the students researching the East Harlem community, reading about the history of the area and finding the borders of East Harlem in relation to the rest of Manhattan. They are surprised to discover that the area, now predominantly Hispanic, was once Jewish and, before that, Italian. They find that street names have changed over the years.
After the research comes the trail itself, when Toliver's students, in independent groups, follow their plotted paths through the neighborhood, visiting and photographing the park, shops, and other points of interest along the way, looking for math applications. When they return to class, they create their own books of math problems relating to what they have seen. One group counted how many elevated trains passed the corner of Lexington and 103rd Street in one minute. Then they posed the problem: How many trains would pass in one hour? Another group asked the question: If the jewelry store down the street is having a 40-percent-off sale, how much does a $35 necklace cost? And, if a parking meter costs 25 cents for every 15 minutes, how much money could the meter collect in eight hours?
The books are made of bright construction paper and decorated with student art work. The first page always includes a map of the Math Trail so other students can walk the path and solve the problems. “Now my eighth graders are writing math problems that can be solved by next year's students,” Toliver says. “They not only become problem solvers; they know math well enough to find the problems.”
One of her greatest discoveries on this end-of-the-year project was that students who scored well on tests were not necessarily the ones with the best grasp of mathematical concepts. While walking the trail, one girl pointed to a rooftop and observed that there were two similar triangles in the architecture. When Toliver asked her how she would go about proving this, the girl explained that similar triangles have proportional sides and that the angles would remain the same regardless of the length of the sides. Her answer showed a deep understanding of geometric concepts, yet she had failed three-quarters of Toliver's written tests.
A Family Atmosphere
The tone in Toliver's classroom transcends the academic. She has made school a home for these children. Many of her students are exposed to drugs or crime. Frequently one parent or the other is gone, or a child may be in foster care. Too often a sibling is in jail, and the students are stepping into the life of the street.
Many call such students disadvantaged. Some say they cannot really be taught. But Toliver disagrees. She herself grew up in the South Bronx and East Harlem, and she understands the problems they face. She also realizes that despite their environment, their socioeconomic level, or the example set by many of their peers, her students have arrived at school. School is their chance to rise above the chaos around them and expand their world, and Toliver refuses to let them down. “I don't feel sorry for my students. And I don't want them to feel sorry for themselves,” she says. “I want them to get up and walk and make their lives better. And the way they make their lives better is through education.”
The atmosphere in her classroom is one of mutual respect; it is a place where students feel safe to make mistakes and to ask questions. Discipline is not a problem; the students know she is there to teach and that a certain decorum, a certain amount of consideration, is required. They know Toliver works hard to make math understandable and interesting, and they do not waste her time with distractions.
One student—let's call him Xavier Mendez—was living in a homeless shelter when he came to Toliver's class in 1988. His mother had been released from a mental institution not long before. Their apartment had burned down, leaving them nowhere to go but the shelter. Xavier spoke to almost no one. The other students secretly laughed at him. He began coming to school early to get out of the shelter. One morning at 7:30 Toliver found him crouched in a corner of the hall by her classroom. “If you decide to come in early,” she told him, “you can help me.” He brightened up a bit and became her helper that year. Toliver gave him breakfast in exchange.
The other students, seeing how much Toliver cared for him, gradually began to accept him. Soon Xavier felt safe enough in the classroom that he was not afraid to participate. By the end of the school year, he had opened up, made friends, and shown himself to be an excellent student. It turned out that he was also an artist. When Xavier graduated from eighth grade, Toliver helped him get into a high school art program. In February 1992, Xavier dropped by P.S. 72 to show Toliver his high school diploma. He told her that he had taken advanced courses and was able to finish high school six months early. What's more, he was on his way to Hunter College that very day to plan his spring semester.
Toliver likes to use Xavier as an example of students who need a little extra attention. On the surface they may seem unwilling to learn or impossible to reach, but given the chance and enough care, most will rise to the occasion and begin to learn. “We don't need different methods to teach so-called disadvantaged children,” she says. “We just need teachers who are dedicated and who believe their students can succeed.”
Over the years, Toliver has observed that as her students begin to master the language of mathematics and learn to express themselves clearly, their performance in other classes improves as well. By gaining a firm hold of one subject, they are able to tackle education in general. Toliver's basic goal, beneath the projects, journals, and assignments, is to draw out her students' intelligence, to challenge them to use their minds, to teach them to reason. “No matter what they choose to do in life, students must learn to think,” she says.
The Role of Technology
Philosophic arguments about the appropriate use of technology in education are overshadowed by economic reality at East Harlem Tech. The issue is not whether technology is valuable—that's a given—but whether it's available. There are only 20 working computers in all of P.S. 72.
Toliver feels strongly that her students must learn to use computers, and learn to use them well, to be prepared to work in the 21st century. Whenever possible, she has her students type assignments in the computer lab. By teaming up with the computer teacher, she succeeded in getting the students to use computers to write simple programs relating to geometric formulas and for other math exercises. “If I had computers in my classroom, I'd certainly integrate them into my lessons,” Toliver says. “But right now, we're having trouble affording calculators.”
With the money she received from her Presidential Award, Toliver is purchasing software and two computers for her school's computer lab, but the process of acquiring enough equipment has been slow. Her primary hope is that initiatives to bring technology into schools will emphasize equal access for all students. “Students are going to need more and more education in order to find a rather basic job,” she says. “But we can't prepare them unless we have the technology.”
A Model Teacher
When teachers visit Toliver's classroom, one of their first observations is that this teacher of nearly 30 years is not “burnt out.” Her response is that she has never given up being a student in life and has never stopped looking for new ways to teach or avenues of knowledge. It is her love of learning that she hopes to pass on to her students, whatever careers they may choose. This, she says, is the greatest contribution a teacher can make. “It is a thrill to hear that my students have finished high school and gone on to college, for I know they are continuing to challenge themselves and will really do something in life.”
Toliver always hopes some of her students will become teachers, but only a few have done so over the years. Recently, however, after she appeared on a television special, five students in a class of 35 told her they wanted to become teachers. “I became a real-life role model,” she says. “It was wonderful to see young students taking pride in education, because we need more people who love to teach.”
And Toliver does love to teach. She is working as a mentor to other teachers in an effort to reach all of the students in her school. She laughs at the suggestion that she would ever leave the classroom. “What else would I do?” she asks. “I'm a teacher.”
Kay Toliver is a senior associate of the Foundation for Advancements in Science and Education (FASE), a Los Angeles-based nonprofit organization. She is working with FASE to create “The Eddie Files,” a TV series that will introduce 8- to 10-year-old students to the world of math through the eyes of Eddie, a fictitious student in Toliver's classroom. With math teacher Jaime Escalante, she is contributing to “Interactions: Real Math—Real Careers,” a multimedia tool that connects pre-algebra math principles to real life in scenarios featuring professionals in varied careers. It will be published by D.C. Heath in spring 1994. For more information on these projects, contact FASE at
-
626-793-5300, or
236 West Mountain St., Suite 105
Pasadena, CA 91103
Arwen Larson, a writer and research associate with FASE, is contributing to a book by the foundation on the future of education technology.
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