We Love Math! - teaching techniques - Brief Article

Innovative, multiple-intelligence math practices that boost learning and fun

All students can and should learn math--every good teacher of mathematics believes this. But how individual students learn, and what fires their imaginations, is a complex and challenging question.

Among the math teachers who appear here, none found one "right way" to approach the subject. These standout teachers agree that educators must be aware of the bigger picture in math even as we are teaching the basics. We have to constantly challenge ourselves. We must keep learning. That takes imagination and, as eighth-grade Massachusetts teacher Marcie Abramson says, the ability to "never lose the sense of being a student."

Picture Book Math

Math, like an exciting piece of literature, has many unexpected twists, turns, and shifts in the plot. And, like a story, math does not have just one possible outcome. Kathy Shultz, a fifth-grade teacher at Holmes Elementary School in Darien, Connecticut, knows that students sometimes see math as a one-way street. "They feel that there is only one answer, and when they find it, they move on to the next problem and solve that," she says. Her goal is to get children to see math as affording numerous possibilities--as fascinating as any tale they could ever read.

A large part of Schultz's math program incorporates manipulatives, writing, and, of course, literature. To teach attributes of geometric figures, she uses The Important Book, by Margaret Wise Brown (HarperCollins, 1999), encouraging students to follow the format of the text as they describe uses for favorite geometric shapes. After reading The True Story of the Three Little Pigs by a Wolf, by John Sciezka (Penguin, 1997), Schultz challenges students with questions such as "If the pigs' lawyer needs to be paid, which of the following payment methods works better?"

After the kids figure out a solution to a problem, they work together to "design their own problems based on the knowledge they gained from the activity," says Schultz. "They come up with questions that are twice as hard as the ones any book, or I, could come up with!"

Schultz is amazed that so many of her students say they absolutely love math. They are also clear about what types of math activities excite them. Anything related to games and stories works well with the kids, but "they hate anything having to do with a rote sheet or opening the textbook." It's not a surprise, then, that Schultz seeks to find creative ways to meet the NCTM standards.

Many parents, however, learned math in a rote fashion themselves, and can be nervous when presented with problems and solutions they don't understand. To meet the problem, Schultz has planned a Family Math Night for this spring. "This will really open the parents' eyes to what their kids are doing."

Not knowing every answer can be OK even for a teacher, says Schultz. If students see their teacher as nervous and always looking for the one right answer, they will mimic her actions. "When you as a teacher don't know the answer or fail to come up with a different solution, celebrate it!" she asserts. "Students need to know that their teacher is human and doesn't know everything.... Let students' knowledge lead the lesson."

Open-ended Problems

Angela Andrews proves that it's possible for someone who hated math as a student to become an excellent and inspirational math teacher. A self-described "math anxious" student, Andrews had always found math irrelevant and incomprehensible. "My whole school career was filled with meaningless mathematics," she says. "My well-intentioned teachers answered my inquiries with comments such as: 'Yours is not to question why--just invert and multiply!"'

Andrews, a multi-grade teacher at the Scott Elementary School in Naperville, Illinois, knows that to answer children's questions with integrity, she must truly understand her subject. That's why she's always working to better understand elementary mathematics. Sometimes that means repairing the false assumptions that were passed on by her own teachers--who gave her the tools to solve a problem, but may not have fathomed the "whys" beyond the "how-tos." "I am constantly ... revisiting my early understanding of math and trying to make sense of it."

Andrews likens one of her favorite classroom activities to the Japanese "open approach" to problem solving. "At the beginning of the year, I ask my students to fill out a card with information about their families, hobbies, sports, talents, pets, and so on," she explains. "Then I use this information to design challenging math problems which are open-ended and solvable through a variety of methods." One example of such a problem: "Bobby got a $1.00 birthday check from his grandma. Before his mom would cash it, he had to tell her all the different ways she could give him $1.00 if she only had coins. How many ways can you think of?"

Students and teacher come to an agreement: The students will not ask for any help from parents or peers, and the teacher will not penalize them in any way for incorrect answers. "This arrangement builds an atmosphere of safety, and allows students the freedom to solve the problem in an unconventional manner," says Andrews.