School & District Management

Teachers Helped to Mine Vocational Classes For Math

By Sean Cavanagh — February 06, 2007 7 min read
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Jeff Linko began his career in an auto dealership, as a mechanic for DaimlerChrysler. Life under the hood suited him. He specialized in transmissions, though he could also repair brakes, steering, air conditioning systems—pretty much anything—with confidence and joy.

A few years later, he began a career in teaching, hoping to foster that passion among high school students in auto-technology classes. Over time, though, he realized that his gifts as a mechanic masked his shortcomings in another area crucial to his teaching: mathematics.

“When I got to math, I would feel very, very vulnerable. I couldn’t make the connections,” Mr. Linko said. “I thought, it’s about time I got comfortable with this.”

Read a summary of “Building Academic Skills in Context: Testing the Value of Enhanced Math Learning in CTE,” posted by the National Research Center for Career and Technical Education. The full text of the report also is available.

Today, the teacher from Lenape Technical School in Ford City, Pa., is more at ease with the subject, and he believes he’s more effective at presenting it to students. He gives credit to a new instructional model he followed that seeks to identify and expand the use of math already found in career and technical courses, in subjects from auto repair to health to business marketing.

That classroom model was designed by researchers at the University of Minnesota-Twin Cities, who recently conducted a national study to gauge its effectiveness in improving students’ math achievement. The results have encouraged supporters of career and technical education, also known as vocational education. Students in the study saw their scores rise on two prominent tests of math ability, after receiving instruction through the classroom model.

“We’re not telling teachers to teach anything different—only to emphasize math when appropriate,” said James R. Stone, the director of the University of Minnesota’s National Research Center for Career and Technical Education, and the study’s principal author. “It’s about getting teachers and students to see math as a tool to solve a workplace problem. The effect is that kids no longer fear math.”

Don’t Force It

The university research center worked with 131 career and technical education teachers and about 3,000 students in conducting the study during the 2004-05 academic year. Teachers like Mr. Linko went through several days of training, aimed at helping them identify and emphasize “naturally occurring” math within their occupational classes. The idea was not to have teachers seek to force algebra, geometry, or statistics into vocational class outside their natural contexts.

“You can’t just walk into a career and technical education class and say, ‘Today, kids, we’re going to talk about math,’ ” Mr. Stone said in an interview last month.

He later explained his findings at a Jan. 26 seminar on Capitol Hill, attended by congressional aides, lobbyists, school and youth advocates, and others. The event was arranged by the American Youth Policy Forum, a Washington nonprofit organization that supports college- and workforce-preparation efforts.

Improving the academic quality of occupational courses can have a major impact, Mr. Stone argued. Ninety-five percent of public school high school students take at least one vocational course, and more than one-third take three or more classes. Mr. Stone sees potential to strengthen vocational students’ skills in other academic areas, such as science and literacy, using approaches similar to the math model tested in his study.

‘Embedded’ Math

Backers of career and technical education have sought for years to dispel the idea that those classes do not challenge students academically.

In 2004, a federal report to Congress found that vocational students lagged behind their peers in reading and math achievement. That study also found that teachers of those courses had poorer state-licensure scores and were less likely to have a four-year college degree than educators in other subjects.

But supporters of such programs say test scores and other measures are deceiving, because many students who enroll in career and technical courses come with long-standing academic weaknesses.

Vocational students can succeed in math if it is presented in a less abstract way, said Jo Boaler, who has researched that issue extensively. Ms. Boaler, an education professor at Sussex University, in England, has studied vocational students after they enter the workforce; she found that many were astonished at how relevant—and digestible—math became upon leaving school.

Mechanical Devices

A research project by University of Minnesota scholars tests the effects of a strategy for helping career and technical teachers identify and emphasize the math lessons in their occupational courses. A participant from a Pennsylvania high school uses a common formula in his auto-tech class for that purpose.

Teacher Jeff Linko at Lenape Technical School uses a formula for piston displacement that describes the cycle of a piston in a car:


Mr. Linko then uses that formula to introduce students to the mathematical formula for the volume of a cylinder, which they are likely to encounter in math classes and standardized tests:


SOURCE: National Research Center for Career and Technical Education

They said, “ ‘Now I’m in my work, I see math everywhere,’ ” Ms. Boaler said. “ ‘Why didn’t I get this in school?’ ”

Ricardo A. Hernandez, the lead research analyst in the office of vocational and adult education at the U.S. Department of Education, which financed the Minnesota study, said federal officials are trying to encourage more high-quality research on effective strategies for improving the academic quality of vocational programs. The new study meets those higher standards, he said.

Participating teachers in the Minnesota study, who were volunteers, were asked to follow seven general principles in identifying and enhancing math topics in career and technical classes. Those guidelines include gauging students’ math knowledge beforehand; using “bridging language” to move students from “shop talk” to “math talk,” as Mr. Stone puts it; and gradually shifting to more math-specific language that students would likely encounter in math classes and tests.

Many of the vocational teachers participating in the study, Mr. Linko included, had taken little math coursework beyond high school. He and other teachers were asked to find math teachers—preferably in their own schools—to tutor them and help them present math in vocational settings.

Mr. Linko worked with Joe Fullerton, an administrator at Lenape Technical School and a former math teacher. They attended the research project’s training sessions together, and met during the year to craft lessons.

One piece of math they decided to highlight in Mr. Linko’s auto-tech class emerged out of a formula the teacher uses to describe the stroke of an auto piston. (See above chart.) That formula uses the number 4 as its denominator. Occasionally, a student would ask Mr. Linko what the 4 stood for.

“I’d have to tell them I didn’t know,” he admitted.

Mr. Fullerton helped him use the piston calculation to move to a more math-specific formula, to measure the volume of a cylinder. Now, if students encounter the math formula in class or on a test, they will recognize it, the two men say.

“Our test scores are increasing,” said Mr. Fullerton, referring to the Pennsylvania state exams. “I really believe that’s a result of what we’re doing in the study.”

Test-Score Gains

The study’s researchers cite other ways teachers can mine math embedded in their career and technical courses.

Teachers in construction classes often use what is known as the 3:4:5 ratio in measuring angles; that language can lead students into a deeper understanding of the Pythagorean theorem, for example. In business and marketing classes, students are told about “maximizing” profits and “break even” points, concepts that can help them understand linear programming, the authors say.

Unlike some vocational education strategies, the study did not allow for team teaching. Teachers such as Mr. Linko were expected to cover all the math on their own, and consult with math tutors outside class. Having teachers with separate skills teaching separate concepts, the study’s authors reasoned, would encourage students to think of math as isolated from career and technical lessons.

Students taking part in the study were pretested on three assessments: TerraNova, an international test of math ability; Accuplacer, a college-placement test administered by the College Board; and WorkKeys, a test designed by ACT Inc. that the authors saw as connected to workforce skills.

At the end of a year using the study’s model, students’ scores on TerraNova and Accuplacer rose by statistically significant margins. Scores on the WorkKeys test also rose, though by less than 1 percent, not considered significant.

Perhaps most impressively, the researchers say, students taught using the study’s model made strong gains when compared on a curve against their peers—scoring in the 71st percentile of those who were not exposed to the model, on the TerraNova test.

During his presentation in Washington, Mr. Stone noted that the math performance of U.S. high school students on the National Assessment of Educational Progress has remained mostly flat for three decades. That stagnation has occurred despite rising state and local academic requirements in math, and an increased number of academically demanding courses. Policymakers, Mr. Stone suggested, need to promote math learning in different contexts—including career and technical education—if they want to reach more students.

“Maybe it’s not how much we offer kids during that high school experience,” Mr. Stone said, after presenting a graphic showing the flat NAEP scores, “but how we offer it.”

Coverage of education research is supported in part by a grant from the Spencer Foundation.
A version of this article appeared in the February 07, 2007 edition of Education Week as Teachers Helped to Mine Vocational Classes for Math


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