* A working draft of resources and reports from an NSF-sponsored
project intended to strengthen the role of mathematics in Advanced
Technological Education (ATE) programs. Intended as a resource for ATE
faculty and members of the mathematical community. Comments are welcome
by e-mail to the project directors:
Susan L. Forman or
Lynn A. Steen. *

- Selecting tasks in order to cover mathematics rather than to explore and solve interesting problems.
- Overlooking interesting or challenging mathematics that lies embedded beneath the surface of many workplace tasks.
- Imposing unwarranted structure on a contextually rich problem in the interest of ensuring appropriate mathematical coverage.
- Believing that complex problems require sophisticated mathematics and that there is something wrong with solutions that use elementary techniques.
- Choosing problems that fail to help students prepare for higher achievement in mathematics.
- Presenting workplace tasks as if they are mathematics worksheets, thereby sterilizing the context of everything that makes it problematic.
- Lacking conceptual continuity and intellectual growth in the sequencing of tasks in which mathematical activities are embedded.
- Failing to bring mathematical closure (including concepts, vocabulary, methods, generalizations) at the conclusion of an open-ended project.
- Not allowing sufficient reflection on the process of mathematical
modeling:
- on accomplishments and limitations;
- on process and results;
- on opportunities and cautions.

- Unless ATE programs make a conscious effort to support strong mathematics, they may inadvertantly widen the traditional skills gap between students aiming for a B.A. and those looking for immediate career opportunities.
- Since students tend to forget much of what they once learned in mathematics courses, there is a strong tendency to "dumb down" curricular materials to the level of what students remember rather than posing problems with whatever mathematical requirements are inherent in the problem.
- Industry's expectation of graduates' mathematical level are often not those of mathematics teachers. For both financial and legal reasons, industry typically expects the least quantitative skills required for the job. Teachers, however, expect students to learn as much as possible to ensure strong preparation for further education. To succeed, ATE projects must serve both these broader mathematics purposes as well as specific industry purposes.
- In some areas--accuracy, timeliness, clarity--industry expectations are typically much higher than those of the educational system. High performance work demands near-perfection, what industry calls "six-sigma" standards. Unless ATE programs elevate students' internal standards to match those of industry, they may leave graduates unprepared for the expectations of modern employment.
- Good problems may excite faculty so much that they forget that they are supposed to teach mathematics. Unless a conscious effort is made to bring mathematics to the foreground at appropriate places, it is easy for both students and teachers to lose sight of mathematics entirely.

**Copyright © 1999.**
*Last Updated:* October 12, 1999.
*Comments to:*
Susan L. Forman or
Lynn A. Steen.