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# Mathematical Skills Required in ATE Programs

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.

ATE projects depend on both mathematical skills and problem-solving strategies. Although problem-solving strategies are relatively similar in different contexts, required skills differ significantly from one application to another. The following inventory illustrates the range of mathematical skills found in one or another ATE setting:
• Carrying out arithmetic calculations by hand and by calculator.
• Reasoning and calculating with percentages and ratios.
• Measuring things, recognizing tolerances, estimating error.
• Using and converting among formulas, tables, and graphs.
• Calculating angles, areas, and volumes.
• Finding averages, ranges, and medians in appropriate contexts.
• Understanding and employing irrational, real, and complex numbers.
• Solving simple algebraic equations.
• Displaying data (pie and bar charts; histograms, scatter plots).
• Applying the Pythagorean theorem.
• Solving simultaneous equations.
• Using triangle trigonometry to calculate unknown lengths or angles.
• Reasoning with standard deviation and the normal error curve.
• Factoring, simplifying, and manipulating algebraic expressions.
• Proving basic theorems of Euclidean geometry.
• Sketching and calculating dimensions of three-dimensionsional objects.
• Using exponential and logarithmic functions.
• Working with trigonometric functions, and graphs
• Calculating probabilities and combinatorial mathematics.
• Using control charts and tests of statistical significance.
• Applying equations and graphs of parabolas, ellipses, hyperbolas.
• Calculating and applying derivatives and integrals.

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Supported by the Advanced Technological Education (ATE) program at the National Science Foundation. Opinions and information on this site are those of the authors and do not represent the views of either the ATE program or the National Science Foundation.

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