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Section 3
3.1
Expression of Departmental philosophy and mission in terms of Departmental
student learning outcomes (for each major/track! concentration)
As stated in Section 1.1 the mission of the Department is to provide a large and diverse student
population with high quality programs that combine a thorough foundation of applicable
mathematical techniques with a theoretic background and training in critical thinking. Students
can succeed in careers if the set of skills, knowledge, and dispositions they possess is sufficient
enough to guarantee a lifetime of continued intellectual growth. For a mathematician, these traits
are embodied in his/her analytical, computational, and communication skills. In addition to
possession of such skills a student's success depends on their ability to apply these skills and
knowledge in a deliberate way to solve problems and make decisions. Students that are adept at
this are highly sought after by graduate schools and employers.
Therefore, in order to maximize a student's success, the Department's curricula and associated
student learning outcomes feature six main areas, which together provide a focus for our
program. These six areas include:
1. Mathematical Understanding
2. Algorithmic Thinking
3. Critical Thinking
4. Problem-solving and Modeling
5. Technology
6. Active-learning and life-long learning
As seen in Matrix 1, students are exposed to many of the Student Learning Outcomes in multiple
courses. We believe that we have been successful in achieving most (if not all) of these
outcomes. In order to demonstrate this, the Department has implemented an ongoing Outcomes
Assessment Plan. The Plan can be found in Appendix 9 and the results are in Section 6.
3.1 Department's Student Learning Outcomes
The student learning outcomes listed below are the outcomes for the Major in Mathematics as
well as the Minors in Mathematics and Mathematics/Statistics.
Student Learning Outcomes
1. Mathematical Understanding: The Relationships between mathematical ideas
We list below specific objectives for this area; to avoid constant repetition we omit “the
student...".
A. Supplies reasons for steps that are justifiable in a given computation, construction or proof,
showing a comprehension of the use of definitions, axioms, and theorems in carrying out a
coherent proof.
B. Rephrases mathematical ideas in equivalent linguistic form.
C. Describes, verbally or in a written essay, relationships among concepts within a single area
,
of mathematics studied by the student.
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D. Describes, verbally or in a written essay, interrelationships between different areas of
mathematics.
E. Indicates insight into mathematical phenomena; sees how and why the facts are part of a
larger body of knowledge.
F. Reads and interprets mathematical writing that is new to the student, but that relates to the
topics that are a part of the student's program.
G. Writes clear, correct mathematical exposition.
H. Generalizes facts and concepts in a broader theory.
I. Demonstrated correct use of mathematical notation and data types.
J. Describes the abstract unity behind mathematical systems of various types, demonstrating
a comprehension of concepts such as isomorphism and congruence, homomorphism and
similarity.
1. Algorithmic Thinking
A. Uses algorithms that are found by others.
(i)
Executes algorithms and draws the appropriate conclusions
(ii)
Describes the sequence of steps for standard algorithms
(iii)
Is able to program a calculator or computer to perform standard algorithms
B. Understands the logic behind algorithms
(i)
Recognizes when the hypotheses hold that permit an algorithm to be used.
(ii)
Explains what may go wrong with an algorithm when hypotheses are ignored.
(iii)
Explains why an algorithm works, using good notation and appropriate
diagrams.
(iv)
Devises variations of known algorithms.
C. Designs new algorithms to solve problems
(i)
Identifies a class of problems solvable by a common process.
(ii)
Estimates the complexity of an algorithm and replaces cumbersome ones by
more efficient procedures.
3. Critical Thinking
A. Identifies the assumptions that lie behind mathematical models.
B. Discusses the hypotheses for mathematical theorems, and gives counterexamples to show
that hypotheses cannot be weakened.
C. Gives counterexamples to show when converses of theorems fail.
D. Discusses consequences of ignoring one or more of the hypotheses of a theorem, or one or
more assumptions underlying a model.
E. Explores alternative definitions of mathematical concepts and alternative sets of
hypotheses to improve theorems and mathematical models.
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4. Problem-solving and Modeling
A. Models mathematical and applied problems.
(i)
Constructs diagrammatic problem representations that reveal the underlying
structure of a given problem.
(ii)
Sets up one or more mathematical equations or inequalities whose solutions
approximate the solutions of a real-life problem.
(iii)
Applies known models to analogous situations.
B. Uses an organized, coherent plan to search for a procedure that leads to a solution to a
given problem.
(i)
Breaks a problem into simpler component parts.
(ii)
Solves similar problems for simpler special cases to gain insight into the main
problem.
(iii)
Reduces the given problem to one already solved, that is, uses the
transform/solve/invert technique.
5. Technology
A. Uses calculators and computer software to implement mathematical algorithms.
B. Carries out calculator and computer experiments to gain insight into mathematical
phenomena.
C. Makes conjectures based on experimental results, and uses further calculator and computer
explorations to refute the conjectures or gather additional evidence supporting the
conjectures.
D. Writes programs for programmable calculators or computer to carry out numerical and
graphical algorithms.
6. Active learning and life-long learning
A. Independently explores mathematical concepts.
(i)
Reads mathematical books and articles independently.
(ii)
Reports orally or in writing on results of investigations, historical development
of topics in mathematics, or solutions to problems.
B. Discusses mathematics with fellow students and faculty.
C. Participates in Seminars, problem solving sessions, or out-of-class presentations on
mathematics.
D. Forms allegiances to mathematics through memberships in professional societies or
professional friendships.
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Matrix 1: Departmental Student Learning Outcomes and Required courses in which the students are exposed to the knowledge, skills, and
dispositions related to each outcome for the Mathematics Major
SLO #
Department Student learning Outcomes
Course(s) where the SLO is met
1.
Mathematical Understanding: The Relationships between mathematical ideas
1.A
Supplies reasons for steps that are justifiable in a given computation, construction or
proof, showing a comprehension of the use of definitions, axioms, and theorems in
carrying out a coherent proof.
281, 424, 425, 457
1.B
Rephrases mathematical ideas in equivalent linguistic form.
281, 424, 425, 457
1.C
Describes, verbally or in a written essay, relationships among concepts within a single
area of mathematics studied by the student.
281, 424, 425, 457
1.D
Describes, verbally or in a written essay, interrelationships between different areas of
mathematics.
281, 424, 425, 457
1.E
Indicates insight into mathematical phenomena; sees how and why the facts are part
of a larger body of knowledge.
281, 424, 425, 457
1.F
Reads and interprets mathematical writing that is new to the student, but that relates
to the topics that are a part of the student's program.
281, 424, 425, 457
1.G
Writes clear, correct mathematical exposition.
281, 424, 425, 457
1.H
Generalizes facts and concepts in a broader theory.
201, 202, 203, 281, 346, 446, 424, 425, 457
1.I
Demonstrated correct use of mathematical notation and data types.
201, 202, 203, 281, 346, 446, 424, 425, 457
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1.J
Describes the abstract unity behind mathematical systems of various types,
demonstrating a comprehension of concepts such as isomorphism and congruence,
homomorphism and similarity.
2
Algorithmic Thinking
424, 425, 457
2.A
Uses algorithms that are found by others.
281
2.B
Understands the logic behind algorithms
281
2.C
Designs new algorithms to solve problems
281
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3
Critical Thinking
3.A
Identifies the assumptions that lie behind mathematical models.
201, 202, 203, 281, 346, 446
3.B
Discusses the hypotheses for mathematical theorems, and gives counterexamples to
show that hypotheses cannot be weakened.
281, 424, 425, 457
3.C
Gives counterexamples to show when converses of theorems fail.
281, 424, 425, 457
3.D
Discusses consequences of ignoring one or more of the hypotheses of a theorem, or
one or more assumptions underlying a model.
281, 424, 425, 457
3.E
Explores alternative definitions of mathematical concepts and alternative sets of
hypotheses to improve theorems and mathematical models.
281, 424, 425, 457
4
Problem-solving and Modeling
4.A
Models mathematical and applied problems.
201, 202, 203, 346, 446
4.B
Uses an organized, coherent plan to search for a procedure that leads to a solution to
a given problem.
201, 202, 203, 346, 446
5.
Technology
5.A
Uses calculators and computer software to implement mathematical algorithms.
201, 202, 203, 346, 446
5.B
Carries out calculator and computer experiments to gain insight into mathematical
phenomena.
201, 202, 203, 346, 446
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5.C
Makes conjectures based on experimental results, and uses further calculator and
computer explorations to refute the conjectures or gather additional evidence
supporting the conjectures.
201, 202, 203, 346, 446
5.C
Writes programs for programmable calculators or computer to carry out numerical
and graphical algorithms.
201, 202, 203, 346, 446
6.
Active learning and life-long learning
6.A
Independently explores mathematical concepts.
All courses
6.B
Discusses mathematics with fellow students and faculty.
All courses
6.C
Participates in Seminars, problem solving sessions, or out-of-class presentations on
mathematics.
6.D
Forms allegiances to mathematics through memberships in professional societies or
professional friendships.
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Matrix 2: Departmental student learning outcomes and out-of-class activities in which the students are exposed to the knowledge, skills, and
dispositions related to each outcome for the Mathematics major
Departmental Student Learning Outcome
In what specific out-of-class activities will students be prepared for this learning
outcome?
1
Mathematical Understanding
Seminars, Problem Solving Sessions, Math Club Activities
2
Algorithmic Thinking
Seminars, Problem Solving Sessions, Math Club Activities
3
Critical Thinking
Seminars, Problem Solving Sessions, Math Club Activities
4
Problem-Solving and modeling
Seminars, Problem Solving Sessions, Math Club Activities
5
Technology
Seminars, Problem Solving Sessions, Math Club Activities
6
Active-learning and Life-long learning
Seminars, Problem Solving Sessions, Conference Participation, Joining Mathematical
associations, Participating in Math Club Activities
SLO #
Matrix 3: Contribution of Departmental Curriculum to Basic General Education Skills
General Education Skill
Nature of Support for Skill in the
Departmental Curriculum
Courses in which this skill is taught or
reinforced
College-level writing
Assignments with extensive writing including
feed back and revisions
MTH 425, MTH 457, MTH 432
Quantitative skills
Assignments/problems given
All courses
Computer skills
Labs/projects
Courses listed in Section 5.6.1
Critical Thinking skills
Assignments/problems given
All courses
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