# Undergraduates

## Assessment

### Quantitative Literacy

Annual assessment of student performance on primary general education courses (Math 1050 and Stat 1040) is accomplished through a common final exam for each course. Each course objective is associated with a set of representative problem types that assess the objective. Each semester the common final exams are created by a group of instructors, led by the course coordinator, by selecting and adjusting the representative problem types associated with the course objectives.

### Preparation for Calculus

To assess the effectiveness of math 1050 as a calculus preparatory course, approximately 100 students who have completed and passed math 1050 will be randomly selected each year, and their subsequent performance in a calculus class (math 1210 or math 1100) will be examined and compared with another randomly selected group of calculus students who qualified for a calculus course by means other than math 1050 from USU.

### Developmental Mathematics

**Identifying Mathematical Proficiency**

There are two assessments that are used to determine the mathematical proficiency of students at USU prior to their placement into a mathematics or statistics course: the American College Test (ACT) and the Accuplacer exam. The scores for each exam and the associated courses that students are allowed to register for based on those scores can be seen here.

**Appropriate and Efficient Remedial Coursework**As a preliminary means of assessing the effectiveness of math 0995, there were two questions that were considered:

- Do students spend less time in remedial coursework now that math 0995 is offered as a replacement of math 0990 and math 1010?
- Is math 0995 a course that sufficiently prepares students to succeed in math 1050?

In order to answer these questions, the following data was collected:

- Passing rates for math 0990 and math 1010 from the fall 2012, spring 2013, summer 2013, and fall 2013 semesters. These semesters represent the last four semesters before math 0995 became an option for students as a remedial course for math 1050 preparation.
- Passing rates for math 0995 from the summer 2015, fall 2015, spring 2016, and summer 2016 semesters.
- These represent the four semesters where math 0995 was the only remedial course option for math 1050 preparation.
- Passing rates for math 1050 for the spring 2013, summer 2013, fall 2013, spring 2014, and summer 2014 semesters. These are semesters where math 0995 was not an option as a remedial course for math 1050 preparation.
- Passing rates for math 1050 for the fall 2015, spring 2016, and summer 2016 semesters. These are semesters where math 0995 was the only option as a remedial course for math 1050 preparation.

This assessment reflects a preliminary investigation into the success of math 0995. Further data will be collected to better understand the effect of the course. The Department of Mathematics and Statistics intends to continue assessing data from the first year of math 0995 to determine the following:

- What is the passing rate for all math 1050 students broken down by how the prerequisite was satisfied?
- Math 0995
- ACT score
- Math placement score
- Remedial course from transfer from another institution

- A comparison of random samples of students who attempted to qualify for math 1050 by starting with an 0990 course and a random sample of students who attempted to qualify for math 1050 by starting with an 0995 course.
- Proportion who eventually qualified for math 1050
- Proportion who eventually passed math 1050
- The number of remedial math credits registered for in an attempt to satisfy prerequisites. This will take into account repeats of courses failed or dropped.

- What is an estimated savings to the Department of Mathematics and Statistics due to math 0995 as a replacement for math 0990 and math 1010?
- How do the course ratings from student evaluations compare for math 0990, math 1010, and math 0995?

## Data-Based Decision Making

The Department of Mathematics and Statistics regularly restructures and enhances the undergraduate curriculum in response to student feedback and performance, course enrollments and evaluations, self-study and Regents reviews, professional and market trends, and new faculty expertise and research interests. The Department pays particular attention to recommendations from the profession – as best implemented in the context of USU’s mission and our existing strengths and capabilities – including the recent National Research Council report The Mathematical Sciences in 2025 (2013, National Academies Press).

The feedback and information from across these resources have led to these recent and ongoing programmatic changes:

- (2015-2017) A new interdisciplinary data science degree program, in collaboration with Management Information Systems, Economics and Finance, and Computer Science, to better prepare students for the growing demands of big data and analytics. (Master's of Data Analytics degree program received final approval from the Board of Regents in July, 2017.)
- (2014-2017) Additional courses in statistical computing and data science, including R programming, SAS programming, and statistical methods for big data.
- (2016-2017) A significant reworking of courses in applied and computational mathematics, along with mathematical biology, to provide more 1- and 2-credit offerings, and greater flexibility and breadth, and an additional 4000-level course in mathematical computing.
- (2016-2018) An initiative to hire new faculty with expertise in mathematical computing and numerical methods, to enhance and update our undergraduate curriculum. (A new assistant professor in mathematical computing hired spring 2017. Ongoing search for a professor in Data Science and Analytics.)
- (2017) Introduction of an additional course in discrete mathematics, to better serve students with interests in mathematical computing and computer science.
- (2016) Revision of mathematics content course requirements for Elementary and Special Education Majors, to extend the former single content course for elementary teachers (Math 2020 Introduction to Logic and Geometry) into a 2-semester sequence: Math 2010 (Algebraic Thinking & Number Sense for Elementary School Teachers), and a revised Math 2020 (Euclidean Geometry & Statistics for Elementary School Teachers).
- (2016-2017) Engagement in the Mathematics Teacher Education (MTE) Partnership, due to the success of our field-based mathematics teacher preparation program. The MTE-Partnership was established to “transform secondary mathematics teacher preparation” to ensure an adequate supply of teacher candidates who can promote mathematical excellence in their future students, leading to college and career readiness in accordance with documents such as the Common Core State Standards for Mathematics (CCSSM) and the Mathematics Education of Teachers II (METII). Using a Networked Improvement Community model, USU has collaborated with a research action cluster focused on developing MODULES for improving specialized mathematical knowledge for teaching in Statistics, Modeling, Geometry and Algebra

## Program Learning Objectives

Mathematics is the Queen of the Sciences … She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.

### Quantitative Literacy

An essential role of the Department of Mathematics and Statistics is to provide the courses and resources required for students to fulfill the quantitative literacy (QL) requirement within their individual general education programs. The common learning objectives for the QL courses at Utah State University are:

- Understand mathematical and statistical models including formulas, tables, and graphs, and be able to draw inferences from them.
- Characterize and interpret mathematical data that is presented symbolically, visually, numerically, or verbally.
- Utilize arithmetic, algebraic, geometric, and statistical models or appropriate combinations of these models to solve problems.

The courses that are offered and coordinated by the Department of Mathematics and Statistics that are intended to satisfy these learning objectives at a general education level and are recognized by the state board of regents as meeting the requirements for QL are Stat 1040 (Introduction to Statistics), Stat 1045 (Introduction to Statistics with Elements of Algebra), and Math 1050 (College Algebra). Course objectives have been identified for each of these courses and each course objective is associated with one of the three QL learning objectives listed above.

### Preparation for Calculus

Math 1050 is recognized by the state board of regents as a course that will fulfill the general education quantitative literacy requirement. However, the Department of Mathematics and Statistics also considers math 1050 an integral component of the precalculus curriculum. Therefore, an additional math 1050 course objective is to provide prospective calculus students the necessary experience, understanding, and abilities in algebra that are required skills required to successfully complete a study of calculus. The course objectives defined for math 1050 were established both to satisfy the QL learning objectives as well as this calculus preparation objective.

### Developmental Mathematics

The Department of Mathematics and Statistics recognizes a responsibility to recognize and provide support to students whose mathematical understanding and abilities are insufficient to successfully complete a QL course.

The program goals for developmental mathematics are:

- Be able to identify the mathematical proficiency of students and place them into courses or suggest appropriate remediation that will increase their likelihood of success in their individual program of studies.
- Provide support, remediation, and courses that prepare students to successfully complete their QL requirement.

A recent report indicates that remedial education for college and university students in the United States costs $1.5 billion annually1. Also, full-time students seeking bachelor’s degrees who are required to take remedial courses in their first year are 74 percent more likely to drop out of college. In response to this data, the Department of Mathematics and Statistics has developed a remedial, four-credit course to prepare students for college algebra. This new course, math 0995, has replaced two previously required remedial courses, math 0990 and math 1010.

(1) Nguyen-Barry, M., & Dannenberg, M. (April 2016). Out of Pocket: The High Cost of Inadequate High Schools and High School Student Achievement on College Affordability. Education Reform Now. Retrieved from edreformnow

### Bachelor of Science/Arts in Mathematics Learning Objectives: The Seeds of a Mathematician

The learning objectives of all undergraduate programs with a focus in Mathematics are based on this observation attributed to Gauss. The courses comprising the major have been chosen to ensure the student obtains the fundamental algorithmic and computational skills, incisive thinking skills, and analytical mindset sufficient for participating in any kind of science or for becoming a Mathematician.

Learning objectives the Mathematics major are achieved through courses which may be categorized in three ways: **Foundational Skills** courses, **Intellectually Transformative** courses, and **Mathematical Fluency** courses. Foundational Skills courses consist of courses taken by intra- and inter-departmental and inter-college students and are intended to give students the algorithmic and computational skills needed in any discipline regardless of major. These courses develop computational skills and begin to develop symbolic fluency and comfort with abstraction. Intellectually Transformative courses are intended to acclimate the student to the thinking styles and philosophies indigenous to theoretical Mathematics. These courses build on the foundation obtained from the Foundational Skills courses, especially on the abilities engendered by the symbolic manipulations, turning those skills into a fluency with a language useful in all disciplines but with a focus tuned more for the development sought in the final category of courses. The Mathematical Fluency courses introduce the student to the ideas from which the topics in Foundational Skills courses were borne. These courses empower the student to succeed in graduate-level courses as well as give them the skills employers hiring mathematicians value: dynamic problem solving skills coupled with technically precise thinking and analytical skills. Technical communication skills are also developed and tested within the guidelines of rigorous proof.

The objective of all BS degrees is, very briefly, to produce mathematicians poised for industry, or for scientific or academic research. All specializations consist of courses from the three categories described above: 1000- to 2000-level courses are the Foundational Skills courses; 3000-level and 4000-level courses constitute the Intellectually Transformative courses; 4000- and 5000-level courses constitute the Mathematical Maturation courses.

**Foundational Skills Courses**

All Mathematics majors develop mastery of foundational algorithmic skills including symbolic manipulation from three major areas: calculus, linear algebra, and differential equations. Calculus studies the mathematics of change and of motion. The skills developed in the courses MATH 1210, Calculus I), MATH 1220 (Calculus II), and MATH 2210 (Multivariable Calculus) prepare all students from the future physicists and engineers to mathematicians for the applications and manipulations of formulas indigenous to their respective disciplines that deal with change and motion. I Linear Algebra students master the solution of systems of equations and abstract the process into something applicable to all disciplines that involve any calculation whatsoever --- from optimization problems such as Linear Programs to projection problems such as Least-Squares curve fitting. Additionally, in MATH 2270 (Linear Algebra), students develop a vocabulary for matrices and a variety of their factorizations that are used in applications from computer graphics and image recognition to solving systems of equations. The course MATH 2280 (Ordinary Differential Equations) prepares students for the applying models based on change and equips with the vocabulary and basic skills needed to find solutions or to identify instances where solutions will be difficult, if not impossible to find. The mastery of the skills developed is assessed in these courses.

**Intellectually Transformative Courses**

It is at the level of Intellectually Transformative courses that the various Mathematics major specializations begin to diverge based on the needs of the courses deemed optimal with respect to the specialization. The transformative courses introduce the Mathematics major to ideas and ways of thinking engendered in the mathematical sciences. Ideas like the power of abstraction are communicated via the language of Algebra, of Sets, or Geometry. Thinking tuned with the philosophy of axiomatic systems is developed via the process of proof. The development of abstraction and proof akin to algebra is developed and assessed in MATH 4310 (Introduction to Algebraic Structures). The language of Set Theory and of Logic is developed and assessed on MATH 3310 (Discrete Math), and that of Geometry in MATH 3110 (Modern Geometry).

**Mathematical Fluency Courses**

The languages and ways of thinking developed in the Intellectually Transformative courses provide the field on which the final learning objectives are played out. In the courses aimed at producing a budding mathematician students develop a deep understanding of the algorithmic skills and computational skills from which the degree grew. Skills with using Logic, Set Theory, Algebra, and the axiomatic methods previously introduced are developed via the study the real number system and functions and operations of calculus in the courses MATH 4200 (Foundations of Analysis), MATH 5210 (Introduction to Analysis I), and MATH 5220 (Introduction to Analysis II). In fact, the theory underpinning all Foundational Skills courses is addressed in the 5000-level courses. The theory of the methods and content in MATH 2270 (Linear Algebra) is addressed in MATH 5340 (Theory of Linear Algebra), that of MATH 1210, 1220, and 2210 (Calculus sequence) and much of MATH 2280 (Differential Equations) is addressed in MATH 4200, 5210, and 5220.

Proficiency in the communication of mathematical arguments, such as proof, is developed in essentially all 5000-level mathematics courses, whence many 5000-level mathematics courses are designated as Communications Intensive and contribute the USU’s University Studies program.

The communication, analysis, symbolic computation, manipulation of axioms, and thinking within the confines of logic are all assessed in these courses.