A half-dozen high-school math students tell a remarkably similar story. Last year they didn't understand algebra. They came to class, listened to the teacher, tried to do the homework...
A half-dozen high-school math students tell a remarkably similar story.
Last year they didn’t understand algebra. They came to class, listened to the teacher, tried to do the homework and failed.
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This year, using a computer-based program called Cognitive Tutor, these students are progressing steadily and staying engaged.
Mukilteo, Everett and Marysville high schools are among about 60 schools in the state that are turning to the software program to teach math to struggling students. Research indicates that Cognitive Tutor, an interactive program that analyzes students’ strengths and weaknesses and allows them to work at their own pace, significantly increases math skills.
Teachers are excited about the results, particularly among students who had given up on math. But the computer-based program is expensive. Mariner High School in the Mukilteo district needed to build and equip a computer lab before school started in September. The software can be more costly than a standard mathematics textbook.
“We purchased it because we saw the good results in other districts,” said Lloy Schaaf, the director of curriculum and professional development for Mukilteo schools. “Integrating technology and cooperative learning in math seemed to have a huge impact.”
In comparisons made over the past two decades, U.S. students’ math skills have lagged behind those of other developed countries. On the high-stakes Washington Assessment of Student Learning (WASL), math scores at many schools are significantly lower than reading and writing scores.
Algebra is where many students lose their way because the mathematics begins to get abstract, said Steve Ritter, the head of research for Carnegie Learning, a private educational-technology company that markets Cognitive Tutor. He said the math program tries to make the subject more concrete by bridging from students’ life experiences to problems that can be solved by algebraic equations.
The Cognitive Tutor program also differs from traditional algebra classes in that it provides immediate feedback. Instead of making the same mistake on a dozen homework problems, a student finds out right away if his or her approach is wrong.
Developed by learning theorists at Carnegie Mellon University, Cognitive Tutor is one of the few math programs to be included in the national What Works Clearinghouse, which identifies programs and products whose effectiveness is backed by scientific evidence.
Administrators in Mukilteo said they used federal grants and “scraped and scratched” to purchase Cognitive Tutor for the district’s two traditional high school and its alternative high school. The district is paying about $52,000 for a seven-year site license, which breaks down to about $60 per student using the program. Math textbooks sell for $55 to $80.
Some smaller districts and individual schools say the cost prevents them from offering Cognitive Tutor despite its demonstrated success.
Ritter acknowledged that in the past the program had been priced too high for many smaller schools and for schools that wanted to use it for only one or two classes. But he said the company adjusted its pricing in June to permit a single class of students to use it for $1,725 a year.
Results “really exciting”
At Mariner High, students in first period Algebra 1A sit in a darkened computer lab working intently at a series of problems. These are students who failed a previous math class or who teachers thought could benefit from a more hands-on, investigative approach. About 350 mostly freshmen and sophomores are enrolled at Mariner, or about one in four students at those grade levels.
On the computer screen, Cognitive Tutor poses real-world questions, such as how long it takes an airplane to fly from Sydney, Australia, to San Francisco and how much time it takes to reach points along the way.
Each problem involves writing an equation, solving for a variable and plotting the answers on a graph.
Teacher Kathleen Church said she has been amazed at both the sophistication of the math and the number of students who previously would have “completely tuned out by now.”
“The results are really exciting,” she said. “I can’t wait to see their test scores.”
In the computer lab, students can ask for hints from the Cognitive Tutor program. The software, which employs a form of artificial intelligence, offers guidance and repeats similar types of problems until the student masters a skill.
The program isn’t teaching the kids by itself. Students spend part of their time in the lab and the rest in class, where Church uses a workbook and group exercises that are part of the Cognitive Tutor curriculum package.
“Most of these kids haven’t had success in the past,” Church said. “They may not have passed a math class in three years. Now they’re saying, ‘I can do this.’ “
Justin Akins, a ninth-grader, has progressed through problems at a quicker pace than any other student in class.
Last year, he said, he “wasn’t so good.” This year?
“I’m moving pretty fast.”
College now “on radar”
Gary Plano, a former Mukilteo curriculum director who is now with the Kent School District, said Kent officials realized about four years ago that many ninth-graders weren’t being exposed to the concepts on the 10th-grade WASL.
He said the district searched for a program capable of teaching algebra to ninth-graders who weren’t performing at their grade level. The district in 2001 launched a pilot study of Cognitive Tutor with 150 students who hadn’t taken algebra.
At the end of the first year, 90 students wanted to continue with Cognitive Tutor geometry. At the end of the third year, 30 students elected to take advanced algebra or trigonometry.
“This group of students would never have taken algebra or geometry, and now they had four-year universities on their radar,” Plano said.
Plano also did his doctoral dissertation about the effectiveness of Cognitive Tutor in the Kent School District during the 2002-03 school year. All eighth-grade students who received lower than a C in math were assigned Cognitive Tutor for ninth-grade algebra. Students with a C or better were assigned to a traditional algebra course.
The gains made by the Cognitive Tutor students were “significantly greater” than the gains in the conventional class, Plano said. The gains were even more pronounced for students learning English and for low-income students, he said.
“The role of teacher changes to become more of a facilitator and coach rather than a person imparting knowledge,” Plano said.
But he was quick to add that the personal relationship between teachers and students is one of the keys to successful learning.
“Some people have voiced a fear that teachers will be replaced by machines and computers,” he said. “I don’t believe that will happen.”
Kevin Judd, a former Mukilteo math teacher who now works for Carnegie Learning, said he has heard criticism that the transition from the interactive computer program to a traditional text-based math class can be difficult.
“It’s a different kind of learning. I don’t think it’s a problem of the software but of the transition,” Judd said.
At Mariner High, Church said she wants kids to realize they can succeed.
“My goal is they’ll walk out of here ready to try another year of math,” she said.
Lynn Thompson: 425-745-7807 or firstname.lastname@example.org