July 17, 2012
Kelley Donoghue’s ninth-grade math class in Lowell, Massachusetts, looks like any other. The whiteboard behind her contains neat columns of red numbers and variables in different combinations. A hastily written calendar broadcasts the dates of math review sessions and, finally, of the MCAS exam, the high-stakes test that her students will take at the end of 10th grade.
In front of Donoghue are 12 students with pencils at the ready, even on this warm May afternoon, for today’s lesson on the language and logic of algebra. They attend to problems in their workbooks, sometimes looking up to help a classmate or ask for help. And though Donoghue is initially greeted by silence when she poses a question to the class, soon she is treated to a series of thoughtful responses before students’ faces disappear again into their workbooks.
What visitors to the class aren’t likely to realize is these students are here because they scored poorly on the mathematics section of the MCAS exam last spring. "Other teachers would probably say that these aren’t their best kids," says Donoghue. "But for some reason, the way this group works, the students like being here, and they like to work most of the time."
Transition to success
So what’s behind the change of heart? Donoghue works tirelessly with her students every day, but she also credits the curriculum she is using: Transition to Algebra.
Created by EDC, Transition to Algebra (TTA) was designed with students like Donoghue’s in mind: middle- and high-school students who have struggled in math and who need support with the fundamentals of algebra. The TTA materials help develop habits such as persevering through problems and communicating about mathematical ideas that are key to success in algebra—and which are also emphasized in the new Common Core State Standards for mathematics.
What makes the TTA materials different from traditional pre-algebra programs is a focus on puzzles and mathematical discussion. Puzzles that require both logic and mathematical knowledge help build the reasoning skills needed for algebraic ideas, and teachers use these experiences to create a "culture of conversation" around mathematics.
One problem, for example, shows a small mobile with red diamonds, green clovers, orange stars, and a blue crescent hanging below. The student’s job is to figure out the value of each symbol based on the stated weight of the mobile (in this problem, the weight is 24 generic units) and its arrangement within the structure. Make no mistake—there are important algebraic ideas at work here, but the problem allows students to tackle them using their existing knowledge of balance. Lower on the same page, algebraic problems in more familiar form appear.
Donoghue believes that TTA’s puzzle approach has helped interest her students and pushed them to care more about math. "I’ve been surprised at how well the kids can understand it, because sometimes it’s hard for me to do," she says. "But I think they like knowing that it takes me a couple minutes to figure out the puzzles, too."
Fun with puzzles
EDC’s Jane Kang has been on the TTA development team for the past year. She says that although some teachers initially expressed apprehension about the puzzle-based approach during professional development workshops at the beginning of the program, seeing students enjoy—and persist with—the math problems has been an eye-opening experience.
"The teachers didn’t necessarily think that their students could do these problems," Kang says. "Experiences like the workshop got some teachers to think, 'I can do more of this in my class' and 'kids can really do this.'"
Kang has observed Donoghue as well as other teachers in Lowell and Malden who are field testing the curriculum. She thinks that the TTA approach works because it is not a skill-and-drill program.
"Students know that this is a math catch-up class, but they say they have fun," she says. "It’s important that they have good experiences and enjoy the puzzles. We want them to build a positive relationship with math."
In fact, the students in Donoghue’s class are taking a double dose of mathematics—in addition to TTA, they are enrolled in a separate Algebra I course, which Donoghue also teaches. She says that this combination of courses has helped a number of her students improve their math skills, and that many students are able to apply what they learn in her TTA section to the more formal algebra course.
Down the hall, a similar scenario is playing out in Samnang Hor’s classroom. Students huddle over problems in small clusters, and Hor glides from group to group, asking questions and delivering individual instruction. A sense of quiet industriousness pervades the room.
Like Donoghue, Hor sees some of these students twice a day—once for the math seminar using TTA and once for the regular section of algebra. "Some of them are kind of put off a little bit in the regular algebra class, whereas they like to participate a little more in [TTA] because of the puzzles," he explains.
The minutes ticking down until the end of class, Hor invites a student to the whiteboard to simplify an expression containing exponents. The student takes the marker from Hor and solves the problem as if it were second nature.
This doesn’t surprise Hor; he sees it happen often. "The Transition to Algebra approach gives them a sense of achievement," he says. "They are able to be successful."