# B.A. in Mathematics Department of Mathematical Sciences School of Science and Technology

```Department of Mathematical
Sciences
School of Science and Technology
B.A. in Mathematics
CIP Code: 27.0101
Program Code: 150
Program Quality Improvement Report 2009-2010
1
Student-Learning Outcomes
1.
Knowledge of Mathematical Content
1.a. Demonstrate a conceptual understanding of and procedural facility
with basic calculus concepts.
1.b. Apply concepts from algebra, geometry, and trigonometry in solving
problems involving calculus.
1.c. Use the principles of multiple variable calculus.
1.d. Apply basic set operations.
1.e. Apply basic propositional and predicate logic.
1.f. Use the concepts of relation and equivalence relation.
1.g. Apply fundamental ideas of linear algebra.
1.h. Demonstrate competency with ordinary differential equations and
their applications.
1.i. Apply the concept of sequence &amp; infinite series.
1.j. Apply major concepts of abstract algebra.
1.k. Analyze functions of one and two variables.
Program Quality Improvement Report 2009-2010
2
Student-Learning Outcomes
2.
Knowledge of Reasoning and Proof.
2.a. Develop and evaluate mathematical arguments and proofs.
2.b. Select and use various types of reasoning and methods of proof.
3.
Knowledge of Mathematical Representation and Problem Solving
3.a. Solve problems that arise in mathematics and those involving
mathematics and other contexts.
3.b. Select, apply and translate among mathematical representations to
solve problems.
Knowledge of Mathematical Communication
4.a. Communicate mathematical thinking coherently and clearly to peers,
faculty and others.
4.b. Use the language of mathematics to express ideas precisely.
4.
Program Quality Improvement Report 2009-2010
3
Student-Learning Outcomes
5.
Knowledge of Technology
5.a. Use knowledge of mathematics to select and use appropriate
technological tools, such as, but not limited to, graphing calculators and
computer algebra systems (e.g. Mathematica and MATLAB).
5.b. Solve problems using an object oriented programming language and its
corresponding operating system.
Program Quality Improvement Report 2009-2010
4
Alignment of Learning Outcomes
Alignment with Cameron University's Mission Statement
“Cameron University provides a diverse and dynamic student body access to quality
educational opportunities; … prepares students for professional success, responsible
citizenship, life-long learning, and meaningful contributions to a rapidly changing
world ...”
• Dissemination of knowledge
• Appreciation of mathematics
• Beauty of mathematics in solving real world application
problems
• Strong foundation of mathematics for acquiring knowledge,
skills, and attitudes for a lifetime of learning
private or government sectors
Program Quality Improvement Report 2009-2010
5
Alignment of Learning Outcomes
Alignment with School of Science and Technology’s
Mission Statement
“The mission of the Cameron University School of Science and Technology is to
educate students in an intellectual atmosphere based on excellence in academic
work, …to deliver student support which gives our students the skills and confidence
to excel as lifelong learners; to ensure success of graduates in a diverse and everchanging environment;… and to support community efforts relevant to the School
mission.”
• Strong knowledge base and quantitative skills
• Gain useful skills as well as an appreciation for the subject
• Tutoring opportunities
• Internship opportunities
Program Quality Improvement Report 2009-2010
6
Alignment of Learning Outcomes
Alignment with Department of Mathematical Sciences’
Mission Statement
The mission of the Mathematical Sciences Department at Cameron University is to
provide quality educational experiences in all mathematics and statistics courses
…provide all students, both majors and non-majors, with the knowledge and skills
needed for life-long learning, as well as an appreciation for the beauty and power of
mathematics… majors will acquire a broad and solid base in mathematics, enabling
them to continue their education in graduate school or to pursue careers in teaching,
industry, or government.
• Mathematical knowledge and skills needed to excel in their
• Appreciation for the beauty and power of mathematics
Program Quality Improvement Report 2009-2010
7
Alignment of Learning Outcomes
Alignment with Cameron University’s Strategic Plan
• Tools necessary for graduates to successfully compete in the
job market both today and into the future
• Familiarity with present technologies
• Ability to communicate mathematics effectively
• Solid foundation in mathematics
• Tutoring opportunities
• Internship opportunities
Program Quality Improvement Report 2009-2010
8
Program Assessment Measures
Direct Measures
•
Entry-level Assessment
•
•
•
Mid-level Assessment
•
•
•
Calculus and Analytical Geometry Final Questions
Technology for Mathematics Assessment
Mid-level Assessment Exam
Upper-level Assessment
•
•
Major Field Achievement Test
Differential Equations Assessment
Program Quality Improvement Report 2009-2010
9
Program Assessment Measures
Indirect Measures
•
Program Quality Improvement Report 2009-2010
10
Report on Previously Chosen Priority
Outcomes
Learning Outcome 1.a
Demonstrate a conceptual understanding of and procedural
facility with basic calculus concepts.
This outcome is assessed by all of the assessments presently
developed, but we chose to focus upon the entry-level
assessment in MATH2215 – Calculus &amp; Analytical Geometry I.
Program Quality Improvement Report 2009-2010
11
Report on Previously Chosen Priority
Outcomes
Learning Outcome 1.a
A pre-test was developed and administered in all Calculus I and
Elementary Calculus courses to assess the students' ability with
algebra and trigonometry (Calculus I only). Based upon the
results of this pre-test, students demonstrating serious
deficiencies in these areas were then to be referred to the
Mathematics Laboratory for additional help and were to meet
with the instructor of the course during office hours to improve
their skills.
Program Quality Improvement Report 2009-2010
12
Report on Previously Chosen Priority
Outcomes
Learning Outcome 1.b
Apply concepts from algebra, geometry, and trigonometry in
solving problems involving calculus.
This outcome is assessed by most of the assessments given, but
was chosen to be part of the previous outcome, since both
were chosen to be part of the improvements to MATH2215.
Program Quality Improvement Report 2009-2010
13
Report on Previously Chosen Priority
Outcomes
Learning Outcome 2.b
Select and use various types of reasoning and methods of proof.
This outcome was not assessed by any of the assessments, so
was chosen so an assessment could be developed.
Program Quality Improvement Report 2009-2010
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Report on Previously Chosen Priority
Outcomes
Learning Outcome 2.b
Proofs are presently being collected from all students in a
particular class in order to evaluate the class as a whole.
Program Quality Improvement Report 2009-2010
15
Student-learning Outcome and Measurements
Outcome 1.b
MEASUREMENTS OF STUDENT LEARNING OR SERVICE OUTCOME
PROGRAM
OUTCOME
1.b.
Apply concepts
from algebra,
geometry, and
trigonometry in
solving problems
involving calculus
CURRICULUM
AREA OR TARGET
AUDIENCE
Required courses
MATH 2215
MATH 2235
MATH 2244
MATH 4483
Measurements
Entry level –
Embedded
questions in final
for MATH 2215
Mid level –
Questions on midlevel assessment
test given in MATH
2613
Upper level – MFT
Methods used to
determine validity
of measurement
instruments
Methods used
to determine
reliability of
measurements
Questions were
developed by
subcommittee of
faculty to align
with learning
outcome (Entry
level and Mid
level)
Questions are
determined to
be correct or
not (only one
correct
MFT is nationally
normed tested
From ETS
Program Quality Improvement Report 2009-2010
Schedule for
measurements
MATH 2215 –
Every semester
MATH 2613 –
Every Fall
semester
MATH 4483 –
Every Spring
semester
16
Student-learning Outcome and Measurements
Outcome 1.b
Entry-level Assessment
Number and Percentage of Students Scoring in Each Category
Learning
Outcome
1.b.
Matching Correct Interpretation for
Integrals – 3 or 2 correct
Correct Interpretation for
Derivatives – 5 or 4 correct
Correct Differential Equation
Correct Rate of Change
Correct Area
Evaluated Limit Correctly
Fall 2007 –
Sum 2008
(41 total)
Fall 2008Sum 2009
(70 total)
Fall 2009Sum 2010
(80 Total)
34 (83%)
41 (59%)
62 (78%)
38 (93%)
42 (60%)
67 (84%)
29 (71%)
21 (51%)
29 (71%)
27 (66%)
27 (39%)
18 (26%)
7 (10%)
4 (6%)
48 (60%)
41 (51%)
40 (50%)
36 (45%)
Program Quality Improvement Report 2009-2010
17
Student-learning Outcome and Measurements
Outcome 1.b
Mid-level Assessment
Percentage of Students Scoring in Each Category
Percent of
Percent of
Percent of
correct
correct
correct
n =14
n=18
n=13
Learning Outcome
Apply concepts from algebra,
geometry and trigonometry in
solving problems involving
calculus (1.b.) *
Percent of
correct
n=13
Fall 2006
Fall 2007
Fall 2008
Fall 2009
43%
50%
46%
54%
*Two additional questions were added covering this learning outcome for the Fall 2007 test.
Program Quality Improvement Report 2009-2010
18
Student-learning Outcome and Measurements
Outcome 1.b
Mid-level Assessment Exam
Percentage of Students Scoring in Each Category
1.b.
Fall 2007 (n=18)
Fall 2008 (n=13)
Fall 2009 (n=14)
Does Not Meet
Standards
Meets
Standards
Exceeds
Standards
Total
50%
38%
29%
33%
54%
57%
17%
8%
14%
100%
100%
100%
Program Quality Improvement Report 2009-2010
19
Student-learning Outcome and Measurements
Outcome 1.b
Major Field Achievement Test
Average and National Percentages for Students Scoring in Each Category
Scores are formatted as follows: Average of Raw Scores (Percentage of National Average)
Overall
1.b: Calculus Indicator
Spring 2005 (n=18)
149.2 (35%)
30.1 (30%)
Spring 2006 (n=16)
145.7 (10%)
29.3 (20%)
Spring 2007 (n=6)
140.0 (1%)
31.0 (25%)
Spring 2008 (n=7)
159.0 (65%)
37.0 (60%)
Spring 2009 (n=8)
151.0 (30%)
33.0 (35%)
Spring 2010 (n=9)
151.0 (40%)
31.0 (25%)
Program Quality Improvement Report 2009-2010
20
Student-learning Outcome and Measurements
Outcome 1.b
MFT Multi-Year Trend Analysis for Percentiles
70
60
Overall
1.b
Percentage
50
40
30
20
10
0
2005
2006
2007
2008
2009
2010
Year
Program Quality Improvement Report 2009-2010
21
Student-learning Outcome and Measurements
Outcome 1.b
Differential Equation Project
Percentage of Students Successfully Completing Each Criteria
Criteria
(Along with objective tested.)
Spring 2008
(n=7)
Spring 2009
(n=13)
Spring 2010
(n=16)
Initial Value Problems are correctly evaluated. (1.a.)
100%
100%
100%
Analytical differentiation is successfully carried out.
(1.a.)
Analytical integration is successfully carried out. (1.a.)
100%
100%
100%
100%
100%
100%
Program Quality Improvement Report 2009-2010
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Action Plan for Student-Learning Outcome
Outcome 1.b
The initial results of the calculus pre-test determined that a
surprising majority of students were deficient in their ability to
solve the problems given on the pre-test. In discussing these
results, the consensus was to forego the pre-test and instead
focus on addressing these issues in College Algebra by instituting
a common final exam to be used in all sections of College
Algebra. This will be used to ensure a uniform level of
knowledge and understanding between all sections and may be
expanded in the future to the remedial algebra courses.
Program Quality Improvement Report 2009-2010
23
Student-learning Outcome and Measurements
Outcome 2.b
MEASUREMENTS OF STUDENT LEARNING OR SERVICE OUTCOME
PROGRAM
OUTCOME
2.b.
Select and use
various types of
reasoning and
methods of proof
CURRICULUM
AREA OR TARGET
AUDIENCE
MATH2613
MATH3013
MATH3213
MATH3302
MATH3613
MATH4423
MATH4483
Measurements
Methods used to
determine validity
of measurement
instruments
Methods used
to determine
reliability of
measurements
Schedule for
measurements
None currently –
plan
Program Quality Improvement Report 2009-2010
24
Action Plan for Student-Learning Outcome
Outcome 2.b
Develop a rubric to assess the proofs collected in Foundations
of Mathematics (MATH 2613), Linear Algebra (MATH 3013),
Abstract Algebra (MATH 3213) and Introduction to Real
Analysis (MATH 4483). This rubric will then be used by a
faculty member who is not teaching the respective course to
grade the proofs. Data collected will be analyzed to determine
students’ performance on learning outcome 2.b.
Program Quality Improvement Report 2009-2010
25
Student-learning Outcome and Measurements
Outcome 5.a
MEASUREMENTS OF STUDENT LEARNING OR SERVICE OUTCOME
PROGRAM
OUTCOME
5.a.
Use knowledge of
mathematics to
select and use
appropriate
technologies
tools, such as,
but not limited
to, graphing
calculators or
computer algebra
systems (e.g.
Mathematica and
MATLAB)
CURRICULUM
AREA OR TARGET
AUDIENCE
MATH1001
MATH2215
MATH3001
MATH3013
MATH3302
MATH4113
MATH4433
STAT3023
STAT3113
Measurements
Methods used to
determine validity
of measurement
instruments
Methods used
to determine
reliability of
measurements
Schedule for
measurements
None currently –
plan
Program Quality Improvement Report 2009-2010
26
Action Plan for Student-Learning Outcome
Outcome 5.a
With the approval of MATH 1001 and MATH 3001, assessments
are still needed for these classes in order to measure how well
students are meeting objective 5.a. These assessments will likely
have to be tailored to the particular technology used.
Program Quality Improvement Report 2009-2010
27
Working In Discipline
Other
Summer 2009
0
2
0
Fall 2009
0
1
1
Spring 2010
0
2
0
Total
0
5
1