Department of Mathematical Sciences School of Science and Technology

Department of Mathematical Sciences

School of Science and Technology

B.A. in MathematicsCIP Code: 27.0101Program Code: 150

1Program Quality Improvement Report 2009-2010

Student-Learning Outcomes


1. Knowledge of Mathematical Content1.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 & infinite series. 1.j. Apply major concepts of abstract algebra. 1.k. Analyze functions of one and two variables.



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 Solving3.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. 4. 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.



5. Knowledge of Technology5.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.


Alignment of Learning OutcomesAlignment 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• Graduates pursue graduate studies or obtain careers in

private or government sectors


Alignment of Learning OutcomesAlignment 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 ever-changing 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


Alignment of Learning OutcomesAlignment 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 desired academic program• Appreciation for the beauty and power of mathematics


Alignment of Learning OutcomesAlignment 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 9

Program Assessment MeasuresDirect Measures

• Entry-level Assessment• Calculus and Analytical Geometry Final Questions• Technology for Mathematics Assessment

• Mid-level Assessment• Mid-level Assessment Exam• Technology for Advanced Mathematical Assessment

• Upper-level Assessment• Major Field Achievement Test• Differential Equations Assessment

Program Quality Improvement Report 2009-2010 10

Program Assessment Measures

Indirect Measures

• The Written Survey of Graduates

Report on Previously Chosen Priority Outcomes

Learning Outcome 1.aDemonstrate 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 & Analytical Geometry I.


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.



Learning Outcome 1.bApply 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.



Learning Outcome 2.bSelect 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.



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.



Student-learning Outcome and MeasurementsOutcome 1.b

PROGRAM OUTCOME

CURRICULUM AREA OR TARGET AUDIENCE

MEASUREMENTS OF STUDENT LEARNING OR SERVICE OUTCOME

Measurements

Methods used to determine validity of measurement instruments

Methods used to determine reliability of measurements

Schedule for measurements

1.b.Apply concepts from algebra, geometry, and trigonometry in solving problems involving calculus

Required coursesMATH 2215MATH 2235MATH 2244MATH 4483

Entry level – Embedded questions in final for MATH 2215

Mid level – Questions on mid-level assessment test given in MATH 2613

Upper level – MFT

Questions were developed by subcommittee of faculty to align with learning outcome (Entry level and Mid level)

MFT is nationally normed tested

Questions are determined to be correct or not (only one correct answer)

From ETS

MATH 2215 – Every semester

MATH 2613 – Every Fall semester

MATH 4483 – Every Spring semester


17

Entry-level AssessmentNumber and Percentage of Students Scoring in Each Category

LearningOutcome Task

Fall 2007 –Sum 2008(41 total)

Fall 2008- Sum 2009 (70 total)

Fall 2009- Sum 2010 (80 Total)

1.b. Matching Correct Interpretation for Integrals – 3 or 2 correct 34 (83%) 41 (59%) 62 (78%)Correct Interpretation for Derivatives – 5 or 4 correct 38 (93%) 42 (60%) 67 (84%)Correct Differential Equation 29 (71%) 27 (39%) 48 (60%)Correct Rate of Change 21 (51%) 18 (26%) 41 (51%)Correct Area 29 (71%) 7 (10%) 40 (50%)Evaluated Limit Correctly 27 (66%) 4 (6%) 36 (45%)

Program Quality Improvement Report 2009-2010


18

*Two additional questions were added covering this learning outcome for the Fall 2007 test.

Mid-level Assessment Percentage of Students Scoring in Each Category

Percent of correct answers

n =14


n=18

Percent of correct

answers n=13


n=13

Learning Outcome Fall 2006 Fall 2007 Fall 2008 Fall 2009Apply concepts from algebra, geometry and trigonometry in solving problems involving calculus (1.b.) *

43% 50% 46% 54%




Mid-level Assessment ExamPercentage of Students Scoring in Each Category

Does Not Meet Standards

Meets Standards

Exceeds Standards

Total

1.b. Fall 2007 (n=18) 50% 33% 17% 100% Fall 2008 (n=13) 38% 54% 8% 100% Fall 2009 (n=14) 29% 57% 14% 100%



Major Field Achievement TestAverage 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%)



MFT Multi-Year Trend Analysis for Percentiles

0

10

20

30

40

50

60

70

2005 2006 2007 2008 2009 2010

Year

Per

cen

tag

e

Overall1.b



Differential Equation ProjectPercentage 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.)

100% 100% 100%

Analytical integration is successfully carried out. (1.a.) 100% 100% 100%


Action Plan for Student-Learning OutcomeOutcome 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 OUTCOME



Measurements




2.b.Select and use various types of reasoning and methods of proof

MATH2613MATH3013MATH3213MATH3302MATH3613MATH4423MATH4483

None currently – Please see action plan



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.


Action Plan for Student-Learning OutcomeOutcome 2.b

PROGRAM OUTCOME



Measurements




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)

MATH1001MATH2215MATH3001MATH3013MATH3302MATH4113MATH4433STAT3023STAT3113

None currently – Please see action plan


Student-learning Outcome and MeasurementsOutcome 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.


Action Plan for Student-Learning OutcomeOutcome 5.a

Published information on graduates

28

Academic Year 09-10 Entered Graduate School Working In Discipline Other

Summer 2009 0 2 0

Fall 2009 0 1 1

Spring 2010 0 2 0

Total 0 5 1


Questions?


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Department of Mathematical Sciences School of Science and Technology

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