National Council of Teachers of Mathematics--
Standards and Education-for-Work: A Promising Equation

Work in Progress at the University of Wisconsin-Madison

by Victor M. Hernández-Gantes and Lisa Nieri

In mathematics, something can be said to be "elegant" if it is useful, clear, no more complex than necessary (yet just as complex as necessary), and gets the job done. In "getting the job done" of integrating academic and hands-on education, the vision of the National Council of Teachers of Mathematics (NCTM) Standards offers some unique opportunities.


The integration of academic and vocational-technical education is central to the core principles of current school reforms in vocational education and has received much deserved attention in recent years. However, ideas of what integration means, how academic and vocational teachers can work together, and what processes and materials facilitate integration are still not quite clear. Recognizing this need for clarification, federal funding strategies and requirements have clearly suggested that curriculum and teaching efforts need to be directly aligned with a number of academic fields including mathematics, science, and communications.

Of these, the combined fields of mathematics and vocational education offer rich opportunities for teacher collaboration, as well as integrated learning opportunities for all students. The role of mathematics is clearly important given the wide range of applications in the workplace characterized by the use of complex technologies, and by the great potential for integration with technical subjects both at the secondary and post-secondary levels. The NCTM Curriculum and Evaluation Standards have provided an excellent framework to link school-based mathematics and school-to-work initiatives.

The question that remains is, how can we bring mathematics and vocational teachers together to work effectively on integration reflecting authentic teaching and learning for all students? A first step in answering this question is to identify and learn from sites with quality efforts in mathematics-vocational education integration. Thus, in the spring of 1995, staff at the University of Wisconsin-Madison began conducting a two-year project to identify and study the characteristics of integrated mathematics-vocational education initiatives in secondary and post-secondary institutions which have adopted the Standards. The objectives of the project are to:

Program Identification

The National Center for Research in Mathematical Sciences Education (NCRMSE) has conducted work designed primarily to examine how schools are implementing efforts to reform and improve mathematics instruction. Based on NCRMSE work, survey instruments were designed for this study. To choose the sites to be surveyed, selected national officers of teacher organizations, directors of mathematics and vocational-technical education, and State education department consultants were contacted in Spring 1995. These educators were asked to identify/nominate schools and two-year post-secondary institutions using the NCTM Standards and engaged in integration practices in different vocational contexts.

A total of 86 program nominations were received during the search (80 high schools, 6 two-year college programs). To determine the general nature and extent of integration efforts, a survey was conducted during the fall of 1995 asking site representatives (mathematics-vocational teachers, program coordinators) to describe: integration formats, the extent to which the Standards are being implemented, activities supporting integration, and demographic information describing the institutional profile.

Case Studies of Promising Sites

Based on survey information, four sites were selected for in-depth description of mathematics/vocational-technical education integration efforts. Selection criteria involved an analysis of the extent of: integration efforts, implementation of the Standards, and institutional support for integration practices. Selected sites include three high school programs and a community college program. This is consistent with the literature on integrating academic and vocational education which indicates a heavy emphasis on secondary forms of integration as compared to efforts in post-secondary education.

All four programs reported implementing integration in several ways, ranging from content integration by individual teachers to program-wide efforts, applying great emphasis to using the core components of the NCTM Standards, and conducting a number of supporting activities which facilitate the integration work of collaborating instructors. All in all, each program approaches integration practices in unique ways based on available resources, experience, and administrative support and leadership.

Developing an interest in learning. All programs evolved from the need to improve academic performance and student interest in learning. The typical situation before implementation of education reforms included poor academic performance and high drop-out rates. Students were not motivated to learn and teacher morale was low. The general picture across the sites was not encouraging.

New administrative personnel provided strong leadership and direction for implementing reforms. A common vision was developed by seeking guidance from organizations such as the Southern Regional Education Board (SREB), Coalition of Essential Schools, and the formation of partnerships with key stakeholders in the community. Legislation principles and documents outlining changes needed to implement education reforms were also heavily consulted and studied to reinforce a common vision for change.

The results of this process included restructuring efforts focusing on integration of academic and vocational education through career pathways, revisiting the school curriculum, gaining teacher participation, and providing relevant and timely professional development activities. To accomplish this, strong leadership and a common vision for change appeared to be critical across all the sites.

Integration Format. Integration models vary across the four sites from the simple, but functional, arrangements of a series of integrated courses and instructors collaborating, formally and informally, in teams to the concept of a magnet school. However, in each case, models were modified in a variety of ways to accommodate the specific needs and circumstances of the institution. For example, an academy format was modified to involve the whole school so as to not "let anyone off the hook" and make sure everybody had an incentive to work on integrated projects.

Math programs which were typically tracked across all sites were restructured in alignment with a thematic program, and a coherent series of "applied mathematics" courses were made available for all students at each site. Creative scheduling arrangements (for example, arena, block scheduling) were also negotiated with all faculty at each site to permit collaborative work among teachers and allow the delivery of a more flexible restructured curriculum where more common planning was required.

Another critical common characteristic includes flexible and faculty-controlled professional development activities to expose and provide instructors with conceptual and practical understandings needed for implementing integration. This was possible due to an institutional climate in which instructors are treated as professionals and because the level of trust with the administration was high. Overall, at each site there appeared to be a culture receptive to implementing much needed change.

Implementing the NCTM Standards. The restructured mathematics curriculum educators developed at each site required new ways to teach integrated concepts. Thus, a key factor for success in integrating mathematics in occupational contexts was to engage instructors in developing curriculum based on their own needs, aligned with their restructured program, and based on the NCTM Standards and SCANS competencies. Thus, the core principles underlying the Standards are emphasized across the four sites being studied.

In general, the focus on problem solving and communication skills seemed to be more prominent. Methods of assessment ranged from traditional paper-and-pencil tests to highly non-traditional strategies which are used more frequently. The strategy is to use traditional methods as a supplement to alternative strategies. For example, students are assessed with criteria checklists, communication among teachers, rubrics and portfolios of students' work. These strategies are not conducted in a routine manner. As one facilitator put it: "The assessment criteria is not just a checklist that is passed around for signatures. It is used to let the students know where they are and what they have to do to complete the activity as they go along. It is like a road map. We're always checking them off and letting them know how they're doing, if they're going in the right direction."

In encouraging students to think critically and better understand the world around them, math can be very valuable in establishing promising connections to their education and career paths. Math provides a rich source of applications for solving real-world problems encountered not only at work but in everyday activities. By exercising the power of doing math as opposed to just knowing math, students can turn an otherwise "hard" subject into an elegant vehicle for producing more authentic and lasting learning. Linking the NCTM Standards and education-for-work seems, indeed, a promising equation.

For further information about this project, please contact:

Victor M. Hernández
University of Wisconsin-Madison
964 Educational Sciences Building
1025 West Johnson Street
Madison, WI 53706-1796
Phone: (608) 265-4578
Fax: (608) 262-3063

Victor M. Hernández is an NCRVE project director and an assistant researcher at the Center on Education and Work, where he served as the principal investigator. Lisa Nieri contributed to this research as a project assistant.

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