Two Approaches to Problem Solving: An Outline
Modeling with Data: Empirical Modeling
Demonstrate the following steps in fitting a model to data relative
to a phenomenon.
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Formulate the key problem or question. (Understand the problem.)
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Communicate your preconceptions.
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Discuss the limitations, assumptions, and scope of your investigation.
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Collect and organize data.
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Analyze and interpret data.
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Choose and fit an appropriate model by varying parameters and testing goodness
of fit by an identified numberical criterion (sum of errors, average error,
percent error).
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Summarize and report findings. (Reflect, describe, formulate, evaluate,
support, generalize, and suggest.)
Modeling from Theory: Mathematical Modeling
Demonstrate the following steps in solving a real world problem.
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Understand the problem.
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Identify the important features.
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Make assumptions and simplifications.
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Define variables.
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Use sub-models.
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Establish relationships between variables.
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Solve.
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Interpret, validate, and critique the model.
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Make improvements.
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Explain the outcome.
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Prepare a report.
Always demonstrate appropriate and effective use of technology
in executing the steps in either of the two processes.
Here are some actions to avoid in the model development
phases of exercises. However, these actions may be employed in the
evaluation or critique of your models if you give reference credit to the
device, software, or source:
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The use of a calculator’s or software application’s pre-programmed curve
fitting procedures.
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Copying a formula or rule from a reference source..
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