Subtracting a 'gifted' gap in math education

Even students who don't have as much background knowledge coming into the program excel, Lizon says. "They see things that I don't see. They amaze me." She recalls a girl looking at patterns placed on the windows that represented various numbers multiplied together. Some were examples such as 6 x 6. "She figured out the concept of square numbers just by looking at those arrays on the windows ... and she figured out the why. That's the thing about M3 ... it's not just rote computation."

Teachers are trained to pose open-ended questions to children and invite them to challenge ideas. The respect and focus is palpable in Kirsten Sanderson's classroom, where the Charter Oak fifth-graders in M3 gather once a day for an hour.

At the whiteboard, Ms. Sanderson writes 3/4 + 4/4 = 7/8 and then asks, "Can you add fractions like this?" The students let out a collective groan and say "No." But she pushes them to explain why. One boy says that you can't add the denominators (the numbers on the bottom) that way, because "it's like a pie in slices, and that's final."

After reviewing the concept of equivalent fractions, she sets them to work on an exercise related to ratios. They have to draw the windows for a fun house at a carnival, based on certain rules, and write explanations.

Today, Ann Marie Spinelli, leader of the M3 professional development team, is here for her weekly visit. She leans down to see the work of Ashley, a petite girl decked out in pink, who excitedly shares with her an observation: No matter what length she chooses for the window, it turns out to be a square because the directions tell her to draw it on a one-to-one ratio.

Sanderson asks three students to show their work on the overhead projector and explain it to the class. But this isn't about rewarding students for getting it "right." When one of them says, "I'm not sure if my answer is right or wrong," Sanderson replies: "Maybe some of your mathematician friends can help you." There's not a hint of embarrassment, and after several suggestions from students, he corrects his formula.

That's an aspect of this class that Kevin particularly likes: "We have 'rights and obligations' in class. We're allowed to challenge an idea, but if we're wrong [or] the other person's wrong, we both learn something," says Kevin (a pseudonym used at the request of school officials). He also enjoys exercises called "Think Deeply," where he figures out multiple elements of a word problem and explains his answers. "We get really into it ... and then time flies."

"I really liked pushing the oranges with our noses," says Becca, another student, of an exercise they did built around "Wacky World Records." "We were doing line graphs. It was really interesting to see what rate you went at," she explains.

Some of Becca's homework exercises don't look too familiar to her mom. "It made me feel kind of proud that I kind of understood it better than my own mom," she says with a laugh.

The project does bring parents along, though. The teachers send home regular newsletters with math activities for parents and kids to do together. Last year, after a series of lessons on probability, families came in for a Math Night in which they played games of chance the students had designed to favor the house (the event was also a fundraiser for a service project). The kids were giddy at first, Sanderson says, and then they had to "fess up" and explain the probability involved in the games.

'One of the most impressive programs' in 30 years

Project M3 was examined by independent consultant Susan Carroll, president of Words and Numbers Research in Torrington, Conn. "I've evaluated programs for 30 years, and this is one of the most impressive I've ever seen," she says by phone. On both multiple-choice tests and open-ended questions used to measure grasp of concepts and problem-solving, students did better than peers who showed the same potential but weren't placed in M3 classes.

In Hartford, a district next to West Hartford where many schools have low test scores, students from M3 are entering accelerated math in middle school, "and it's the first time these schools have sent kids to that program," Gavin says. Having seen the benefits, principals are asking for the curriculum to be developed for higher and lower grades.

The third- and fourth-grade M3 curriculum is already for sale and is being used in 43 states, Gavin says. Educators as far away as Singapore have expressed interest in using the curriculum to increase the critical thinking and creativity in their classrooms.

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