Results from a National Study of Mathematics in Career and Technical Education

A Forum — January 26, 2007

Many high school students, particularly those enrolled in career and technical education (CTE) courses, do not have the mathematical skills necessary for today’s jobs or college entrance requirements. Mathematical concepts are found in all areas of CTE, but are often not explicitly visible to teachers and students. The National Research Center for Career and Technical Education (NRCCTE) recently completed a group randomized trial (GRT) study designed to test a model for enhancing mathematics instruction in high school CTE courses by emphasizing the mathematic principles already embedded in the CTE curriculum. The project was designed to help CTE students make meaningful relationships between basic mathematical principles and related concepts in their CTE classes.  To achieve this, CTE teachers in the experimental group were coached by math teachers on how to enhance and teach the mathematical principles naturally occurring in the CTE curriculum.  Students would then be able to manipulate concepts from either class and apply them accordingly.  Presenters at this forum included the research director, two teachers who are using the tested model, and the program officer from the U.S. Department of Education which funded the research.

Ric Hernandez, Program Officer in the U.S. Department of Education (ED) Office of Vocational and Adult Education, noted that the recently reauthorized Perkins Act calls for dissemination of research on best practices that improve career education. ED is working to improve research rigor and the project discussed at this forum addressed four key research priorities: mathematics, secondary schools, professional development, and student achievement data.

James R. Stone III, Director of the National Research Center for Career and Technical Education, called attention to the fact that scores on the National Assessment of Educational Progress (NAEP) have moved very little in thirty years even though students are taking more math and science. Therefore, as he says, “we need to look at how we are teaching math.” The context of CTE courses is rich in math even though these courses do not emphasize development of math skills. A goal of the Math-in-CTE research was to test the possibility that enhancing the embedded mathematics in technical education courses could build math skills without reducing technical skill development.

Stone explained that volunteer teachers in auto technology, information technology, agriculture, health occupations, and business/marketing were randomly assigned to experimental or control groups. Many of the CTE teachers had no math training and some did not have a college degree. CTE and math teachers worked together to create lessons that focused on the naturally occurring math in the curriculum. Teachers in the control classes were to follow their existing lesson plans with no changes.  Ongoing direct and indirect math support was provided to the CTE teachers in the experimental group throughout the school year. All participating teachers in experimental and control classes received a stipend.

The Math Enhancement Process being tested included seven elements of pedagogy:

• introduce the CTE lesson

• assess students’ math awareness

• work through the embedded example

• work through related, contextual examples

• work through traditional math examples

• demonstrate students’ understanding

• formal assessment

CTE lessons were able to address such math concepts as number relations, computation, measurement, geometry and spatial sense, statistics and data analysis, patterns, functions, algebra, and problem solving. In some cases, the lessons refreshed or reinforced material students had seen earlier in their math classes.

After one year in which about 10% of class time was devoted to math-enhanced lessons, students in the experimental groups performed significantly better than the control classes on two of three standardized tests (TerraNova and Accuplacer). There was improvement on the WorkKeys test as well, though it was not considered enough to be statistically significant. In four of the five career areas, there was no difference in retention and development of occupational skills. In the fifth area, there was a large improvement in skill development which Stone attributed to the math-rich content of the occupation itself.

Stone identified several keys to success for this Math-in-CTE model:

• Develop and sustain a true community of practice between CTE and math teachers;

• Begin with the CTE curriculum, not with the math curriculum;

• Understand math as an essential workplace skill;

• Maximize the math already inherent in the CTE curriculum; and

• Enable CTE teachers to become teachers of “math-in-CTE”, not math teachers.

Stone believes a particularly significant indicator of the model’s success is the fact that 70% of the teachers who used it during the study continued using the model even after the study was over and they were no longer being compensated. Teachers in the control group had been given all the materials at the end of the study but only 20% were following the model. “This shows the value of intensive professional development,” said Stone.

Stone said there are other areas that could be evaluated. Additional research could test a model focusing on math throughout a program, not just in a single class. It might also be possible to focus on other academic subjects within the CTE curriculum, such as science or literacy. But there is also a tipping point – how much math (science, literacy) can you include in a class before it is no longer a CTE class?

With state education requirements demanding more years of math in their curricula, CTE courses could provide a viable alternative for students to earn the needed math credits to graduate high school.  Stone explained that while awarding math credits for CTE courses using mathematical principles is a positive step, CTE teachers and administrators should be cautious.  Once CTE courses gain mathematic applicable credit, CTE instructors may find more restrictions and guidelines to ensure that math is actually being taught to their students.  In addition, many of the CTE instructors are not professionally trained as math teachers.  Stone raised the concern that in time, CTE courses could disappear and simply become another math class for students to enroll in.  Additionally, students may not be attracted to CTE courses if the curriculum becomes too mathematically-focused.

Stone concluded that Math-in-CTE is a powerful, evidence-based strategy for improving student math skills; it is a way but not necessarily the only way to help high school students master math. It is not a substitute for traditional math, but CTE classes can be a lab to help students master what they do not understand. The National Research Center is now providing technical assistance in four states interested in developing the Math-in-CTE model. Stone suggested that working with states, rather than school districts, in order to create larger communities of practice and enable teachers to collaborate outside their own schools, might be an effective strategy.

Jeff Linko and Joe Fullerton are both teachers at Lenape Technical School in suburban Pittsburgh. Linko is a teacher in the automotive repair program. Fullerton is a math teacher and program development specialist. They worked together during the Math-in-CTE study. Their collaboration was critical, according to Linko, who said the math teacher guides the CTE instructor through the difficult steps.

Fullerton said CTE made math relevant to students for whom content has to pass the ‘who cares’ test. “I would teach a formula in math and a student would say, ‘hey, we’re learning that in auto tech’ and everyone in class sees that the kid who’s usually goofing off suddenly knows something, so interest in math spreads.” Fullerton said students see a connection between their technical area and math class and they begin to take ownership of the learning process. “Our test scores aren’t as high as we’d like, but they are improving, and it’s a direct impact of what we do with this study,” concluded Fullerton.

Linko believes test scores improved in part because students developed a common vocabulary between math and auto tech. The bore of a piston is the same as the diameter of a circle; the stroke of a piston is also the height of a cylinder; piston displacement is the same as volume. The students who had taken higher level math courses used mathematical formulas in auto tech; other students linked standardized test questions to the auto tech examples. Linko said the Math-in-CTE program worked for all levels of students because students were able to help each other. Linko said the auto tech students became more comfortable asking and answering math-related questions; as a teacher, he became more comfortable explaining basic formulas used by auto technicians.

Fullerton said students from other career areas began to make math connections to their disciplines on their own.  In the end, both Linko and Fullerton said that other teachers in other disciplines wanted to learn more and participate in the process.

The results achieved in this study did not require school-wide reform efforts such as leadership or cultural changes. The improved mathematical performance of the students in the experimental groups was produced by assembling teams of teachers in a single occupational area and providing them with a process and a pedagogy through which they could successfully enhance the math in their own curricula. Essential to the model was the ongoing teamwork between CTE instructors and their math partners in an authentic community of practice.

Highlights from Question and Answer Session

 

In response to a question about the need for students to learn algebra instead of other kinds of math, Hernandez said studies consistently show that algebra is a gateway course to postsecondary success because of the rigor it requires. Stone acknowledged that there is some algebra that is needed to be successful in the workplace, although he argued for giving more importance to statistics. ACT has published a report, Ready for College Ready for Work, which documents the need for math skills in work. (http://www.act.org/path/policy/pdf/ReadinessBrief.pdf)

When asked if the Math-in-CTE model could be extended to comprehensive high schools or other subject areas such as dance or history, Fullerton said the challenge would be making non-math teachers comfortable teaching outside their subject expertise. Stone said the approach of addressing real problems in real settings could extend to other academic areas. “We compartmentalize too much in high school,” he added. “Elementary school is much more holistic.”

Stone was asked if the Math-in-CTE model worked because it was tested with willing volunteers rather than the CTE workforce as a whole. He acknowledged that the test group was a select group. Using product marketing analogies, Stone said that if you can get the innovators and early adopters in any group to buy into a plan, you are more likely to have success with the broader population. He also recommended that this teaching model be included in the pre-service curriculum for teacher education.

Hernandez said federal officials were particularly impressed that the people who participated in the Math-in-CTE study wanted to continue using the model after the study and the funding ended.

 

Resources

Building Academic Skills in Context: Testing the Value of Enhanced Math Learning in CTE -  full report http://www.aypf.org/forumbriefs/2007/Resources/MathLearningFinalStudy.pdf

National Research Center for Career and Technical Education http://www.nccte.org/

Lenape Technical School http://www.lenape.k12.pa.us/

Presenters Bio

Dr. James Stone is a native of Washington D.C. He earned his B.S. and Ed.D. degrees at Virginia Polytechnic Institute and State University and a Master’s in School Administration at George Mason University. He currently is a professor in the Department of Work and Human Resource Education at the University of Minnesota.

Dr. Stone was part of the team that developed the successful bid for the National Centers in Career and Technical Education (1999), where he served as the Deputy Director of the National Research Center for Career and Technical Education with responsibilities for developing new research initiatives. He has served as Director since August 2002. He has also served on the Editorial Board of the Journal of Vocational Education Research and as Editor.

Responsible for more than $5 million in external grants focusing primarily on the role of schools in linking youth and adults to the workplace, Dr. Stone has maintained an active program of research over the past twenty years. He directed or co-directed eight studies in the National Center for Research in Vocational Education. He is the lead researcher on the Math-in-CTE study and he has authored or co-authored more than 60 research reports, journal articles, or books. Nine of his studies received outstanding research awards. Dr. Stone has also presented more than 200 papers, speeches and workshops.

Beyond the traditional forms of disseminating research results, Dr. Stone has worked directly with schools and school systems supporting efforts to improve occupationally oriented education. He worked for more than five years with Oakland California Public Schools helping to implement a community based, school-to-work plan that included career academy development and school-based enterprises. He worked with a Minneapolis high school in partnership with the American Indian OIC to develop a program targeted at urban Indian youth. He recently completed a study of postsecondary occupational/technical education in Minnesota. Dr. Stone is currently working with school districts and states interested in implementing the Math-in-CTE approach to curriculum integration.

Dr. Ricardo (Ric) Hernandez is the Lead Research Analyst in the Policy, Research, and Evaluation Staff of the Office of Vocational and Adult Education, U.S. Department of Education.  He has been with OVAE for nine years and was the Branch Chief of the Program Improvement Branch under the prior Division of National Programs and has been responsible for managing a variety of research activities in CTE as well as Adult Education. One of his major project management responsibilities is the National Research Center for Career and Technical Education.  He has worked closely with the Dr. Stone to develop the Center’s research portfolio for each year of its grant.   The Math-in-CTE study was a result of this collaboration between the National Center and OVAE.  Dr. Hernandez has a Masters (MS) and Doctorate (Ph.D.) in Adult and Vocational Education from the University of Connecticut.

Joseph Fullerton, a 1997 graduate of Slippery Rock University of Pennsylvania, has been at Lenape Technical School for the past eight years. He began as a math teacher, focusing on algebra and statistics. For the past three years, he has been the Program Development Specialist, focusing on curriculum at Lenape and career awareness for Armstrong County. Fullerton has also been an active participant in the National Math Study.

Jeff Linko, a graduate of Indiana University of Pennsylvania, has been teaching at Lendape Tech for 18 years. Linko is ASE certified in all eight areas of automotive repair. He has been an active participant in the National Math STudy and is a proponent of teaching mathematics/automotive technology to all students.

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