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Determined to raise the mathematics skills of elementary school students, Vermont state education officials launched the Vermont Mathematics Initiative in 1999. Elementary teachers learn algebra, geometry, problem solving, and calculus so they can better understand and explain math to their students. Included: Lessons from the Vermont Mathematics Initiative

Algebra, trigonometry, and calculus are not topics often associated with elementary school teachers.

Vermont education officials, however, calculate that a professional development program in mathematics for elementary teachers will add up to better math comprehension for them and better math skills for their students.

Called the Vermont Math Initiative (VMI), teachers in the three-year program learn higher-level math in a way they can understand and then take that increased understanding to their classrooms. At the end of the program, teachers receive a master's degree in education with a specialty in K-6 mathematics education.

VMI's goal is to prepare 300 math teachers with advanced degrees by 2005; those teachers will then instruct other teachers and help shape mathematics instruction in their schools. Currently, 105 teachers from 76 schools are enrolled in the program, which began in 1999. Vermont has about 3,200 elementary school teachers in 350 K-5 or K-6 elementary schools.

"In traditional staff development, teachers learn how to teach math to kids -- not mathematics itself," says Dr. Kenneth Gross, director of the program and a professor of mathematics and education at the University of Vermont. To prepare to teach reading, teachers do not just read books at the level of their students, he notes. "My idea was to train teachers to think like mathematicians. This is not baby math. We are teaching college-level math in such a way that they can assimilate it and translate it to fit their own K-6 classes."

TEACHER, ADMINSTRATOR COMMITMENT

Teachers who are accepted into the program take four math courses a year at the University of Vermont, two during a two-week session in the summer and one each during three weekends in the fall and the spring. A mentor is assigned to each teacher in the program.

VMI instructors are from the University of Vermont and other colleges in the state. Office hours are held at different locations during the year so teachers can get help with homework and discuss with other teachers how they are integrating the math into their lessons.

School administrators are expected to support the VMI teachers. When teachers apply to the program, their principals have to sign the applications and submit statements outlining how they envision the training being applied in their schools. After the first year of the program, teachers and principals attend a three-day workshop on implementing VMI-based instruction.

Deborah Armitage, a mathematics consultant for the Vermont Department of Education and a former elementary school teacher, says the state sees enormous benefits from the program. "For the first time, teachers are seeing the why and the when of what they are doing," Armitage tells Education World. "They understand where the math is leading. They have crossed a line -- instead of just doing math, they are experiencing math and understanding math."

LEAVE THE CALCULATORS HOME

Gross, who also runs math programs for gifted high school students and adults who want to improve their math skills, began developing the program about five years ago, after staff from the Vermont Department of Education approached him with concerns about student math skills. The DOE officials realized that any curriculum changes were doomed to fail if teachers did not have a grasp of the material, Gross says. "If you don't understand the math, then all you are doing is teaching activities."

In setting up the program, Gross says, he had two primary criteria: to offer challenging material and to treat teachers as professionals. "Society undervalues teaching and education; teachers are overworked and underpaid and asked to teach everything and be psychologists. I wanted teachers in this program to be treated liked the CEOs of corporations." That meant holding the program in an attractive setting, providing accommodations, and providing lunch, he says.

The state's department of education, school districts, individual schools, and the Windham Foundation fund the VMI. The state pays half of each teacher's tuition for the program; the teacher's school and school district pay the other half. Tuition is $840 per course, which includes room and board.

The VMI courses cover arithmetic, probability, statistics, algebra, trigonometry, and calculus. Teachers are forbidden to use any mathematical formula until they are able to derive it, Armitage says. One of the first courses is called Math as a Second Language, which brings together arithmetic, algebra, and geometry to show that they are different approaches to the same subject, Gross says. "You can teach algebra in kindergarten or first grade if you understand the math behind it."

A subtraction problem, for example, can be turned into an algebra problem, if you change 9 - 5=? to 5 + x =9, solve for x, and x=4. "Subtraction and division are really algebra," says Gross.

ADDING UP THE BENEFITS

Teachers come into the program with various levels of math skills and several told Education World that they were amazed at how much they have learned and how their confidence has grown.

"It's everything I wanted and 100 times more," says Connie Cannon, who teaches fifth grade at the Dorset School in Dorset, Vermont. She is in her second year of the program. "I'm excited to be immersed in math again, and I've bonded with the other teachers and made some close friends."

After taking the Math as a Second Language course, Cannon says, topics such as probability, trigonometry, and calculus are much clearer. "I would never have expected to be able to do this. I never understood them the way I understand them now."

Cannon has taught for 26 years. She majored in fine arts as an undergraduate and has a master's degree in education. She says she took only one or two math-related courses in graduate school. "Nothing prepared me for teaching math."

Now, Cannon says, she knows multiple ways of solving problems. For example, when she was in school, she was taught when solving a problem such as 43 - 29 to automatically cross out the 4 and add a 1 to the 3, without really understanding the math behind it. Now Cannon explains to her students that because the top number is 43, in order to do the subtraction, they borrow one group of 10 from the 40 and add it to the 3, making it 13.

"This has made me more confident," Cannon says of the program. "I have a better foundation so I can help students better."

Kathleen Nolan, a third-year VMI participant who teaches middle school math at Island Pond School in Island Pond, Vermont, says she finally is learning the concepts behind certain applications.

"I learned math one way: memorize the procedures, the steps, and the process," says Nolan, who has taught for 27 years. "Now I need to teach differently so the kids understand better. Now I can see the connections, I understand the concepts in many different ways, so I can teach in many different ways."

Adjusting her thinking also has taken some time, according to Cannon. "I'm starting with more of a math background than some people, so it has been a challenge to slow myself down and ask 'why?' It's been a widening experience."

FIGHTING THE PHOBIA

Many elementary school teachers' lack of strong math skills often dates back to their own school experience, says Gross. "Many people become math phobic and don't feel good about math," he explains to Education World. "If I tell someone I'm a mathematician or teach math, nine of ten people say to me it was their least favorite or worst subject."

New math curricula were introduced in the late 1980s, but often teachers were not prepared to teach it, Gross adds. "They threw in topics previously foreign to the K-6 and K-12 curriculum, such as statistics and problem solving; they introduced topics teachers had not studied in school."

Teacher preparation programs usually do not include many mathematics or science courses, Gross says. "Elementary teachers have so many subjects to learn. There has been an emphasis on pedagogy and process versus content in terms of mathematics and science preparation. The teacher training community has not put a premium on knowing mathematics, and many teachers come in loathing it."

Cannon and Nolan agree. "Education majors need more math and science; everyone has to teach it," Cannon says of elementary teachers. "A lot of elementary teachers shy away from math," Nolan comments. "It wasn't their strong suit. But I think math education is changing at the college level."

Vermont is looking into revamping its teacher education programs to include more math content and is also considering a science program for elementary teachers similar to VMI. VMI may be expanded to middle school teachers as well, Gross says.

Armitage, of the state education department, praises the dedication of teachers in the VMI program. Even though elementary teachers spend only about one-seventh of their day teaching math, "they are still willing to give up their time for this," he notes.

The teachers know that they are preparing more math-literate students. "If I can make math fun, they'll be golden," Cannon says of her students.