M 450-Applied Mathematics

Assessment Coordinator:  Lisa Davis and Mark Pernarowski

According to the below description of Applied Mathematics Program Learning Outcomes and Assessment, all six students majoring in the Applied Mathematics option who are currently enrolled in either section of M 450 were assessed for Outcomes 3 and 4. 

Outcome 3

Students demonstrate the ability to set up mathematical models and critically interpret their results.

Outcome 4

Students select and implement an appropriate mathematical technique needed to analyze and validate mathematical models.

Evaluation

One assignment was used in this assessment. Two problems selected from a midterm exam given by both instructors. Student performance on the first question was used to assess outcome 3, and student performance on second question was used to assess outcome The first question involved a dimensional analysis and subsequent interpretation of relationships among relevant physical quantities given in the problem. The second question asked students to identify dimensions relevant to the given problem, and then they were asked to non-dimensionalize the given differential equation so that the resulting dimensionless equation had a certain form.

Results

Of the six students assessed, four indicated excellent performance and two indicated acceptable performance. Of the six students assessed, two showed excellent performance, one showed an acceptable performance, two gave a marginal performance and one performance was unacceptable.

Assessed Exceptional Acceptable Marginal Unacceptable
LO 3 4 2 0 0
LO 4 2 1 2 1

Recommendations

We have no recommendations at this time.

Program Learning Outcomes

LO# Students should demonstrate the ability to:
1. Derive numerical methods for approximating the solution of problems of continuous mathematics (M 441, M 442).
2. Implement a variety of numerical algorithms using appropriate technology (M 441, M 442).
3. Set up mathematical models and critically interpret their results (M 450, M451).
4. Select and implement an appropriate mathematical technique needed to analyze and validate mathematical models (M 450, M 451).

Curriculum Map and Assessment Schedule

Course LO 1 LO 2 LO 3 LO 4 Assessment Schedule
M441 X X     Even fall semesters
M442 X X     Odd spring semesters
M450     X X Odd fall semesters
M451     X X Even spring semesters

Rubric

LO  Unacceptable Marginal Acceptable Excellent
1

The work is not correct and complete because either concepts are used improperly or key ideas are missing or the organization is unlikely to work even if a few
more ideas were inserted.

 The work is not
correct and complete because one or two
significant ideas are missing, but the terms are properly defined and the work shows a type of organization that might well work if the right ideas were inserted in the proper
places. Also, the work is "marginal" if most of the work is leading toward a correct argument, but a false statement is inserted.		 The work is almost
correct with relevant
concepts used and ideas that could work, but not well‐organized, for example, with some steps out of order, or with something relatively minor incomplete.		 The work is fully
correct and complete, with the relevant concepts properly employed and ideas that work, and the steps well‐organized into a proper sequence
2 If the work is not
correct and complete
because either there are fundamental gaps in understanding of
the underlying scientific principles or in the understanding of the appropriate technique and its implementation.		 The work is not
correct and complete because one or two
significant ideas are missing, but the majority of the ingredients are present.		 The work is almost
correct with relevant
assumptions addressed and the correct algorithm chosen with an implementation that
could work, but is
implemented with a minor misunderstanding of a technique or a minor error in other elements of the computations.		 The work is fully correct and complete, with a full
understanding of the
underlying mathematical
assumptions that deem a particular mathematical
technique applicable to a given model and with an appropriate knowledge of
the main principles and techniques related to the implementation of a particular form of analysis, mathematical or numerical.
3 The work is not correct
and complete because
either there are
fundamental gaps in
understanding of the
underlying mathematical
assumptions or in the understanding of the appropriate technique and its implementation. 		 The work is not
correct and complete because one or two significant components of the analysis or of the implementation are missing, but the majority of the ingredients are
present.		 The work is almost
correct with relevant
scientific concepts and
mathematical
techniques that could
work, but not well organized, with a minor omission,
misunderstanding, or
inadequate choice of
mathematical
technique.		 The work is fully correct and complete, with the complete understanding of the scientific principles
of the modeled problem and with employment of
the appropriate
mathematical techniques.
4 The work is not
correct and complete
because either there
are fundamental gaps
in understanding of
the underlying
mathematical
assumptions or in the
understanding of the
appropriate technique
and its implementation. 		 The work is not correct and complete because one or two significant
components of the
analysis or of the
implementation are missing, but the majority of the ingredients are present.		 The work is almost
correct with relevant
assumptions addressed
and the correct
algorithm chosen with
an implementation that
could work, but is
implemented with a
minor
misunderstanding of a
technique or a minor
error in other elements
of the computations.		 The work is fully correct
and complete, with a full understanding of the underlying mathematical
assumptions that deem a particular mathematical
technique applicable to a given model and with an appropriate knowledge of
the main principles and techniques related to the implementation of a particular form of analysis, mathematical or numerical.

Threshold

At least half of the majors in each of the courses are assessed as "excellent" or "acceptable" for all the learning outcomes. 

 

PDF of M450 Assessment Report