Mathematics For Measurement:
“Math for practical arts”
Mary Parker (mparker@austincc.edu)
and Hunter Ellinger (hunter@ellinger.org)
Saturday, January 14, 2006 Joint Mathematics Meetings San Antonio, Texas
Detailed
materials at http://www.schoolsupport.net/MFM/
Algebra
Review - Solving Equations and Evaluating Expressions
Rounding
Using
a Calculator
Formulas
- Computing and Graphing
Using
a Spreadsheet
Angles
and Construction of Diagrams
Linear
Equations - Algebra
Linear
Models - Word Problems
Introduction
to Data and Modeling
Propagation
of Errors due to Rounding
Introduction
to Trigonometry
Trigonometric
Ratios and Relationships
Computing
with Approximate Numbers: Significant Digits
Measurement
Sensitivity: Sensitivity of a Formula to Errors in Input Values
Communicating
the Results of Computing with Approximate Numbers
Curve
Fitting: Separating "Signal" from "Noise"
Describing Noise in Measured Values: Standard Deviation
Propagation
of Noise I: One Measured Input Value into a Formula.
Sine
and Cosine Formulas on Larger Intervals
Solving
General Triangles
The
"Ambiguous Case"
Removing Bias from a Measurement Process: Calibration
Propagation of Noise, Part II: Averaging Multiple Measurements
– A Useful Rule
Propagation of Noise, Part III: Combining Measured Input
Values – Empirical Method
Propagation of Noise, Part IV: Combining Measured Input Values – Other Rules
Solving Applications Problems (students select project problems from teacher-supplied list)
The main purpose is to make connections between mathematical thinking and the sophisticated practical thinking of which students are already capable.
The urgency of this goal stems from the deep alienation from mathematics that the majority of students feel by the time they enter college.
The standard school sequence is simplistic applications of increasingly sophisticated techniques, rather than the increasingly sophisticated application of simple techniques that would be much more effective.
Sophistication is largely drawn from concepts (e.g., measurement-process stability) that students have already developed in practical contexts – MFM is a course designed for adults
Practical arts majors form a significant minority of the enrollment of American community colleges -- more focused, attention to individual topics is more dependent on the perceived relevance, often active resistance to abstract generalizations. But substantial practical vocational experience, skill at detecting the oversimplifications.
MFM is an attempt to recapture “sophisticated application of simple techniques” while also enhancing student competence with important tools (e.g., spreadsheet programs, technical drawing), concepts (e.g., noise propagation, error sensitivity), and techniques (e.g., curve-fitting, practical trigonometry).
Measurement is an area with which almost all adult have substantial experience, is relevant to almost all vocational areas, is connected to math requiring only limited prerequisite skills, is of immediate utility (practical & math), is related to advanced topics, and is well suited for investigation with spreadsheets (a robust tool of lifelong utility).
[1]
Enable students to state much of their existing quantitative knowledge about
their areas of specialization in terms of numeric values and appropriate
formulaic relationships, and give them confidence in the utility and relevance
of such statements.
[2]
Enhance the ability of students to communicate on measurement-related matters
with engineers or similar mathematically-adept leaders of their communities of
vocational practice.
[3]
Provide, for each area of mathematical technique learned, concrete methods that
can be used to check, illustrate, and approximate it (such as graphs for
functional formulas and scale diagrams for trigonometric problems).
Diagrams Spreadsheets: formulas, data, fitting, statistics RoundingàApproximationàNoise
Cross-references to slope, graphing, approximation, formulas, calculators, trigonometry
Noise measurement, propagation (both empirical and theoretical); calibration for errors
PRELIMINARY