Principles
of Mathematics Cluster
Basic Statistical Variation
Participants develop data collection, analysis,
and presentation skills; a working understanding
of measures of central tendency, variability,
and the normal curve; an increased comfort level
with statistics; and an awareness of the usefulness
of statistics to manufacturing.
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Module
College Algebra Applications
This module introduces the activity-based,
competency-based instruction in mathematics that
characterizes all the modules in the curriculum.
It reviews competencies that participants are
expected to have developed from secondary school
or from other instruction and applies them in
a variety of authentic learning tasks (ALTs).
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Module
Differentiation
The study of calculus splits into two subdivisions:
differentiation and integration. Differentiation
focuses on derivatives (the product), differentiation
(the process used to make derivatives), and some
of the various uses for derivatives.
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Module
Further Applications of Trigonometry
Further Applications of Trigonometry
introduces participants to two aspects of trigonometry:
trigonometry as it was originally—and is
currently—used for measuring large, remote,
and unreachable distances, and trigonometry as
it is used in its newer role, describing cyclical
processes.
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Integration
The study of calculus splits into two subdivisions:
differentiation and integration. Integration
focuses on the reversal of the process of differentiation
in order to determine the functional relationship
between variables. The module emphasizes the application
of integration to establish volume, velocity,
and various applications of "the area under the
curve."
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Module
Precision, Accuracy, and Tolerance
A manufacturing engineering technician must
have a thorough understanding of the importance
of precision and accuracy. This module gives participants
experience in identifying the importance of tolerances
based on customers' needs. In addition, participants
use a variety of measuring devices to learn about
precision and accuracy.
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Module
Probability, Sampling, and Hypothesis Testing
Probability, Sampling, and Hypothesis Testing
introduces participants to: modern exploratory
data analysis, randomized sampling, a working
understanding of the Central Limit Theorem, a
working understanding of error and risk, confidence
interval building/interpretation, and hypothesis
testing/interpretation. This module also helps
participants develop a new sense of appreciation
for the power of statistics and the major role
it plays in science and technology.
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Module
Statistical Distributions
Statistical Distributions introduces participants
to the analysis of statistical distributions,
including: collecting data, using graphical calculators,
and solving real-world problems. In addition,
participants learn how to determine a product
warranty period using data which illustrate normal
distribution.
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Module
Statistical Experiments
Participants gain competence in sampling, making
inferences, and testing hypotheses by designing
and conducting statistical experiments with realistic
data.
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Module
Units and Conversions
This module provides participants with an understanding
of units and conversions, including: methods for
calculating conversion factors with nonstandard
units, conversions of specifications between the
US and metric systems, advantages of using the
metric system, and problem-solving through dimensional
analysis.
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Module
Vector Analysis
Participants learn the definition of vectors,
learn how to mathematically manipulate them, and
apply them to a variety of real physical systems.
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Module
Visualizations Through Geometry
Visualizations Through Geometry goes
beyond the traditional use of geometry as a tool
for measurement, enabling participants to recognize
geometry as a carrier of other types of information
and to view geometry as a visual metaphor illustrating
relationships.
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Module
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