# Mathematics

- Mission Statement
The mathematics department mission is to provide students with the knowledge and problem solving skills necessary to competently integrate mathematics into their personal and professional lives. Faculty endeavor to create an environment that makes that possible. Quality teaching of relevant courses and supervision of student projects including undergraduate research are central objectives.

The mathematics department is committed to providing excellent opportunities for all students: students majoring in mathematics, students majoring in science or engineering fields that depend heavily on mathematics, future teachers, in-service teachers, and all students seeking to improve their quantitative literacy. The department offers curriculum that attends to the needs of the diverse educational and career goals of our students. Since mathematics is relevant to numerous fields, many of our course offerings are designed in a manner sensitive to other disciplines. A common emphasis in all our courses is the process of mathematical thinking and problem solving, as these skills will serve all students during college and for years to come.

Mathematics and mathematics education are rapidly developing fields, and since the best teachers are those who remain active in their discipline, we engage in mathematical and educational research, in service teacher training, and course and curriculum development. Professional and scholarly work is both expected and encouraged.

- Student Learning Outcomes
- Certificate (Not Applicable)
- Associate Degree
The Associate of Science (AS) degree in Mathematics provides foundational knowledge and skills in mathematics as well as the ability to think logically and independently, analyze results and reflect on findings. The associate degree is often the first step toward careers in science, engineering, or economics.

Students who receive an Associate of Science degree in Mathematics at Weber State University will have:

- 1. Knowledge of and the ability to apply the concepts of differential and integral calculus.
- 2. Knowledge of and the ability to apply the concepts of series and to utilize various integration techniques and their applications.
- 3. Knowledge of and the ability to apply the concepts of three-dimensional spaces, multivariable calculus, and vector calculus.
- 4. Knowledge of and ability to apply matrix techniques as well as the language and concepts of vector spaces and transformations.

- Bachelor Degree
Mathematics Teaching Major (Math Teaching Emphasis):

Students who receive bachelor degrees in Mathematics Teaching at Weber State University are expected to have:

- Knowledge of and the ability to apply the concepts of differentiable, integral, and multivariable calculus.
- Knowledge of and ability to apply the concepts of matrices and Euclidean vector spaces, and ordinary differential equations.
- Ability to comprehend and write proofs that are logically, grammatically, and mathematically correct.
- Knowledge of basic probability and statistics, analysis, and number theory.
- Knowledge of and ability to teach concepts of high school level mathematics.

Applied Mathematics Major (Applied Emphasis):Students who receive bachelor degrees in Applied Mathematics at Weber State University are expected to have:

- Knowledge of and the ability to apply the concepts of differentiable, integral, and multivariable calculus.
- Knowledge of and ability to apply the concepts of matrices and Euclidean vector spaces, and ordinary differential equations.
- Knowledge and ability to apply the concepts of several areas of applied mathematics (probability and statistics, numerical analysis, partial differential equations, etc.).
- Ability to comprehend and write correct mathematical arguments.

Program Learning Outcomes for a Mathematics Major by Emphasis:

Using the goals above as a basis, the following learning outcomes based on skills and topic knowledge for each emphasis were established.

Mathematics Major (Regular Emphasis):- Students who receive bachelor degrees in Mathematics at Weber State University are expected to have:
- Knowledge of and the ability to apply the concepts of differentiable, integral, and multivariable calculus.
- Knowledge of and ability to apply the concepts of matrices and Euclidean vector spaces, and ordinary differential equations.
- Ability to comprehend and write proofs that are logically, grammatically, and mathematically correct.
- Knowledge of and ability to prove results in analysis and algebra curriculum.

In a review of the courses required for Mathematics majors it was determined that each required course contributes to each of the following goals: Mathematics majors should gain a substantive knowledge and comprehension of the major ideas in the core areas of their fields of study. All mathematics majors should learn a fundamental set of skills that will enable them to succeed in an ever changing world, including problem solving and independent learning, technology and communication. Students pursuing Mathematics Minors, Mathematics Teaching Minors, or Elementary Mathematics Endorsements should be able to effectively apply appropriate mathematical ideas and/or teaching approaches in their field. Mathematics students should enjoy resources that are sufficient for achieving their goals. While obtaining mathematical knowledge, they should also have a reasonable freedom in the choice of their courses.

The education of a student is a cooperative effort between the student, many faculty in different disciplines, and other university community members such as advisors, librarians, administrators, etc. The Mathematics Department controls only one aspect of this effort, namely the teaching of mathematics. However, this document states overall desirable following goals for students of mathematics: Mathematics majors should gain a substantive knowledge and comprehension of the major ideas in the core areas of their fields of study.

- Mathematics: The main topics are modern and linear algebra and analysis of real-valued functions.
- Applied Mathematics: The main topics are numerical and statistical analysis, linear algebra, mathematical modeling and differential equations.
- Mathematics Teaching: The main mathematical topics are the ones contained in mathematics courses required for certification. Mathematics teaching majors should also learn effective approaches for teaching mathematics.
- All mathematics majors should learn a fundamental set of skills that will enable them to succeed in an ever changing world. Problem Solving & Independent Learning: They should be adequately trained to apply their mathematical knowledge in both familiar and new situations. They should also be able to seek new knowledge to help in those endeavors.
- Technology: They should learn to use appropriate technology, such as computers, as an aide in investigating mathematical problems and teaching.
- Communication: They should learn to successfully communicate mathematical ideas and solutions of problems with others at the appropriate level. Students pursuing Mathematics Minors, Mathematics Teaching Minors, or Elementary Mathematics Endorsements should be able to effectively apply appropriate mathematical ideas and/or teaching approaches in their field. Mathematics service courses should meet the overall varied needs of client departments. Students in these courses should obtain the required mathematical knowledge.

The B.S. in Mathematics with emphasis in Computational Statistics and Data Science has the following learning goals for students:

- Students will understand the theoretical, conceptual, and applied underpinnings of Statistics.
- Students will understand the theoretical, conceptual, and applied underpinnings of Data Science.
- Students will demonstrate fundamentals and fluency in computation.
- Students will effectively analyze and reason with data.
- Students will be able to effectively communicate their results.

- Certificate (Not Applicable)
- Curriculum Grid
- Program and Contact Information
From data mining to forensics, mathematics is the language of choice for an ever increasing number of disciplines. The scientist, the engineer, the actuary, the financial planner -- all use algebra, geometry, calculus and statistics. But also the voter needs to understand these concepts, albeit at a less advanced level, to reach informed decisions about a multitude of issues from utility rates and retirement saving to information security and global warming.

The Department of Mathematics offers a variety of courses (from general interest to advanced levels of applicability), two minors, departmental honors, and three majors. The Mathematics major may be the best choice for someone planning to go directly to graduate school; the Applied Mathematics major prepares one for a job that uses mathematics; the Mathematics Teaching major prepares students to be teachers of mathematics in elementary through high school.

**Contact Information:**Contact InformationSandra Fital-Akelbek, ChairMathematics DepartmentWeber State University1415 Edvalson St., Dept 2517Ogden UT, 84408-2517**Location:**Tracy Hall Science Center, TY 381801 626-6097 - Assessment Plan
Assessment is an ongoing process in the Mathematics Department. Externally, broad reviews are conducted regularly by the Board of Regents and by Northwest, ABET, and NCATE accrediting agencies. These generally include reviews of departmental offerings, course content, textbooks, and examinations. In these reviews experienced professionals usually compare our program with others and provide the department with reports detailing its perceived strengths and weaknesses. Other programs also undergo similar external reviews. Based on all these reviews and in consultation with client departments, the Mathematics Department makes necessary changes for improvement of its program.

Internally, the Mathematics Department reviews its entire curriculum periodically, has dialogs with client departments, re-evaluates textbooks annually, keeps current on national curriculum trends, and studies course grade distributions from time to time. In addition, faculty share and review examinations, regularly collect student evaluations of teaching, and undergo annual reviews for merit. Faculty also consult with local school districts, graduate schools, and employers.

Data Collection:

- In data collection a balance must be reached between the cost (time, money, etc.) and usefulness of the data while not imposing unreasonable demands on faculty, university resources, students and graduates. There is no single nationally accepted method, such as standardized testing, for overall assessment. While the core topics of most courses are the same nationally, there is no consensus with regard to the importance or depth of coverage of each topic. Any national comparison would be further complicated by differing entrance standards and missions of universities.
- Many evaluation criteria cannot be quantified with a simple numerical scale. For example, there is no national ranking for textbooks. Thus, while the Mathematics Department does review textbooks annually, and uses those reviews to select high quality textbooks, little would be gained from further analysis. This is also true for many other collection/evaluation methods listed below.
- The following are feasible means of data collection which can lead to a meaningful assessment. Much of these data could be collected through one instrument, such as a survey, while others have been studied for many years.
- College Graduation Exit Survey Post-graduate Survey Input from Client Departments Feedback from General Education Assessment Textbook Evaluation Exam Evaluation Distribution of Grades in Mathematics Courses Distribution of Grades in Client Courses Student Research and Contests Results
- Mathematics service courses should meet the overall varied needs of client departments. Students in these courses should obtain the required mathematical knowledge.

Measurable Course Learning Outcomes and Action Plan for Program Courses beyond QL courses:

- Course learning outcomes for each of the required courses for math majors and elementary majors are listed Appendix H. The curriculum impact grids in C. 5. show the extent to which these learning outcomes impact the program learning outcomes for the math majors. The outcomes are available electronically to department members on the department’s network drive. Each time a course above 1080 is taught the instructor will target each of the course learning outcomes with test questions or papers or projects and report the on the student completion rates. See the section on QL below for the assessment plan for the QL course Math 1030, 1040, 1050, 1080. Thresholds will be established according to Bloom’s Taxonomy and method of measurement in the range of 65% to 70%. For example a question on a midterm exam is more immediate and will have a rate of 70% while a question on a comprehensive final could have a rate of 65%. Projects or papers will have a rate 70 %. If the completion rates do not meet the thresholds then there will be discussions with the appropriate committee and department to determine the reason and formulate a course of action such as new texts, new approaches, additional homework, etc.

Assessment Grid The following grid states how and at what level of effectiveness (High, Medium, or Low) the data collected can be used in assessment of the department’s program goals:

- Mathematics majors should gain a substantive knowledge and comprehension of the major ideas in the core areas of their fields of study (pure mathematics, applied mathematics, mathematics teaching). All mathematics majors should learn a fundamental set of skills that will enable them to succeed in an ever changing world, including problem solving and independent learning, technology and communication. Students pursuing Mathematics Minors, Mathematics Teaching Minors, or Elementary Mathematics Endorsements should be able to effectively apply appropriate mathematical ideas and/or teaching approaches in their field.
- To draw accurate conclusions it will be necessary that the data sets be sufficiently large, be from target populations, and be reliable. In order to generate larger data sets, in some instances groups like majors, minors, and client students, will be lumped together, while in others, such as graduate acceptance rate, the data will be accumulated over several years. For accurate targeting it will be necessary to subdivide some groups, like minors, teaching minors and elementary mathematics endorsements. Finally, the surveys and their results should also be analyzed for unintended biases and reliability of data.

The Mathematics Department is doing the following:

- Maintaining an address file of graduates. Administering, over time, exit interviews and a questionnaire that inquires about results of standardized tests, acceptance to graduate school, curriculum strengths and weaknesses, obtaining employment, quality of job training, obtaining advanced degrees, teaching effectiveness, etc. Performing surveys of majors that make inquiries about courses and reasons they choose or changed major. Study the results of general education assessment and then respond in appropriate ways. Establish and maintain measurable program learning outcomes and measurable course learning outcomes. Target questions on tests and finals that access whether students are meeting the course learning outcomes and collect the data for the evidence of learning spreadsheets. In courses where appropriate, access student papers and/or projects and collect data on these and report on the completion rates.
- Graduate School Acceptance
- Graduate Degrees Earned
- Classroom Observations of Student Teachers
- Profile of Entering Students
- Course evidence of learning grids for courses within the majors
- Course evidence of learning grids for the general education QL courses
- Course evidence of learning grids for courses for elementary major courses

- Assessment Report Submissions
- Program Review

*This information is part of the cyclical program review process. Details such as mission statements, learning outcomes, etc., are updated as part of the biennial assessment reporting process, an integral component of program review.*